FLUENT 6.1 User's Guide

FLUENT 6.1

February 2003

User’s Guide

Licensee acknowledges that use of Fluent Inc.’s products can only provide an imprecise estimation of possible future performance and that additional testing and analysis, independent of the Licensor’s products, must be conducted before any product can be finally developed or commercially introduced. As a result, Licensee agrees that it will not rely upon the results of any usage of Fluent Inc.’s products in determining the final design, composition or structure of any product.

c 2003 by Fluent Inc. Copyright All rights reserved. No part of this document may be reproduced or otherwise used in any form without express written permission from Fluent Inc.

Airpak, FIDAP, FLUENT, GAMBIT, Icepak, MixSim, and POLYFLOW are registered trademarks of Fluent Inc. All other products or name brands are trademarks of their respective holders.

Fluent Inc. Centerra Resource Park 10 Cavendish Court Lebanon, NH 03766

Volume 1 1 2 3 4 5 6 7

Getting Started User Interface Reading and Writing Files Unit Systems Reading and Manipulating Grids Boundary Conditions Physical Properties

Volume 2 8 9 10 11 12 13 14 15 16 17 18 19

Modeling Basic Fluid Flow Modeling Flow in Moving and Deforming Zones Modeling Turbulence Modeling Heat Transfer Introduction to Modeling Species Transport and Reacting Flows Modeling Species Transport and Finite-Rate Chemistry Modeling Non-Premixed Combustion Modeling Premixed Combustion Modeling Partially Premixed Combustion The Composition PDF Transport Model Modeling Pollutant Formation Predicting Aerodynamically Generated Noise

Volume 3 20 21 22 23 24 25 26 27 28 29 30 A

Introduction to Modeling Multiphase Flows Discrete Phase Models General Multiphase Models Modeling Solidification and Melting Using the Solver Grid Adaption Creating Surfaces for Displaying and Reporting Data Graphics and Visualization Alphanumeric Reporting Field Function Definitions Parallel Processing FLUENT Model Compatibility

Using This Manual

What’s In This Manual The FLUENT User’s Guide tells you what you need to know to use FLUENT. It is divided into three volumes: • Volume 1 contains introductory information, as well as information about the user interface, file import and export, unit systems, grids, boundary conditions, and physical properties. • Volume 2 contains information about modeling fluid flow, moving zones, turbulence, heat transfer, species transport and reacting flows, pollutant formation, and acoustics. • Volume 3 contains information about flows that involve multiple phases, including solidification and melting, calculating a solution (including information about parallel processing) and postprocessing the results. A bibliography and an index for all three volumes of the User’s Guide are also provided, along with a nomenclature list.

! Under U.S. and international copyright law, Fluent is unable to distribute copies of the papers listed in the bibliography, other than those published internally by Fluent. Please use your library or a document delivery service to obtain copies of copyrighted papers. A brief description of what’s in each chapter follows: Volume 1 • Chapter 1, Getting Started, describes the capabilities of FLUENT and the way in which it interacts with other Fluent Inc. and third-party programs. It also advises you on how to choose the appropriate solver formulation for your application, gives an overview of the problem setup steps, and presents a sample session that you can work through at your own pace. Finally, this chapter provides information about accessing the FLUENT manuals on CD-ROM or in the installation area. • Chapter 2, User Interface, describes the mechanics of using the graphical user interface, the text interface, and the on-line help. It also provides instructions for remote and batch execution. (See the separate Text Command List for information about specific text interface commands.)

c Fluent Inc. January 28, 2003

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Using This Manual

• Chapter 3, Reading and Writing Files, contains information about the files that FLUENT can read and write, including hardcopy files. • Chapter 4, Unit Systems, describes how to use the standard and custom unit systems available in FLUENT. • Chapter 5, Reading and Manipulating Grids, describes the various sources of computational grids and explains how to obtain diagnostic information about the grid and how to modify it by scaling, translating, and other methods. This chapter also contains information about the use of non-conformal grids. • Chapter 6, Boundary Conditions, explains the different types of boundary conditions available in FLUENT, when to use them, how to define them, and how to define boundary profiles and volumetric sources and fix the value of a variable in a particular region. It also contains information about porous media and lumped parameter models. • Chapter 7, Physical Properties, explains how to define the physical properties of materials and the equations that FLUENT uses to compute the properties from the information that you input. Volume 2 • Chapter 8, Modeling Basic Fluid Flow, describes the governing equations and physical models used by FLUENT to compute fluid flow (including periodic flow, swirling and rotating flows, compressible flows, and inviscid flows), as well as the inputs you need to provide to use these models. • Chapter 9, Modeling Flows in Moving and Deforming Zones, describes the use of single rotating reference frames, multiple moving reference frames, mixing planes, sliding meshes, and dynamic meshes in FLUENT. • Chapter 10, Modeling Turbulence, describes FLUENT’s models for turbulent flow and when and how to use them. • Chapter 11, Modeling Heat Transfer, describes the physical models used by FLUENT to compute heat transfer (including convective and conductive heat transfer, natural convection, radiative heat transfer, and periodic heat transfer), as well as the inputs you need to provide to use these models. • Chapter 12, Introduction to Modeling Species Transport and Reacting Flows, provides an overview of the models available in FLUENT for species transport and reactions, as well as guidelines for selecting an appropriate model for your application.

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Using This Manual

• Chapter 13, Modeling Species Transport and Finite-Rate Chemistry, describes the finite-rate chemistry models in FLUENT and how to use them. This chapter also provides information about modeling species transport in non-reacting flows. • Chapter 14, Modeling Non-Premixed Combustion, describes the non-premixed combustion model and how to use it. This chapter includes details about using prePDF. • Chapter 15, Modeling Premixed Combustion, describes the premixed combustion model and how to use it. • Chapter 16, Modeling Partially Premixed Combustion, describes the partially premixed combustion model and how to use it. • Chapter 17, The Composition PDF Transport Model, describes the composition PDF transport model and how to use it. • Chapter 18, Modeling Pollutant Formation, describes the models for the formation of NOx and soot and how to use them. • Chapter 19, Predicting Aerodynamically Generated Noise, describes the acoustics model and how to use it. Volume 3 • Chapter 20, Introduction to Modeling Multiphase Flows, provides an overview of the models for multiphase flow (including the discrete phase, VOF, mixture, and Eulerian models), as well as guidelines for selecting an appropriate model for your application. • Chapter 21, Discrete Phase Models, describes the discrete phase models available in FLUENT and how to use them. • Chapter 22, General Multiphase Models, describes the general multiphase models available in FLUENT (VOF, mixture, and Eulerian) and how to use them. • Chapter 23, Modeling Solidification and Melting, describes FLUENT’s model for solidification and melting and how to use it. • Chapter 24, Using the Solver, describes the FLUENT solvers and how to use them. • Chapter 25, Grid Adaption, explains the solution-adaptive mesh refinement feature in FLUENT and how to use it. • Chapter 26, Creating Surfaces for Displaying and Reporting Data, explains how to create surfaces in the domain on which you can examine FLUENT solution data.


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Using This Manual

• Chapter 27, Graphics and Visualization, describes the graphics tools that you can use to examine your FLUENT solution. • Chapter 28, Alphanumeric Reporting, describes how to obtain reports of fluxes, forces, surface integrals, and other solution data. • Chapter 29, Field Function Definitions, defines the flow variables that appear in the variable selection drop-down lists in FLUENT panels, and tells you how to create your own custom field functions. • Chapter 30, Parallel Processing, explains the parallel processing features in FLUENT and how to use them. This chapter also provides information about partitioning your grid for parallel processing. • Appendix A, FLUENT Model Compatibility, presents a chart outlining the compatibility of several FLUENT model categories.

What’s in the Other Manuals In addition to this User’s Guide, there are several other manuals available to help you use FLUENT and its associated programs: • The Tutorial Guide contains a number of example problems with complete detailed instructions, commentary, and postprocessing of results. • The UDF Manual contains information about writing and using user-defined functions (UDFs). • The Text Command List provides a brief description of each of the commands in FLUENT’s text interface. • The GAMBIT manuals teach you how to use the GAMBIT preprocessor for geometry creation and mesh generation.

Typographical Conventions Several typographical conventions are used in this manual’s text to facilitate your learning process. • An exclamation point (!) in the margin marks an important note or warning. • Different type styles are used to indicate graphical user interface menu items and text interface menu items (e.g., Iso-Surface panel, surface/iso-surface command).

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Using This Manual

• The text interface type style is also used when illustrating exactly what appears on the screen or exactly what you need to type into a field in a panel. The information displayed on the screen is enclosed in a large box to distinguish it from the narrative text, and user inputs are often enclosed in smaller boxes. • A mini flow chart is used to indicate the menu selections that lead you to a specific command or panel. For example, Define −→Boundary Conditions... indicates that the Boundary Conditions... menu item can be selected from the Define pull-down menu, and display −→grid indicates that the grid command is available in the display text menu. The words before the arrows invoke menus (or submenus) and the arrows point from a specific menu toward the item you should select from that menu. In this manual, mini flow charts usually precede a description of a panel or command, or a screen illustration showing how to use the panel or command. They allow you to look up information about a command or panel and quickly determine how to access it without having to search the preceding material. • The menu selections that will lead you to a particular panel are also indicated (usually within a paragraph) using a “/”. For example, Define/Materials... tells you to choose the Materials... menu item from the Define pull-down menu.

Mathematical Conventions ~ • Where possible, vector quantities are displayed with a raised arrow (e.g., ~a, A). Boldfaced characters are reserved for vectors and matrices as they apply to linear algebra (e.g., the identity matrix, I). • The operator ∇, referred to as grad, nabla, or del, represents the partial derivative of a quantity with respect to all directions in the chosen coordinate system. In Cartesian coordinates, ∇ is defined to be ∂ ∂ ∂ ~ı + ~ + ~k ∂x ∂y ∂z ∇ appears in several ways: – The gradient of a scalar quantity is the vector whose components are the partial derivatives; for example, ∇p =


∂p ∂p ∂p ~ı + ~ + ~k ∂x ∂y ∂z

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Using This Manual

– The gradient of a vector quantity is a second-order tensor; for example, in Cartesian coordinates, ∇(~v ) =

!

∂ ∂ ∂ ~ı + ~ + ~k vx~ı + vy~ + vz~k ∂x ∂y ∂z

This tensor is usually written as         

∂vx ∂x

∂vx ∂y

∂vx ∂z

∂vy ∂x

∂vy ∂y

∂vy ∂z

∂vz ∂x

∂vz ∂y

∂vz ∂z

        

– The divergence of a vector quantity, which is the inner product between ∇ and a vector; for example, ∇ · ~v =

∂vx ∂vy ∂vz + + ∂x ∂y ∂z

– The operator ∇ · ∇, which is usually written as ∇2 and is known as the Laplacian; for example, ∇2 T =

∂2T ∂2T ∂2T + + ∂x2 ∂y 2 ∂z 2

∇2 T is different from the expression (∇T )2 , which is defined as 2

(∇T ) =

∂T ∂x

!2

∂T + ∂y

!2

∂T + ∂z

!2

• An exception to the use of ∇ is found in the discussion of Reynolds stresses in Chapter 10, where convention dictates the use of Cartesian tensor notation. In this chapter, you will also find that some velocity vector components are written as u, v, and w instead of the conventional v with directional subscripts.

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Using This Manual

When To Call Your Support Engineer The Fluent support engineers can help you to plan your CFD modeling projects and to overcome any difficulties you encounter while using FLUENT. If you encounter difficulties we invite you to call your support engineer for assistance. However, there are a few things that we encourage you to do before calling: • Read the section(s) of the manual containing information on the commands you are trying to use or the type of problem you are trying to solve. • Recall the exact steps you were following that led up to and caused the problem. • Write down the exact error message that appeared, if any. • For particularly difficult problems, save a journal or transcript file of the FLUENT session in which the problem occurred. This is the best source that we can use to reproduce the problem and thereby help to identify the cause.


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Using This Manual

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Contents

1 Getting Started

1-1

1.1

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-1

1.2

Program Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-2

1.3

Program Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-3

1.4

Overview of Using FLUENT . . . . . . . . . . . . . . . . . . . . . . . . .

1-5

1.4.1

Planning Your CFD Analysis . . . . . . . . . . . . . . . . . . . .

1-5

1.4.2

Problem Solving Steps . . . . . . . . . . . . . . . . . . . . . . . .

1-6

Starting FLUENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-7

1.5.1

Single-Precision and Double-Precision Solvers . . . . . . . . . . .

1-7

1.5.2

Starting FLUENT on a UNIX System . . . . . . . . . . . . . . .

1-8

1.5.3

Starting FLUENT on a Windows System . . . . . . . . . . . . . . 1-10

1.5.4

Startup Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

1.5

1.6

Choosing the Solver Formulation . . . . . . . . . . . . . . . . . . . . . . 1-13

1.7

Accessing the FLUENT Manuals . . . . . . . . . . . . . . . . . . . . . . . 1-17

1.8

1.7.1

Viewing the Manuals . . . . . . . . . . . . . . . . . . . . . . . . 1-17

1.7.2

Printing the Manuals . . . . . . . . . . . . . . . . . . . . . . . . 1-22

Sample Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24 1.8.1

Outline of Procedure . . . . . . . . . . . . . . . . . . . . . . . . 1-24

1.8.2

Reading and Checking the Grid . . . . . . . . . . . . . . . . . . 1-26

1.8.3

Selecting the Solver Formulation . . . . . . . . . . . . . . . . . . 1-28

1.8.4

Defining Physical Models . . . . . . . . . . . . . . . . . . . . . . 1-29

1.8.5

Specifying Fluid Properties . . . . . . . . . . . . . . . . . . . . . 1-29

1.8.6

Specifying Boundary Conditions . . . . . . . . . . . . . . . . . . 1-31

1.8.7

Adjusting Solution Controls . . . . . . . . . . . . . . . . . . . . . 1-32


TOC-1

CONTENTS

1.8.8

Saving the Case File . . . . . . . . . . . . . . . . . . . . . . . . . 1-33

1.8.9

Solving the Problem . . . . . . . . . . . . . . . . . . . . . . . . . 1-35

1.8.10

Saving the Results . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40

1.8.11

Examining the Results

1.8.12

Exiting from FLUENT . . . . . . . . . . . . . . . . . . . . . . . . 1-42

1.8.13

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-42

. . . . . . . . . . . . . . . . . . . . . . . 1-41

2 User Interface 2.1

2.2

2.3

2.4

2.5

TOC-2

2-1

Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-1

2.1.1

Console . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-1

2.1.2

Dialog Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-5

2.1.3

Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-9

2.1.4

Graphics Display Windows . . . . . . . . . . . . . . . . . . . . . 2-16

2.1.5

Customizing the Graphical User Interface (UNIX Systems Only) 2-19

Text User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21 2.2.1

Text Menu System . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21

2.2.2

Text Prompt System

2.2.3

Interrupts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27

2.2.4

System Commands

2.2.5

Text Menu Input from Character Strings . . . . . . . . . . . . . 2-28

. . . . . . . . . . . . . . . . . . . . . . . . 2-23

. . . . . . . . . . . . . . . . . . . . . . . . . 2-27

Using On-Line Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29 2.3.1

Using the GUI Help System . . . . . . . . . . . . . . . . . . . . . 2-29

2.3.2

Using the Text Interface Help System . . . . . . . . . . . . . . . 2-34

Remote Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-35 2.4.1

Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 2-35

2.4.2

Steps for Running on a Remote Machine

2.4.3

Starting the Solver Manually on the Remote Machine . . . . . . 2-36

2.4.4

Executing Remotely by Reading a Case File . . . . . . . . . . . . 2-37

. . . . . . . . . . . . . 2-35

Batch Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37


CONTENTS

2.5.1

Background Execution on UNIX Systems . . . . . . . . . . . . . 2-37

2.5.2

Batch Execution Options . . . . . . . . . . . . . . . . . . . . . . 2-39

2.6

Checkpointing a FLUENT Simulation . . . . . . . . . . . . . . . . . . . . 2-40

2.7

Exiting the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41

3 Reading and Writing Files 3.1

3.2

3.3

3-1

Shortcuts for Reading and Writing Files . . . . . . . . . . . . . . . . . .

3-2

3.1.1

Default File Suffixes . . . . . . . . . . . . . . . . . . . . . . . . .

3-2

3.1.2

Binary Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-2

3.1.3

Detecting File Format . . . . . . . . . . . . . . . . . . . . . . . .

3-3

3.1.4

Recent File List . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-3

3.1.5

Reading and Writing Compressed Files . . . . . . . . . . . . . .

3-3

3.1.6

Tilde Expansion (UNIX Systems Only) . . . . . . . . . . . . . .

3-5

3.1.7

Automatic Numbering of Files . . . . . . . . . . . . . . . . . . .

3-5

3.1.8

Disabling the Overwrite Confirmation Prompt . . . . . . . . . .

3-6

Reading Mesh Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-6

3.2.1

Reading TGrid Mesh Files . . . . . . . . . . . . . . . . . . . . . .

3-6

3.2.2

Reading and Importing GAMBIT and GeoMesh Mesh Files . . . .

3-6

3.2.3

Reading preBFC Unstructured Mesh Files . . . . . . . . . . . . .

3-7

3.2.4

Importing preBFC Structured Mesh Files . . . . . . . . . . . . .

3-7

3.2.5

Importing ANSYS Files . . . . . . . . . . . . . . . . . . . . . . .

3-7

3.2.6

Importing I-DEAS Universal Files . . . . . . . . . . . . . . . . . .

3-7

3.2.7

Importing NASTRAN Files . . . . . . . . . . . . . . . . . . . . .

3-8

3.2.8

Importing PATRAN Neutral Files . . . . . . . . . . . . . . . . . .

3-8

3.2.9

Importing Meshes and Data in CGNS Format . . . . . . . . . . .

3-8

3.2.10

Reading a New Grid File . . . . . . . . . . . . . . . . . . . . . .

3-9

Reading and Writing Case and Data Files . . . . . . . . . . . . . . . . .

3-9

3.3.1

Reading and Writing Case Files . . . . . . . . . . . . . . . . . .

3-9

3.3.2

Reading and Writing Data Files . . . . . . . . . . . . . . . . . . 3-10


TOC-3

CONTENTS

3.3.3

Reading and Writing Case and Data Files Together

. . . . . . . 3-11

3.3.4

Automatic Saving of Case and Data Files . . . . . . . . . . . . . 3-11

3.4

Reading FLUENT/UNS and RAMPANT Case and Data Files . . . . . . . 3-12

3.5

Importing FLUENT 4 Case Files . . . . . . . . . . . . . . . . . . . . . . . 3-12

3.6

Importing FIDAP Neutral Files . . . . . . . . . . . . . . . . . . . . . . . 3-13

3.7

Creating and Reading Journal Files . . . . . . . . . . . . . . . . . . . . . 3-13 3.7.1

3.8

Creating Transcript Files . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 3.8.1

3.9

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14

Reading and Writing Profile Files . . . . . . . . . . . . . . . . . . . . . . 3-15

3.10 Reading and Writing Boundary Conditions

. . . . . . . . . . . . . . . . 3-17

3.11 Writing a Boundary Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 3-17 3.12 Saving Hardcopy Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18 3.12.1

Using the Graphics Hardcopy Panel . . . . . . . . . . . . . . . . . 3-18

3.13 Exporting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 3.13.1

Using the Export Panel . . . . . . . . . . . . . . . . . . . . . . . 3-23

3.13.2

Export File Formats . . . . . . . . . . . . . . . . . . . . . . . . . 3-26

3.14 Grid-to-Grid Solution Interpolation . . . . . . . . . . . . . . . . . . . . . 3-30 3.14.1

Performing Grid-to-Grid Solution Interpolation . . . . . . . . . . 3-30

3.14.2

Format of the Interpolation File . . . . . . . . . . . . . . . . . . 3-31

3.15 Reading Scheme Source Files . . . . . . . . . . . . . . . . . . . . . . . . 3-33 3.16 The .fluent File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33 3.17 Saving the Panel Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33 3.18 Formats of Case and Data Files . . . . . . . . . . . . . . . . . . . . . . . 3-34

TOC-4

3.18.1

Formatting Conventions in Binary and Formatted Files . . . . . 3-34

3.18.2

Grid Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35

3.18.3

Other (Non-Grid) Case Sections . . . . . . . . . . . . . . . . . . 3-48

3.18.4

Data Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-51


CONTENTS

4 Unit Systems

4-1

4.1

Restrictions on Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-2

4.2

Units in Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-2

4.3

Built-In Unit Systems in FLUENT . . . . . . . . . . . . . . . . . . . . . .

4-3

4.4

Customizing Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-4

5 Reading and Manipulating Grids 5.1

5.2

5.3

5.4

5-1

Grid Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5-2

5.1.1

Examples of Acceptable Grid Topologies . . . . . . . . . . . . . .

5-2

5.1.2

Choosing the Appropriate Grid Type . . . . . . . . . . . . . . .

5-2

Grid Requirements and Considerations . . . . . . . . . . . . . . . . . . . 5-11 5.2.1

Geometry/Grid Requirements

. . . . . . . . . . . . . . . . . . . 5-11

5.2.2

Mesh Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12

Grid Import . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14 5.3.1

GAMBIT Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

5.3.2

GeoMesh Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

5.3.3

TGrid Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

5.3.4

preBFC Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

5.3.5

ICEMCFD Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 5-15

5.3.6

Grid Files from Third-Party CAD Packages . . . . . . . . . . . . 5-15

5.3.7

FLUENT/UNS and RAMPANT Case Files . . . . . . . . . . . . . 5-21

5.3.8

FLUENT 4 Case Files . . . . . . . . . . . . . . . . . . . . . . . . 5-21

5.3.9

FIDAP Neutral Files . . . . . . . . . . . . . . . . . . . . . . . . . 5-21

5.3.10

Reading Multiple Mesh Files . . . . . . . . . . . . . . . . . . . . 5-22

Non-Conformal Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-24 5.4.1

Non-Conformal Grid Calculations . . . . . . . . . . . . . . . . . 5-24

5.4.2

Requirements and Limitations of Non-Conformal Grids . . . . . 5-26

5.4.3

Using a Non-Conformal Grid in FLUENT . . . . . . . . . . . . . 5-28

5.4.4

Starting From a FLUENT/UNS or RAMPANT Case . . . . . . . . 5-30


TOC-5

CONTENTS

5.5

5.6

5.7

Checking the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-30 5.5.1

Grid Check Information . . . . . . . . . . . . . . . . . . . . . . . 5-30

5.5.2

Repairing Duplicate Shadow Nodes

. . . . . . . . . . . . . . . . 5-32

Reporting Grid Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 5-33 5.6.1

Grid Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-33

5.6.2

Memory Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34

5.6.3

Grid Zone Information

5.6.4

Partition Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 5-36

. . . . . . . . . . . . . . . . . . . . . . . 5-35

Modifying the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-36 5.7.1

Scaling the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-37

5.7.2

Translating the Grid . . . . . . . . . . . . . . . . . . . . . . . . . 5-38

5.7.3

Merging Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-39

5.7.4

Separating Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-41

5.7.5

Creating Periodic Zones . . . . . . . . . . . . . . . . . . . . . . . 5-46

5.7.6

Slitting Periodic Zones

5.7.7

Fusing Face Zones . . . . . . . . . . . . . . . . . . . . . . . . . . 5-48

5.7.8

Slitting Face Zones . . . . . . . . . . . . . . . . . . . . . . . . . . 5-49

5.7.9

Extruding Face Zones . . . . . . . . . . . . . . . . . . . . . . . . 5-50

5.7.10

Reordering the Domain and Zones . . . . . . . . . . . . . . . . . 5-51

5.7.11

Deleting, Deactivating, and Activating Zones . . . . . . . . . . . 5-52

. . . . . . . . . . . . . . . . . . . . . . . 5-47

6 Boundary Conditions 6.1

TOC-6

6-1

Overview of Defining Boundary Conditions . . . . . . . . . . . . . . . .

6-2

6.1.1

Available Boundary Types . . . . . . . . . . . . . . . . . . . . .

6-2

6.1.2

The Boundary Conditions Panel . . . . . . . . . . . . . . . . . . .

6-3

6.1.3

Changing Boundary Zone Types . . . . . . . . . . . . . . . . . .

6-3

6.1.4

Setting Boundary Conditions . . . . . . . . . . . . . . . . . . . .

6-4

6.1.5

Copying Boundary Conditions . . . . . . . . . . . . . . . . . . .

6-5

6.1.6

Selecting Boundary Zones in the Graphics Display . . . . . . . .

6-6


CONTENTS

6.2

6.3

6.4

6.5

6.6

6.1.7

Changing Boundary Zone Names . . . . . . . . . . . . . . . . . .

6-6

6.1.8

Defining Non-Uniform Boundary Conditions

. . . . . . . . . . .

6-7

6.1.9

Defining Transient Boundary Conditions . . . . . . . . . . . . . .

6-7

6.1.10

Saving and Reusing Boundary Conditions . . . . . . . . . . . . .

6-9

Flow Inlets and Exits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-10 6.2.1

Using Flow Boundary Conditions . . . . . . . . . . . . . . . . . . 6-10

6.2.2

Determining Turbulence Parameters . . . . . . . . . . . . . . . . 6-11

Pressure Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . . 6-17 6.3.1

Inputs at Pressure Inlet Boundaries . . . . . . . . . . . . . . . . 6-17

6.3.2

Default Settings at Pressure Inlet Boundaries . . . . . . . . . . . 6-23

6.3.3

Calculation Procedure at Pressure Inlet Boundaries . . . . . . . 6-23

Velocity Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 6-25 6.4.1

Inputs at Velocity Inlet Boundaries

6.4.2

Default Settings at Velocity Inlet Boundaries . . . . . . . . . . . 6-30

6.4.3

Calculation Procedure at Velocity Inlet Boundaries . . . . . . . . 6-30

Mass Flow Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . 6-32 6.5.1

Inputs at Mass Flow Inlet Boundaries . . . . . . . . . . . . . . . 6-32

6.5.2

Default Settings at Mass Flow Inlet Boundaries . . . . . . . . . . 6-38

6.5.3

Calculation Procedure at Mass Flow Inlet Boundaries . . . . . . 6-38

Inlet Vent Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 6-40 6.6.1

6.7

6.9

Inputs at Inlet Vent Boundaries . . . . . . . . . . . . . . . . . . 6-40

Intake Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 6-42 6.7.1

6.8

. . . . . . . . . . . . . . . . 6-25

Inputs at Intake Fan Boundaries . . . . . . . . . . . . . . . . . . 6-42

Pressure Outlet Boundary Conditions . . . . . . . . . . . . . . . . . . . 6-44 6.8.1

Inputs at Pressure Outlet Boundaries . . . . . . . . . . . . . . . 6-44

6.8.2

Default Settings at Pressure Outlet Boundaries . . . . . . . . . . 6-48

6.8.3

Calculation Procedure at Pressure Outlet Boundaries . . . . . . 6-48

Pressure Far-Field Boundary Conditions . . . . . . . . . . . . . . . . . . 6-50 6.9.1

Inputs at Pressure Far-Field Boundaries . . . . . . . . . . . . . . 6-50


TOC-7

CONTENTS

6.9.2

Default Settings at Pressure Far-Field Boundaries . . . . . . . . 6-52

6.9.3

Calculation Procedure at Pressure Far-Field Boundaries . . . . . 6-52

6.10 Outflow Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 6-54 6.10.1

FLUENT’s Treatment at Outflow Boundaries . . . . . . . . . . . 6-54

6.10.2

Using Outflow Boundaries . . . . . . . . . . . . . . . . . . . . . . 6-55

6.10.3

Mass Flow Split Boundary Conditions . . . . . . . . . . . . . . . 6-56

6.10.4

Other Inputs at Outflow Boundaries . . . . . . . . . . . . . . . . 6-57

6.11 Outlet Vent Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 6-58 6.11.1

Inputs at Outlet Vent Boundaries . . . . . . . . . . . . . . . . . 6-58

6.12 Exhaust Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 6-60 6.12.1

Inputs at Exhaust Fan Boundaries . . . . . . . . . . . . . . . . . 6-60

6.13 Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6-62 6.13.1

Inputs at Wall Boundaries . . . . . . . . . . . . . . . . . . . . . 6-62

6.13.2

Default Settings at Wall Boundaries . . . . . . . . . . . . . . . . 6-78

6.13.3

Shear-Stress Calculation Procedure at Wall Boundaries . . . . . 6-78

6.13.4

Heat Transfer Calculations at Wall Boundaries . . . . . . . . . . 6-78

6.14 Symmetry Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 6-81 6.14.1

Examples of Symmetry Boundaries . . . . . . . . . . . . . . . . . 6-81

6.14.2

Calculation Procedure at Symmetry Boundaries . . . . . . . . . 6-82

6.15 Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 6-84 6.15.1

Examples of Periodic Boundaries . . . . . . . . . . . . . . . . . . 6-84

6.15.2

Inputs for Periodic Boundaries . . . . . . . . . . . . . . . . . . . 6-84

6.15.3

Default Settings at Periodic Boundaries . . . . . . . . . . . . . . 6-85

6.15.4

Calculation Procedure at Periodic Boundaries . . . . . . . . . . . 6-85

6.16 Axis Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6-87 6.17 Fluid Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-88 6.17.1

Inputs for Fluid Zones . . . . . . . . . . . . . . . . . . . . . . . . 6-88

6.18 Solid Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-91 6.18.1

TOC-8

Inputs for Solid Zones . . . . . . . . . . . . . . . . . . . . . . . . 6-91


CONTENTS

6.19 Porous Media Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6-93 6.19.1

Limitations and Assumptions of the Porous Media Model . . . . 6-94

6.19.2

Momentum Equations for Porous Media . . . . . . . . . . . . . . 6-94

6.19.3

Treatment of the Energy Equation in Porous Media . . . . . . . 6-96

6.19.4

Treatment of Turbulence in Porous Media . . . . . . . . . . . . . 6-97

6.19.5

Effect of Porosity on Transient Scalar Equations . . . . . . . . . 6-97

6.19.6

User Inputs for Porous Media . . . . . . . . . . . . . . . . . . . . 6-98

6.19.7

Modeling Porous Media Based on Physical Velocity . . . . . . . . 6-109

6.19.8

Solution Strategies for Porous Media . . . . . . . . . . . . . . . . 6-110

6.19.9

Postprocessing for Porous Media . . . . . . . . . . . . . . . . . . 6-111

6.20 Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6-112 6.20.1

Fan Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-112

6.20.2

User Inputs for Fans . . . . . . . . . . . . . . . . . . . . . . . . . 6-113

6.20.3

Postprocessing for Fans . . . . . . . . . . . . . . . . . . . . . . . 6-119

6.21 Radiator Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 6-120 6.21.1

Radiator Equations . . . . . . . . . . . . . . . . . . . . . . . . . 6-120

6.21.2

User Inputs for Radiators . . . . . . . . . . . . . . . . . . . . . . 6-122

6.21.3

Postprocessing for Radiators . . . . . . . . . . . . . . . . . . . . 6-127

6.22 Porous Jump Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 6-129 6.23 Non-Reflecting Boundary Conditions . . . . . . . . . . . . . . . . . . . . 6-131 6.23.1


6.23.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-132

6.23.3

Using the Non-Reflecting Boundary Conditions . . . . . . . . . . 6-140

6.24 User-Defined Fan Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-141 6.24.1

Steps for Using the User-Defined Fan Model . . . . . . . . . . . . 6-141

6.24.2

Example of a User-Defined Fan . . . . . . . . . . . . . . . . . . . 6-142

6.25 Heat Exchanger Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-150 6.25.1

Overview and Restrictions of the Heat Exchanger Models . . . . 6-151

6.25.2

Heat Exchanger Model Theory . . . . . . . . . . . . . . . . . . . 6-152


TOC-9

CONTENTS

6.25.3

Using the Heat Exchanger Model . . . . . . . . . . . . . . . . . . 6-158

6.25.4

Using the Heat Exchanger Group . . . . . . . . . . . . . . . . . . 6-167

6.25.5

Postprocessing for the Heat Exchanger Model . . . . . . . . . . . 6-174

6.26 Boundary Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-174 6.26.1

Boundary Profile Specification Types . . . . . . . . . . . . . . . 6-175

6.26.2

Boundary Profile File Format . . . . . . . . . . . . . . . . . . . . 6-176

6.26.3

Using Boundary Profiles . . . . . . . . . . . . . . . . . . . . . . . 6-177

6.26.4

Reorienting Boundary Profiles . . . . . . . . . . . . . . . . . . . 6-180

6.27 Fixing the Values of Variables . . . . . . . . . . . . . . . . . . . . . . . . 6-183 6.27.1

Overview of Fixing the Value of a Variable . . . . . . . . . . . . 6-183

6.27.2

Procedure for Fixing Values of Variables in a Zone . . . . . . . . 6-185

6.28 Defining Mass, Momentum, Energy, and Other Sources . . . . . . . . . . 6-187 6.28.1

Procedure for Defining Sources . . . . . . . . . . . . . . . . . . . 6-188

6.29 Coupling Boundary Conditions with GT-Power . . . . . . . . . . . . . . 6-192 6.29.1

Requirements and Restrictions . . . . . . . . . . . . . . . . . . . 6-192

6.29.2

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-193

6.30 Coupling Boundary Conditions with WAVE . . . . . . . . . . . . . . . . 6-195 6.30.1

Requirements and Restrictions . . . . . . . . . . . . . . . . . . . 6-195

6.30.2

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-196

7 Physical Properties 7.1

7.2

TOC-10

7-1

Setting Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . .

7-2

7.1.1

Material Types . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7-3

7.1.2

Using the Materials Panel . . . . . . . . . . . . . . . . . . . . . .

7-3

7.1.3

Defining Properties Using Temperature-Dependent Functions . .

7-8

7.1.4

Customizing the Materials Database . . . . . . . . . . . . . . . . 7-12

Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14 7.2.1

Defining Density for Various Flow Regimes . . . . . . . . . . . . 7-14

7.2.2

Input of Constant Density

. . . . . . . . . . . . . . . . . . . . . 7-15


CONTENTS

7.3

7.4

7.5

7.6

7.7

7.2.3

Inputs for the Boussinesq Approximation . . . . . . . . . . . . . 7-15

7.2.4

Density as a Profile Function of Temperature . . . . . . . . . . . 7-15

7.2.5

Incompressible Ideal Gas Law . . . . . . . . . . . . . . . . . . . . 7-16

7.2.6

Ideal Gas Law for Compressible Flows . . . . . . . . . . . . . . . 7-16

7.2.7

Composition-Dependent Density for Multicomponent Mixtures . 7-17

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19 7.3.1

Input of Constant Viscosity . . . . . . . . . . . . . . . . . . . . . 7-19

7.3.2

Viscosity as a Function of Temperature . . . . . . . . . . . . . . 7-19

7.3.3

Defining the Viscosity Using Kinetic Theory

7.3.4

Composition-Dependent Viscosity for Multicomponent Mixtures

7.3.5

Viscosity for Non-Newtonian Fluids . . . . . . . . . . . . . . . . 7-24

. . . . . . . . . . . 7-22 7-22

Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29 7.4.1

Input of Constant Thermal Conductivity . . . . . . . . . . . . . 7-29

7.4.2

Thermal Conductivity as a Function of Temperature . . . . . . . 7-29

7.4.3

Defining the Thermal Conductivity Using Kinetic Theory . . . . 7-30

7.4.4

Composition-Dependent Thermal Conductivity for Multicomponent Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-30

7.4.5

Anisotropic Thermal Conductivity for Solids . . . . . . . . . . . 7-32

Specific Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-36 7.5.1

Input of Constant Specific Heat Capacity . . . . . . . . . . . . . 7-36

7.5.2

Specific Heat Capacity as a Function of Temperature . . . . . . . 7-37

7.5.3

Defining Specific Heat Capacity Using Kinetic Theory . . . . . . 7-37

7.5.4

Specific Heat Capacity as a Function of Composition . . . . . . . 7-37

Radiation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-38 7.6.1

Absorption Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 7-38

7.6.2

Scattering Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 7-40

7.6.3

Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-41

7.6.4

Reporting the Radiation Properties . . . . . . . . . . . . . . . . 7-41

Mass Diffusion Coefficients


. . . . . . . . . . . . . . . . . . . . . . . . . 7-42

TOC-11

CONTENTS

7.7.1

Fickian Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-42

7.7.2

Full Multicomponent Diffusion . . . . . . . . . . . . . . . . . . . 7-43

7.7.3

Thermal Diffusion Coefficients . . . . . . . . . . . . . . . . . . . 7-44

7.7.4

Mass Diffusion Coefficient Inputs . . . . . . . . . . . . . . . . . . 7-45

7.7.5

Mass Diffusion Coefficient Inputs for Turbulent Flow . . . . . . . 7-50

7.8

Standard State Enthalpies . . . . . . . . . . . . . . . . . . . . . . . . . . 7-50

7.9

Standard State Entropies . . . . . . . . . . . . . . . . . . . . . . . . . . 7-51

7.10 Molecular Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . 7-51 7.11 Kinetic Theory Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 7-51 7.12 Operating Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-53 7.12.1

The Effect of Numerical Roundoff on Pressure Calculation in LowMach-Number Flow . . . . . . . . . . . . . . . . . . . . . . . . . 7-53

7.12.2

Operating Pressure, Gauge Pressure, and Absolute Pressure . . . 7-53

7.12.3

Setting the Operating Pressure . . . . . . . . . . . . . . . . . . . 7-53

7.13 Reference Pressure Location . . . . . . . . . . . . . . . . . . . . . . . . . 7-55 7.14 Real Gas Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-55 7.14.1

The NIST Real Gas Model . . . . . . . . . . . . . . . . . . . . . 7-55

7.14.2

The User-Defined Real Gas Model . . . . . . . . . . . . . . . . . 7-59

8 Modeling Basic Fluid Flow

8-1

8.1

Overview of Physical Models in FLUENT . . . . . . . . . . . . . . . . . .

8-2

8.2

Continuity and Momentum Equations . . . . . . . . . . . . . . . . . . .

8-3

8.3

Periodic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8-5

8.3.1

Overview and Limitations . . . . . . . . . . . . . . . . . . . . . .

8-5

8.3.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8-6

8.3.3

User Inputs for the Segregated Solver . . . . . . . . . . . . . . .

8-8

8.3.4

User Inputs for the Coupled Solvers . . . . . . . . . . . . . . . .

8-9

8.3.5

Monitoring the Value of the Pressure Gradient . . . . . . . . . . 8-10

8.3.6

Postprocessing for Streamwise-Periodic Flows . . . . . . . . . . . 8-10

8.4

TOC-12

Swirling and Rotating Flows . . . . . . . . . . . . . . . . . . . . . . . . . 8-11


CONTENTS

8.5

8.6

8.4.1

Overview of Swirling and Rotating Flows . . . . . . . . . . . . . 8-12

8.4.2

Physics of Swirling and Rotating Flows . . . . . . . . . . . . . . 8-13

8.4.3

Turbulence Modeling in Swirling Flows . . . . . . . . . . . . . . 8-14

8.4.4

Grid Setup for Swirling and Rotating Flows . . . . . . . . . . . . 8-15

8.4.5

Modeling Axisymmetric Flows with Swirl or Rotation . . . . . . 8-15

Compressible Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-20 8.5.1

When to Use the Compressible Flow Model . . . . . . . . . . . . 8-21

8.5.2

Physics of Compressible Flows . . . . . . . . . . . . . . . . . . . 8-22

8.5.3

Modeling Inputs for Compressible Flows . . . . . . . . . . . . . . 8-23

8.5.4

Floating Operating Pressure . . . . . . . . . . . . . . . . . . . . 8-24

8.5.5

Solution Strategies for Compressible Flows . . . . . . . . . . . . 8-26

8.5.6

Reporting of Results for Compressible Flows . . . . . . . . . . . 8-27

Inviscid Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-28 8.6.1

Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-28

8.6.2

Setting Up an Inviscid Flow Model . . . . . . . . . . . . . . . . . 8-30

8.6.3

Solution Strategies for Inviscid Flows . . . . . . . . . . . . . . . 8-30

8.6.4

Postprocessing for Inviscid Flows . . . . . . . . . . . . . . . . . . 8-31

9 Modeling Flows in Moving and Deforming Zones

9-1

9.1

Overview of Moving Zone Approaches . . . . . . . . . . . . . . . . . . .

9-2

9.2

Flow in a Rotating Reference Frame . . . . . . . . . . . . . . . . . . . .

9-3

9.2.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9-3

9.2.2

Equations for a Rotating Reference Frame . . . . . . . . . . . . .

9-3

9.2.3

Grid Setup for a Single Rotating Reference Frame . . . . . . . .

9-8

9.2.4

Problem Setup for a Single Rotating Reference Frame . . . . . .

9-9

9.2.5

Choosing the Relative or Absolute Velocity Formulation . . . . . 9-10

9.2.6

Solution Strategies for a Rotating Reference Frame . . . . . . . . 9-10

9.2.7

Postprocessing for a Single Rotating Reference Frame . . . . . . 9-12

9.3

The Multiple Reference Frame (MRF) Model . . . . . . . . . . . . . . . 9-13


TOC-13

CONTENTS

9.4

9.5

9.6

TOC-14

9.3.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-13

9.3.2

The MRF Formulation . . . . . . . . . . . . . . . . . . . . . . . 9-16

9.3.3

Grid Setup for Multiple Reference Frames . . . . . . . . . . . . . 9-17

9.3.4

Problem Setup for Multiple Reference Frames . . . . . . . . . . . 9-18

9.3.5

Solution Strategies for Multiple Reference Frames

9.3.6

Postprocessing for Multiple Reference Frames . . . . . . . . . . . 9-19

. . . . . . . . 9-19

The Mixing Plane Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-20 9.4.1


9.4.2

Mixing Plane Theory . . . . . . . . . . . . . . . . . . . . . . . . 9-21

9.4.3

Problem Setup for a Mixing Plane Model . . . . . . . . . . . . . 9-25

9.4.4

Solution Strategies for Problems with Mixing Planes . . . . . . . 9-30

9.4.5

Postprocessing for the Mixing Plane Model . . . . . . . . . . . . 9-30

Sliding Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-31 9.5.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-31

9.5.2

Sliding Mesh Theory . . . . . . . . . . . . . . . . . . . . . . . . . 9-35

9.5.3

Setup and Solution of a Sliding Mesh Problem . . . . . . . . . . 9-38

9.5.4

Postprocessing for Sliding Meshes . . . . . . . . . . . . . . . . . 9-42

Dynamic Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-44 9.6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-44

9.6.2

Dynamic Mesh Conservation Equations . . . . . . . . . . . . . . 9-45

9.6.3

Dynamic Mesh Update Methods . . . . . . . . . . . . . . . . . . 9-46

9.6.4

Solid-Body Kinematics . . . . . . . . . . . . . . . . . . . . . . . 9-54

9.6.5

Problem Setup for Dynamic Meshes . . . . . . . . . . . . . . . . 9-56

9.6.6

Setting Dynamic Mesh Modeling Parameters . . . . . . . . . . . 9-57

9.6.7

Specifying the Motion of Dynamic Zones . . . . . . . . . . . . . 9-62

9.6.8

Previewing the Dynamic Mesh . . . . . . . . . . . . . . . . . . . 9-67

9.6.9

Defining In-Cylinder Events . . . . . . . . . . . . . . . . . . . . . 9-68

9.6.10

Guidelines for Setting Up an In-Cylinder Case . . . . . . . . . . 9-75

9.6.11

Crevice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-84


CONTENTS

10 Modeling Turbulence 10.1 Introduction

10-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1

10.2 Choosing a Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . 10-2 10.2.1

Reynolds-Averaged Approach vs. LES . . . . . . . . . . . . . . . 10-2

10.2.2

Reynolds (Ensemble) Averaging . . . . . . . . . . . . . . . . . . 10-3

10.2.3

Boussinesq Approach vs. Reynolds Stress Transport Models . . . 10-4

10.2.4

The Spalart-Allmaras Model . . . . . . . . . . . . . . . . . . . . 10-5

10.2.5

The Standard k- Model

10.2.6

The RNG k- Model . . . . . . . . . . . . . . . . . . . . . . . . . 10-6

10.2.7

The Realizable k- Model . . . . . . . . . . . . . . . . . . . . . . 10-7

10.2.8

The Standard k-ω Model . . . . . . . . . . . . . . . . . . . . . . 10-8

10.2.9

The Shear-Stress Transport (SST) k-ω Model . . . . . . . . . . . 10-8

. . . . . . . . . . . . . . . . . . . . . . 10-6

10.2.10 The v 2 -f Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-8 10.2.11 The Reynolds Stress Model (RSM) . . . . . . . . . . . . . . . . . 10-9 10.2.12 Computational Effort: CPU Time and Solution Behavior . . . . 10-9 10.3 The Spalart-Allmaras Model . . . . . . . . . . . . . . . . . . . . . . . . . 10-10 10.3.1

Transport Equation for the Spalart-Allmaras Model . . . . . . . 10-10

10.3.2

Modeling the Turbulent Viscosity . . . . . . . . . . . . . . . . . 10-11

10.3.3

Modeling the Turbulent Production . . . . . . . . . . . . . . . . 10-11

10.3.4

Modeling the Turbulent Destruction . . . . . . . . . . . . . . . . 10-12

10.3.5

The DES Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-13

10.3.6

Model Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-13

10.3.7

Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 10-13

10.3.8

Convective Heat and Mass Transfer Modeling . . . . . . . . . . . 10-14

10.4 The Standard, RNG, and Realizable k- Models . . . . . . . . . . . . . . 10-15 10.4.1


10.4.2

The RNG k- Model . . . . . . . . . . . . . . . . . . . . . . . . . 10-16

10.4.3

The Realizable k- Model . . . . . . . . . . . . . . . . . . . . . . 10-19

10.4.4

Modeling Turbulent Production in the k- Models . . . . . . . . 10-23


. . . . . . . . . . . . . . . . . . . . . . 10-15

TOC-15

CONTENTS

10.4.5

Effects of Buoyancy on Turbulence in the k- Models . . . . . . . 10-23

10.4.6

Effects of Compressibility on Turbulence in the k- Models . . . 10-24

10.4.7

Convective Heat and Mass Transfer Modeling in the k- Models . 10-25

10.5 The Standard and SST k-ω Models . . . . . . . . . . . . . . . . . . . . . 10-26 10.5.1

The Standard k-ω Model . . . . . . . . . . . . . . . . . . . . . . 10-26

10.5.2

The Shear-Stress Transport (SST) k-ω Model . . . . . . . . . . . 10-31

10.6 The Reynolds Stress Model (RSM) . . . . . . . . . . . . . . . . . . . . . 10-35 10.6.1

The Reynolds Stress Transport Equations . . . . . . . . . . . . . 10-35

10.6.2

Modeling Turbulent Diffusive Transport . . . . . . . . . . . . . . 10-36

10.6.3

Modeling the Pressure-Strain Term . . . . . . . . . . . . . . . . . 10-37

10.6.4

Effects of Buoyancy on Turbulence . . . . . . . . . . . . . . . . . 10-39

10.6.5

Modeling the Turbulence Kinetic Energy . . . . . . . . . . . . . 10-40

10.6.6

Modeling the Dissipation Rate . . . . . . . . . . . . . . . . . . . 10-40

10.6.7

Modeling the Turbulent Viscosity . . . . . . . . . . . . . . . . . 10-41

10.6.8

Boundary Conditions for the Reynolds Stresses . . . . . . . . . . 10-41

10.6.9

Convective Heat and Mass Transfer Modeling . . . . . . . . . . . 10-42

10.7 The Large Eddy Simulation (LES) Model . . . . . . . . . . . . . . . . . 10-43 10.7.1

Filtered Navier-Stokes Equations . . . . . . . . . . . . . . . . . . 10-44

10.7.2

Subgrid-Scale Models . . . . . . . . . . . . . . . . . . . . . . . . 10-45

10.7.3

Boundary Conditions for the LES Model . . . . . . . . . . . . . 10-47

10.8 Near-Wall Treatments for Wall-Bounded Turbulent Flows . . . . . . . . 10-47 10.8.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-47

10.8.2

Wall Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-49

10.8.3

Enhanced Wall Treatment . . . . . . . . . . . . . . . . . . . . . . 10-56

10.9 Grid Considerations for Turbulent Flow Simulations . . . . . . . . . . . 10-61

TOC-16

10.9.1

Near-Wall Mesh Guidelines for Wall Functions . . . . . . . . . . 10-61

10.9.2

Near-Wall Mesh Guidelines for the Enhanced Wall Treatment . . 10-62

10.9.3

Near-Wall Mesh Guidelines for the Spalart-Allmaras Model . . . 10-62

10.9.4

Near-Wall Mesh Guidelines for the k-ω Models . . . . . . . . . . 10-63


CONTENTS

10.9.5

Near-Wall Mesh Guidelines for Large Eddy Simulation . . . . . . 10-63

10.10 Problem Setup for Turbulent Flows . . . . . . . . . . . . . . . . . . . . . 10-64 10.10.1 Turbulence Options . . . . . . . . . . . . . . . . . . . . . . . . . 10-65 10.10.2 Defining Turbulence Boundary Conditions . . . . . . . . . . . . . 10-71 10.10.3 Providing an Initial Guess for k and (or k and ω) . . . . . . . . 10-73 10.11 Solution Strategies for Turbulent Flow Simulations . . . . . . . . . . . . 10-75 10.11.1 Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-75 10.11.2 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-75 10.11.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-76 10.11.4 RSM-Specific Solution Strategies . . . . . . . . . . . . . . . . . . 10-76 10.11.5 LES-Specific Solution Strategies . . . . . . . . . . . . . . . . . . 10-77 10.12 Postprocessing for Turbulent Flows . . . . . . . . . . . . . . . . . . . . . 10-79 10.12.1 Custom Field Functions for Turbulence . . . . . . . . . . . . . . 10-81 10.12.2 Postprocessing LES Statistics . . . . . . . . . . . . . . . . . . . . 10-82 10.12.3 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-82 11 Modeling Heat Transfer

11-1

11.1 Overview of Heat Transfer Models in FLUENT . . . . . . . . . . . . . . . 11-1 11.2 Convective and Conductive Heat Transfer . . . . . . . . . . . . . . . . . 11-1 11.2.1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-2

11.2.2

User Inputs for Heat Transfer . . . . . . . . . . . . . . . . . . . . 11-6

11.2.3

Solution Process for Heat Transfer . . . . . . . . . . . . . . . . . 11-9

11.2.4

Reporting and Displaying Heat Transfer Quantities . . . . . . . . 11-10

11.2.5

Exporting Heat Flux Data . . . . . . . . . . . . . . . . . . . . . 11-12

11.3 Radiative Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-13 11.3.1

Introduction to Radiative Heat Transfer . . . . . . . . . . . . . . 11-14

11.3.2

Choosing a Radiation Model . . . . . . . . . . . . . . . . . . . . 11-16

11.3.3

The Discrete Transfer Radiation Model (DTRM) . . . . . . . . . 11-19

11.3.4

The P-1 Radiation Model . . . . . . . . . . . . . . . . . . . . . . 11-22


TOC-17

CONTENTS

11.3.5

The Rosseland Radiation Model . . . . . . . . . . . . . . . . . . 11-26

11.3.6

The Discrete Ordinates (DO) Radiation Model . . . . . . . . . . 11-28

11.3.7

The Surface-to-Surface (S2S) Radiation Model . . . . . . . . . . 11-38

11.3.8

Radiation in Combusting Flows

11.3.9

Overview of Using the Radiation Models

. . . . . . . . . . . . . . . . . . 11-41 . . . . . . . . . . . . . 11-44

11.3.10 Selecting the Radiation Model . . . . . . . . . . . . . . . . . . . 11-46 11.3.11 Defining the Ray Tracing for the DTRM . . . . . . . . . . . . . . 11-47 11.3.12 Computing or Reading the View Factors for the S2S Model . . . 11-49 11.3.13 Defining the Angular Discretization for the DO Model . . . . . . 11-55 11.3.14 Defining Non-Gray Radiation for the DO Model . . . . . . . . . 11-56 11.3.15 Defining Material Properties for Radiation . . . . . . . . . . . . 11-57 11.3.16 Setting Radiation Boundary Conditions . . . . . . . . . . . . . . 11-58 11.3.17 Setting Solution Parameters for Radiation . . . . . . . . . . . . . 11-63 11.3.18 Solving the Problem . . . . . . . . . . . . . . . . . . . . . . . . . 11-66 11.3.19 Reporting and Displaying Radiation Quantities . . . . . . . . . . 11-67 11.3.20 Displaying Rays and Clusters for the DTRM . . . . . . . . . . . 11-69 11.4 Periodic Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-71 11.4.1


11.4.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-72

11.4.3

Modeling Periodic Heat Transfer . . . . . . . . . . . . . . . . . . 11-73

11.4.4

Solution Strategies for Periodic Heat Transfer . . . . . . . . . . . 11-75

11.4.5

Monitoring Convergence . . . . . . . . . . . . . . . . . . . . . . . 11-76

11.4.6

Postprocessing for Periodic Heat Transfer . . . . . . . . . . . . . 11-76

11.5 Buoyancy-Driven Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-78

TOC-18

11.5.1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-78

11.5.2

Modeling Natural Convection in a Closed Domain . . . . . . . . 11-78

11.5.3

The Boussinesq Model . . . . . . . . . . . . . . . . . . . . . . . . 11-79

11.5.4

User Inputs for Buoyancy-Driven Flows . . . . . . . . . . . . . . 11-79

11.5.5

Solution Strategies for Buoyancy-Driven Flows . . . . . . . . . . 11-82


CONTENTS

11.5.6

Postprocessing for Buoyancy-Driven Flows . . . . . . . . . . . . 11-83

12 Introduction to Modeling Species Transport and Reacting Flows

12-1

12.1 Overview of Species and Reaction Modeling . . . . . . . . . . . . . . . . 12-1 12.2 Approaches to Reaction Modeling . . . . . . . . . . . . . . . . . . . . . . 12-1 12.2.1

Generalized Finite-Rate Model . . . . . . . . . . . . . . . . . . . 12-2

12.2.2

Non-Premixed Combustion Model . . . . . . . . . . . . . . . . . 12-2

12.2.3

Premixed Combustion Model . . . . . . . . . . . . . . . . . . . . 12-2

12.2.4

Partially Premixed Combustion Model . . . . . . . . . . . . . . . 12-3

12.2.5

Composition PDF Transport Combustion Model . . . . . . . . . 12-3

12.3 Choosing a Reaction Model . . . . . . . . . . . . . . . . . . . . . . . . . 12-3 13 Modeling Species Transport and Finite-Rate Chemistry

13-1

13.1 Volumetric Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2 13.1.1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2

13.1.2

Overview of User Inputs for Modeling Species Transport and Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11

13.1.3

Enabling Species Transport and Reactions and Choosing the Mixture Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-13

13.1.4

Defining Properties for the Mixture and Its Constituent Species . 13-15

13.1.5

Defining Boundary Conditions for Species . . . . . . . . . . . . . 13-30

13.1.6

Defining Other Sources of Chemical Species . . . . . . . . . . . . 13-30

13.1.7

Solution Procedures for Chemical Mixing and Finite-Rate Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-30

13.1.8

Postprocessing for Species Calculations . . . . . . . . . . . . . . 13-34

13.1.9

Importing a Chemical Mechanism from CHEMKIN . . . . . . . . 13-35

13.2 Wall Surface Reactions and Chemical Vapor Deposition . . . . . . . . . 13-36 13.2.1

Overview of Surface Species and Wall Surface Reactions . . . . . 13-36

13.2.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-36

13.2.3

User Inputs for Wall Surface Reactions . . . . . . . . . . . . . . 13-41

13.2.4

Solution Procedures for Wall Surface Reactions . . . . . . . . . . 13-42


TOC-19

CONTENTS

13.2.5

Postprocessing for Surface Reactions . . . . . . . . . . . . . . . . 13-42

13.3 Particle Surface Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 13-43 13.3.1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-43

13.3.2

User Inputs for Particle Surface Reactions . . . . . . . . . . . . . 13-47

13.3.3

Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-48

13.4 Species Transport Without Reactions . . . . . . . . . . . . . . . . . . . . 13-49 14 Modeling Non-Premixed Combustion

14-1

14.1 Description of the Equilibrium Mixture Fraction/ PDF Model . . . . . . 14-1 14.1.1

Benefits and Limitations of the Non-Premixed Approach . . . . . 14-2

14.1.2

Details of the Non-Premixed Approach . . . . . . . . . . . . . . 14-2

14.1.3

Restrictions and Special Cases for the Non-Premixed Model . . . 14-18

14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry . . . . . 14-22 14.2.1

Single-Mixture-Fraction Approach . . . . . . . . . . . . . . . . . 14-22

14.2.2

Two-Mixture-Fraction Approach . . . . . . . . . . . . . . . . . . 14-23

14.2.3

The Look-Up Table Concept . . . . . . . . . . . . . . . . . . . . 14-25

14.3 User Inputs for the Non-Premixed Equilibrium Model . . . . . . . . . . . 14-29 14.3.1

Problem Definition Procedure in prePDF . . . . . . . . . . . . . . 14-29

14.3.2

Informational Messages and Errors Reported by prePDF . . . . . 14-68

14.3.3

Non-Premixed Model Input and Solution Procedures in FLUENT 14-72

14.3.4

Modeling Liquid Fuel Combustion Using the Non-Premixed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-84

14.3.5

Modeling Coal Combustion Using the Non-Premixed Model . . . 14-84

14.4 The Laminar Flamelet Model . . . . . . . . . . . . . . . . . . . . . . . . 14-91

TOC-20

14.4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-91

14.4.2

Restrictions and Assumptions . . . . . . . . . . . . . . . . . . . . 14-92

14.4.3

The Flamelet Concept . . . . . . . . . . . . . . . . . . . . . . . . 14-92

14.4.4

Flamelet Generation . . . . . . . . . . . . . . . . . . . . . . . . . 14-95

14.4.5

Flamelet Import . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-98


CONTENTS

14.4.6

User Inputs for the Laminar Flamelet Model . . . . . . . . . . . 14-100

14.5 Adding New Species to the prePDF Database . . . . . . . . . . . . . . . 14-118 15 Modeling Premixed Combustion

15-1

15.1 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.1.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1

15.1.2

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-2

15.2 Premixed Combustion Theory . . . . . . . . . . . . . . . . . . . . . . . . 15-3 15.2.1

Propagation of the Flame Front . . . . . . . . . . . . . . . . . . 15-3

15.2.2

Turbulent Flame Speed . . . . . . . . . . . . . . . . . . . . . . . 15-4

15.2.3

Premixed Combustion Model Formulation in FLUENT . . . . . . 15-8

15.2.4

Calculation of Temperature . . . . . . . . . . . . . . . . . . . . . 15-8

15.2.5

Calculation of Density . . . . . . . . . . . . . . . . . . . . . . . . 15-9

15.3 Using the Premixed Combustion Model . . . . . . . . . . . . . . . . . . 15-10 15.3.1

Enabling the remixed Combustion Model . . . . . . . . . . . . . 15-10

15.3.2

Choosing an Adiabatic or Non-Adiabatic Model

15.3.3

Modifying the Constants for the Premixed Combustion Model . . 15-11

15.3.4

Defining Physical Properties for the Unburnt Mixture . . . . . . 15-12

15.3.5

Setting Boundary Conditions for the Progress Variable . . . . . . 15-13

15.3.6

Initializing the Progress Variable . . . . . . . . . . . . . . . . . . 15-13

15.3.7

Postprocessing for Premixed Combustion Calculations . . . . . . 15-13

15.3.8

Starting from a FLUENT 5 Premixed Combustion Case File . . . 15-15

16 Modeling Partially Premixed Combustion

. . . . . . . . . 15-11

16-1


Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1

16.1.2

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1

16.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-2 16.2.1

Calculation of Scalar Quantities . . . . . . . . . . . . . . . . . . 16-2

16.2.2

Laminar Flame Speed . . . . . . . . . . . . . . . . . . . . . . . . 16-3


TOC-21

CONTENTS

16.3 Using the Partially Premixed Combustion Model . . . . . . . . . . . . . 16-4 16.3.1

Setup and Solution Procedure . . . . . . . . . . . . . . . . . . . 16-4

16.3.2

Modifying the Unburnt Mixture Property Polynomials in prePDF 16-5

17 The Composition PDF Transport Model

17-1


Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1

17.1.2

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1

17.2 Composition PDF Transport Theory . . . . . . . . . . . . . . . . . . . . 17-2 17.2.1

Solution of the PDF Transport Equation . . . . . . . . . . . . . 17-3

17.2.2

Particle Convection . . . . . . . . . . . . . . . . . . . . . . . . . 17-3

17.2.3

Particle Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-4

17.2.4

Particle Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-5

17.2.5

The ISAT Algorithm

. . . . . . . . . . . . . . . . . . . . . . . . 17-7

17.3 Using the Composition PDF Transport Model . . . . . . . . . . . . . . . 17-9 17.3.1

Enabling the Composition PDF Transport Model . . . . . . . . . 17-10

17.3.2

Setting Integration Parameters . . . . . . . . . . . . . . . . . . . 17-10

17.3.3

Selecting the Particle Mixing Model . . . . . . . . . . . . . . . . 17-12

17.3.4

Defining the Solution Parameters . . . . . . . . . . . . . . . . . . 17-12

17.3.5

Monitoring the Solution . . . . . . . . . . . . . . . . . . . . . . . 17-12

17.3.6

Monitoring ISAT . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-14

17.3.7

Efficient Use of ISAT . . . . . . . . . . . . . . . . . . . . . . . . 17-15

17.3.8

Unsteady Composition PDF Transport Simulations . . . . . . . . 17-16

17.3.9

Compressible Composition PDF Transport Simulations . . . . . 17-16

17.3.10 Postprocessing for Composition PDF Transport Calculations . . 17-17 18 Modeling Pollutant Formation

18-1

18.1 NOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1

TOC-22

18.1.1


18.1.2

Governing Equations for NOx Transport . . . . . . . . . . . . . . 18-3


CONTENTS

18.1.3

Thermal NOx Formation . . . . . . . . . . . . . . . . . . . . . . 18-3

18.1.4

Prompt NOx Formation . . . . . . . . . . . . . . . . . . . . . . . 18-8

18.1.5

Fuel NOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . 18-11

18.1.6

NOx Formation From Reburning . . . . . . . . . . . . . . . . . . 18-22

18.1.7

NOx Formation in Turbulent Flows

18.1.8

Using the NOx Model . . . . . . . . . . . . . . . . . . . . . . . . 18-26

. . . . . . . . . . . . . . . . 18-23

18.2 Soot Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-32 18.2.1


18.2.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-33

18.2.3

Using the Soot Models

. . . . . . . . . . . . . . . . . . . . . . . 18-36

19 Predicting Aerodynamically Generated Noise

19-1


Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-2

19.1.2

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-2

19.2 Acoustics Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-3 19.3 Using the Acoustics Model . . . . . . . . . . . . . . . . . . . . . . . . . . 19-5 19.3.1

Enabling the Acoustics Model . . . . . . . . . . . . . . . . . . . 19-6

19.3.2

Setting Model Parameters . . . . . . . . . . . . . . . . . . . . . . 19-7

19.3.3

Specifying Source Surfaces . . . . . . . . . . . . . . . . . . . . . 19-8

19.3.4

Specifying Acoustics Receivers . . . . . . . . . . . . . . . . . . . 19-11

19.3.5

Postprocessing for the Acoustics Model . . . . . . . . . . . . . . 19-13

20 Introduction to Modeling Multiphase Flows

20-1

20.1 Multiphase Flow Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2 20.2 Examples of Multiphase Systems . . . . . . . . . . . . . . . . . . . . . . 20-4 20.3 Approaches to Multiphase Modeling . . . . . . . . . . . . . . . . . . . . 20-4 20.3.1

The Euler-Lagrange Approach . . . . . . . . . . . . . . . . . . . 20-4

20.3.2

The Euler-Euler Approach . . . . . . . . . . . . . . . . . . . . . 20-5

20.4 Choosing a Multiphase Model . . . . . . . . . . . . . . . . . . . . . . . . 20-6


TOC-23

CONTENTS

20.4.1

General Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . 20-6

20.4.2

Detailed Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . 20-7

21 Discrete Phase Models

21-1

21.1 Overview and Limitations of the Discrete Phase Models . . . . . . . . . 21-1 21.1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-1

21.1.2

Particles in Turbulent Flows . . . . . . . . . . . . . . . . . . . . 21-2

21.1.3

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-2

21.1.4

Overview of Discrete Phase Modeling Procedures . . . . . . . . . 21-4

21.2 Trajectory Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-5 21.2.1

Equations of Motion for Particles . . . . . . . . . . . . . . . . . . 21-5

21.2.2

Turbulent Dispersion of Particles . . . . . . . . . . . . . . . . . . 21-11

21.2.3

Particle Erosion and Accretion . . . . . . . . . . . . . . . . . . . 21-17

21.3 Heat and Mass Transfer Calculations . . . . . . . . . . . . . . . . . . . . 21-18 21.3.1

Particle Types in FLUENT . . . . . . . . . . . . . . . . . . . . . 21-18

21.3.2

Law 1/Law 6: Inert Heating or Cooling . . . . . . . . . . . . . . 21-19

21.3.3

Law 2: Droplet Vaporization . . . . . . . . . . . . . . . . . . . . 21-21

21.3.4

Law 3: Droplet Boiling . . . . . . . . . . . . . . . . . . . . . . . 21-24

21.3.5

Law 4: Devolatilization . . . . . . . . . . . . . . . . . . . . . . . 21-25

21.3.6

Law 5: Surface Combustion . . . . . . . . . . . . . . . . . . . . . 21-34

21.4 Spray Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-40 21.4.1

Atomizer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-40

21.4.2

Droplet Collision Model . . . . . . . . . . . . . . . . . . . . . . . 21-55

21.4.3

Spray Breakup Models

21.4.4

Dynamic Drag Model . . . . . . . . . . . . . . . . . . . . . . . . 21-66

. . . . . . . . . . . . . . . . . . . . . . . 21-58

21.5 Coupling Between the Discrete and Continuous Phases . . . . . . . . . . 21-68 21.6 Overview of Using the Discrete Phase Models . . . . . . . . . . . . . . . 21-71 21.7 Discrete Phase Model Options . . . . . . . . . . . . . . . . . . . . . . . . 21-71 21.7.1

TOC-24

Including Radiation Heat Transfer to the Particles . . . . . . . . 21-71


CONTENTS

21.7.2

Including the Thermophoretic Force on the Particles . . . . . . . 21-71

21.7.3

Including a Coupled Heat-Mass Solution on the Particles . . . . 21-73

21.7.4

Including Brownian Motion Effects on the Particles . . . . . . . . 21-73

21.7.5

Including Saffman Lift Force Effects on the Particles . . . . . . . 21-73

21.7.6

Monitoring Erosion/Accretion of Particles at Walls . . . . . . . . 21-73

21.7.7

Alternate Drag Laws

21.7.8

User-Defined Functions . . . . . . . . . . . . . . . . . . . . . . . 21-74

. . . . . . . . . . . . . . . . . . . . . . . . 21-73

21.8 Particle Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-74 21.8.1

Inputs for Particle Tracking . . . . . . . . . . . . . . . . . . . . . 21-74

21.8.2

Options for Spray Modeling . . . . . . . . . . . . . . . . . . . . . 21-75

21.9 Setting Initial Conditions for the Discrete Phase . . . . . . . . . . . . . . 21-76 21.9.1

Overview of Initial Conditions . . . . . . . . . . . . . . . . . . . 21-76

21.9.2

Injection Types

21.9.3

Particle Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-79

21.9.4

Creating, Copying, Deleting, and Listing Injections . . . . . . . . 21-79

21.9.5

Defining Injection Properties . . . . . . . . . . . . . . . . . . . . 21-81

21.9.6

Point Properties for Single Injections . . . . . . . . . . . . . . . . 21-84

21.9.7

Point Properties for Group Injections . . . . . . . . . . . . . . . 21-84

21.9.8

Point Properties for Cone Injections . . . . . . . . . . . . . . . . 21-88

21.9.9

Point Properties for Surface Injections . . . . . . . . . . . . . . . 21-90

. . . . . . . . . . . . . . . . . . . . . . . . . . . 21-77

21.9.10 Point Properties for Plain-Orifice Atomizer Injections . . . . . . 21-91 21.9.11 Point Properties for Pressure-Swirl Atomizer Injections . . . . . 21-91 21.9.12 Point Properties for Air-Blast/Air-Assist Atomizer Injections . . 21-92 21.9.13 Point Properties for Flat-Fan Atomizer Injections . . . . . . . . . 21-93 21.9.14 Point Properties for Effervescent Atomizer Injections . . . . . . . 21-93 21.9.15 Modeling Turbulent Dispersion of Particles . . . . . . . . . . . . 21-94 21.9.16 Custom Particle Laws . . . . . . . . . . . . . . . . . . . . . . . . 21-96 21.9.17 Defining Properties Common to More Than One Injection . . . . 21-97 21.10 Setting Boundary Conditions for the Discrete Phase . . . . . . . . . . . 21-100


TOC-25

CONTENTS

21.10.1 Discrete Phase Boundary Condition Types . . . . . . . . . . . . 21-100 21.10.2 Inputs for Discrete Phase Boundary Conditions . . . . . . . . . . 21-104 21.11 Setting Material Properties for the Discrete Phase . . . . . . . . . . . . . 21-105 21.11.1 Summary of Property Inputs . . . . . . . . . . . . . . . . . . . . 21-105 21.11.2 Setting Discrete-Phase Physical Properties . . . . . . . . . . . . 21-105 21.12 Calculation Procedures for the Discrete Phase . . . . . . . . . . . . . . . 21-113 21.12.1 Parameters Controlling the Numerical Integration . . . . . . . . 21-113 21.12.2 Performing Trajectory Calculations . . . . . . . . . . . . . . . . 21-116 21.12.3 Resetting the Interphase Exchange Terms . . . . . . . . . . . . . 21-120 21.12.4 Parallel Processing for the Discrete Phase Model . . . . . . . . . 21-120 21.13 Postprocessing for the Discrete Phase . . . . . . . . . . . . . . . . . . . . 21-121 21.13.1 Graphical Display of Trajectories . . . . . . . . . . . . . . . . . . 21-121 21.13.2 Reporting of Trajectory Fates . . . . . . . . . . . . . . . . . . . . 21-124 21.13.3 Step-by-Step Reporting of Trajectories . . . . . . . . . . . . . . . 21-128 21.13.4 Reporting Current Positions for Unsteady Tracking . . . . . . . . 21-129 21.13.5 Reporting of Interphase Exchange Terms and Discrete Phase Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-131 21.13.6 Trajectory Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 21-132 21.13.7 Histogram Reporting of Samples . . . . . . . . . . . . . . . . . . 21-133 21.13.8 Summary Reporting of Current Particles . . . . . . . . . . . . . 21-134 21.13.9 Postprocessing of Erosion/Accretion Rates . . . . . . . . . . . . 21-136 22 General Multiphase Models

22-1

22.1 Choosing a General Multiphase Model . . . . . . . . . . . . . . . . . . . 22-2 22.1.1

Overview and Limitations of the VOF Model . . . . . . . . . . . 22-2

22.1.2

Overview and Limitations of the Mixture Model . . . . . . . . . 22-3

22.1.3

Overview and Limitations of the Eulerian Model . . . . . . . . . 22-5

22.2 Volume of Fluid (VOF) Model . . . . . . . . . . . . . . . . . . . . . . . 22-7

TOC-26

22.2.1

The Volume Fraction Equation . . . . . . . . . . . . . . . . . . . 22-7

22.2.2

Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-8


CONTENTS

22.2.3

The Momentum Equation . . . . . . . . . . . . . . . . . . . . . . 22-8

22.2.4

The Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . 22-8

22.2.5

Additional Scalar Equations . . . . . . . . . . . . . . . . . . . . 22-9

22.2.6

Interpolation Near the Interface . . . . . . . . . . . . . . . . . . 22-9

22.2.7

Time Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 22-12

22.2.8

Surface Tension and Wall Adhesion . . . . . . . . . . . . . . . . 22-13

22.3 Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-16 22.3.1

Continuity Equation for the Mixture . . . . . . . . . . . . . . . . 22-16

22.3.2

Momentum Equation for the Mixture . . . . . . . . . . . . . . . 22-17

22.3.3

Energy Equation for the Mixture . . . . . . . . . . . . . . . . . . 22-17

22.3.4

Relative (Slip) Velocity and the Drift Velocity . . . . . . . . . . . 22-18

22.3.5

Volume Fraction Equation for the Secondary Phases . . . . . . . 22-19

22.4 Eulerian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-20 22.4.1

Volume Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 22-20

22.4.2

Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . 22-21

22.4.3

Interphase Exchange Coefficients . . . . . . . . . . . . . . . . . . 22-25

22.4.4

Solids Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-30

22.4.5

Solids Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 22-32

22.4.6

Granular Temperature . . . . . . . . . . . . . . . . . . . . . . . . 22-33

22.4.7

Description of Heat Transfer . . . . . . . . . . . . . . . . . . . . 22-34

22.4.8

Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . 22-35

22.4.9

Solution Method in FLUENT . . . . . . . . . . . . . . . . . . . . 22-42

22.5 Description of Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . 22-44 22.5.1

Unidirectional Constant Mass Transfer . . . . . . . . . . . . . . . 22-44

22.5.2

UDF-Prescribed Mass Transfer . . . . . . . . . . . . . . . . . . . 22-44

22.5.3

Mass Transfer through Cavitation . . . . . . . . . . . . . . . . . 22-45

22.6 Setting Up a General Multiphase Problem . . . . . . . . . . . . . . . . . 22-50 22.6.1

Steps for Using the General Multiphase Models . . . . . . . . . . 22-51

22.6.2

Additional Guidelines for Eulerian Multiphase Simulations . . . . 22-52


TOC-27

CONTENTS

22.6.3

Enabling the Multiphase Model and Specifying the Number of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-53

22.6.4

Selecting the VOF Formulation . . . . . . . . . . . . . . . . . . . 22-54

22.6.5

Defining a Homogeneous Multiphase Flow . . . . . . . . . . . . . 22-56

22.6.6

Defining Mass Transfer Effects . . . . . . . . . . . . . . . . . . . 22-56

22.6.7

Including Cavitation Effects . . . . . . . . . . . . . . . . . . . . . 22-57

22.6.8

Overview of Defining the Phases . . . . . . . . . . . . . . . . . . 22-58

22.6.9

Defining Phases for the VOF Model . . . . . . . . . . . . . . . . 22-58

22.6.10 Defining Phases for the Mixture Model . . . . . . . . . . . . . . 22-62 22.6.11 Defining Phases for the Eulerian Model . . . . . . . . . . . . . . 22-64 22.6.12 Defining Heat Transfer for the Eulerian Model . . . . . . . . . . 22-71 22.6.13 Including Body Forces . . . . . . . . . . . . . . . . . . . . . . . . 22-72 22.6.14 Setting Time-Dependent Parameters for the VOF Model . . . . . 22-72 22.6.15 Selecting a Turbulence Model for an Eulerian Multiphase Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-74 22.6.16 Setting Boundary Conditions . . . . . . . . . . . . . . . . . . . . 22-75 22.6.17 Setting Initial Volume Fractions . . . . . . . . . . . . . . . . . . 22-89 22.6.18 Inputs for Compressible VOF and Mixture Model Calculations . 22-89 22.6.19 Inputs for Solidification/Melting VOF Calculations . . . . . . . . 22-90 22.7 Solution Strategies for General Multiphase Problems . . . . . . . . . . . 22-90 22.7.1

Solution Strategies for the VOF Model . . . . . . . . . . . . . . . 22-90

22.7.2

Solution Strategies for the Mixture Model . . . . . . . . . . . . . 22-91

22.7.3

Solution Strategies for the Eulerian Model . . . . . . . . . . . . . 22-92

22.8 Postprocessing for General Multiphase Problems . . . . . . . . . . . . . 22-93

TOC-28

22.8.1

Available Postprocessing Variables . . . . . . . . . . . . . . . . . 22-93

22.8.2

Displaying Velocity Vectors for Individual Phases . . . . . . . . . 22-95

22.8.3

Reporting Fluxes for Individual Phases . . . . . . . . . . . . . . 22-95

22.8.4

Reporting Forces on Walls for Individual Phases . . . . . . . . . 22-95

22.8.5

Reporting Flow Rates for Individual Phases . . . . . . . . . . . . 22-95


CONTENTS

23 Modeling Solidification and Melting

23-1

23.1 Overview and Limitations of the Solidification/Melting Model . . . . . . 23-1 23.1.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-1

23.1.2

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-2

23.2 Theory for the Solidification/Melting Model . . . . . . . . . . . . . . . . 23-3 23.2.1

Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-3

23.2.2

Momentum Equations . . . . . . . . . . . . . . . . . . . . . . . . 23-4

23.2.3

Turbulence Equations . . . . . . . . . . . . . . . . . . . . . . . . 23-5

23.2.4

Species Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 23-5

23.2.5

Pull Velocity for Continuous Casting . . . . . . . . . . . . . . . . 23-6

23.2.6

Contact Resistance at Walls . . . . . . . . . . . . . . . . . . . . 23-7

23.3 Using the Solidification/Melting Model . . . . . . . . . . . . . . . . . . . 23-8 23.3.1

Setup Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-8

23.3.2

Procedures for Modeling Continuous Casting . . . . . . . . . . . 23-10

23.3.3

Solution Procedure

23.3.4

Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-11

24 Using the Solver

. . . . . . . . . . . . . . . . . . . . . . . . . 23-11

24-1

24.1 Overview of Numerical Schemes . . . . . . . . . . . . . . . . . . . . . . . 24-2 24.1.1

Segregated Solution Method . . . . . . . . . . . . . . . . . . . . 24-2

24.1.2

Coupled Solution Method . . . . . . . . . . . . . . . . . . . . . . 24-4

24.1.3

Linearization: Implicit vs. Explicit . . . . . . . . . . . . . . . . . 24-4

24.2 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-7 24.2.1

First-Order Upwind Scheme . . . . . . . . . . . . . . . . . . . . . 24-8

24.2.2

Power-Law Scheme

24.2.3

Second-Order Upwind Scheme . . . . . . . . . . . . . . . . . . . 24-10

24.2.4

QUICK Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-10

24.2.5

Central-Differencing Scheme . . . . . . . . . . . . . . . . . . . . 24-11

24.2.6

Linearized Form of the Discrete Equation . . . . . . . . . . . . . 24-12


. . . . . . . . . . . . . . . . . . . . . . . . . 24-8

TOC-29

CONTENTS

24.2.7

Under-Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 24-12

24.2.8

Temporal Discretization . . . . . . . . . . . . . . . . . . . . . . . 24-12

24.2.9

Evaluation of Derivatives . . . . . . . . . . . . . . . . . . . . . . 24-15

24.3 The Segregated Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-16 24.3.1

Discretization of the Momentum Equation . . . . . . . . . . . . . 24-16

24.3.2

Discretization of the Continuity Equation . . . . . . . . . . . . . 24-17

24.3.3

Pressure-Velocity Coupling . . . . . . . . . . . . . . . . . . . . . 24-19

24.3.4

Steady-State and Time-Dependent Calculations . . . . . . . . . . 24-22

24.4 The Coupled Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-23 24.4.1

Governing Equations in Vector Form . . . . . . . . . . . . . . . . 24-23

24.4.2

Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-24

24.4.3

Time Marching for Steady-State Flows . . . . . . . . . . . . . . . 24-27

24.4.4

Temporal Discretization for Unsteady Flows . . . . . . . . . . . . 24-29

24.5 Multigrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-30 24.5.1

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-30

24.5.2

Multigrid Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-32

24.5.3

Algebraic Multigrid (AMG) . . . . . . . . . . . . . . . . . . . . . 24-35

24.5.4

Full-Approximation Storage (FAS) Multigrid . . . . . . . . . . . 24-39

24.6 Overview of How to Use the Solver . . . . . . . . . . . . . . . . . . . . . 24-42 24.7 Choosing the Discretization Scheme

. . . . . . . . . . . . . . . . . . . . 24-43

24.7.1

First Order vs. Second Order . . . . . . . . . . . . . . . . . . . . 24-43

24.7.2

Other Discretization Schemes . . . . . . . . . . . . . . . . . . . . 24-44

24.7.3

Choosing the Pressure Interpolation Scheme . . . . . . . . . . . . 24-44

24.7.4

Choosing the Density Interpolation Scheme . . . . . . . . . . . . 24-44

24.7.5

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-45

24.8 Choosing the Pressure-Velocity Coupling Method . . . . . . . . . . . . . 24-46

TOC-30

24.8.1

SIMPLE vs. SIMPLEC . . . . . . . . . . . . . . . . . . . . . . . 24-46

24.8.2

PISO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-47

24.8.3

User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-47


CONTENTS

24.9 Setting Under-Relaxation Factors . . . . . . . . . . . . . . . . . . . . . . 24-48 24.10 Changing the Courant Number . . . . . . . . . . . . . . . . . . . . . . . 24-49 24.10.1 Courant Numbers for the Coupled Explicit Solver . . . . . . . . 24-49 24.10.2 Courant Numbers for the Coupled Implicit Solver

. . . . . . . . 24-50

24.10.3 User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-50 24.11 Turning On FAS Multigrid . . . . . . . . . . . . . . . . . . . . . . . . . 24-51 24.11.1 Setting Coarse Grid Levels . . . . . . . . . . . . . . . . . . . . . 24-51 24.12 Setting Solution Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-53 24.13 Initializing the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-55 24.13.1 Initializing the Entire Flow Field . . . . . . . . . . . . . . . . . . 24-55 24.13.2 Patching Values in Selected Cells . . . . . . . . . . . . . . . . . . 24-57 24.14 Performing Steady-State Calculations . . . . . . . . . . . . . . . . . . . . 24-59 24.15 Performing Time-Dependent Calculations . . . . . . . . . . . . . . . . . 24-60 24.15.1 User Inputs for Time-Dependent Problems . . . . . . . . . . . . 24-62 24.15.2 Adaptive Time Stepping

. . . . . . . . . . . . . . . . . . . . . . 24-67

24.15.3 Postprocessing for Time-Dependent Problems . . . . . . . . . . . 24-69 24.16 Monitoring Solution Convergence . . . . . . . . . . . . . . . . . . . . . . 24-70 24.16.1 Monitoring Residuals . . . . . . . . . . . . . . . . . . . . . . . . 24-70 24.16.2 Monitoring Statistics . . . . . . . . . . . . . . . . . . . . . . . . 24-77 24.16.3 Monitoring Forces and Moments . . . . . . . . . . . . . . . . . . 24-78 24.16.4 Monitoring Surface Integrals . . . . . . . . . . . . . . . . . . . . 24-82 24.16.5 Monitoring Volume Integrals . . . . . . . . . . . . . . . . . . . . 24-85 24.17 Animating the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-88 24.17.1 Defining an Animation Sequence . . . . . . . . . . . . . . . . . . 24-89 24.17.2 Playing an Animation Sequence . . . . . . . . . . . . . . . . . . 24-92 24.17.3 Saving an Animation Sequence . . . . . . . . . . . . . . . . . . . 24-95 24.17.4 Reading an Animation Sequence . . . . . . . . . . . . . . . . . . 24-97 24.18 Executing Commands During the Calculation . . . . . . . . . . . . . . . 24-97 24.18.1 Specifying the Commands to be Executed . . . . . . . . . . . . . 24-97


TOC-31

CONTENTS

24.18.2 Defining Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-98 24.18.3 Saving Files During the Calculation . . . . . . . . . . . . . . . . 24-100 24.19 Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 24-100 24.19.1 Judging Convergence . . . . . . . . . . . . . . . . . . . . . . . . 24-101 24.19.2 Step-by-Step Solution Processes . . . . . . . . . . . . . . . . . . 24-102 24.19.3 Modifying Algebraic Multigrid Parameters . . . . . . . . . . . . 24-103 24.19.4 Setting FAS Multigrid Parameters . . . . . . . . . . . . . . . . . 24-108 24.19.5 Modifying Multi-Stage Time-Stepping Parameters . . . . . . . . 24-111 25 Grid Adaption

25-1

25.1 Using Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-2 25.1.1

Adaption Example . . . . . . . . . . . . . . . . . . . . . . . . . . 25-2

25.1.2

Adaption Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . 25-4

25.2 The Static Adaption Process . . . . . . . . . . . . . . . . . . . . . . . . 25-6 25.2.1

Adaption and Mask Registers . . . . . . . . . . . . . . . . . . . . 25-6

25.2.2

Hanging Node Adaption . . . . . . . . . . . . . . . . . . . . . . . 25-8

25.2.3

Conformal Adaption . . . . . . . . . . . . . . . . . . . . . . . . . 25-10

25.2.4

Conformal vs. Hanging Node Adaption . . . . . . . . . . . . . . 25-13

25.3 Boundary Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-14 25.3.1

Boundary Adaption Example . . . . . . . . . . . . . . . . . . . . 25-14

25.3.2

Steps for Performing Boundary Adaption . . . . . . . . . . . . . 25-14

25.4 Gradient Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-18 25.4.1

Gradient Adaption Approach . . . . . . . . . . . . . . . . . . . . 25-18

25.4.2

Steady Gradient Adaption Example . . . . . . . . . . . . . . . . 25-20

25.4.3

Steps for Performing Gradient Adaption . . . . . . . . . . . . . . 25-20

25.5 Dynamic Gradient Adaption . . . . . . . . . . . . . . . . . . . . . . . . . 25-23 25.5.1

Dynamic Gradient Adaption Approach . . . . . . . . . . . . . . 25-23

25.6 Isovalue Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-25 25.6.1

TOC-32

Isovalue Adaption Example . . . . . . . . . . . . . . . . . . . . . 25-25


CONTENTS

25.6.2

Steps for Performing Isovalue Adaption . . . . . . . . . . . . . . 25-25

25.7 Region Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-28 25.7.1

Defining a Region . . . . . . . . . . . . . . . . . . . . . . . . . . 25-28

25.7.2

Region Adaption Example . . . . . . . . . . . . . . . . . . . . . 25-28

25.7.3

Steps for Performing Region Adaption . . . . . . . . . . . . . . . 25-30

25.8 Volume Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-32 25.8.1

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-32

25.8.2

Volume Adaption Example . . . . . . . . . . . . . . . . . . . . . 25-32

25.8.3

Steps for Performing Volume Adaption . . . . . . . . . . . . . . 25-34

25.9 y + and y ∗ Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-35 25.9.1

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-35

25.9.2

y + Adaption Example . . . . . . . . . . . . . . . . . . . . . . . . 25-35

25.9.3

Steps for Performing y + or y ∗ Adaption . . . . . . . . . . . . . . 25-35

25.10 Managing Adaption Registers . . . . . . . . . . . . . . . . . . . . . . . . 25-38 25.10.1 Manipulating Adaption Registers . . . . . . . . . . . . . . . . . . 25-39 25.10.2 Modifying Adaption Marks . . . . . . . . . . . . . . . . . . . . . 25-41 25.10.3 Displaying Registers . . . . . . . . . . . . . . . . . . . . . . . . . 25-42 25.10.4 Adapting to Registers . . . . . . . . . . . . . . . . . . . . . . . . 25-44 25.11 Grid Adaption Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-44 25.12 Improving the Grid by Smoothing and Swapping . . . . . . . . . . . . . 25-48 25.12.1 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-48 25.12.2 Face Swapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-51 25.12.3 Combining Skewness-Based Smoothing and Face Swapping . . . 25-53 26 Creating Surfaces for Displaying and Reporting Data

26-1

26.1 Using Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-2 26.2 Zone Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-3 26.3 Partition Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-4 26.4 Point Surfaces


. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-6

TOC-33

CONTENTS

26.4.1

Using the Point Tool

. . . . . . . . . . . . . . . . . . . . . . . . 26-7

26.5 Line and Rake Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-9 26.5.1

Using the Line Tool . . . . . . . . . . . . . . . . . . . . . . . . . 26-10

26.6 Plane Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-13 26.6.1

Using the Plane Tool . . . . . . . . . . . . . . . . . . . . . . . . 26-15

26.7 Quadric Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-18 26.8 Isosurfaces

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-20

26.9 Clipping Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-22 26.10 Transforming Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-24 26.11 Grouping, Renaming, and Deleting Surfaces . . . . . . . . . . . . . . . . 26-26 27 Graphics and Visualization

27-1

27.1 Basic Graphics Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 27-2 27.1.1

Displaying the Grid . . . . . . . . . . . . . . . . . . . . . . . . . 27-2

27.1.2

Displaying Contours and Profiles . . . . . . . . . . . . . . . . . . 27-10

27.1.3

Displaying Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 27-17

27.1.4

Displaying Pathlines . . . . . . . . . . . . . . . . . . . . . . . . . 27-25

27.1.5

Displaying Results on a Sweep Surface . . . . . . . . . . . . . . . 27-31

27.2 Customizing the Graphics Display . . . . . . . . . . . . . . . . . . . . . 27-33 27.2.1

Overlay of Graphics . . . . . . . . . . . . . . . . . . . . . . . . . 27-33

27.2.2

Opening Multiple Graphics Windows . . . . . . . . . . . . . . . 27-34

27.2.3

Controlling Captions . . . . . . . . . . . . . . . . . . . . . . . . . 27-35

27.2.4

Adding Text to the Graphics Window . . . . . . . . . . . . . . . 27-36

27.2.5

Changing the Colormap . . . . . . . . . . . . . . . . . . . . . . . 27-39

27.2.6

Adding Lights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-43

27.2.7

Modifying the Rendering Options . . . . . . . . . . . . . . . . . 27-46

27.3 Controlling the Mouse Button Functions . . . . . . . . . . . . . . . . . . 27-49 27.4 Modifying the View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-51 27.4.1

TOC-34

Scaling, Centering, Rotating, Translating, and Zooming the Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-51


CONTENTS

27.4.2

Controlling Perspective and Camera Parameters . . . . . . . . . 27-54

27.4.3

Saving and Restoring Views . . . . . . . . . . . . . . . . . . . . . 27-56

27.4.4

Mirroring and Periodic Repeats . . . . . . . . . . . . . . . . . . . 27-58

27.5 Composing a Scene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-61 27.5.1

Selecting the Object(s) to be Manipulated . . . . . . . . . . . . . 27-62

27.5.2

Changing an Object’s Display Properties . . . . . . . . . . . . . 27-62

27.5.3

Transforming Geometric Objects in a Scene . . . . . . . . . . . . 27-65

27.5.4

Modifying Isovalues . . . . . . . . . . . . . . . . . . . . . . . . . 27-67

27.5.5

Modifying Pathline Attributes . . . . . . . . . . . . . . . . . . . 27-69

27.5.6

Deleting an Object from the Scene . . . . . . . . . . . . . . . . . 27-70

27.5.7

Adding a Bounding Frame . . . . . . . . . . . . . . . . . . . . . 27-70

27.6 Animating Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-72 27.6.1

Creating an Animation . . . . . . . . . . . . . . . . . . . . . . . 27-73

27.6.2

Playing an Animation . . . . . . . . . . . . . . . . . . . . . . . . 27-74

27.6.3

Saving an Animation . . . . . . . . . . . . . . . . . . . . . . . . 27-75

27.6.4

Reading an Animation File . . . . . . . . . . . . . . . . . . . . . 27-77

27.6.5

Notes on Animation . . . . . . . . . . . . . . . . . . . . . . . . . 27-77

27.7 Creating Videos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-78 27.7.1

Recording Animations To Video . . . . . . . . . . . . . . . . . . 27-78

27.7.2

Equipment Required . . . . . . . . . . . . . . . . . . . . . . . . . 27-79

27.7.3

Recording an Animation with FLUENT . . . . . . . . . . . . . . 27-79

27.7.4

General Information . . . . . . . . . . . . . . . . . . . . . . . . . 27-87

27.8 Histogram and XY Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-87 27.8.1

Plot Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-87

27.8.2

XY Plots of Solution Data . . . . . . . . . . . . . . . . . . . . . 27-89

27.8.3

XY Plots of File Data . . . . . . . . . . . . . . . . . . . . . . . . 27-94

27.8.4

XY Plots of Circumferential Averages . . . . . . . . . . . . . . . 27-96

27.8.5

XY Plot File Format . . . . . . . . . . . . . . . . . . . . . . . . 27-98

27.8.6

Residual Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-99


TOC-35

CONTENTS

27.8.7

Solution Histograms . . . . . . . . . . . . . . . . . . . . . . . . . 27-99

27.8.8

Modifying Axis Attributes . . . . . . . . . . . . . . . . . . . . . 27-100

27.8.9

Modifying Curve Attributes . . . . . . . . . . . . . . . . . . . . . 27-103

27.9 Turbomachinery Postprocessing . . . . . . . . . . . . . . . . . . . . . . . 27-105 27.9.1

Defining the Turbomachinery Topology . . . . . . . . . . . . . . 27-105

27.9.2

Generating Reports of Turbomachinery Data . . . . . . . . . . . 27-108

27.9.3

Displaying Turbomachinery Averaged Contours . . . . . . . . . . 27-117

27.9.4

Displaying Turbomachinery 2D Contours . . . . . . . . . . . . . 27-118

27.9.5

Generating Averaged XY Plots of Turbomachinery Solution Data 27-121

27.9.6

Globally Setting the Turbomachinery Topology . . . . . . . . . . 27-122

27.9.7

Turbomachinery-Specific Variables . . . . . . . . . . . . . . . . . 27-123

27.10 Fast Fourier Transform (FFT) Postprocessing . . . . . . . . . . . . . . . 27-123 27.10.1 Limitations of the FFT Algorithm . . . . . . . . . . . . . . . . . 27-124 27.10.2 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-124 27.10.3 Fast Fourier Transform (FFT) . . . . . . . . . . . . . . . . . . . 27-125 27.10.4 Using the FFT Utility . . . . . . . . . . . . . . . . . . . . . . . . 27-126 28 Alphanumeric Reporting

28-1

28.1 Reporting Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-1 28.2 Fluxes Through Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . 28-2 28.2.1

Generating a Flux Report . . . . . . . . . . . . . . . . . . . . . . 28-2

28.3 Forces on Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-4 28.3.1

Computing Forces and Moments . . . . . . . . . . . . . . . . . . 28-4

28.3.2

Generating a Force or Moment Report . . . . . . . . . . . . . . . 28-5

28.4 Projected Surface Area Calculations . . . . . . . . . . . . . . . . . . . . 28-6 28.5 Surface Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-7 28.5.1

Computing Surface Integrals . . . . . . . . . . . . . . . . . . . . 28-8

28.5.2

Generating a Surface Integral Report . . . . . . . . . . . . . . . 28-10

28.6 Volume Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-12

TOC-36


CONTENTS

28.6.1

Computing Volume Integrals . . . . . . . . . . . . . . . . . . . . 28-12

28.6.2

Generating a Volume Integral Report . . . . . . . . . . . . . . . 28-14

28.7 Histogram Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-15 28.8 Reference Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-16 28.8.1

Setting Reference Values . . . . . . . . . . . . . . . . . . . . . . 28-16

28.8.2

Setting the Reference Zone . . . . . . . . . . . . . . . . . . . . . 28-17

28.9 Summary Reports of Case Settings . . . . . . . . . . . . . . . . . . . . . 28-18 28.9.1

Generating a Summary Report . . . . . . . . . . . . . . . . . . . 28-18

29 Field Function Definitions

29-1

29.1 Node and Cell Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-1 29.1.1

Cell Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-1

29.1.2

Node Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-2

29.2 Velocity Reporting Options . . . . . . . . . . . . . . . . . . . . . . . . . 29-3 29.3 Field Variables Listed by Category . . . . . . . . . . . . . . . . . . . . . 29-5 29.4 Alphabetical Listing of Field Variables and Their Definitions . . . . . . . 29-17 29.5 Custom Field Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-45 29.5.1

Creating a Custom Field Function . . . . . . . . . . . . . . . . . 29-45

29.5.2

Manipulating, Saving, and Loading Custom Field Functions . . . 29-47

29.5.3

Sample Custom Field Functions . . . . . . . . . . . . . . . . . . 29-49

30 Parallel Processing

30-1

30.1 Introduction to Parallel Processing . . . . . . . . . . . . . . . . . . . . . 30-1 30.2 Starting the Parallel Version of the Solver . . . . . . . . . . . . . . . . . 30-4 30.2.1

Starting the Parallel Solver on a UNIX System . . . . . . . . . . 30-4

30.2.2

Starting the Parallel Solver on a LINUX System . . . . . . . . . 30-7

30.2.3

Starting the Parallel Solver on a Windows System . . . . . . . . 30-10

30.3 Using a Parallel Network of Workstations . . . . . . . . . . . . . . . . . 30-13 30.3.1

Configuring the Network . . . . . . . . . . . . . . . . . . . . . . 30-13

30.3.2

The Hosts Database . . . . . . . . . . . . . . . . . . . . . . . . . 30-16


TOC-37

CONTENTS

30.3.3

Checking Network Connectivity . . . . . . . . . . . . . . . . . . 30-17

30.4 Partitioning the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-18 30.4.1

Overview of Grid Partitioning . . . . . . . . . . . . . . . . . . . 30-18

30.4.2

Partitioning the Grid Automatically . . . . . . . . . . . . . . . . 30-19

30.4.3

Partitioning the Grid Manually . . . . . . . . . . . . . . . . . . . 30-21

30.4.4

Grid Partitioning Methods . . . . . . . . . . . . . . . . . . . . . 30-26

30.4.5

Checking the Partitions . . . . . . . . . . . . . . . . . . . . . . . 30-33

30.4.6

Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 30-35

30.5 Checking and Improving Parallel Performance . . . . . . . . . . . . . . . 30-36 30.5.1

Checking Parallel Performance . . . . . . . . . . . . . . . . . . . 30-36

30.5.2

Optimizing the Parallel Solver . . . . . . . . . . . . . . . . . . . 30-36

30.6 Running Parallel FLUENT under SGE . . . . . . . . . . . . . . . . . . . 30-38 30.6.1

Overview of FLUENT and SGE Integration . . . . . . . . . . . . 30-38

30.6.2

Configuring SGE for FLUENT . . . . . . . . . . . . . . . . . . . . 30-39

30.6.3

Running a FLUENT Simulation under SGE . . . . . . . . . . . . 30-42

30.7 Running Parallel FLUENT under LSF . . . . . . . . . . . . . . . . . . . . 30-43 30.7.1

Overview of FLUENT and LSF Integration . . . . . . . . . . . . . 30-43

30.7.2

Checkpointing and Restarting . . . . . . . . . . . . . . . . . . . 30-44

30.7.3

Configuring LSF for FLUENT

30.7.4

Submitting a FLUENT Job . . . . . . . . . . . . . . . . . . . . . 30-46

30.7.5

Checkpointing FLUENT Jobs . . . . . . . . . . . . . . . . . . . . 30-47

30.7.6

Restarting FLUENT Jobs . . . . . . . . . . . . . . . . . . . . . . 30-47

30.7.7

Migrating FLUENT Jobs . . . . . . . . . . . . . . . . . . . . . . . 30-47

30.7.8

Using FLUENT and LSF . . . . . . . . . . . . . . . . . . . . . . . 30-48

A FLUENT Model Compatibility

. . . . . . . . . . . . . . . . . . . 30-45

A-1

A.1 FLUENT Model Compatibility Chart . . . . . . . . . . . . . . . . . . . . A-1

TOC-38


Chapter 1.

Getting Started

This chapter provides an introduction to FLUENT, an explanation of its capabilities, and instructions for starting the solver and choosing the solver formulation. In addition, a sample session is presented. The sample session assumes that the grid file has already been generated. The grid file is included on the documentation CD. • Section 1.1: Introduction • Section 1.2: Program Structure • Section 1.3: Program Capabilities • Section 1.4: Overview of Using FLUENT • Section 1.5: Starting FLUENT • Section 1.6: Choosing the Solver Formulation • Section 1.7: Accessing the FLUENT Manuals • Section 1.8: Sample Session

1.1

Introduction

FLUENT is a state-of-the-art computer program for modeling fluid flow and heat transfer in complex geometries. FLUENT provides complete mesh flexibility, solving your flow problems with unstructured meshes that can be generated about complex geometries with relative ease. Supported mesh types include 2D triangular/quadrilateral, 3D tetrahedral/hexahedral/pyramid/wedge, and mixed (hybrid) meshes. FLUENT also allows you to refine or coarsen your grid based on the flow solution. FLUENT is written in the C computer language and makes full use of the flexibility and power offered by the language. Consequently, true dynamic memory allocation, efficient data structures, and flexible solver control are all made possible. In addition, FLUENT uses a client/server architecture, which allows it to run as separate simultaneous processes on client desktop workstations and powerful compute servers, for efficient execution, interactive control, and complete flexibility of machine or operating system type. All functions required to compute a solution and display the results are accessible in FLUENT through an interactive, menu-driven interface. The user interface is written in a language called Scheme, a dialect of LISP. The advanced user can customize and enhance the interface by writing menu macros and functions. Contact your support engineer for details.


1-1

Getting Started

1.2

Program Structure

Your FLUENT package includes the following products: • FLUENT, the solver. • prePDF, the preprocessor for modeling non-premixed combustion in FLUENT. • GAMBIT, the preprocessor for geometry modeling and mesh generation. • TGrid, an additional preprocessor that can generate volume meshes from existing boundary meshes. • filters (translators) for import of surface and volume meshes from CAD/CAE packages such as ANSYS, CGNS, I-DEAS, NASTRAN, PATRAN, and others. Figure 1.2.1 shows the organizational structure of these components.

! Note that a “grid” is the same thing as a “mesh”; the two words are used interchangeably here and throughout this manual. GAMBIT

Geometry or Mesh

⋅ geometry setup

Packages

⋅ 2D/3D mesh generation

2D/3D Mesh

Other CAD/CAE

Boundary Mesh

Boundary and/or Volume Mesh

prePDF ⋅ calculation of PDF look-up tables

PDF files

FLUENT ⋅ mesh import and adaption ⋅ physical models ⋅ boundary conditions ⋅ material properties ⋅ calculation ⋅ postprocessing

TGrid Mesh

⋅ 2D triangular mesh ⋅ 3D tetrahedral mesh ⋅ 2D or 3D hybrid mesh

Mesh

Figure 1.2.1: Basic Program Structure

You can create your geometry and grid using GAMBIT. See the GAMBIT documentation for details. You can also use TGrid to generate a triangular, tetrahedral, or hybrid volume mesh from an existing boundary mesh (created by GAMBIT or a third-party CAD/CAE

1-2


1.3 Program Capabilities

package). See the TGrid User’s Guide for details. It is also possible to create grids for FLUENT using ANSYS (Swanson Analysis Systems, Inc.), CGNS (CFD general notation system), or I-DEAS (SDRC); or MSC/ARIES, MSC/PATRAN, or MSC/NASTRAN (all from MacNeal-Schwendler Corporation). Interfaces to other CAD/CAE packages may be made available in the future, based on customer requirements, but most CAD/CAE packages can export grids in one of the above formats. Once a grid has been read into FLUENT, all remaining operations are performed within the solver. These include setting boundary conditions, defining fluid properties, executing the solution, refining the grid, and viewing and postprocessing the results. Note that preBFC and GeoMesh are the names of Fluent preprocessors that were used before the introduction of GAMBIT. You may see some references to preBFC and GeoMesh in this manual, for those users who are still using grids created by these programs.

1.3

Program Capabilities

The FLUENT solver has the following modeling capabilities: • 2D planar, 2D axisymmetric, 2D axisymmetric with swirl (rotationally symmetric), and 3D flows • Quadrilateral, triangular, hexahedral (brick), tetrahedral, prism (wedge), pyramid, and mixed element meshes • Steady-state or transient flows • Incompressible or compressible flows, including all speed regimes (low subsonic, transonic, supersonic, and hypersonic flows) • Inviscid, laminar, and turbulent flows • Newtonian or non-Newtonian flows • Heat transfer, including forced, natural, and mixed convection, conjugate (solid/fluid) heat transfer, and radiation • Chemical species mixing and reaction, including homogeneous and heterogeneous combustion models and surface deposition/reaction models • Free surface and multiphase models for gas-liquid, gas-solid, and liquid-solid flows • Lagrangian trajectory calculation for dispersed phase (particles/droplets/bubbles), including coupling with continuous phase • Cavitation model • Phase change model for melting/solidification applications


1-3

Getting Started

• Porous media with non-isotropic permeability, inertial resistance, solid heat conduction, and porous-face pressure jump conditions • Lumped parameter models for fans, pumps, radiators, and heat exchangers • Inertial (stationary) or non-inertial (rotating or accelerating) reference frames • Multiple reference frame (MRF) and sliding mesh options for modeling multiple moving frames • Mixing-plane model for modeling rotor-stator interactions, torque converters, and similar turbomachinery applications with options for mass conservation and swirl conservation • Dynamic mesh model for modeling domains with moving and deforming mesh • Volumetric sources of mass, momentum, heat, and chemical species • Material property database • Extensive customization capability via user-defined functions • Dynamic (two-way) coupling with GT-Power and WAVE • Acoustics module (documented separately) • Magnetohydrodynamics (MHD) module (documented separately) • Continuous fiber module (documented separately) FLUENT is ideally suited for incompressible and compressible fluid flow simulations in complex geometries. Fluent Inc. also offers other solvers that address different flow regimes and incorporate alternative physical models. Additional CFD programs from Fluent Inc. include Airpak, FIDAP, Icepak, MixSim, and POLYFLOW.

1-4


1.4 Overview of Using FLUENT

1.4

Overview of Using FLUENT

FLUENT uses unstructured meshes in order to reduce the amount of time you spend generating meshes, simplify the geometry modeling and mesh generation process, model more-complex geometries than you can handle with conventional, multi-block structured meshes, and let you adapt the mesh to resolve the flow-field features. FLUENT can also use body-fitted, block-structured meshes (e.g., those used by FLUENT 4 and many other CFD solvers). FLUENT is capable of handling triangular and quadrilateral elements (or a combination of the two) in 2D, and tetrahedral, hexahedral, pyramid, and wedge elements (or a combination of these) in 3D. This flexibility allows you to pick mesh topologies that are best suited for your particular application, as described in Section 5.1.2. You can adapt all types of meshes in FLUENT in order to resolve large gradients in the flow field, but you must always generate the initial mesh (whatever the element types used) outside of the solver, using GAMBIT, TGrid, or one of the CAD systems for which mesh import filters exist.

1.4.1

Planning Your CFD Analysis

When you are planning to solve a problem using FLUENT, you should first give consideration to the following issues: • Definition of the Modeling Goals: What specific results are required from the CFD model and how will they be used? What degree of accuracy is required from the model? • Choice of the Computational Model: How will you isolate a piece of the complete physical system to be modeled? Where will the computational domain begin and end? What boundary conditions will be used at the boundaries of the model? Can the problem be modeled in two dimensions or is a three-dimensional model required? What type of grid topology is best suited for this problem? • Choice of Physical Models: Is the flow inviscid, laminar, or turbulent? Is the flow unsteady or steady? Is heat transfer important? Will you treat the fluid as incompressible or compressible? Are there other physical models that should be applied? • Determination of the Solution Procedure: Can the problem be solved simply, using the default solver formulation and solution parameters? Can convergence be accelerated with a more judicious solution procedure? Will the problem fit within the memory constraints of your computer, including the use of multigrid? How long will the problem take to converge on your computer? Careful consideration of these issues before beginning your CFD analysis will contribute significantly to the success of your modeling effort. When you are planning a CFD project, take advantage of the customer support provided to all FLUENT users.


1-5

Getting Started

1.4.2

Problem Solving Steps

Once you have determined the important features of the problem you want to solve, you will follow the basic procedural steps shown below. 1. Create the model geometry and grid. 2. Start the appropriate solver for 2D or 3D modeling. 3. Import the grid. 4. Check the grid. 5. Select the solver formulation. 6. Choose the basic equations to be solved: laminar or turbulent (or inviscid), chemical species or reaction, heat transfer models, etc. Identify additional models needed: fans, heat exchangers, porous media, etc. 7. Specify material properties. 8. Specify the boundary conditions. 9. Adjust the solution control parameters. 10. Initialize the flow field. 11. Calculate a solution. 12. Examine the results. 13. Save the results. 14. If necessary, refine the grid or consider revisions to the numerical or physical model. Step 1 of the solution process requires a geometry modeler and grid generator. You can use GAMBIT or a separate CAD system for geometry modeling and grid generation. You can also use TGrid to generate volume grids from surface grids imported from GAMBIT or a CAD package. Alternatively, you can use supported CAD packages to generate volume grids for import into TGrid or into FLUENT (see Section 5.3). For more information on creating geometry and generating grids using each of these programs, please refer to their respective manuals. In Step 2, you will start the 2D or 3D solver as described in Section 1.5. The details of steps 3–14 are covered in later sections of this guide. (See Section 1.6 for details about step 5.) The menu you need to use for each solution step is shown in Table 1.4.1.

1-6


1.5 Starting FLUENT

Table 1.4.1: Overview of the FLUENT Menus Solution Step 3. Import the grid. 4. Check the grid. 5. Select the solver formulation. 6. Choose basic equations. 7. Material properties. 8. Boundary conditions. 9. Adjust solution controls. 10. Initialize the flow field. 11. Calculate a solution. 12. Examine the results.

13. Save the results. 14. Adapt the grid.

1.5

Menu File menu Grid menu Define menu Define menu Define menu Define menu Solve menu Solve menu Solve menu Display menu Plot menu Report menu File menu Adapt menu

Starting FLUENT

The way you start FLUENT will be different for UNIX and Windows systems, as described below in Sections 1.5.2 and 1.5.3. The installation process (described in the separate installation instructions for your computer type) is designed to ensure that the FLUENT program is launched when you follow the appropriate instructions. If it is not, consult your computer systems manager or your Fluent support engineer.

1.5.1

Single-Precision and Double-Precision Solvers

Both single-precision and double-precision versions of FLUENT are available on all computer platforms. For most cases, the single-precision solver will be sufficiently accurate, but certain types of problems may benefit from the use of a double-precision version. Several examples are listed below: • If your geometry has features of very disparate length scales (e.g., a very long, thin pipe), single-precision calculations may not be adequate to represent the node coordinates. • If your geometry involves multiple enclosures connected via small-diameter pipes (e.g., automotive manifolds), mean pressure levels in all but one of the zones can be quite large (since you can set only one global reference pressure location). Doubleprecision calculations may therefore be necessary to resolve the pressure differences that drive the flow, since these will typically be much smaller than the pressure levels.


1-7

Getting Started

• For conjugate problems involving high thermal-conductivity ratios and/or highaspect-ratio grids, convergence and/or accuracy may be impaired with the singleprecision solver, due to inefficient transfer of boundary information.

1.5.2

Starting FLUENT on a UNIX System

There are several ways to start FLUENT on a UNIX system: • Start the appropriate version from the command line. • Start the solver from the command line without specifying a version, and then use the Select Solver panel to choose the appropriate version. • Start the solver from the command line without specifying a version, and then read in a case file (or a case file and data file) to start the appropriate version.

Specifying the Solver Version from the Command Line When you start FLUENT from the command line, you can specify the dimensionality of the problem (2D or 3D), as well as whether you want a single- or double-precision calculation: fluent 2d runs the two-dimensional, single-precision solver, fluent 3d runs the three-dimensional, single-precision solver, fluent 2ddp runs the two-dimensional, double-precision solver, and fluent 3ddp runs the three-dimensional, double-precision solver. See Section 30.2 for information about starting the parallel solvers.

Specifying the Solver Version in the Select Solver Panel If you type fluent on the command line with no arguments, the startup console window (the text window and the main menu bar) will appear as shown in Figure 1.5.1. You can start a single-precision version of FLUENT by typing 2d or 3d at the version> prompt. For a double-precision version, type 2ddp or 3ddp.

1-8


1.5 Starting FLUENT

Figure 1.5.1: Console Window at Startup

If you would rather use the GUI to start the correct version, select the Run... menu item in the File menu. File −→Run... The Select Solver panel will appear as shown in Figure 1.5.2, and you can pick the appropriate version. (You can also start FLUENT on a remote machine or start the parallel version from this panel, as described in Sections 2.4 and 30.2.) You will normally follow the steps below to start a solver from the panel: 1. Specify a 2D or 3D solver by turning the 3D option on or off under Versions. 2. Specify the precision by turning the Double Precision option on or off under Versions. 3. Click the Run button. If the program executable is not in your search path, you can specify a complete pathname to the executable in the Program text entry box before clicking Run.

Specifying the Solver Version by Reading a Case File As discussed above, if you type fluent on the command line without specifying a version argument, the console window will appear as shown in Figure 1.5.1. You can then automatically execute the appropriate solver by selecting a case file or case and data files


1-9

Getting Started

Figure 1.5.2: The FLUENT version can be selected from the Select Solver panel

using the File/Read/Case... or File/Read/Case & Data... menu item (see Section 3.3) or using the read-case or read-case-data command in the version text menu. File −→ Read −→Case... File/Read/Case... or read-case starts the solver that is appropriate for the specified case file and then reads in the file. File −→ Read −→Case & Data... File/Read/Case & Data... or read-case-data starts the solver that is appropriate for the specified case file and then reads in the specified case and data files (where the case and data files have the same name with .cas and .dat extensions, respectively).

1.5.3

Starting FLUENT on a Windows System

There are two ways to start FLUENT on a Windows system: • Click the Start button, select the Programs menu, select the Fluent.Inc menu, and then select the FLUENT 6 program item. (Note that if the default “Fluent.Inc” program group name was changed when FLUENT was installed, you will find the FLUENT 6 menu item in the program group with the new name that was assigned, rather than in the Fluent.Inc program group.) • Start from an MS-DOS Command Prompt window by typing fluent 2d (for the 2D single-precision solver), fluent 3d (for the 3D single-precision solver), fluent

1-10


1.5 Starting FLUENT

2ddp (for the 2D double-precision solver), or fluent 3ddp (for the 3D doubleprecision solver) at the prompt. Before doing so, however, you must first modify your user environment so that the MS-DOS Command utility will find fluent. You can do this by selecting the program item “Set Environment”, which is also found in the Fluent.Inc program group. This program will add the Fluent.Inc directory to your command search path. From the MS-DOS Command Prompt window, you can also start the parallel version of FLUENT. To start the parallel version on x processors, type fluent version -tx at the prompt, replacing version with the desired solver version (2d, 3d, 2ddp, or 3ddp) and x with the number of processors (e.g., fluent 3d -t3 to run the 3D version on 3 processors). For information about the parallel version of FLUENT, see Chapter 30.

1.5.4

Startup Options

To obtain information about available versions, releases, etc. before starting up the solver, you can type fluent -help. Available options are as shown below: Usage: fluent [version] [-help] [options] options: -cl following argument passed to fluent, -cxarg following argument passed to cortex, -cx host:p1:p2 connect to the specified cortex process, -driver [ opengl | x11 | null ], sets the graphics driver (available drivers vary by platform), -env show environment variables, -g run without gui or graphics, -gr run without graphics, -gu run without gui, -hcl following argument passed to fluent host, -help this listing, -i journal read the specified journal file, -loadx load mpp from host x, -lsf run fluent under LSF, -manspa manually spawn compute nodes, -n no execute, -ncl following argument passed to fluent node, -nocheck disable checks for valid license file and server, -pathx specify root path x to Fluent.Inc, -post run a post-processing-only executable, -project x write project x start and end times to license log, -px specify communicator x, -r list all releases, -rx specify release x,


1-11

Getting Started

-sge run fluent under Sun Grid Engine, -sgeckpt ckpt_obj, set Checkpointing object to ckpt_obj for SGE, -sgepe fluent_pe min_n-max_n, set parallel environment for SGE to fluent_pe, min_n and max_n are number of min and max nodes requested, -v list all versions, -vx specify version x, -tx specify number of processors x,

! On Windows systems, only -cx, -driver, -env, -gu (with restrictions), -help, -i journal, -r, -rx, -v, -vx, and -tx are available. The first three options are for specifying arguments for FLUENT and Cortex. Cortex is a process that provides the user interface and graphics for FLUENT. The option -cx host:p1:p2 is used only when you are starting the solver manually (see Section 1.5.2). If you type fluent -driver, you can specify the graphics driver to be used in the solver session (e.g., fluent -driver xgl). Typing fluent -env will list all environment variables before running FLUENT. fluent -g will run Cortex without graphics and without the graphical user interface. This option is useful if you are not on an X Window display or if you want to submit a batch job. fluent -gu will run Cortex without the graphical user interface and fluent -gr will run Cortex without graphics. (On Windows systems, fluent -gu will run FLUENT keeping it in a minimized window; if you maximize the window, the GUI will be available. This option can be used in conjunction with the -i journal option to run a job in “background” mode.) To start the solver and immediately read a journal file, type fluent -i journal, replacing journal with the name of the journal file you want to read. The -nocheck option speeds up the solver startup by not checking to see if the license server is running. This is useful if you know that the license daemon is running or you would rather not try to start it if it is not running (e.g., if you do not have privileges to do so). fluent -post will run a version of the solver that allows you to set up a problem or perform postprocessing, but will not allow you to perform calculations. The -project x option allows you to record CPU time for individual “projects” separately. If a job is started by typing fluent -project x (where x is replaced by the name of the project), extra information related to CPU time will be written to the license manager log file (usually license.log in the license subdirectory of your FLUENT installation directory). To determine the CPU time for the project, add the USER CPU and SYSTEM CPU values that appear in license.log. See the installation notes for more information about the license manager. Typing fluent version -r, replacing version with the desired version, will list all releases of the specified version. fluent -rx will run release x of FLUENT. You may

1-12


1.6 Choosing the Solver Formulation

specify a version as well, or you can wait and specify the version when prompted by the solver. fluent -v will list the available versions. fluent -vx will run version x of FLUENT. You can type fluent -n or use the -n option in conjunction with any of the others to see where the (specified) executable is without actually running it. The remaining options are used in association with the parallel solver. -hcl is used to pass an argument to the FLUENT host process and -ncl is used to pass an argument to the FLUENT compute node process(es). -loadx is used to start the parallel compute node processes on a dedicated parallel machine from its remote front-end machine (x). -manspa is used to disable the default automatic spawning of compute node processes. -px specifies the use of parallel communicator x, where x can be any of the communicators listed in Section 30.2.1. -pathx specifies the root path (path) to the Fluent.Inc installation directory. -tx specifies that x processors are to be used. For more information about starting the parallel version of FLUENT, see Section 30.2.

1.6

Choosing the Solver Formulation

FLUENT provides three different solver formulations: • segregated • coupled implicit • coupled explicit All three solver formulations will provide accurate results for a broad range of flows, but in some cases one formulation may perform better (i.e., yield a solution more quickly) than the others. The segregated and coupled approaches differ in the way that the continuity, momentum, and (where appropriate) energy and species equations are solved: the segregated solver solves these equations sequentially (i.e., segregated from one another), while the coupled solver solves them simultaneously (i.e., coupled together). Both formulations solve the equations for additional scalars (e.g., turbulence or radiation quantities) sequentially. The implicit and explicit coupled solvers differ in the way that they linearize the coupled equations. See Section 24.1 for more details about the three solver formulations. Note that the segregated solver is the formulation previously used by FLUENT 4 and FLUENT/UNS, and the coupled explicit solver is the formulation previously used by RAMPANT. The segregated solver traditionally has been used for incompressible and mildly compressible flows. The coupled approach, on the other hand, was originally designed for high-speed compressible flows. Both approaches are now applicable to a broad range of


1-13

Getting Started

flows (from incompressible to highly compressible), but the origins of the coupled formulation may give it a performance advantage over the segregated solver for high-speed compressible flows. By default, FLUENT uses the segregated solver, but for high-speed compressible flows (as discussed above), highly coupled flows with strong body forces (e.g., buoyancy or rotational forces), or flows being solved on very fine meshes, you may want to consider the coupled implicit solver instead. This solver couples the flow and energy equations, which often results in faster solution convergence. A trade-off involved in the use of the coupled implicit solver is that it requires more memory (1.5 to 2 times) than the segregated solver. For cases where the use of the coupled implicit solver is desirable, but your machine does not have sufficient memory, you can use the segregated solver or the coupled explicit solver instead. The coupled explicit solver also couples the flow and energy equations, but it requires less memory than the coupled implicit solver. It will, however, usually take longer to reach a converged solution with the coupled explicit solver than with the coupled implicit solver.

! Note that the segregated solver provides several physical models that are not available with the coupled solvers: • Cavitation model • Fixed variable option • Physical velocity formulation for porous media • Volume-of-fluid (VOF) model • Multiphase mixture model • Eulerian multiphase model • Non-premixed combustion model • Premixed combustion model • Partially premixed combustion model • Composition PDF transport model • Soot and NOx models • Rosseland radiation model • Melting/solidification model • Specified mass flow rate for streamwise periodic flow

1-14


1.6 Choosing the Solver Formulation

• Shell conduction model • Floating operating pressure The following features are available with the coupled solvers, but not with the segregated solver: • Real gas model • User-defined real gas model • NIST real gas model • Non-reflecting boundary conditions • Stiff chemistry solver option for laminar flames

User Inputs for Solver Selection To choose one of the three solver formulations, you will use the Solver panel (Figure 1.6.1). Define −→ Models −→Solver... To use the segregated solver, retain the default selection of Segregated under Solver. To use the coupled implicit solver, select Coupled under Solver and Implicit (the default) under Formulation. To use the coupled explicit solver, select Coupled under Solver and Explicit under Formulation.


1-15

Getting Started

Figure 1.6.1: The Solver Panel

1-16


1.7 Accessing the FLUENT Manuals

1.7

Accessing the FLUENT Manuals

As described in Section 2.3, FLUENT’s on-line help gives you access to the FLUENT documentation through HTML files, which can be viewed with your standard web browser (e.g., Netscape Communicator). For printing, Adobe Acrobat PDF versions of the manuals are also provided. This section describes how to access the FLUENT manuals outside of FLUENT (i.e., not through the FLUENT on-line help utility). See Section 2.3.1 for information about accessing the manuals through the on-line help. You can access the manuals directly from the CD or, if the files have been installed in your Fluent Inc. installation area, you can also access them there. See the separate installation instructions for your platform type for information about installing the files from the documentation CD.

! The comments in this chapter about accessing files in the installation area assume that all files on the documentation CD have been installed. If the files you are looking for are not in the installation area, you will need to install them or access them directly from the CD. The following sections provide information about accessing the manuals: • Section 1.7.1: Viewing the Manuals • Section 1.7.2: Printing the Manuals

1.7.1

Viewing the Manuals

To view the manuals, you will generally make use of the HTML files, either in the installation area or on the documentation CD. You will also need a web browser. If you do not have one, contact your Fluent support engineer and ask for the Netscape Communicator CD-ROM.

How to Access the HTML Files in the Installation Area If the files on the documentation CD have been installed, you can view the HTML versions of the manuals by pointing your browser to path/Fluent.Inc/fluent6.1/help/index.htm where Fluent.Inc is the directory in which FLUENT has been installed, and you must replace path by the path to the directory where Fluent.Inc is located. If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to browse through your directories to find the file.


1-17

Getting Started

This will bring up the FLUENT documentation “home” page (Figure 1.7.1), from which you can select the HTML version of the particular FLUENT manual you want to view.

Figure 1.7.1: The FLUENT Documentation Home Page

How to Access the HTML Files on the CD The procedure for viewing the manuals directly on the CD differs slightly for UNIX and Windows systems: • For UNIX systems, you can view the manuals by inserting the CD into your CDROM drive and pointing your browser to the following file: /cdrom/fluent6.1/help/index.htm where cdrom must be replaced by the name of your CD-ROM drive.

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If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to browse through your directories to find the file. • For Windows systems, you can view the manuals by inserting the CD into your CD-ROM drive and pointing your browser to the following file: cdrom:\fluent6.1\help\Index.htm where cdrom must be replaced by the drive letter of your CD-ROM drive (e.g., E). If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to select the CD-ROM drive (which will be named Fluent inc, followed by the letter for the CD-ROM drive) and choose the appropriate file. This will bring up the FLUENT documentation “home” page (Figure 1.7.1), from which you can select the HTML version of the particular FLUENT manual you want to view.

Navigating the Manuals When you are viewing a manual in your browser, a set of navigation buttons will appear at the upper right and lower right corners of the HTML page, as shown in Figure 1.7.2.

Figure 1.7.2: Navigation Buttons

The navigation buttons are as follows: Next will take you to the next page in the manual. Note that this is not the same function as the “Forward” button of your browser. Up will take you to the first page of the current manual division (chapter or section). Previous will take you to the page just before the current one in the manual. Note that this is not the same function as the “Back” button of your browser. Index will take you to the index for the manual.


1-19

Getting Started

Contents will take you to the table of contents for the manual. Return to Home will take you to the FLUENT documentation home page (Figure 1.7.1). Search will display a full text search popup window (Figure 1.7.3). Note that these buttons will not necessarily appear on all pages, and in some cases, they will appear, but be inactive; in such cases, they will be “grayed out”, as the Previous and Up buttons are in Figure 1.7.2.

Finding Information in the Manuals Three tools are available to help you find the information you are looking for in a manual. Index The index gives an alphabetical list of keywords, each linked to relevant sections of the manual. You can access the index by clicking the Index button that appears at the top and bottom of the page. Note that the Index button will not appear if the manual does not have an index. In a larger manual, the index will be split into a number of pages, each containing keywords starting with a particular letter; in this case, the Index button will take you to the “A” index page. Table of Contents The table of contents gives a list of the titles of the chapters, sections, and subsections of the manual in the order in which they appear. Each title is linked to the corresponding chapter or section. You can access the table of contents by clicking the Contents button that appears at the top and bottom of the page. Note that the Contents button will not appear if the manual does not have a table of contents. Browser Search The full text search engine (Figure 1.7.3) allows you to search the HTML manual for either single or multiple keywords. You can access the full text search engine by clicking the Search button that appears at the top of the page. To display the popup window and use the search engine, Javascript should be enabled in your web browser. Note that the Javascript search engine has been optimized for Netscape 4.7 and later, and Internet Explorer 5.5 and later. To use the search engine, enter a specific term or keyword(s) in the text field and click the Search button. By default, the search engine will look for pages that contain any keyword input (Boolean OR). If you insert a + before the keyword input, then the search engine will look for pages that contain all of the keywords provided in the text field (Boolean AND).

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Search results appear in the lower half of the search engine popup window. When search results extend below the bottom edge of the window, activate scroll bars by selecting the lower portion of the window and pressing the button on the keyboard.

Figure 1.7.3: The Full Text Search Engine You can also use the search capability provided by your browser to find words or expressions on a single page. For example, you can use the Edit/Find in Page... menu item in Netscape Communicator to search for the word “turbulence” on a page of the manual.

Typographical Conventions Throughout the manuals, mini flow charts are used to indicate the menu selections that lead you to a specific command or panel. Words in green invoke menus (or submenus) and are connected by arrows that point from a specific menu toward the item you should select from that menu.

! An exclamation point (!) at the beginning of a line marks an important note or warning.


1-21

Getting Started

Printing Portions of a Manual Although you can print pages of a manual from your browser, a much higher-quality printout can be obtained by using the PDF files provided on your documentation CD. See Section 1.7.2 for details.

Modifying the Appearance of the Manuals There are a few things that you might want to change about the way your browser displays the manuals in order to increase their usefulness. Font Size The absolute size of the text that you will see when viewing your FLUENT documentation is dependent on a number of factors, including the resolution of your monitor screen. You can adjust the text size by changing the default font size in the preferences menu of your browser. In Netscape Communicator, for example, select the Edit/Preferences... menu item and then choose the Appearance category, where you will find the Fonts controls. Try several sizes to see the effect on the appearance of the manuals, and choose the one that is best for you. Page Width While reading a manual, you may find a figure that is wider than your browser’s window. As a result, some of the figure will be hidden from view. To see all of the figure, you can use the horizontal scroll bar at the bottom of your browser’s window, or increase your browser’s window size. You might also want to adjust the window size to increase or decrease the page width to a comfortable reading width. Tool Tips When viewing the manuals with certain browsers, information about a figure will be displayed if you put your cursor over it. However, this information is not meaningful for most users, and you might find it somewhat distracting. On some browsers, you can disable the display of “Tool Tips” in the preferences menu.

1.7.2

Printing the Manuals

Adobe Acrobat PDF files are provided for printing all or part of the manuals. You can also print individual HTML pages from your browser, but it is recommended that you use the PDF files instead if you are printing a long section, in order to obtain a higher-quality printout.

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About the PDF Files The PDF files are appropriate for viewing and printing with Adobe Acrobat Reader, which is available for most UNIX and Windows systems. These files are distinguished by a .pdf suffix in their file names.

! For the purpose of easier on-line document navigation, the PDF files contain active hyperlinks in the table of contents and index. In addition, active hyperlinks have been applied to all cross-references to chapters, sections, figures, tables, and bibliography entries. Note that you can select the paper size to which you are printing in Adobe Acrobat Reader by selecting the File/Print Setup... menu item and choosing the desired Paper size. If the page is too large to fit on your paper size, you can reduce it by selecting the File/Print... menu item and enabling the Shrink to Fit option. If you do not have Adobe Acrobat Reader, you can download it (at no cost) from www.adobe.com. If you are not able to download files from the Internet, contact your Fluent support engineer and ask for the Adobe Acrobat Reader CD-ROM.

How to Access the PDF Files in the Installation Area If the PDF files on the documentation CD have been installed, you can access them by pointing your browser to path/Fluent.Inc/fluent6.1/help/index.htm where Fluent.Inc is the directory in which FLUENT has been installed, and you must replace path by the path to the directory where Fluent.Inc is located. If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to browse through your directories to find the file. This will bring up the FLUENT documentation “home” page (Figure 1.7.1), from which you can select the PDF file(s) for the particular FLUENT manual you want. For large manuals, PDF files are provided for the individual chapters in addition to a single PDF file for the entire manual.

How to Access the PDF Files on the CD The procedure for accessing the PDF files directly on the CD differs slightly for UNIX and Windows systems: • For UNIX systems, you can access the files by inserting the CD into your CD-ROM drive and pointing your browser to the following file:


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Getting Started

/cdrom/fluent6.1/help/index.htm where cdrom must be replaced by the name of your CD-ROM drive. If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to browse through your directories to find the file. • For Windows systems, you can access the files by inserting the CD into your CDROM drive and pointing your browser to the following file: cdrom:\fluent6.1\help\Index.htm where cdrom must be replaced by the drive letter of your CD-ROM drive (e.g., E). If, for example, you are using Netscape Communicator as your browser, select the File/Open Page... menu item and click the Choose File... button to select the CD-ROM drive (which will be named Fluent inc, followed by the letter for the CD-ROM drive) and choose the appropriate file. This will bring up the FLUENT documentation “home” page (Figure 1.7.1), from which you can select the PDF file(s) for the particular FLUENT manual you want. For large manuals, PDF files are provided for the individual chapters in addition to a single PDF file for the entire manual.

1.8

Sample Session

To demonstrate the use of the problem-solving and postprocessing capabilities of FLUENT, you can make use of a grid file provided on the documentation CD to solve a very simple problem. The grid file was created to solve the problem illustrated in Figure 1.8.1. In this problem, a cavity in the shape of a 60◦ rhombus, 0.1 m on a side, contains air at constant density and is driven by the top wall which moves to the right with a speed of 0.1 m/s. With a Reynolds number of about 500, the flow is laminar.

1.8.1

Outline of Procedure

The driven cavity flow shown in Figure 1.8.1 is a simple 2D problem in which the flow is laminar, there is no heat transfer, and there are no special physical models to consider. In addition, the overall problem geometry, grid, and boundary locations and types have already been defined in the grid generator. You can simply read the grid file, with all this information, into FLUENT. The modeling steps you will follow in this sample FLUENT session are reduced to the following:

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1.8 Sample Session u wall = 0.1 m/s 60

o

D

θ = 60o

ρ = 1.0 kg/m3 D

µ = 2.0 E-05 kg/m-s D = 0.1 m Re ∼

ρ uwall D ∼ 500 µ

Figure 1.8.1: Fluid Flow in a Driven Cavity

• Read the grid file and check it. • Select the default segregated solver. • Define the physical models. • Specify the fluid properties. • Specify the boundary conditions. • Save the problem setup. • Initialize the solution. • Calculate the solution. • Save the results. • Examine the results. Before beginning, you should copy the grid file from the documentation CD to your working directory (i.e., the directory in which you are going to start the solver). The grid file for this tutorial is (for UNIX systems) /cdrom/fluent6.1/help/tutfiles/sample/cavity.msh or (for Windows systems) cdrom:\fluent6.1\help\tutfiles\sample\cavity.msh where cdrom must be replaced by the drive letter of your CD-ROM drive.


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Getting Started

1.8.2

Reading and Checking the Grid

Start the 2D version of FLUENT (see Section 1.5).

Reading the Grid To read in the quadrilateral grid file, select the File/Read/Case... menu item. File −→ Read −→Case... The Select File dialog box will appear, as shown in Figure 1.8.2. A case file, in general, contains the grid, boundary conditions, and solution control parameters. The grid file is a subset of this, and the grid in this example has been saved in FLUENT format, so you can read it in the same manner as a full case file. (To read a grid file that was saved in another format, you would use the appropriate item in the File/Import submenu.)

Figure 1.8.2: Reading the Grid

If the file containing the grid you want to use is shown in Files, you can double-click the left mouse button on its name to begin reading it. If it is not shown, you can modify the path shown in Filter to include the file you are searching for, or you can type the complete name of the file in the box labeled Case File, and then click OK. In this example the file cavity.msh is selected. FLUENT will report its progress in the console window as it reads the grid.

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1.8 Sample Session

Checking the Grid After you read in the grid, you should check its validity by selecting the Grid/Check menu item. Grid −→Check You should see the domain extents, volume statistics, and connectivity information in the console window, as shown below: Grid Check Domain Extents: x-coordinate: min (m) = 0.000000e+00, max (m) = 1.500000e-01 y-coordinate: min (m) = 0.000000e+00, max (m) = 8.660000e-02 Volume statistics: minimum volume (m3): 7.156040e-05 maximum volume (m3): 7.157349e-05 total volume (m3): 8.660000e-03 Face area statistics: minimum face area (m2): 9.089851e-03 maximum face area (m2): 9.091221e-03 Checking number of nodes per cell. Checking number of faces per cell. Checking thread pointers. Checking number of cells per face. Checking face cells. Checking bridge faces. Checking right-handed cells. Checking face handedness. Checking element type consistency. Checking boundary types: Checking face pairs. Checking periodic boundaries. Checking node count. Checking nosolve cell count. Checking nosolve face count. Checking face children. Checking cell children. Checking storage. Done.

The most common error identified by the grid check is negative volumes in the grid. If the minimum volume is negative, you will need to repair the grid to remove this nonphysical discretization of the solution domain. You may be able to use the Iso-Value... marking ability in the Adapt pull-down menu to locate the problem by marking and displaying cells


1-27

Getting Started

with volumes less than zero (see Section 25.6). For additional information on checking the grid, see Section 5.5.

Displaying the Grid To display the grid, select the Display/Grid... menu item. Display −→Grid... In the resulting Grid Display panel (Figure 1.8.3), click the Display button. This will open a graphics display window and draw the grid. You should see a picture like the one in Figure 1.8.4. Close the Grid Display panel by clicking the Close button.

Figure 1.8.3: The Grid Display Panel

You can zoom in to enlarge the view using the mouse. Move the cursor to a point on the screen that is slightly above and to the left of the cavity. Then, while holding down the middle mouse button, move the cursor down and to the right to a point that is slightly below and to the right of the cavity. When you release the middle mouse button, the portion of the display within the zoom box will be expanded to fill the entire window.

1.8.3

Selecting the Solver Formulation

For this example, the velocities involved are low enough that you can model the problem assuming incompressible flow. For such problems, the segregated solver is appropriate. Since the segregated solver is the default in FLUENT, no change is needed. If you wanted

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1.8 Sample Session

Grid

Oct 15, 2002 FLUENT 6.1 (2d, segregated, lam)

Figure 1.8.4: Grid Display with Default View

to select one of the coupled solvers, you would visit the Solver panel in the Define/Models submenu.

1.8.4

Defining Physical Models

In FLUENT, the default physical model setup is for laminar flow. Since the flow modeled in this example is laminar, you will not need to make any changes to the model settings. If you did need to modify the physical models, you would do so using the Viscous Model panel and other panels in the Define/Models submenu.

1.8.5

Specifying Fluid Properties

To set the fluid properties for your problem, select the Define/Materials... menu item. This will open the Materials panel (Figure 1.8.5). Define −→Materials... If you wanted to use a material other than air you could select it from the materials database (as described in Section 7.1.2), or create your own material (as described in Section 7.1.2). For this problem, you will just make some modifications to the properties for air, the default material. Change the density to 1.0 kg/m3 and the viscosity to 2 × 10−5 kg/m-s. Click Change/Create to save the new values, and then close the panel.


1-29

Getting Started

Figure 1.8.5: The Materials Panel

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1.8 Sample Session

1.8.6

Specifying Boundary Conditions

You can set values for boundary conditions and change boundary types using the Boundary Conditions panel shown in Figure 1.8.6. To open this panel, select the Define/Boundary Conditions... menu item. Define −→Boundary Conditions...

Figure 1.8.6: The Boundary Conditions Panel To set the boundary conditions for a particular zone, select the desired boundary in the Zone list. You can change the boundary type by selecting from the Type list. After you select the correct zone type, you can set the actual boundary condition values by clicking the Set... button. (If you prefer, you can double-click on the boundary zone name in the Zone list instead of clicking the Set... button.) For this example, you need to change the conditions for the moving (top) wall by setting the x velocity to 0.1 m/s to model the moving cavity lid. If you are not sure which of the two wall boundaries represents the moving (top) wall, you can click your right mouse button on the top wall boundary in the graphics window (which is still showing the grid display of Figure 1.8.4). The zone information will be printed in the FLUENT console window, and wall-2 will be selected automatically in the Zone list in the Boundary Conditions panel. Now click the Set... button to open the Wall panel shown in Figure 1.8.7. To set the wall velocity, you will need to turn on the Moving Wall option. When you do so, the Wall panel will expand to show the wall motion information (see Figure 1.8.8). By default, Translational motion is selected and the velocity Direction is set to X, so you can simply set the Speed to 0.1. (Note that since the adjacent fluid zone is not moving—as


1-31

Getting Started

Figure 1.8.7: The Wall Panel

it would be if you were modeling a rotating reference frame—you need not worry about the specification of relative or absolute motion; they are equivalent.) After you have entered this value, click OK to save your settings and close the panel. The only other boundary in this problem is the wall boundary on the remaining three sides of the cavity (wall-5). For this example, the default wall boundary conditions (no motion) will be used, so no further action is needed. Click the Close button in the Boundary Conditions panel to close it.

1.8.7

Adjusting Solution Controls

You can change the default settings for the under-relaxation factors, multigrid parameters, and other flow solver parameters in the panels that are opened from the Solve/Controls submenu. These settings are described in Chapter 24. Normally, you will not need to change these parameters. For this problem, the default settings are adequate.

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1.8 Sample Session

Figure 1.8.8: The Wall Panel for a Moving Wall

Enabling Residual Plotting The problem setup is almost complete. You will now turn on the graphical residual monitoring so that you can easily watch the progress of the solution. To do this, select the Solve/Monitors/Residual... menu item to open the Residual Monitors panel shown in Figure 1.8.9. Solve −→ Monitors −→Residual... Under Options, turn on the Plot option to activate the graphical display of residuals during the calculation, and then click OK.

1.8.8

Saving the Case File

Your inputs that define the problem are stored in the case file. You must save this file in order to continue your analysis in a future FLUENT session. (The results that you compute will be stored in a separate file, the data file.)


1-33

Getting Started

Figure 1.8.9: The Residual Monitors Panel

1-34


1.8 Sample Session

To save the case file, select the File/Write/Case... menu item. The Select File dialog box will appear, as shown in Figure 1.8.10. File −→ Write −→Case...

Figure 1.8.10: Saving a Case File Keep the default name (cavity.cas) in the Case File text entry box. Click OK to save the file cavity.cas.

1.8.9

Solving the Problem

Initializing the Flow Before iterating, you must initialize the flow field to provide a starting point for the solution. You have a choice of computing the initial solution from the settings of one (or all) of the boundary conditions or entering flow-field values individually. Select the Solve/Initialize/Initialize... menu item to open the Solution Initialization panel shown in Figure 1.8.11. Solve −→ Initialize −→Initialize... Since a strongly recirculating flow is expected to develop, initialization of all values to 0 is acceptable. Thus you can retain the default values in the panel and initialize the flow by clicking the Init button. Then close the panel.


1-35

Getting Started

Figure 1.8.11: The Solution Initialization Panel

Calculating Now you are ready to begin iterating. Select the Solve/Iterate... menu item. This will open the Iterate panel shown in Figure 1.8.12. Solve −→Iterate...

Figure 1.8.12: The Iterate Panel Enter 10 for the Number of Iterations and click the Iterate button to perform the 10 iterations. When the iterations start, you should see the residual plot in the graphics window. After the 10 iterations are complete, your graphics window should look something like Figure 1.8.13. The residuals are headed downward, which is a good sign. (Note that the

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1.8 Sample Session

actual values of the residuals may differ slightly on different machines, so your plot may not look exactly the same as Figure 1.8.13.)

Residuals continuity x-velocity y-velocity

1e+01

1e+00

1e-01

1e-02

1e-03 1

2

3

4

5

6

7

8

9

10

Iterations

Scaled Residuals


Figure 1.8.13: Residual Plot After 10 Iterations

You will also want to check the flow field to see how it is developing. To view the velocity vectors in the flow field, select the Vectors... menu item in the Display menu. This will open the Vectors panel shown in Figure 1.8.14. Display −→Vectors... The default settings on this panel produce a vector plot colored by velocity magnitude, which is what you want to see. Click the Display button, and you should see a plot similar to Figure 1.8.15. Even after only 10 iterations, the clockwise recirculation pattern in the cavity is clearly visible. It looks like the solution is proceeding in an acceptable manner, so you can just ask for more iterations to complete the solution. Enter 90 for the Number of Iterations in the Iterate panel, and click Iterate. The solution is converged to the default tolerances after a total of about 50 iterations. At this point, your residual plot will look something like Figure 1.8.16. (Note that the exact number of iterations required for the solution to converge may vary on different computers.) You are now ready to save the data and look at the converged results.


1-37

Getting Started

Figure 1.8.14: The Vectors Panel

1-38


1.8 Sample Session

4.61e-02 4.38e-02 4.15e-02 3.92e-02 3.69e-02 3.46e-02 3.23e-02 3.00e-02 2.77e-02 2.54e-02 2.31e-02 2.08e-02 1.85e-02 1.62e-02 1.39e-02 1.16e-02 9.26e-03 6.96e-03 4.65e-03 2.35e-03 4.45e-05

Velocity Vectors Colored By Velocity Magnitude (m/s)

Nov 27, 2002 FLUENT 6.1 (2d, segregated, lam)

Figure 1.8.15: Velocity Vectors After 10 Iterations

Residuals continuity x-velocity y-velocity

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05 0

5

10

15

20

25

30

35

40

45

50

Iterations

Scaled Residuals


Figure 1.8.16: Residuals After Convergence


1-39

Getting Started

1.8.10

Saving the Results

As discussed earlier, when the case file was saved, inputs that define the problem and the results computed by FLUENT are stored in two separate files: the case file and the data file. You must save both files in order to resume your analysis in a future FLUENT session. Note that FLUENT does not automatically save these files for you. Although you already saved the case file before you began the calculation, it is a good idea to save it again, along with the data file. To save the case and data files, select the File/Write/Case & Data... menu item. The Select File dialog box will appear, as shown in Figure 1.8.17. File −→ Write −→Case & Data...

Figure 1.8.17: Saving Case and Data Files Enter the name you would like for the case and data files in the Case/Data File field. If you keep the default name, FLUENT will save a case file called cavity.cas and a data file called cavity.dat. Click the OK button after entering the filename to save the files. Since the case file cavity.cas already exists, FLUENT will ask you if it is OK to overwrite it. You can click OK in the Warning dialog box (Figure 1.8.18) and FLUENT will write both files. Note that after terminating this session, you could start a new FLUENT session, read the

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1.8 Sample Session

Figure 1.8.18: Confirming the Overwrite

case file and data file, and resume your analysis or modify the sample problem.

1.8.11

Examining the Results

Plotting Contours You have already seen how to make a velocity vector plot. Now select the Contours... menu item in the Display menu. This will open the Contours panel shown in Figure 1.8.19. Display −→Contours...

Figure 1.8.19: The Contours Panel


1-41

Getting Started

In the upper drop-down list under Contours Of, select Velocity..., and then select Stream Function in the lower list. Click the Display button. The resulting display should appear as shown in Figure 1.8.20. Close the panel when you are finished displaying contours.

5.07e-04 4.82e-04 4.57e-04 4.31e-04 4.06e-04 3.81e-04 3.55e-04 3.30e-04 3.04e-04 2.79e-04 2.54e-04 2.28e-04 2.03e-04 1.78e-04 1.52e-04 1.27e-04 1.01e-04 7.61e-05 5.07e-05 2.54e-05 0.00e+00

Contours of Stream Function (kg/s)

Nov 27, 2002 FLUENT 6.1 (2d, segregated, lam)

Figure 1.8.20: Contours of Stream Function

1.8.12

Exiting from FLUENT

When you are finished examining the results, and you have saved your case and data files, you can end the FLUENT session by selecting the File/Exit menu item. File −→Exit

1.8.13

Summary

This example has been designed to show you how to use FLUENT to solve a very simple problem. Example problems of increasing difficulty are solved in the FLUENT Tutorial Guide where the different physical models and solution parameters that are available in FLUENT are illustrated in greater detail.

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Chapter 2.

User Interface

The user interface to FLUENT consists of a graphical interface with pull-down menus, panels, and dialogs, as well as a textual command line interface. Each is described in this chapter. Information about on-line help and remote and batch execution is also included. • Section 2.1: Graphical User Interface • Section 2.2: Text User Interface • Section 2.3: Using On-Line Help • Section 2.4: Remote Execution • Section 2.5: Batch Execution • Section 2.6: Checkpointing a FLUENT Simulation • Section 2.7: Exiting the Program

2.1

Graphical User Interface

The graphical user interface (GUI) is made up of four main components: a console window, control panels, dialog boxes, and graphics windows. When you use the GUI, you will be interacting with one of these components at all times. Figure 2.1.1 is a sample screen shot showing all of the GUI components. The four GUI components are described in detail in subsequent sections. On UNIX systems, the attributes of the GUI (including colors and text fonts) can be customized to better match your platform environment. This is described in Section 2.1.5.

2.1.1

Console

The FLUENT Console is the main window that controls the execution of the program. When using the Console to interact with FLUENT, you have a choice between a text user interface (TUI) and a graphical user interface (GUI). The Console contains a terminal emulator for the TUI and a menu bar for the GUI.


2-1

User Interface

Figure 2.1.1: Screen Shot Showing GUI Components

2-2


2.1 Graphical User Interface

Figure 2.1.2: The Console

Terminal Emulator The terminal emulator is similar in behavior to “xterm” or other UNIX command shell tools, or to the MS-DOS Command Prompt window on Windows systems. It allows you to interact with the TUI menu. More information on the TUI can be found in Section 2.2. All textual output from the program is printed in the terminal emulator, and all typing is displayed on the bottom line. As the number of text lines grows, the lines will be scrolled off the top of the window. The scroll bar on the right allows you to go back and look at the preceding text. The terminal emulator accepts to let you interrupt the program while it is working. It also lets you perform text copy and paste operations between the Console and other X Window (or Windows) applications (that support copy and paste). The following steps show you how to perform a copy and paste operation on a UNIX system: 1. Move the pointer to the beginning of the text to be copied. 2. Press and hold down the left mouse button. 3. Move the pointer to the end of the text (text should be highlighted). 4. Release the left mouse button. 5. Move the pointer to the target window.


2-3

User Interface

6. Press the middle mouse button to “paste” the text. On a Windows system, you will follow the steps below to copy text to the clipboard: 1. Move the pointer to the beginning of the text to be copied. 2. Press and hold down the left mouse button. 3. Move the pointer to the end of the text (text should be highlighted). 4. Release the left mouse button. 5. Press the and keys together.

Menu Bar The menu bar organizes the GUI menu hierarchy using a set of pull-down menus. A pull-down menu contains items that perform commonly executed actions. Figure 2.1.3 shows the (UNIX) Help pull-down menu.

Figure 2.1.3: The Help Pull-Down Menu

To select a pull-down menu item with the mouse, follow the procedure outlined below: 1. Move the pointer to the name of the pull-down menu. 2. Click the left mouse button to display the pull-down menu. 3. Move the pointer to the item you wish to select and click it. 4. Release the left mouse button.

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In addition to using the mouse, you can also select a pull-down menu item using the keyboard. Each pull-down menu label or menu item contains one underlined character, known as the mnemonic. Pressing the key plus the mnemonic character of a pulldown menu will display the menu. Once the pull-down menu is selected and displayed, you can type a mnemonic character associated with an item to select that item. If at any time you wish to cancel a menu selection while a pull-down menu is posted, you can press the key. For example, to display the Help menu and select the Using Help... option, press h, then h. A pull-down menu item may also have an accelerator key associated with it. An accelerator key can be used to select a menu item without displaying the pull-down menu. If a menu item has an associated accelerator key, the key will be shown to the right of the item. For example, if a pull-down menu contains the item Iterate... Ctrl+I, you can select this item by holding down the key and pressing the “I” key.

2.1.2

Dialog Boxes

Dialog boxes are used to perform simple input/output tasks, such as issuing warning and error messages, or asking a question requiring a yes or no answer. A dialog box is a separate “temporary” window that appears when FLUENT needs to communicate with you. When a dialog box appears on your screen, you should take care of it before moving on to other tasks. Once you have tended to the dialog box, it will be closed, and then you can continue. Each type of dialog box is described below.

Information Dialog Box

The Information dialog box is used to report some information that FLUENT thinks you should know. Once you have read the information, you can click the OK button to close the dialog box.


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User Interface

Warning Dialog Box

The Warning dialog box is used to warn you of a potential problem and ask you whether or not you want to proceed with the current operation. If you click the OK button, the operation will proceed. If you click the Cancel button, the operation will be canceled.

Error Dialog Box

The Error dialog box is used to alert you that an error that has occurred. Once you have read the error information, you can click the OK button to close the dialog box.

Working Dialog Box

The Working dialog box is displayed when FLUENT is busy performing a task. This is a special dialog box, because it requires no action by you. It is there to let you know that you must wait. When the program is finished, it will close the dialog box automatically. You can, however, abort the task that is being performed by clicking the Cancel button.

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Question Dialog Box

The Question dialog box is used to ask you a question that requires a yes or no answer. You can click the appropriate button to answer the question.

Select File Dialog Box

The Select File dialog box enables you to choose a file for reading or writing. You can use it to look at your system directories and select a file. Note that the appearance of the Select File dialog box will not always be the same. The version shown above will appear in almost all cases, but it will be different if you are loading external data files for use in an XY plot (see Sections 27.8.2 and 27.8.3). In such cases, the dialog box will look like the following version.


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User Interface

The steps for file selection are as follows: 1. Go to the appropriate directory. You can do this in two different ways: • Enter the path to the desired directory in the Filter text entry box and then press the key or click the Filter button. Be sure to include the final / character in the pathname, before the optional search pattern (described below). • Double-click a directory, and then a subdirectory, etc. in the Directories list until you reach the directory you want. You can also click once on a directory and then click the Filter button, instead of double-clicking. Note that the “.” item represents the current directory and the “..” item represents the parent directory. 2. Specify the file name by selecting it in the Files list or entering it in the File text entry box (if available) at the bottom of the dialog box. The name of this text entry box will change depending on the type of file you are selecting (Case File, Journal File, etc.).

!

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Note that if you are searching for an existing file with a nonstandard extension, you may need to modify the “search pattern” at the end of the path in the Filter text entry box. For example, if you are reading a data file, the default extension in the search path will be *.dat*, and only those files that have a .dat extension



will appear in the Files list. If you want files with a .DAT extension to appear in the Files list, you can change the search pattern to *.DAT*. If you want all files in the directory to be listed in the Files list, enter just * as the search pattern. 3. If you are reading multiple XY-plot data files, the selected file will be added to the list of XY File(s). You can choose another file, following the instructions above, and it will also be added to this list. (If you accidentally select the wrong file, you can choose it in the XY File(s) list and click the Remove button to remove it from the list of files to be read.) Repeat until all of the desired files are in the XY File(s) list. 4. If you are writing a case, data, or radiation file, use the Write Binary Files check box to specify whether the file should be written as a text or binary file. You can read and edit a text file, but it will require more storage space than the same file in binary format. Binary files take up less space and can be read and written by FLUENT more quickly. 5. Click the OK button to read or write the specified file. Shortcuts for this step are as follows: • If your file appears in the Files list and you are not reading an XY file, doubleclick it instead of just selecting it. This will automatically activate the OK button. (If you are reading an XY file, you will always have to click OK yourself. Clicking or double-clicking will just add the selected file to the XY File(s) list.) • If you entered the name of the file in the File text entry box, you can press the key instead of clicking the OK button. File selection on Windows systems is accomplished using the standard Windows Select File dialog box. See documentation regarding your Windows system for further instructions.

2.1.3

Panels

Panels are used to perform more complicated input tasks. Similar to a dialog box, a panel is displayed in a separate window, but working with a panel is more akin to filling out a form. Each panel is unique and employs various types of input controls that make up the form. The types of controls you will see are described further in this section. When you have finished entering data in a panel’s controls, you will need to apply the changes you have made, or abort the changes, if desired. For this task, each panel falls into one of two behavioral categories, depending on how it was designed.


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User Interface

The first category of panels is used in situations where it is desirable to apply the changes and immediately close the panel. This type of panel includes two button controls as described below: OK applies any changes you have made to the panel, then closes the panel. Cancel closes the panel, ignoring any changes you have made. An example of this type of panel is shown below:

The other category of panels is used in situations where it is desirable to keep the panel displayed on the screen after changes have been applied. This makes it easy to quickly go back to that panel and make more changes. Panels used for postprocessing and grid adaption often fall into this category. This type of panel includes two button controls as described below: Apply applies any changes you have made to the panel, but does not close the panel. The name of this button is often changed to something more descriptive. For example, many of the postprocessing panels use the name Display for this button, and the adaption panels use the name Adapt. Close closes the panel. An example of this type of panel is shown below:

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All panels include the following button used to access on-line help: Help displays information about the controls in the panel. The help information will appear in your web browser. Each type of input control utilized by the panels is described below. Note that the examples shown here are for a UNIX system; if you are working on a Windows system, your panel controls may look slightly different, but they will work exactly as described here.

Tab

Much like the tabs on a notebook divider, tabs in panels are used to mark the different sections into which a panel is divided. A panel that contains many controls may be divided into different sections to reduce the amount of screen space it occupies. You can access each section of the panel by “clicking” the left mouse button on the corresponding tab. A click is one press and release of the mouse button.


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User Interface

Button

A button, also referred to as a push button, is used to perform a function indicated by the button label. To activate a button, place the pointer over the button and click the left mouse button.

Check Box

A check box, also referred to as a check button, is used to turn on/off an item or action indicated by the check box label. Click the left mouse button on the check box to toggle the state.

Radio Buttons

Radio buttons are a set of check boxes with the condition that only one can be set in the “on” position at a time. When you click the left mouse button on a radio button, it will be turned on, and all others will be turned off. Radio buttons appear either as diamonds (as shown above) or as circles.

Text Entry

A text entry lets you type text input. It will often have a label associated with it to indicate the purpose of the entry.

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Integer Number Entry

An integer number entry is similar to a text entry except it allows only integer numbers to be entered (e.g., 10, -10, 50000 and 5E4). You may find it easier to enter large integer numbers using scientific notation. For example, you could enter 350000 or 3.5E5. The integer number entry also has arrow buttons that allow you to easily increase or decrease its value. For most integer number entry controls, the value will be increased (or decreased) by one when you click an arrow button. You can increase the size of the increment by holding down a keyboard key while clicking the arrow button. The keys used are shown below: Key Factor of Increase Shift 10 Ctrl 100

Real Number Entry

A real number entry is similar to a text entry, except it allows only real numbers to be entered (e.g., 10, -10.538, 50000.45 and 5.72E-4). In most cases, the label will show the units associated with the real number entry.

Single-Selection List

A single-selection list contains zero or more items. Each item is printed on a separate line in the list. You can select an item by placing the pointer over the item line and clicking


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User Interface

with the left mouse button. The selected item will become highlighted. Selecting another item will deselect the previously selected item in the list. Many panels will also accept a double-click in order to invoke the panel action that is associated with the list selection (see information on the panel of interest for more details).

Multiple-Selection List

A multiple selection list is similar to a single-selection list, except it allows for more than one selected item at a time. When you click the left mouse button on an item, its selection state will toggle. Clicking on an unselected item will select it. Clicking on a selected item will deselect it. To select a range of items in a multiple-selection list, you can select the first desired item, and then select the last desired item while holding down the key. The first and last items, and all the items between them, will be selected. You can also click and drag the left mouse button to select multiple items. There are two small buttons in the upper right corner of the multiple selection list that accelerate the task of selecting or deselecting all the items in the list. Clicking on the first button will select all items. Clicking on the second button will deselect all items.

Drop-Down List

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A drop-down list is a hidden single-selection list that shows only the current selection to save space. When you want to change the selection, follow the steps below: 1. Click the arrow button to display the list. 2. Place the pointer over the new list item. 3. Click the left mouse button on the item to make the selection and close the list. If you wish to abort the selection operation while the list is displayed, you can move the pointer anywhere outside the list and click the left mouse button.

Scale

The scale is used to select a value from a predefined range by moving a slider. The number shows the current value. To change the value, follow one of the procedures below: 1. Place the pointer over the slider. 2. Press and hold down the left mouse button. 3. Move the pointer along the slider bar to change the value. 4. Release the left mouse button. or 1. Place the pointer over the slider and click the left mouse button. 2. Using the arrow keys on the keyboard, move the slider bar left or right to change the value.


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User Interface

Figure 2.1.4: Sample Graphics Display Window

2.1.4

Graphics Display Windows

Graphics display windows (e.g., Figure 2.1.4) are separate windows that display the program’s graphical output. The Display Options panel can be used to change the attributes of the graphics display or to open another display window. The Mouse Buttons panel can be used to set the action taken when a mouse button is pressed in the display window.

! To cancel a display operation, press while data are being processed in preparation for graphical display. You cannot cancel the operation after the program begins to draw in the graphics window. For Windows systems, there are special features for printing the contents of the graphics window directly. These features are not available on UNIX systems.

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Printing the Contents of the Graphics Display Window (Windows Systems Only) If you are using the Windows version of FLUENT, the graphics window’s system menu, displayed by clicking in the upper-left corner of the graphics window, contains the usual system commands, such as move, size, and close. Along with the system commands, FLUENT adds three more commands to the menu for printer and clipboard support. These commands are described below: Copy to Clipboard places a copy of the current picture into the Microsoft Windows clipboard. Some attributes of the copied picture can be changed using the Page Setup panel. The size of your graphics window affects the size of the text fonts used in the picture. For best results, experiment with the graphics window size and examine the resulting clipboard picture using the Windows clipboard viewer. Print... displays the Microsoft Windows Print dialog box, which enables you to send a copy of the picture to a printer. Some attributes of the copied picture can be changed using the Page Setup panel. Still more attributes of the final print can be specified within the Microsoft Windows Print and Print Setup dialog boxes (see documentation for Microsoft Windows and your printer for details). Page Setup... displays the Page Setup panel, which allows you to change attributes of the picture copied to the clipboard, or to a printer.

Page Setup Panel (Windows Systems Only) To open the Page Setup panel, select the Page Setup... menu item in the graphics display window’s system menu. Controls Color allows you to specify a color or non-color picture. Color selects a color picture. Gray Scale selects a gray-scale picture. Monochrome selects a black-and-white picture. Color Quality allows you to specify the color mode used for the picture. True Color creates a picture defined by RGB values. This assumes that your printer or display has at least 65536 colors, or “unlimited colors”. Mapped Color creates a picture that uses a colormap. This is the right choice for devices that have 256 colors. Dithered Color creates a dithered picture that uses 20 colors or less.


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User Interface

Figure 2.1.5: The Page Setup Panel (Windows Systems Only)

Clipboard Formats allows you to choose the desired format copied to the clipboard. The size of your graphics window can affect the size of the clipboard picture. For best results, experiment with the graphics window size and examine the resulting clipboard picture using the Windows clipboard viewer. Bitmap is a bitmap copy of the graphics window. DIB Bitmap is a device-independent bitmap copy of the graphics window. Metafile is a Windows Metafile. Enhanced Metafile is a Windows Enhanced Metafile. Picture Format allows you to specify a raster or a vector picture. Vector creates a vector picture. This format will have a higher resolution when printed, but some large 3D pictures may take a long time to print. Raster creates a raster picture. This format will have a lower resolution when printed, but some large 3D pictures may take much less time to print. Printer Scale % controls the amount of the page that the printed picture will cover. Decreasing the scaling will effectively increase the margin between the picture and the edge of the paper. Options contains options that control other attributes of the picture.

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Landscape Orientation (Printer) specifies the orientation of the picture. If selected, the picture is made in landscape mode; otherwise, it is made in portrait mode. This option is applicable only when printing. Reverse Foreground/Background specifies that the foreground and background colors of the picture will be swapped. This feature allows you to make a copy of the picture with a white background and a black foreground, while the graphics window is displayed with a black background and white foreground.

2.1.5

Customizing the Graphical User Interface (UNIX Systems Only)

On UNIX systems, you may wish to customize the graphical user interface by changing attributes such as text color, background color, and text fonts. The program will try to provide default text fonts that are satisfactory for your platform’s display size, but in some cases customization may be necessary if the default text fonts make the GUI too small or too large on your display, or if the default colors are undesirable. The GUI in FLUENT is based on the X Window System Toolkit and OSF/Motif. The attributes of the GUI are represented by X Window “resources”. If you are unfamiliar with the X Window System Resource Database, please refer to any documentation you may have that describes how to use the X Window System or OSF/Motif applications. The default X Window resource values for a medium resolution display are shown below: ! ! General resources ! Fluent*geometry: +0-0 Fluent*fontList: *-helvetica-bold-r-normal--12-* Fluent*MenuBar*fontList: *-helvetica-bold-r-normal--12-* Fluent*XmText*fontList: *-fixed-medium-r-normal--13-* Fluent*XmTextField*fontList: *-fixed-medium-r-normal--13-* Fluent*foreground: black Fluent*background: gray75 Fluent*activeForeground: black Fluent*activeBackground: gray85 Fluent*disabledTextColor: gray55 Fluent*XmToggleButton.selectColor: green Fluent*XmToggleButtonGadget.selectColor: green Fluent*XmText.translations:\ #overrideDelete: delete-previous-character() Fluent*XmTextField.translations:\ #overrideDelete: delete-previous-character()


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User Interface

! ! Console resources ! Fluent*ConsoleText.rows: 24 Fluent*ConsoleText.columns: 80 Fluent*ConsoleText.background: linen ! ! Help Viewer resources ! Fluent*Hyper.foreground: black Fluent*Hyper.background: linen Fluent*Hyper.hyperColor: SlateBlue3 Fluent*Hyper*normalFont:\ *-new century schoolbook-medium-r-normal--12-* Fluent*Hyper*hyperFont:\ *-new century schoolbook-bold-r-normal--12-* Fluent*Hyper*texLargeFont:\ *-new century schoolbook-bold-r-normal--14-* Fluent*Hyper*texBoldFont:\ *-new century schoolbook-bold-r-normal--12-* Fluent*Hyper*texFixedFont:\ *-courier-bold-r-normal--12-* Fluent*Hyper*texItalicFont:\ *-new century schoolbook-medium-i-normal--12-* Fluent*Hyper*texMathFont:\ *-symbol-medium-r-normal--14-* Fluent*Hyper*texSansFont:\ *-helvetica-bold-r-normal--12-* To customize one or more of the resources for a particular user, place appropriate resource specification lines in that user’s file $HOME/.Xdefaults or whatever resource file is loaded by the X Window System on the user’s platform. To customize one or more of the resources for several users at a site, place the resource specification lines in an application defaults resource file called Fluent. This file should then be installed in a directory such as /usr/lib/X11/app-defaults, or on SUN workstations, the directory may be /usr/openwin/lib/app-defaults. See documentation regarding your platform for more information.

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2.2 Text User Interface

2.2

Text User Interface

The text interface (TUI) uses, and is written in, a dialect of Lisp called Scheme. Users familiar with Scheme will be able to use the interpretive capabilities of the interface to create customized commands.

2.2.1

Text Menu System

The text menu system provides a hierarchical interface to the program’s underlying procedural interface. Because it is text based, you can easily manipulate its operation with standard text-based tools: input can be saved in files, modified with text editors, and read back in to be executed. Because the text menu system is tightly integrated with the Scheme extension language, it can easily be programmed to provide sophisticated control and customized functionality. The menu system structure is similar to the directory tree structure of UNIX operating systems. When you first start FLUENT, you are in the “root” menu and the menu prompt is simply a caret. >

To generate a listing of the submenus and commands in the current menu, simply press . > adapt/ display/ define/ file/

grid/ parallel/ plot/ report/

solve/ surface/ view/ exit

By convention, submenu names end with a / to differentiate them from menu commands. To execute a command, just type its name (or an abbreviation). Similarly, to move down into a submenu, enter its name or an abbreviation. When you move into the submenu, the prompt will change to reflect the current menu name. > display /display> set /display/set>

To move back to the previously occupied menu, type q or quit at the prompt.


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User Interface

/display/set> q /display>

You can move directly to a menu by giving its full pathname. /display> /file /display//file>

In the above example, control was passed from /display to /file without stopping in the root menu. Therefore, when you quit from the /file menu, control will be passed directly back to /display. /display//file> q /display>

Furthermore, if you execute a command without stopping in any of the menus along the way, control will again be returned to the menu from which you invoked the command. /display> /file start-journal jrnl Input journal opened on file "jrnl". /display>

The text menu system provides on-line help for menu commands. The text menu on-line help system is described in Section 2.3.2.

Command Abbreviation To select a menu command, you do not need to type the entire name; you can type an abbreviation that matches the command. The rules for matching a command are as follows: A command name consists of phrases separated by hyphens. A command is matched by matching an initial sequence of its phrases. Matching of hyphens is optional. A phrase is matched by matching an initial sequence of its characters. A character is matched by typing that character. If an abbreviation matches more than one command, then the command with the greatest number of matched phrases is chosen. If more than one command has the same number of matched phrases, then the first command to appear in the menu is chosen.

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For example, each of the following will match the command set-ambientcolor: setambient-color, s-a-c, sac, and sa. When abbreviating commands, sometimes your abbreviation will match more than one command. In such cases, the first command is selected. Occasionally, there is an anomaly such as lint not matching lightinginterpolation because the li gets absorbed in lights-on? and then the nt doesn’t match interpolation. This can be resolved by choosing a different abbreviation, such as liin, or l-int.

Scheme Evaluation If you enter an open parenthesis, (, at the menu prompt, then that parenthesis and all characters up to and including the matching closing parenthesis are passed to Scheme to be evaluated, and the result of evaluating the expression is displayed.

> (define a 1) a > (+ a 2 3 4) 10

Aliases Command aliases can be defined within the menu system. As with the UNIX csh shell, aliases take precedence over command execution. The following aliases are predefined in Cortex: error, pwd, chdir, ls, ., and alias. error displays the Scheme object that was the “irritant” in the most recent Scheme error interrupt. pwd prints the working directory in which all file operations will take place. chdir will change the working directory. ls lists the files in the working directory. alias displays the list of symbols currently aliased.

2.2.2

Text Prompt System

Commands require various arguments, including numbers, filenames, yes/no responses, character strings, and lists. A uniform interface to this input is provided by the text prompt system. A prompt consists of a prompt string, followed by an optional units string enclosed in parentheses, followed by a default value enclosed in square brackets


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User Interface

filled grids? [no] shrink-factor [0.1] line-weight [1] title [""]

The default value for a prompt is accepted by typing a or a , (comma).

! Note that a comma is not a separator. It is a separate token that indicates a default value. The sequence “1,2” results in three values; the number 1 for the first prompt, the default value for the second prompt, and the number 2 for the third prompt. A short help message can be displayed at any prompt by entering a ?. (See Section 2.3.2.) To abort a prompt sequence, simply press .

Numbers The most common prompt type is a number. Numbers can be either integers or reals. Valid numbers are, for example, 16, -2.4, .9E5, and +1E-5. Integers can also be specified in binary, octal, and hexadecimal form. The decimal integer 31 can be entered as 31, #b11111, #o37, or #x1f. In Scheme, integers are a subset of reals, so you do not need a decimal point to indicate that a number is real; 2 is just as much a real as 2.0. If you enter a real at an integer prompt, any fractional part will simply be truncated; 1.9 will become 1.

Booleans Some prompts require a yes-or-no response. A yes/no prompt will accept either yes or y for a positive response, and no or n for a negative response. yes/no prompts are used for confirming potentially dangerous actions such as overwriting an existing file, exiting without saving case, data, mesh, etc. Some prompts require actual Scheme boolean values (true or false). These are entered with the Scheme symbols for true and false, #t and #f.

Strings Character strings are entered in double quotes, e.g., "red". Plot titles and plot legend titles are examples of character strings. Character strings can include any characters, including blank spaces and punctuation.

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Symbols Symbols are entered without quotes. Zone names, surface names, and material names are examples of symbols. Symbols must start with an alphabetical character (i.e., a letter), and cannot include any blank spaces or commas.

Filenames Filenames are actually just character strings. For convenience, filename prompts do not require the string to be surrounded with double quotes. If, for some exceptional reason, a filename contains an embedded space character, then the name must be surrounded with double quotes. One consequence of this convenience is that filename prompts do not evaluate the response. For example, the sequence

> (define fn "valve.ps") fn > hc fn

will end up writing a hardcopy file with the name fn, not valve.ps. Since the filename prompt did not evaluate the response, fn did not get a chance to evaluate "valve.ps" as it would for most other prompts.

Lists Some functions in FLUENT require a “list” of objects such as numbers, strings, booleans, etc. A list is a Scheme object that is simply a sequence of objects terminated by the empty list, ’(). Lists are prompted for an element at a time, and the end of the list is signaled by entering an empty list. This terminating list forms the tail of the prompted list, and can either be empty or can contain values. For convenience, the empty list can be entered as () as well as the standard form ’(). Normally, list prompts save the previous argument list as the default. To modify the list, overwrite the desired elements and terminate the process with an empty list. For example, element(1) element(2) element(3) element(4)

[()] [()] [()] [()]

1 10 100

creates a list of three numbers: 1, 10, and 100. Subsequently,


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User Interface

element(1) element(2) element(3) element(4) element(5)

[1] [10] [100] [()] 1000 [()]

adds a fourth element. Then element(1) [1] element(2) [10] element(3) [100] ()

leaves only 1 and 10 in the list. Subsequently entering element(1) [1] ,,’(11 12 13)

creates a five element list: 1, 10, 11, 12, and 13. Finally, a single empty list removes all elements element(1) [1] ()

Evaluation All responses to prompts (except filenames, see above) are evaluated by the Scheme interpreter before they are used. You can therefore enter any valid Scheme expression as the response to a prompt. For example, to enter a unit vector with one component equal to 1/3 (without using your calculator), /foo> set-xy x-component [1.0] (/ 1 3) y-component [0.0] (sqrt (/ 8 9))

or, you could first define a utility function to compute the second component of a unit vector, > (define (unit-y x) (sqrt (- 1.0 (* x x)))) unit-y /foo> set-xy x-component [1.0] (/ 1 3) y-component [0.0] (unit-y (/ 1 3))

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Default Value Binding The default value at any prompt is bound to the Scheme symbol “_” (underscore) so that the default value can form part of a Scheme expression. For example, if you want to decrease a default value by one-third, you could enter

shrink-factor [0.8] (/ _ 3)

2.2.3

Interrupts

The execution of the code can be halted using , at which time the present operation stops at the next recoverable location.

2.2.4

System Commands

If you are running FLUENT under a UNIX-based operating system, you can execute system commands with the ! (bang) shell escape character. All characters following the ! up to the next newline character will be executed in a subshell. Any further input related to these system commands must be entered in the window in which you started the program, and any screen output will also appear in that window. (Note that if you started FLUENT remotely, this input and output will be in the window in which you started Cortex.) > !rm junk.* > !vi script.rp

The ls and pwd aliases invoke the UNIX ls and pwd commands in the working directory. The chdir alias changes the program’s current working directory. !ls and !pwd will execute the UNIX commands in the directory in which Cortex was started. The screen output will appear in the window in which you started FLUENT, unless you started it remotely, in which case the output will appear in the window in which you started Cortex. (Note that !chdir or !cd executes in a subshell, so it will not change the working directory either for FLUENT or for Cortex, and it is therefore not useful.) Typing chdir with no arguments will move you to your home directory in the console. Several examples of system commands entered in the console are shown below. The screen output that will appear in the window in which FLUENT was started (or, if you started the program remotely, in the window in which Cortex was started) follows the examples.


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User Interface

Example input (in the FLUENT console): > !pwd > !ls valve.*

Example output (in the window in which FLUENT—or Cortex, if you started the program remotely—was started): /home/cfd/run/valve valve1.cas valve1.msh

2.2.5

valve2.cas

valve2.msh

Text Menu Input from Character Strings

Often, when writing a Scheme extension function for FLUENT, it is convenient to be able to include menu commands in the function. This can be done with ti-menu-load-string. For example, to open graphics window 1, use (ti-menu-load-string "di ow 1") A Scheme loop that will open windows 0 and 1 and display the front view of the grid in window 0 and the back view in window 1 is given by (for-each (lambda (window view) (ti-menu-load-string (format #f "di ow ~a gr view rv ~a" window view))) ’(0 1) ’(front back)) This loop makes use of the format function to construct the string used by menu-load-string. This simple loop could also be written without using menu commands at all, but you need to know the Scheme functions that get executed by the menu commands to do it: (for-each (lambda (window view) (cx-open-window window) (display-grid) (cx-restore-view view)) ’(0 1) ’(front back))

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2.3 Using On-Line Help

String input can also provide an easy way to create aliases within FLUENT. For example, to create an alias that will display the grid, you could type the following: (alias ’dg (lambda () (ti-menu-load-string "/di gr"))) Then any time you enter dg from anywhere in the menu hierarchy, the grid will be drawn in the active window.

! ti-menu-load-string evaluates the string argument in the top level menu. It ignores any menu you may be in when you invoke ti-menu-loadstring. Therefore, the command (ti-menu-load-string "open-window 1 gr")

; incorrect usage

will not work even if you type it from within the display/ menu—the string itself must cause control to enter the display/ menu, as in (ti-menu-load-string "display open-window 1 grid")

2.3

Using On-Line Help

Included in FLUENT is an on-line help facility that provides easy access to the program documentation. Through the graphical user interface, you have the entire User’s Guide and other documentation available to you with the click of a mouse button. The User’s Guide and other manuals are displayed in your web browser, and you can use the hypertext links and the browser’s search and navigation tools (as well as the additional navigation tools described in Section 1.7.1) to find the information you need. • Section 2.3.1: Using the GUI Help System • Section 2.3.2: Using the Text Interface Help System

2.3.1

Using the GUI Help System

There are many ways to access the information contained in the on-line help. You can get reference information from within a panel or (on UNIX machines) request contextsensitive help for a particular menu item or panel. You can also go to the User’s Guide contents page or index, and use the hypertext links there to find the information you are looking for. In addition to the User’s Guide, you can also access the other FLUENT documentation (e.g., the Tutorial Guide or UDF Manual). Note that the Reference Guide, which is the last chapter of the User’s Guide in the on-line help, contains a description of each menu item and panel.


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User Interface

! FLUENT’s help system is HTML-based, so you need to have access to a web browser. You also need to have installed the HTML files from the documentation CD-ROM. See the separate installation instructions for your platform type for information about installing the files from the documentation CD-ROM. This section focuses on the Help menu in FLUENT, and how you can use it (and the Help button in each panel) to access the HTML-based on-line help from within FLUENT. See Section 1.7 for information about accessing the documentation outside of FLUENT. Section 1.7.1 provides additional information about navigating and finding information in the User’s Guide (and other manuals), as well as guidelines for modifying the appearance of the HTML versions of the manuals.

Panel Help To get help about a panel that you are currently using, click the Help button in the panel. The web browser will open to the section of the Reference Guide that explains the function of each item in the panel. In this section you will also find hypertext links to the section(s) of the User’s Guide that discuss how to use the panel and provide related information.

Context-Sensitive Help (UNIX Only) If you want to find out how or when a particular menu item or panel is used, you can use the context-sensitive help feature. Select the Context-Sensitive Help item in the Help pull-down menu. Help −→Context-Sensitive Help With the resulting question-mark cursor, select an item from a pull-down menu. The web browser will open to the section of the User’s Guide that discusses the selected item.

Opening the User’s Guide Table of Contents To see a list of the chapters in the User’s Guide, select the User’s Guide Contents... menu item in the Help pull-down menu. Help −→User’s Guide Contents... Selecting this item will open the web browser to the contents page of the User’s Guide (Figure 2.3.1). Each chapter in the list is a hypertext link that you can click to view that chapter. There is also an Expanded Contents link, which will display a list of contents including all section titles in addition to the chapter titles. Each of these is a link to the corresponding chapter or section of the manual.

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Figure 2.3.1: The FLUENT User’s Guide Contents Page


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User Interface

Opening the User’s Guide Index To see the index for the User’s Guide, select the User’s Guide Index... menu item in the Help pull-down menu. Help −→User’s Guide Index... Selecting this menu item will open the web browser to the “A” page of the index (Figure 2.3.2). You can use the links at the top and bottom of the page to access the index pages for other letters of the alphabet. Next to each entry in the index you will find one or more numbers, which are links. Clicking on one of these links will bring you to the corresponding place in the User’s Guide where the index entry topic is discussed.

Opening the Reference Guide To open the web browser to the first page of the Reference Guide, which contains information about each panel or menu item, arranged by pull-down menu, click the Reference Guide hypertext link near the bottom of the User’s Guide Contents page.

Help on Help You can obtain information about using on-line help by selecting the Using Help... menu item in the Help pull-down menu. Help −→Using Help... When you select this item, the web browser will open to the beginning of this section.

Help for Text Interface Commands There are two ways to find information about text interface commands. You can either go to the Text Command List (which can be accessed using the Help/More Documentation... menu item, as described below), or use the text interface help system described in Section 2.3.2.

Accessing the Other Manuals As noted above, you can access other manuals through the on-line help, in addition to the User’s Guide. (You can also access the User’s Guide in formats other than HTML— namely, Adobe Acrobat PDF—which is recommended if you want to print out an entire chapter or a long section.) To see what other FLUENT manuals are available, select the More Documentation... menu item in the Help pull-down menu. Help −→More Documentation... When you select this item, the web browser will open to the FLUENT documentation “home” page (Figure 1.7.1). See Section 1.7.1 for more details.

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Figure 2.3.2: The FLUENT User’s Guide Index


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User Interface

Version and Release Information You can obtain information about the version and release of FLUENT you are running by selecting the Version... menu item in the Help pull-down menu. Help −→Version...

2.3.2

Using the Text Interface Help System

The text user interface provides context-sensitive on-line help. Within the text menu system, a brief description of each of the commands can be invoked by entering a ? followed by the command in question. Example: > ?dis display/: Enter the display menu.

You can also enter a lone ? to enter “help mode.” In this mode, you need only enter the command or menu name to display the help message. To exit help mode type q or quit as for a normal menu. Example: > ? [help-mode]> di display/: Enter the display menu. [help-mode]> pwd pwd: #[alias] (LAMBDA () (BEGIN (SET! pwd-cmd ((LAMBDA n n) ’system (IF (cx-send ’(unix?)) "pwd" "cd"))) (cx-send pwd-cmd))) [help-mode]> q

Help can also be obtained when you are prompted for information by typing a ? at the prompt.

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2.4 Remote Execution

Example: > display/annotate Annotation text [""] ? Enter the text to annotate the plot with. Annotation text [""]

2.4

Remote Execution

There may be situations when you want to view FLUENT on one machine, but run it on a different (remote) machine. This section explains how to do this.

2.4.1

Overview and Limitations

If FLUENT has been started without a version argument (e.g., 3d), you can select the solver after startup. Starting the solver in this manner allows you to run it on a remote processor. By default, when you type the command to start FLUENT and include the version, you actually start Cortex (a process that provides the user interface and graphics for FLUENT) and Cortex then starts FLUENT on the same processor on which Cortex is running. When you type the startup command without specifying a version, you just start Cortex. This gives you the opportunity to specify a different processor on which to run the solver.

! Note the following limitations when you run FLUENT on a remote UNIX machine from a local Windows machine: • You will not be able to read or write files using the items in the File pull-down menu; use the text commands for reading and writing files instead. See the separate Text Command List for details. • You will not be able to use user-defined functions.

2.4.2

Steps for Running on a Remote Machine

To run FLUENT on a remote processor, you will normally follow the procedure listed below. 1. Start FLUENT by typing the following: • On a UNIX machine, type fluent • On a Windows machine (in an MS-DOS Command Prompt window), type fluent -serv -a


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User Interface

2. Open the Select Solver panel. File −→Run... 3. In the Select Solver panel, under Remote Execution, set the internet name of the remote machine (Hostname), your username at that machine (Username), and your password at that machine (Password). 4. Specify the appropriate solver version under Versions and Options in the Select Solver panel. (More information about these items is available in Sections 1.5 and 30.2.) 5. Click the Run button. If the remote processor refuses to start the solver, you may need to try the procedure described in Section 2.4.3.

2.4.3

Starting the Solver Manually on the Remote Machine

If the remote process fails when you click the Run button in the Select Solver panel (as described in Section 2.4.2), you can use the “listen” option to work around network security devices that prevent Cortex from creating a remote process directly. The procedure is as follows: 1. Click the Listen button in the Select Solver panel or type listen at the version> prompt (and press to accept the default “time out”). FLUENT will print a message telling you what arguments you should use to start the solver on a remote machine. The arguments will be in this format: -cx host:p1:p2 where host is the name of the host Cortex is running on, and :p1:p2 are two colon-separated integers indicating the port numbers being used. 2. Open a telnet or xterm window and log onto the remote machine where you want to launch the solver. 3. In the telnet or xterm window, type the following to start the desired version of FLUENT: fluent version -cx host:p1:p2 replacing version by the version that you wish to run (e.g., 3d), and the host and port numbers by the values displayed above when you clicked Listen in the Select Solver panel or typed listen in the FLUENT console window.

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2.5 Batch Execution

2.4.4

Executing Remotely by Reading a Case File

If you plan to start the appropriate version of FLUENT by reading in a case file (as described in Section 1.5.2), but you wish to run the solver on a remote machine, you can specify the remote machine in the Select Solver panel as described in Section 2.4.2, and then click Apply instead of Run. This will save the settings for remote execution. When you start the solver by specifying a case file, the solver will be run on the specified remote machine.

2.5

Batch Execution

FLUENT can be used interactively, with input from and display to your computer screen, or it can be used in a batch or background mode in which inputs are obtained from and outputs are stored in files. Generally you will perform problem setup, initial calculations, and postprocessing of results in an interactive mode. However, when you are ready to perform a large number of iterative calculations, you may want to run FLUENT in batch or background. This allows the computer resources to be prioritized, enables you to control the process from a file (eliminating the need for you to be present during the calculation), and also provides a record of the calculation history (residuals) in an output file. While the procedures for running FLUENT in a batch mode differ depending on your computer operating system, Section 2.5.1 provides guidance for running in batch/background on UNIX systems.

2.5.1

Background Execution on UNIX Systems

To run FLUENT in background in a C-shell (csh) on a UNIX system, type a command of the following form at the system-level prompt: fluent 2d -g < inputfile >& outputfile & or in a Bourne/Korn-shell, type: fluent 2d -g < inputfile > outputfile 2>&1 & In these examples, • fluent is the command you type to execute FLUENT interactively. • -g indicates that the program is to be run without the GUI or graphics (see Section 1.5). • inputfile is a file of FLUENT commands that are identical to those that you would type interactively.


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User Interface

• outputfile is a file that the background job will create and which will contain the output that FLUENT would normally print to the screen (e.g., the menu prompts and residual reports). • & tells the UNIX system to perform this task in background and to send all standard system errors (if any) to outputfile. The file inputfile can be a journal file created in an earlier FLUENT session, or it can be a file that you have created using a text editor. In either case, the file must consist only of text interface commands (since the GUI is disabled during batch execution). A typical inputfile is shown below: ; Read case file rc example.cas ; Initialize the solution /solve/init/init ; Calculate 50 iterations it 50 ; Write data file wd example50.dat ; Calculate another 50 iterations it 50 ; Write another data file wd example100.dat ; Exit FLUENT exit yes

This example file reads a case file example.cas, initializes the solution, and performs 100 iterations in two groups of 50, saving a new data file after each 50 iterations. The final line of the file terminates the session. Note that the example input file makes use of the standard aliases for reading and writing case and data files and for iterating. (it is the alias for /solve/iterate, rc is the alias for /file/read-case, wd is the alias for /file/write-data, etc.) These predefined aliases allow you to execute commonlyused commands without entering the text menu in which they are found. In general, FLUENT assumes that input beginning with a / starts in the top-level text menu, so if you use any text commands for which aliases do not exist, you must be sure to type in the complete name of the command (e.g., /solve/init/init). Note also that you can include comments in the file. As in the example above, comment lines must begin with a ; (semicolon). An alternate strategy for submitting your batch run, as follows, has the advantage that the outputfile will contain a record of the commands in the inputfile. In this approach, you would submit the batch job in a C-shell using:

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2.5 Batch Execution

fluent 2d -g -i inputfile >& outputfile & or in a Bourne/Korn-shell using: fluent 2d -g -i inputfile > outputfile 2>&1 &

2.5.2

Batch Execution Options

During a typical session, FLUENT may require feedback from you in the event of a problem it encounters. FLUENT usually communicates problems or questions through the use of Error dialog boxes, Warning dialog boxes, or Question dialog boxes. While executing FLUENT in batch mode, you may want to suppress this type of interaction in order to, for example, create journal files more easily. There are three common batch configuration options available to you when running FLUENT in batch mode. You can access these options using the Batch Options panel. File −→Batch Options...

Figure 2.5.1: The Batch Options Panel The Batch Options panel contains the following items: Confirm File Overwrite determines whether FLUENT confirms a file overwrite. This option is turned on by default. Hide Questions allows you to hide Question dialog boxes. This option is turned off by default. Exit on Error allows you to automatically exit from batch mode when an error occurs. This option is turned off by default.


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User Interface

Note that these options are also available in the file/set-batch-options command in the text interface. file −→set-batch-options Any combination of these options can be turned on or off at any given time prior to running in batch mode

2.6

Checkpointing a FLUENT Simulation

The checkpointing feature of FLUENT allows you to save case and data files while your simulation is running. While similar to the autosave feature of FLUENT (Section 3.3.4), which allows you to save files throughout a simulation, checkpointing allows you slightly more control in that you can save a FLUENT job even after you have started the job and did not set the autosave option. Checkpointing also allows you to save case and data files and then exit out of FLUENT. This feature is especially useful when you need to stop a FLUENT job abruptly and save its data. There are two different ways to checkpoint a FLUENT simulation, depending upon how the simulation has been started. 1. FLUENT running under LSF or SGE FLUENT is integrated with load management tools like LSF and SGE. These two tools allow you to checkpoint any job running under them. You can use the standard method provided by these tools to checkpoint the FLUENT job. For more information on using FLUENT and SGE, see Section 30.6. For more information about using FLUENT and LSF, see Section 30.7. 2. Independently running FLUENT When not using tools such as LSF or SGE, a different checkpointing mechanism can be used when running a FLUENT simulation. You can checkpoint a FLUENT simulation by saving case and data files while iterating, or by saving case and data files upon exiting FLUENT. • Saving case and data files while iterating: On UNIX, create a file called check-fluent, i.e., /tmp/check-fluent On Windows NT, create a file called check-fluent.txt, i.e., c:\\temp\check-fluent.txt • Saving case and data files and exiting FLUENT: On UNIX, create a file called check-fluent, i.e.,

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2.7 Exiting the Program

/tmp/exit-fluent On Windows NT, create a file called check-fluent.txt, i.e., c:\\temp\exit-fluent.txt The saved case and data files will have the current iteration number appended to their file names. To change the default location of these saved case and data files, you can use the following Scheme commands: (set! checkpoint/check-filename "pathname") and (set! checkpoint/exit-filename "pathname") where pathname is the path you wish to set as the new default location of the saved case and data files. Also, you can instruct FLUENT to only write data files by entering the following Scheme command: (rpsetvar ’checkpoint/write-case? #f)

2.7

Exiting the Program

You can exit FLUENT by selecting Exit in the File pull-down menu. If the present state of the program has not been written to a file, you will receive a warning message. You can cancel the exit and write the appropriate file(s) or you can continue to exit without saving the case or data.


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User Interface

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Chapter 3.

Reading and Writing Files

During a FLUENT session you may need to import and export several kinds of files. Files that are read include grid, case, data, profile, Scheme, and journal files, and files that are written include case, data, profile, journal, and transcript files. FLUENT also has features that allow you to save panel layouts and hardcopies of graphics windows. You can also export data for use with various visualization and postprocessing tools. These operations are described in the following sections. • Section 3.1: Shortcuts for Reading and Writing Files • Section 3.2: Reading Mesh Files • Section 3.3: Reading and Writing Case and Data Files • Section 3.4: Reading FLUENT/UNS and RAMPANT Case and Data Files • Section 3.5: Importing FLUENT 4 Case Files • Section 3.6: Importing FIDAP Neutral Files • Section 3.7: Creating and Reading Journal Files • Section 3.8: Creating Transcript Files • Section 3.9: Reading and Writing Profile Files • Section 3.10: Reading and Writing Boundary Conditions • Section 3.11: Writing a Boundary Grid • Section 3.12: Saving Hardcopy Files • Section 3.13: Exporting Data • Section 3.14: Grid-to-Grid Solution Interpolation • Section 3.15: Loading Scheme Source Files • Section 3.16: The .fluent File • Section 3.17: Saving the Panel Layout • Section 3.18: Formats of FLUENT Case and Data Files


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3.1

Shortcuts for Reading and Writing Files

FLUENT has several features that make the reading and writing of files very convenient: • Automatic appending or detection of default filename suffixes • Binary file reading and writing • Automatic detection of file format (text/binary) • Recent file list • Reading and writing of compressed files • Tilde expansion • Automatic numbering of files • Ability to disable the overwrite confirmation prompt

3.1.1

Default File Suffixes

There are default file suffixes associated with each type of file that FLUENT reads or writes. For several commonly used files, the solver will automatically append or detect the appropriate suffix when you specify the first part of the filename (the prefix). For example, to write a case file named myfile.cas, you can specify just myfile and FLUENT will automatically append .cas. Similarly, to read the case file named myfile.cas into the solver, you can specify just myfile and FLUENT will automatically search for a file of that name with the suffix .cas. FLUENT will automatically append and detect default suffixes for case and data files. In addition, FLUENT will automatically do this for PDF files and ray files. The appropriate default file suffix will appear in the Select File dialog box for each type of file.

3.1.2

Binary Files

When you write a case, data, or ray file, FLUENT will save a binary file by default. Binary files take up less space than text files and can be read and written by FLUENT more quickly. Note, however, that you cannot read and edit a binary file, as you can do for a text file. If you need to save a text file, turn off the Write Binary Files option in the Select File dialog box when you are writing the file.

! FLUENT can read binary files that were saved on different platforms, but other products, such as TGrid, cannot. If you are planning to read a case file into TGrid on a different platform, you should save a text file from FLUENT.

3-2


3.1 Shortcuts for Reading and Writing Files

3.1.3

Detecting File Format

When you read a case, data, grid, PDF, or ray file, the solver will automatically determine whether it is a text (formatted) or binary file.

3.1.4

Recent File List

There is a shortcut for reading in case and data files that you have recently used in FLUENT. At the bottom of the File/Read submenu there is a list of the four FLUENT case files that you most recently read or wrote. To read one of these files into FLUENT, simply select it in the list. This shortcut allows you to conveniently read a recently-used file without having to select it in the Select File dialog box. Note that the files listed are the four case files that you have used most recently in any FLUENT session, so some may not be appropriate for your current session (e.g., a 3D case file will be listed even if you are running a 2D version of FLUENT). Also, if you read a case file using this shortcut, the corresponding data file will be read only if it has the same base name as the case file (e.g., file1.cas and file1.dat) and it was read (or written) with the case file the last time the case file was read (or written).

3.1.5

Reading and Writing Compressed Files

Reading Compressed Files You can use the Select File dialog box to read files that have been compressed using compress or gzip. If you select a compressed file with a .Z extension, FLUENT will automatically invoke zcat to import the file’s data. If you select a compressed file with a .gz extension, the solver will invoke gunzip to import the file’s data. For example, if you select a file named flow.msh.gz, the solver will report the following message, Reading "| gunzip -c flow.msh.gz"...

indicating that the result of the gunzip is imported into FLUENT via an operating system pipe. You can also type in the filename without any suffix (e.g., if you are not sure whether or not the desired file is compressed). First, the solver attempts to open a file with the input name. If it cannot find a file with that name, it attempts to locate files with default suffixes and extensions appended to the name. For example, if you enter the name file-name, the solver traverses the following list until it finds an existing file:


3-3


• file-name • file-name.gz • file-name.Z • file-name.suffix • file-name.suffix.gz • file-name.suffix.Z where suffix is a common extension to the file, such as .cas or .msh. The solver reports an error if it fails to find an existing file with one of these names.

! For Windows systems, only files that were compressed with gzip (i.e., files with a .gz extension) can be read. Files that were compressed with compress cannot be read into FLUENT on a Windows machine.

! Do not read a compressed ray file; FLUENT will not be able to access the ray tracing information properly from a compressed ray file.

Writing Compressed Files You can use the Select File dialog box to write a compressed file by appending a .Z or .gz extension onto the file name. For example, if you enter flow.gz as the name for a case file, the solver will report the following message: Writing "| gzip -cfv > flow.cas.gz"...

The status message indicates that the case file information is being piped into the gzip command, and that the output of the compression command is being redirected to the file with the specified name. In this particular example, the .cas extension was added automatically.

! For Windows systems, compression can be performed only with gzip; that is, you can write a compressed file by appending .gz to the name, but appending .Z will not result in file compression.

! Do not write a compressed ray file; FLUENT will not be able to access the ray tracing information properly from a compressed ray file.

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3.1 Shortcuts for Reading and Writing Files

3.1.6

Tilde Expansion (UNIX Systems Only)

On UNIX systems, if you specify ~/ as the first two characters of a filename, the ~ will be expanded to be your home directory. Similarly, you can start a filename with ~username/, and the ~username will be expanded to the home directory of “username”. If you specify ~/file as the case file to be written, FLUENT will save the file file.cas in your home directory. You can specify a subdirectory of your home directory as well: if you enter ~/cases/file.cas, FLUENT will save the file file.cas in the cases subdirectory.

3.1.7

Automatic Numbering of Files

There are several special characters that you can include in a filename. Using one of these character strings in your filename provides a shortcut for numbering the files based on various parameters (i.e., iteration number, time step, or total number of files saved so far), because you will not need to enter a new filename each time you save a file. (See also Section 3.3.4 for information about saving and numbering case and data files automatically.) • For unsteady calculations, you can save files with names that reflect the time step at which they are saved by including the character string %t in the file name. For example, you can specify contours-%t.ps for the file name, and the solver will save a file with the appropriate name (e.g., contours-0001.ps if the solution is at the first time step). • To save a file with a name that reflects the iteration at which it is saved, use the character string %i in the file name. For example, you can specify contours-%i.ps for the file name, and the solver will save a file with the appropriate name (e.g., contours-0010.ps if the solution is at the 10th iteration). • To save a hardcopy file with a name that reflects the total number of hardcopy files saved so far in the current solver session, use the character string %n in the file name. This option can be used only for hardcopy files.

! Note that when you use the character strings described above in a filename, you will not be prompted for confirmation before FLUENT overwrites an existing file with the same name. Say, for example, that you are repeatedly using the filename myfile-%t.ps to save hardcopies with names that reflect the current time step. If you have already saved myfile-0001.ps at the first time step and then you restart the calculation and save another hardcopy at the (new) first time step, the solver will overwrite the original myfile-0001.ps without checking with you first.


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3.1.8

Disabling the Overwrite Confirmation Prompt

By default, if you ask FLUENT to write a file with the same name as an existing file in that directory, it will ask you to confirm that it is “OK to overwrite” the existing file. If you do not want the solver to ask you for confirmation before it overwrites existing files, you can choose the file/confirm-overwrite? text command and answer no.

3.2

Reading Mesh Files

Mesh files, also known as grid files, are created with the GAMBIT, TGrid, GeoMesh, and preBFC grid generators, or by several third-party CAD packages. A grid file is—from FLUENT’s point of view—simply a subset of a case file (described in Section 3.3.1). The grid file contains the coordinates of all the nodes, connectivity information that tells how the nodes are connected to one another to form faces and cells, and the zone types and numbers (e.g., wall-1, pressure-inlet-5, symmetry-2) of all the faces. The grid file does not contain any boundary conditions, flow parameters, or solution parameters. For more information about grids, see Chapter 5. To read a native-format mesh file (i.e., a mesh file that has been saved in FLUENT format) into the solver, use the File/Read/Case... menu item, as described in Section 3.3.1. GAMBIT, TGrid, GeoMesh, and preBFC can all write a native-format mesh file. For more information about reading these files, see Sections 5.3.1, 5.3.2, 5.3.3, and 5.3.4. For information on importing an unpartitioned mesh file into the parallel solver using the partition filter, see Section 30.4.4.

3.2.1

Reading TGrid Mesh Files

Since TGrid has the same file format as FLUENT, you can read a TGrid mesh into the solver using the File/Read/Case... menu item. File −→ Read −→Case... For more information about reading TGrid mesh files, see Section 5.3.3.

3.2.2

Reading and Importing GAMBIT and GeoMesh Mesh Files

If you create a FLUENT 5/6, FLUENT/UNS, or RAMPANT grid in GAMBIT or GeoMesh, you can read it into FLUENT using the File/Read/Case... menu item. File −→ Read −→Case... Selecting the Case... menu item will open the Select File dialog box (see Section 2.1.2), in which you will specify the name of the file to be read. If you have saved a neutral file from GAMBIT, rather than a FLUENT grid file, you can import it into FLUENT using the File/Import/GAMBIT... menu item.

3-6


3.2 Reading Mesh Files

File −→ Import −→GAMBIT... For more information about importing files from GAMBIT and GeoMesh, see Sections 5.3.1 and 5.3.2.

3.2.3

Reading preBFC Unstructured Mesh Files

Since preBFC’s unstructured triangular grids have the same file format as FLUENT, you can read a preBFC triangular mesh into the solver using the File/Read/Case... menu item.

! Note that you must save the file using the MESH-RAMPANT/TGRID command. File −→ Read −→Case... For more information about reading preBFC mesh files, see Section 5.3.4.

3.2.4

Importing preBFC Structured Mesh Files

You can read a preBFC structured mesh file into FLUENT using the File/Import/preBFC Structured Mesh... menu item. File −→ Import −→preBFC Structured Mesh... Selecting the preBFC Structured Mesh... menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the preBFC structured mesh file to be read. The solver will read grid information and zone types from the preBFC mesh file. For more information about importing preBFC mesh files, see Section 5.3.4.

3.2.5

Importing ANSYS Files

To read an ANSYS file, use the File/Import/ANSYS... menu item. File −→ Import −→ANSYS... Selecting this menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the ANSYS file to be read. The solver will read grid information from the ANSYS file. For more information about importing ANSYS files, see Section 5.3.6.

3.2.6

Importing I-DEAS Universal Files

I-DEAS Universal files can be read into FLUENT with the File/Import/IDEAS Universal... menu item. File −→ Import −→IDEAS Universal...


3-7


Selecting the IDEAS Universal... menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the I-DEAS Universal file to be read. The solver will read grid information and zone types from the I-DEAS Universal file. For more information about importing I-DEAS Universal files, see Section 5.3.6.

3.2.7

Importing NASTRAN Files

NASTRAN files can be read into FLUENT with the File/Import/NASTRAN... menu item. File −→ Import −→NASTRAN... Selecting the NASTRAN... menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the NASTRAN file to be read. The solver will read grid information from the NASTRAN file. For more information about importing NASTRAN files, see Section 5.3.6.

3.2.8

Importing PATRAN Neutral Files

To read a PATRAN Neutral file zoned by named components (that is, a file in which you have grouped nodes with the same specified group name), use the File/Import/PATRAN... menu item. File −→ Import −→PATRAN... Selecting this menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the PATRAN Neutral file to be read. The solver will read grid information from the PATRAN Neutral file. For more information about importing PATRAN Neutral files, see Section 5.3.6.

3.2.9

Importing Meshes and Data in CGNS Format

You can import meshes in CGNS (CFD general notation system) format into FLUENT using the File/Import/CGNS/Mesh... menu item. File −→ Import −→ CGNS −→Mesh... Note that this feature is available on a limited number of platforms (listed in the release notes). To import a mesh and the corresponding CGNS data, File/Import/CGNS/Mesh & Data... menu item.

you can use the

File −→ Import −→ CGNS −→Mesh & Data...

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3.3 Reading and Writing Case and Data Files

3.2.10

Reading a New Grid File

After you have set up a case file using a particular grid, you can merge a new grid with the existing boundary conditions, material properties, solution parameters, etc. One situation in which you might use this feature is if you have generated a better mesh for a problem you have been working on, and you do not want to reenter all of the boundary conditions, properties, and parameters. You can read in the new grid as long as it has the same zone structure as the original grid.

! The new and original grids should have the same zones, numbered in the same order. A warning is issued if they do not, because inconsistencies could create problems with the boundary conditions.

3.3

Reading and Writing Case and Data Files

Information related to your FLUENT simulation is stored in two files: the case file and the data file. The commands for reading and writing these files are described in the following sections, along with commands for the automatic saving of case and data at specified intervals. A description of the case and data file formats is provided in Section 3.18. • Section 3.3.1: Reading and Writing Case Files • Section 3.3.2: Reading and Writing Data Files • Section 3.3.3: Reading and Writing Case and Data Files Together • Section 3.3.4: Automatic Saving of Case and Data Files Note that FLUENT can read and write either text or binary case and data files; binary files require less storage space and are faster to read and write. To specify whether to write a binary or text file, use the Write Binary Files check button in the Select File dialog box (see Section 2.1.2). In addition, you can read and write either text or binary files in compressed formats (see Section 3.1.5). FLUENT automatically detects the file type when reading.

! If you adapt the grid, you must save a new case file as well as a data file. Otherwise the new data file will not correspond to the case file (they will have different numbers of cells, for example). FLUENT will warn you when you try to exit the program if you have not saved an up-to-date case or data file.

3.3.1

Reading and Writing Case Files

Case files contain the grid, boundary conditions, and solution parameters for a problem, as well as information about the user interface and graphics environment. For information about the format of case files see Section 3.18. The commands used for reading case files


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can also be used to read native-format grid files (as described in Section 3.2) because the grid information is a subset of the case information. You can read a case file using the Select File dialog box (see Section 2.1.2) invoked by selecting the File/Read/Case... menu item. To write a case file, use the Select File dialog box invoked by selecting the File/Write/Case... menu item. File −→ Read −→Case... File −→ Write −→Case... See Section 1.5.2 for information about executing the appropriate version automatically based on the case file that is read.

Default Suffixes By convention, case file names are composed of a root with the suffix .cas. If you conform to this convention, you do not have to type the suffix when prompted for a filename; it will be added automatically. When FLUENT reads a case file, it first looks for a file with the exact name you typed. If a file with that name is not found, it uses the procedure described in Section 3.1.5 to search for the case file. When FLUENT writes a case file, .cas will be added to the name you type unless the name already ends with .cas.

3.3.2

Reading and Writing Data Files

Data files contain the values of the flow field in each grid element and the convergence history (residuals) for that flow field. For information about the format of data files see Section 3.18. You can read a data file using the Select File dialog box (see Section 2.1.2) invoked by selecting the File/Read/Data... menu item. Likewise, you can write a data file using the Select File dialog box invoked by selecting the File/Write/Data... menu item. File −→ Read −→Data... File −→ Write −→Data...

Default Suffixes By convention, data file names are composed of a root with the suffix .dat. If you conform to this convention, you do not have to type the suffix when prompted for a filename; it will be added automatically. When FLUENT reads a data file, it first looks for a file with the exact name you typed. If a file with that name is not found, it uses the procedure described in Section 3.1.5 to search for the data file. When it writes a data file, .dat will be added to the name you type unless the name already ends with .dat.

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3.3 Reading and Writing Case and Data Files

3.3.3

Reading and Writing Case and Data Files Together

A case file and a data file together contain all the information required to restart a solution. Case files contain the grid, boundary conditions, and solution parameters. Data files contain the values of the flow field in each grid element and the convergence history (residuals) for that flow field. You can read a case file and a data file together by using the Select File dialog box (see Section 2.1.2) invoked by selecting the File/Read/Case & Data... menu item. To read both files, select the appropriate case file, and the corresponding data file (same name with .dat suffix) will also be read. To write a case file and a data file, select the File/Write/Case & Data... menu item. File −→ Read −→Case & Data... File −→ Write −→Case & Data... See Section 1.5.2 for information about executing the appropriate version automatically based on the case file that is read.

3.3.4

Automatic Saving of Case and Data Files

You can request FLUENT to automatically save case and data files at specified intervals during a calculation. This is especially useful for time-dependent calculations, since it will allow you to save the results at different time steps without stopping the calculation and performing the save manually. You can also use the auto-save feature for steady-state problems, to examine the solution at different stages in the iteration history. Automatic saving is specified using the Autosave Case/Data panel (Figure 3.3.1). File −→ Write −→Autosave...

Figure 3.3.1: The Autosave Case/Data Panel

You must set the frequency of saves for case and/or data files, and the root filename. Enter the case-saving frequency in the Autosave Case File Frequency field, and the data-


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saving frequency in the Autosave Data File Frequency field. Both values are set to zero by default, indicating that no automatic saving is performed. For steady flows you will specify the frequency in iterations, and for unsteady flows you will specify it in time steps (unless you are using the explicit time stepping formulation, in which case you will specify the frequency in iterations). If you define an Autosave Case File Frequency of 10, for example, a case file will be saved every 10 iterations or time steps. Enter the filename to be used for the autosave files in the Filename field. The iteration or time-step number and an appropriate suffix (.cas or .dat) will be added to the specified root name. If the specified Filename ends in .gz or .Z, appropriate file compression will be performed. (See Section 3.1.5 for details about file compression.) All of the autosave inputs are stored in the case file.

3.4

Reading FLUENT/UNS and RAMPANT Case and Data Files

Case files created by FLUENT/UNS 3 or 4 or RAMPANT 2, 3, or 4 can be read into FLUENT in the same way that current case files are read (see Section 3.3). If you read a case file created by FLUENT/UNS, FLUENT will select the Segregated solver in the Solver panel. If you read a case file created by RAMPANT, FLUENT will select the Coupled Explicit solver formulation in the Solver panel. Data files created by FLUENT/UNS 4 or RAMPANT 4 can be read into FLUENT in the same way that current data files are read (see Section 3.3).

3.5

Importing FLUENT 4 Case Files

You can read a FLUENT 4 case file using the File/Import/FLUENT 4 Case... menu item. File −→ Import −→FLUENT 4 Case... Selecting the FLUENT 4 Case... menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the FLUENT 4 case file to be read. FLUENT will read only grid information and zone types from the FLUENT 4 case file. You must specify boundary conditions, model parameters, material properties, and other information after reading this file. For more information about importing FLUENT 4 case files, see Section 5.3.8.

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3.6 Importing FIDAP Neutral Files

3.6

Importing FIDAP Neutral Files

You can read a FIDAP Neutral file using the File/Import/FIDAP... menu item. File −→ Import −→FIDAP... Selecting the FIDAP... menu item will invoke the Select File dialog box (see Section 2.1.2), in which you will specify the name of the FIDAP file to be read. FLUENT will read grid information and zone types from the FIDAP file. You must specify boundary conditions and other information after reading this file. For more information about importing FIDAP Neutral files, see Section 5.3.9.

3.7

Creating and Reading Journal Files

A journal file contains a sequence of FLUENT commands, arranged as they would be typed interactively into the program or entered through the GUI. GUI commands are recorded as Scheme code lines in journal files. FLUENT creates a journal file by recording everything you type on the command line or enter through the GUI. You may also create journal files manually with a text editor. If you want to include comments in your file, be sure to put a ; (semicolon) at the beginning of each comment line. See Section 2.5.1 for an example. The purpose of a journal file is usually to automate a series of commands rather than entering them repeatedly on the command line. Another use is to produce a record of the input to a program session for later reference, although transcript files are often more useful for this purpose (see Section 3.8). Command input is taken from the specified journal file until its end is reached, at which time control is returned to the standard input (usually the keyboard). Each line from the journal file is echoed to the standard output (usually the screen) as it is read and processed.

! Since a journal file is, by design, just a simple record/playback facility, it knows nothing about the state in which it was recorded or the state in which it is being played back. You should, therefore, try to recreate the state in which the journal was written before you read it into the program. If, for example, your journal file includes an instruction for FLUENT to save a new file with a specified name, you should check that no file with that name exists in your directory before you read in your journal file. If a file with that name does exist and you read in your journal file anyway, when the program reaches the write instruction, it will prompt for a confirmation that it is OK to overwrite the old file. Since no response to the confirmation request is contained in the journal file, FLUENT will not be able to continue following the journal’s instructions. Other conditions that may affect the program’s ability to perform the instructions contained in a journal file can be created by modifications or manipulations that you make within the program. For example, if your journal file creates several surfaces and displays data on those surfaces,


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you must be sure to read in appropriate case and data files before reading the journal file.

! Only one journal file can be open for recording at a time, but you can write a journal and a transcript file simultaneously. You can also read a journal file at any time.

3.7.1

User Inputs

To start the journaling process, select the File/Write/Start Journal... menu item. File −→ Write −→Start Journal... After you enter a name for the file in the Select File dialog box (see Section 2.1.2), journal recording will begin and the Start Journal... menu item will become the Stop Journal menu item. You can end journal recording by selecting Stop Journal, or simply by exiting the program. File −→ Write −→Stop Journal You can read a journal file into the program using the Select File dialog box invoked by selecting the File/Read/Journal... menu item. File −→ Read −→Journal... Journal files are always loaded in the main (i.e., top-level) text menu, regardless of where you are in the text menu hierarchy when you invoke the read command.

3.8

Creating Transcript Files

A transcript file contains a complete record of all standard input to and output from FLUENT (usually all keyboard and GUI input and all screen output). GUI commands are recorded as Scheme code lines in transcript files. FLUENT creates a transcript file by recording everything typed as input or entered through the GUI, and everything printed as output in the text window. The purpose of a transcript file is to produce a record of the program session for later reference. Because they contain messages and other output, transcript files, unlike journal files (see Section 3.7), cannot be read back into the program.

! Only one transcript file can be open for recording at a time, but you can write a transcript and a journal file simultaneously. You can also read a journal file while a transcript recording is in progress.

3.8.1

User Inputs

To start the transcripting process, select the File/Write/Start Transcript... menu item. File −→ Write −→Start Transcript...

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3.9 Reading and Writing Profile Files

After you enter a name for the file in the Select File dialog box (see Section 2.1.2), transcript recording will begin and the Start Transcript... menu item will become the Stop Transcript menu item. You can end transcript recording by selecting Stop Transcript, or simply by exiting the program. File −→ Write −→Stop Transcript

3.9

Reading and Writing Profile Files

Boundary profiles are used to specify flow conditions on a boundary zone of the solution domain. For example, they can be used to prescribe a velocity field on an inlet plane. For more information on boundary profiles, see Section 6.26.

Reading Profile Files Boundary profile files can be read using the Select File dialog box invoked by selecting the File/Read/Profile... menu item. File −→ Read −→Profile...

Writing Profile Files You can also create a profile file from the conditions on a specified boundary or surface. For example, you can create a profile file from the outlet conditions of one case and then read that profile into another case and use the outlet profile data as the inlet conditions for the new case. To write a profile file, you will use the Write Profile panel (Figure 3.9.1). File −→ Write −→Profile... 1. Retain the default option of Define New Profiles. 2. Select the surface(s) from which you want to extract data for the profile(s) in the Surfaces list. 3. Choose the variable(s) for which you want to create profiles in the Values list. 4. Click on the Write... button and specify the profile file name in the resulting Select File dialog box. FLUENT will save the grid coordinates of the data points in the selected surface(s) and the values of the selected variables at those positions. When you read the profile file back into the solver, the “surface” name will be the profile name and the “value” name will be the field name that appears in the drop-down lists in the boundary condition panels.


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Figure 3.9.1: The Write Profile Panel

If you have made any modifications to the boundary profiles since you read them in (e.g., if you reoriented an existing profile to create a new one), or if you wish to store all the profiles used in a case file in a separate file, you can simply select the Write Currently Defined Profiles option and click on the Write... button. All currently defined profiles will be saved in the file you specify in the resulting Select File dialog box. This file can be read back into the solver whenever you wish to use these profiles again.

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3.10 Reading and Writing Boundary Conditions

3.10

Reading and Writing Boundary Conditions

To save all currently-defined boundary conditions to a file, select the write-bc text command and specify a name for the file. file −→write-bc FLUENT will write the boundary conditions, as well as the solver and model settings, to a file using the same format as the “zone” section of the case file. See Section 3.18 for details about the case file format. To read boundary conditions from a file and apply them to the corresponding zones in your model, select the read-bc text command. file −→read-bc FLUENT will set the boundary conditions in the current model by comparing the zone name associated with each set of conditions in the file with the zone names in the model. If the model does not contain a matching zone name for a set of boundary conditions, those conditions will be ignored.

! If you read boundary conditions into a model that contains a different mesh topology (e.g., a cell zone has been removed), you should check the conditions at boundaries within and adjacent to the region of the topological change. This is particularly important for wall zones. If you want FLUENT to apply a set of conditions to multiple zones with similar names, or to a single zone with a name you’re not completely sure of in advance, you can edit the boundary-condition file you saved with the write-bc command to include “wildcards” (*) within the zone names. For example, if you want to apply a particular set of conditions to wall-12, wall-15, and wall-17 in your current model, you should edit the boundarycondition file so that the zone name associated with the desired conditions is wall-*.

3.11

Writing a Boundary Grid

You can write the boundary zones (surface grid) to a file. This file can be read and used by TGrid to produce a volume mesh. You may find this feature useful if you are unsatisfied with a mesh that you obtained from another grid generation program. A boundary grid can be written using the Select File dialog box (see Section 2.1.2) invoked by selecting the File/Write/Boundary Grid... menu item. File −→ Write −→Boundary Grid...


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3.12

Saving Hardcopy Files

Graphics window displays can be saved in various formats, including TIFF, PICT, and PostScript. There may be slight differences, however, between hardcopies and the displayed graphics windows, since hardcopies are generated using the internal software renderer, while the graphics windows may utilize specialized graphics hardware for optimum performance. Many systems provide a utility to “dump” the contents of a graphics window into a raster file. This is generally the fastest method of generating a hardcopy (since the scene is already rendered in the graphics window), and guarantees that the hardcopy will be identical to the window.

3.12.1

Using the Graphics Hardcopy Panel

To set hardcopy parameters and save hardcopy files, you will use the Graphics Hardcopy panel (Figure 3.12.1). File −→Hardcopy...

Figure 3.12.1: The Graphics Hardcopy Panel The procedure for saving a hardcopy file is listed below, followed by details about each step. 1. Choose the hardcopy file format. 2. (optional) Specify the file type, if applicable. 3. Set the coloring. 4. (optional) Define the resolution, if applicable.

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3.12 Saving Hardcopy Files

5. Set any of the options described below. 6. If you are generating a window dump, specify the command to be used for the dump. 7. (optional) Preview the result. 8. Click on the Save... button and enter the filename in the resulting Select File dialog box. (See Section 3.1.7 for information on special features related to filename specification.) If you want to save the current hardcopy settings, but you are not ready to save a hardcopy yet, you can click on the Apply button instead of the Save... button. The applied settings will become the defaults for subsequent hardcopies.

Choosing the Hardcopy File Format To choose the hardcopy file format, select one of the following items in the Format list: EPS (Encapsulated PostScript) output is the same as PostScript output, with the addition of Adobe Document Structuring Conventions (v2) statements. Currently, no preview bitmap is included in EPS output. Often, programs that import EPS files use the preview bitmap to display on-screen, although the actual vector PostScript information is used for printing (on a PostScript device). You can save EPS files in raster or vector format. HPGL is a vector file format designed for pen plotters. The HPGL driver supports a limited set of colors and is not capable of rendering some scenes properly. IRIS Image is the native raster image file format on SGI computers. The IRIS Image driver may not be available on all platforms. JPEG is a common raster file format. PICT is the native graphics file format on Macintosh computers. PICT files may contain either vector or raster information (or both). Typically, “draw” programs generate vector information, while “paint” programs use raster formats. You can choose to save a PICT file in raster or vector format. PPM output is a common raster file format. PostScript is a common vector file format. You can also choose to save a PostScript file in raster format. TIFF is a common raster file format.


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VRML is a graphics interchange format that allows export of 3D geometrical entities that you can display in the FLUENT graphics window. This format can commonly be used by VR systems and in particular the 3D geometry can be viewed and manipulated in a web-browser graphics window.

!

Note that non-geometric entities such as text, titles, color bars, and orientation axis are not exported. In addition, most display or visibility characteristics set in FLUENT, such as lighting, shading method, transparency, face and edge visibility, outer face culling, and hidden line removal, are not explicitly exported but are controlled by the software used to view the VRML file. Window Dump (UNIX systems only) selects a window dump operation for generating the hardcopy. With this format, you will need to specify the appropriate Window Dump Command. See below for details.

Choosing the File Type If you are saving a PostScript, EPS (Encapsulated PostScript), or PICT file, you can choose Raster or Vector as the File Type. A vector file defines the graphics image as a combination of geometric primitives like lines, polygons, and text. A raster file defines the color of each individual pixel in the image. Vector files are usually scalable to any resolution, while raster files have a fixed resolution. Supported vector formats include PostScript, EPS, HPGL, and PICT. Supported raster formats are IRIS image, JPEG, PICT, PPM, PostScript, EPS, and TIFF.

! In general, for the quickest print time, you may want to save vector files for simple 2D displays and raster files for complicated scenes.

Specifying the Color Mode For all formats except the window dump you can specify which type of Coloring you want to use for the hardcopy file. For a color-scale copy select Color, for a gray-scale copy select Gray Scale, and for a black-and-white copy, select Monochrome. Note that most monochrome PostScript devices will render Color images in shades of gray, but to ensure that the color ramp is rendered as a linearly-increasing gray ramp, you should select Gray Scale.

Defining the Resolution For raster hardcopy files, you can control the resolution of the hardcopy image by specifying the size (in pixels). Set the desired Width and Height under Resolution. If the Width and Height are both zero, the hardcopy is generated at the same resolution as the active graphics window. (To check the size of the active window in pixels, you can click on Info in the Display Options panel.)

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3.12 Saving Hardcopy Files

Note that for PostScript, EPS, and PICT files, you will specify the resolution in dots per inch (DPI) instead of setting the width and height.

Hardcopy Options For all hardcopy formats except the window dump, you can control two additional settings under Options. First, you can specify the orientation of the hardcopy using the Landscape Orientation button. If this option is turned on, the hardcopy is made in landscape mode; otherwise, it is made in portrait mode. Second, you can control the foreground/background color using the Reverse Foreground/Background option. If this option is enabled, the foreground and background colors of graphics windows being hardcopied will be swapped. This feature allows you to make hardcopies with a white background and a black foreground, while the graphics windows are displayed with a black background and white foreground. Hardcopy Options for PostScript Files FLUENT provides options that allow you to save PostScript files that can be printed more quickly. The following options can be found in the display/set/hard-copy/driver/ post-format text menu: fast-raster enables a raster file that may be larger than the standard raster file, but will print much more quickly. raster enables the standard raster file. rle-raster enables a run-length encoded raster file that will be about the same size as the standard raster file, but will print slightly more quickly. (This is the default file type.) vector enables the standard vector file. (Vector and raster files are described above.)

Window Dumps (UNIX Systems Only) If you select the Window Dump format, the program will use the specified Window Dump Command to save the hardcopy file. For example, if you want to use xwd to capture a window, you will set the Window Dump Command to xwd -id %w >


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FLUENT will automatically interpret %w to be the ID number of the active window when the dump occurs. In the Select File dialog box that appears when you click on the Save... button, enter the filename for the output from the window dump (e.g., myfile.xwd). If you are planning to make an animation, you might want to save the window dumps into numbered files, using the %n variable. To do this, you will use the same Window Dump Command as that shown in the example above, but for the filename in the Select File dialog box you will enter myfile%n.xwd. Each time you create a new window dump, the value of %n will increase by one, so you do not need to tack numbers onto the hardcopy filenames manually. If you are planning to use the ImageMagick animate program, saving the files in MIFF format (the native ImageMagick format) is more efficient. In such cases, you should use the ImageMagick tool import. For the Window Dump Command you will enter import -window %w (which is the default command). In the Select File dialog box that appears when you click on the Save... button, specify the output format to be MIFF by using the .miff suffix at the end of your filename. The window-dump feature is system- and graphics-driver-specific. Thus the commands available to you for dumping windows will depend heavily on your particular configuration. Another issue to consider when saving window dumps is that the window dump will capture the window exactly as it is displayed, including resolution, colors, transparency, etc. (For this reason, all of the inputs that control these characteristics are disabled in the Graphics Hardcopy panel when you enable the Window Dump format.) If you are using an 8-bit graphics display, you might want to use one of the built-in raster drivers (e.g., TIFF) to generate higher-quality 24-bit color output rather than dumping the 8-bit window.

Previewing the Hardcopy Image Before you save a hardcopy file, you have the option of previewing what the saved image will look like. If you click on Preview, the current settings are applied to the active graphics window so that you can investigate the effects of different options interactively before saving the final, approved hardcopy.

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3.13 Exporting Data

3.13

Exporting Data

The current release of FLUENT allows you to export data to ABAQUS, ANSYS, ASCII, AVS, CGNS, Data Explorer, EnSight (formerly known as MPGS), FAST, Fieldview, I-DEAS, NASTRAN, PATRAN, RadTherm, and Tecplot formats. Section 3.13.1 explains how to save data in these formats, and Section 3.13.2 describes each type of file. Note that only EnSight 6 and Fieldview Case+Data (structured only) files can be exported using the parallel version of FLUENT.

! Since FLUENT cannot import surfaces, if you export a file from FLUENT with surfaces selected, you may not be able to read these files back into FLUENT. TGrid, however, can import surface data (see the TGrid User’s Guide for details).

! If you intend to export data to I-DEAS, you should ensure that your mesh does not contain pyramidal elements, as these are currently not supported by I-DEAS.

3.13.1

Using the Export Panel

To write data that can be imported into one of these products for data visualization and postprocessing, you will use the Export panel (Figure 3.13.1). File −→Export... The procedure is listed below: 1. Select the type of file you want to write in the File Type list. 2. If you chose ABAQUS, ASCII, Data Explorer, I-DEAS Universal, NASTRAN, PATRAN, or Tecplot, select the surface(s) for which you want to write data in the Surfaces list. If no surfaces are selected, the entire domain is exported. For RadTherm files, only wall surfaces will be available. 3. For all file types except ANSYS, FAST Solution, and RadTherm, select the variable(s) for which data is to be saved in the Functions to Write list. 4. (optional) For ABAQUS, ASCII, I-DEAS Universal, NASTRAN, and PATRAN files, select the Loads to be written (Force, Temperature, and/or Heat Flux). Saving these loads will allow you to analyze the structural stresses (fluid pressure or thermal) in an FEA program. Note that loads are written only on boundary walls when the entire domain is exported (i.e., if you select no Surfaces). 5. (optional) For ASCII files, select the Delimiter separating the fields (Comma or Space) and the Location from which the values of scalar functions are to be taken (Node values or Cell-Centered values). 6. (optional) If applicable, define transient export parameters.


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Figure 3.13.1: The Export Panel

• For EnSight 6 and EnSight Case Gold files, turn on the Transient option and specify a value for Append After Timestep and the File Name. All of the geometry, velocity, and scalar files (e.g., file.geo, file.vel, file.scl1, etc.) will be appended after the specified number of timesteps during the solution process. The time values will be written to the EnSight case file (e.g., file.encas), which also lists all of the other exported file names. To save the transient parameters, click on the Apply button. • For formats other than EnSight, use the Execute Commands panel. The text command for exporting to a particular format can be entered directly into the Command text field (or the FLUENT console window if you are defining a macro), and will be of the following general form: file/export/file-type file-name [list-of-surfaces ()] [yes|no] [list-of-scalars q] where items enclosed in square brackets are optional depending on the type

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3.13 Exporting Data

of file being exported. – file-type indicates the type of file being exported. For example, replace file-type by fieldview-uns to indicate Fieldview Unstructured. – file-name indicates (without the extension) the name of the file that you wish to save.

!

By default, FLUENT will not overwrite exported files. Instead, if the specified file name already exists, FLUENT will prompt you with the question OK to overwrite? every time the command is executed. Thus, you will also need to enter a response to this question (yes or no) as part of the text command entered in the Command field. Usually, you will want to export to different files at different time steps. This can be achieved by including a %t in the file-name string. FLUENT will replace the %t with the time step at which the export occurs. For example, a file name of example-%t would be expanded to example-0001 at the first time step and example-0010 at the tenth time step. – list-of-surfaces indicates, for relevant types of files, the list of surfaces (name or ID) that you wish to export. The () input terminates the list. For example, the input outlet-3 wall-2 5 () would select surfaces named outlet-3, wall-2, and also the surface with the ID 5 (note that this is not the zone ID). – list-of-scalars indicates, for relevant types of files, the list of cell functions that you want to write to the exported file. The q input terminates the list. For example, the input x-velocity cell-volume q will select the x velocity and the cell volume. – yes|no indicates, for relevant types of files, that you will need to answer a prompted question (e.g., whether to allow FLUENT to overwrite exported files, whether to enable/disable a particular option, etc.). Certain file types will require more than one yes or no input. See Section 24.18 for more information about executing commands and creating and using command macros. 7. For RadTherm files, select the method of writing the heat transfer coefficient (Heat Transfer Coef.), which can be Flux Based or, if a turbulence model is enabled, Wall Function based. 8. For all file types except transient EnSight files, click on the Write... button to save a file for the specified function(s) in the specified format, using the Select File dialog box.


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3.13.2

Export File Formats

Below, the files that are written when you select each export file type are listed along with the equivalent text commands: ABAQUS a single file (e.g., file.aba) containing coordinates, connectivity, optional loads, zone groups, velocity, and selected scalars will be written. You can specify which scalars you want in the Functions to Write list. Export of data to Abaqus is available only for 3D models and is valid only for solid zones or for those surfaces that lie at the intersection of solid zones. file/export/abaqus file-name list-of-surfaces () yes|no list-of-scalars q ANSYS a single file will be written containing coordinates, connectivity, and the scalars listed below: ‘‘x-velocity’’, ‘‘y-velocity’’, ‘‘z-velocity’’, ‘‘pressure’’, ‘‘temperature’’, ‘‘turb-kinetic-energy’’, ‘‘turb-diss-rate’’, ‘‘density’’, ‘‘viscosity-turb’’, ‘‘viscosity-lam’’, ‘‘viscosity-eff’’, ‘‘thermal-conductivity-lam’’, ‘‘thermal-coductivity-eff’’, ‘‘total-pressure’’, ‘‘total-temperature’’, ‘‘pressure-coefficient’’, ‘‘mach-number’’, ‘‘stream-function’’, ‘‘heat-flux’’, ‘‘heat-transfer-coef’’, ‘‘wall-shear’’, ‘‘specific-heat-cp’’ The file written is an ANSYS results file with a .rfl extension. Note that export to ANSYS is available on a limited number of platforms (listed in the release notes). To read this file into ANSYS, use the following procedure: 1. In ANSYS, go to General Postproc−→ Data and File Options and read the .rfl file generated from FLUENT. 2. Go to Results Summary and click on the first line in the upcoming panel. You will see some information listed in the ANSYS 56 OUTPUT window displaying geomtery informatiom. 3. In the small ANSYS Input window, enter the following commands in order: SET,FIRST /PREP7 ET,1,142 The last command corresponds to FLOTRAN 3D element. If your case is 2D, then this should be replaced by ET,1,141. 4. In the ANSYS MULTIPHYSICS UTITLITY menu, select Plot and then Nodes or Elements, including the nodal solution under Results in the drop-down list. file/export/ansys file-name

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3.13 Exporting Data

ASCII a single ASCII file containing the coordinates, connectivity information, optional loads, and specified scalar function data. You can select the Surfaces for which to save the data. If no surfaces are selected, the data will be written for the entire domain. You can then specify which scalars you want in the Functions to Write list. If you specify the data Location as Node, then the node coordinates and the data values at the node points will be exported. If you choose Cell-Centered, then the cell-centered coordinates and the data values at the cell-centered coordinates will be exported. You can also specify the Delimiter for separating data in the file (Comma or Space). file/export/ascii file-name list-of-surfaces () yes|no list-of-scalars q yes|no AVS an AVS version 4 UCD file containing coordinate and connectivity information and specified scalar function data. You can specify which scalars you want in the Functions to Write list. file/export/avs file-name list-of-scalars q CGNS (CFD general notation system) a single file (e.g., file.cgns) containing coordinates, connectivity, zone information, velocity, and selected scalars will be written. You can specify which scalars you want in the Functions to Write list. file/export/cgns file-name list-of-scalars q Data Explorer a single file (e.g., file.dx) containing coordinate, connectivity, velocity, and specified function data. You can select the Surfaces for which to save the data. If no surfaces are selected, the data will be written for the entire domain. You can then specify which scalars you want in the Functions to Write list. file/export/dx file-name list-of-surfaces () list-of-scalars q EnSight 6 (formerly MPGS) a geometry file (e.g., file.geo) containing the coordinates and connectivity information, a velocity file (e.g., file.vel) containing the velocity, a scalar file (e.g., file.scl1) for each selected variable or function, and an EnSight case file (e.g., file.encas) that contains details about the other exported files. You can specify which scalars you want in the Functions to Write list. See Section 3.13.1 for details about exporting transient data. file/export/ensight file-name list-of-scalars q EnSight Case Gold a geometry file (e.g., file.geo) containing the coordinates and connectivity information, a velocity file (e.g., file.vel) containing the velocity, a scalar file (e.g., file.scl1) for each selected variable or function, and an EnSight case file (e.g., file.encas) that contains details about the other exported files. You can specify the file Format as Binary or ASCII. The major advantage of the binary format is that it takes less time to load the exported files into EnSight. You can specify which scalars you want in the Functions to Write list. file/export/ensight-gold file-name list-of-scalars q yes|no


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FAST a grid file in extended Plot3D format containing coordinates and connectivity, a velocity file containing the velocity, and a scalar file for each selected variable or function. This file type is valid only for triangular and tetrahedral grids. You can specify which scalars you want in the Functions to Write list. file/export/fast-grid file-name FAST Solution a single file containing density, velocity, and total energy data. This file type is valid only for triangular and tetrahedral grids. file/export/fast-solution file-name Fieldview Unstructured a binary file (e.g., file.fvuns) containing coordinate and connectivity information and specified scalar function data, and a regions file (e.g., file.fvuns.fvreg) containing information about the cell zones. The names of the cell zones, along with the grid numbers, are written in the .fvuns.fvreg file. In FIELDVIEW, you will then be able to visualize a single zone while completely turning off all other zones. You can specify which scalars you want in the Functions to Write list. This file type is valid only for 3D grids. file/export/fieldview-uns file-name list-of-scalars q Fieldview Case+Data a FLUENT case file (e.g., file.fvc) that can be read by FIELDVIEW, and a data file (e.g., file.fvd) containing node-averaged values for the selected variables. You can specify which scalars you want in the Functions to Write list. file/export/fieldview file-name list-of-scalars q Fieldview Data a data file containing node-averaged values for the selected variables. You can specify which scalars you want in the Functions to Write list. (For transient simulations, you will often export multiple FIELDVIEW data files but you will usually want to save the case file just once. In such cases, you can use the Fieldview Case+Data option to save the first data set with a case file, and then use the Fieldview Data option to save subsequent data sets without a case file.) file/export/fieldview-data file-name list-of-scalars q I-DEAS Universal a single file containing coordinates, connectivity, optional loads, zone groups, velocity, and selected scalars. You can specify which scalars you want in the Functions to Write list. file/export/ideas file-name list-of-surfaces () yes|no list-of-scalars q NASTRAN a single file (e.g., file.nas) containing coordinates, connectivity, optional loads, zone groups, and velocity. Pressure is written as PLOAD, and heat flux is written as QHBDY data. If wall zones are selected in the Surfaces list, nodal forces are written for the walls. You can choose the Loads to be written (Force, Temperature, and/or Heat Flux). Additionally, you can specify which scalars you want in the Functions to Write list.

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3.13 Exporting Data

file/export/nastran file-name list-of-surfaces () yes|no list-of-scalars q PATRAN a neutral file (e.g., file.neu) containing coordinates, connectivity, optional loads, zone groups, velocity, and selected scalars. Pressure is written as a distributed load. If wall zones are selected in the Surfaces list, nodal forces are written for the walls. You can choose the Loads to be written (Force, Temperature, and/or Heat Flux). Additionally, you can specify which scalars you want in the Functions to Write list. The PATRAN result template file (e.g., file.res tmpl) is written, which lists the scalars present in the nodal result file (e.g., file.rst). file/export/patran-neutral file-name list-of-surfaces () yes|no RadTherm a PATRAN neutral file (e.g., file.neu) containing element velocity components (i.e., the element that is just touching the wall), heat transfer coefficients, and temperatures of the wall for any selected wall surface. The Surfaces list will change to contain only wall surfaces. In the case of turbulence, the heat transfer coefficients (Heat Tran. Coef.) can be chosen to be Flux Based or Wall Function based. If the wall is one-sided, the data are written for one side of the wall. If the wall is two-sided, the data are written for both sides. In the case of wall-wall shadow, the values are written only for the major face. file/export/radtherm file-name list-of-surfaces () yes|no Tecplot a single file containing the coordinates and scalar functions in the appropriate tabular format. You can select the Surfaces for which to save the data. If no surfaces are selected, the data will be written for the entire domain. You can then specify which scalars you want in the Functions to Write list. file/export/tecplot file-name list-of-surfaces () list-of-scalars q

! Note that when you are exporting data for Data Explorer, EnSight 6, EnSight Case Gold, or I-DEAS Universal and the reference zone is not a stationary zone, the data in the velocity fields will be exported by default as velocities relative to the motion specification of that zone. These data are always exported, even if you do not choose to export any scalars. Any velocities that you select to export as scalars in the Functions to Write list (e.g., X Velocity, Y Velocity, Radial Velocity, etc.) will exported as absolute velocities. For all other types of exported files, the velocities exported by default are absolute velocities.


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3.14

Grid-to-Grid Solution Interpolation

FLUENT can interpolate solution data for a given geometry from one grid to another, allowing you to compute a solution using one grid (e.g., hexahedral) and then change to another grid (e.g., hybrid) and continue the calculation using the first solution as a starting point.

3.14.1

Performing Grid-to-Grid Solution Interpolation

The procedure for grid-to-grid solution interpolation is as follows: 1. Set up the model and calculate a solution on the initial grid. 2. Write an interpolation file for the solution data to be interpolated onto the new grid, using the Interpolate Data panel (Figure 3.14.1). File −→Interpolate...

Figure 3.14.1: The Interpolate Data Panel

(a) Under Options, select Write Data. (b) In the Cell Zones list, select the cell zones for which you want to save data to be interpolated.

!

If your case includes both fluid and solid zones, you will need to write the data for the fluid zones and the data for the solid zones to separate files. (c) Choose the variable(s) for which you want to interpolate data in the Fields list. All FLUENT solution variables are available for interpolation.

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3.14 Grid-to-Grid Solution Interpolation

(d) Click on the Write... button and specify the interpolation file name in the resulting Select File dialog box. The file format is described in Section 3.14.2. 3. Set up a new case. (a) Read in the new grid, using the appropriate menu item in the File/Read/ or File/Import/ menu. (b) Define the appropriate models.

!

It is very important that you enable all of the models that were enabled in the original case. If, for example, the energy equation was enabled in the original case and you forget to enable it in the new case, the temperature data in the interpolation file will not be interpolated. (c) Define the boundary conditions, material properties, etc. 4. Read in the data to be interpolated. File −→Interpolate... (a) Under Options, select Read and Interpolate. (b) In the Cell Zones list, select the cell zones for which you want to read and interpolate data. Note that, if the solution has not been initialized, computed, or read, all zones in the Cell Zones list will be selected by default, to ensure that no zone remains without data after the interpolation. If all zones already have data (from initialization or a previously computed or read solution), you can select a subset of the Cell Zones to read and interpolate data onto a specific zone (or zones). (c) Click on the Read... button and specify the interpolation file name in the resulting Select File dialog box.

!

If your case includes both fluid and solid zones, you will need to perform these steps twice (once to interpolate the data for the fluid zones and once to interpolate the data for the solid zones), since the two sets of data were saved to separate files. 5. Lower the under-relaxation factors and calculate on the new grid for a few iterations to avoid sudden changes due to any imbalance of fluxes after interpolation. Then increase the under-relaxation factors and compute a solution on the new grid.

3.14.2

Format of the Interpolation File

The format of the interpolation file is as follows: • The first line is the interpolation file version. It is 1.0 for FLUENT 5 and 2.0 for FLUENT 6.


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• The second line is the dimensionality (2 or 3). • The third line is the total number of points. • The fourth line is the total number of fields (temperature, pressure, etc.) included. • A list of field names follows, from line 5. You can see a complete list of the field names used by FLUENT by selecting the display/contours text command and viewing the available choices for contours of. The list depends on the models turned on. • After the list of field names, comes a list of x, y, and (in 3D) z coordinates for all the data points. • All the field values at all the points in the same order as their names are listed last. The number of coordinate and field points should match the number given in line 3. An example is shown below: 2 2 34800 3 x-velocity pressure y-velocity -0.068062 -0.0680413 ...

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3.15 Reading Scheme Source Files

3.15

Reading Scheme Source Files

A Scheme source file can be loaded in three ways: through the menu system as a scheme file, through the menu system as a journal file, or through Scheme itself. For large source files you will normally use the Select File dialog box (see Section 2.1.2) invoked by selecting the File/Read/Scheme... menu item File −→ Read −→Scheme... or the Scheme load function. > (load "file.scm")

Shorter files can also be loaded with the File/Read/Journal... menu item or the file/ read-journal command in the text interface (or its . or source alias). > . file.scm > source file.scm

In this case, each character of the file is echoed to the console as it is read in the same way as if you were typing the contents of the file in by hand.

3.16

The .fluent File

When starting up, FLUENT looks in your home directory for an optional file called .fluent. If it finds the file, it loads it with the Scheme load function. This file can contain Scheme functions that customize the code’s operation.

3.17

Saving the Panel Layout

The Save Layout command in the File pull-down menu allows you to save the present panel and window layout. Specifically, you can arrange panels and graphics windows on your screen in a preferred configuration and select the File/Save Layout menu item. File −→Save Layout A .cxlayout file is written in your home directory. (If you subsequently arrange different panels and save the layout again, the positions of these panels will be added to the positions of the panels that you saved earlier. If you move a panel for which a position is already saved, and then you save the layout, the new position will be written to the .cxlayout file.) In subsequent sessions, when you open a panel or create a graphics window, it will be positioned based on the saved configuration. Any panel or window


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not specified in the saved configuration will use the default position. Note that the .cxlayout file in your home directory applies to all Cortex applications (i.e., FLUENT, FLUENT/Post, MixSim, and TGrid).

3.18

Formats of Case and Data Files

This section describes the contents and formats of FLUENT case and data files. These files are broken into several sections according to the following guidelines: • Each section is enclosed in parentheses and begins with a decimal integer indicating its type. This integer is different for formatted and binary files, as described in Section 3.18.1. • All groups of items are enclosed in parentheses. This makes skipping to ends of (sub)sections and parsing them very easy. It also allows for easy and compatible addition of new items in future releases. • Header information for lists of items is enclosed in separate sets of parentheses preceding the items, and the items are enclosed in their own parentheses. Descriptions of the sections are grouped according to function. If you are creating grids for FLUENT, you only need to consider the sections described in Section 3.18.2. If you are attempting to import solutions into another postprocessor, you should study Sections 3.18.2 and 3.18.4. Section 3.18.3 describes the sections that store boundary conditions, material properties, and solver control settings. See Section 3.18.1 for details about differences between formatted and binary files. Note that the case and data files may contain other sections that are intended for internal use only.

3.18.1

Formatting Conventions in Binary and Formatted Files

For formatted files, examples of file sections are given in Sections 3.18.2 and 3.18.3. For binary files, the header indices described in this section (e.g., 10 for the node section) are preceded by 20 for single-precision binary data, or by 30 for double-precision binary data (e.g., 2010 or 3010 instead of 10). Also, the end of the binary data is indicated by End of Binary Section 2010 or End of Binary Section 3010 before the closing parameters of the section. An example is shown below (with the binary data represented by periods): (2010 (2 1 2aad 2 3)( . .

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3.18 Formats of Case and Data Files

. ) End of Binary Section 2010)

3.18.2

Grid Sections

Grid sections are stored in the case file. (A “grid” file is a subset of a case file, containing only those sections pertaining to the grid.) Following are descriptions of the currently defined grid sections. The section ID numbers are indicated below in both symbolic and numeric forms. The symbolic representations are available as symbols in a Scheme source file (xfile.scm), which is available from Fluent Inc., or as macros in a C header file (xfile.h), which is located in the following directory in your installation area: /Fluent.Inc/fluent6.x/client/src/xfile.h

Comment Index: Scheme symbol: C macro: Status:

0 xf-comment XF COMMENT optional

Comment sections can appear anywhere in the file (except within other sections), and appear as (0 "comment text") It is recommended that each long section, or group of related sections, be preceded by a comment section explaining what is to follow. For example, (0 "Variables:") (37 ( (relax-mass-flow 1) (default-coefficient ()) (default-method 0) ))

Header Index: Scheme symbol: C macro: Status:


1 xf-header XF HEADER optional

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Header sections can appear anywhere in the file (except within other sections), and appear as (1 "TGrid 2.1.1") The purpose of this section is to identify the program that wrote the file. Although it can appear anywhere, it is typically one of the first sections in the file. Additional header sections indicate other programs that may have been used in generating the file and thus provide a history mechanism showing where the file came from and how it was processed.

Dimensions Index: Scheme symbol: C macro: Status:

2 xf-dimension XF DIMENSION optional

The dimensionality of the grid (2 ND) where ND is 2 or 3. This section is currently supported as a check that the grid has the appropriate dimensionality.

Nodes Index: Scheme symbol: C macro: Status:

10 xf-node XF NODE required

(10 (zone-id first-index last-index type ND)( x1 y1 z1 x2 y2 z2 . . . )) If zone-id is zero, this is a declaration section providing the total number of nodes in the grid. first-index will then be one, last-index will be the total number of nodes in hexadecimal, type is equal to 1, ND is the dimensionality of the grid, and there are no coordinates following. The parentheses for the coordinates are not there either. For example,

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(10 (0 1 2d5 1 2)) If zone-id is greater than zero, it indicates the zone to which the nodes belong. first-index and last-index are then the indices of the nodes in the zone, in hexadecimal. Of course, last-index in each zone must be less than or equal to the value in the declaration section. Type is always equal to 1. ND is an optional argument that indicates the dimensionality of the node data, where ND is 2 or 3. If the number of dimensions in the grid is two, as specified by the Dimensions section described above or in the node header, then only x and y coordinates are present on each line. Below is a two-dimensional example: (10 (1 1 2d5 1.500000e-01 1.625000e-01 . . . 1.750000e-01 2.000000e-01 1.875000e-01 ))

1 2)( 2.500000e-02 1.250000e-02

0.000000e+00 2.500000e-02 1.250000e-02

Because the grid connectivity is composed of integers representing pointers (see Cells and Faces, below), using hexadecimal conserves space in the file and provides for faster file input and output. The header indices are also in hexadecimal so that they match the indices in the bodies of the grid connectivity sections. The zone-id and type are also in hexadecimal for consistency.

Periodic Shadow Faces Index: Scheme symbol: C macro: Status:

18 xf-periodic-face XF PERIODIC FACE required only for grids with periodic boundaries

This section indicates the pairings of periodic faces on periodic boundaries. Grids without periodic boundaries do not have sections of this type. The format of the section is as follows: (18 (first-index last-index periodic-zone shadow-zone)(


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f00 f01 f10 f21 f20 f21 . . . )) where first-index is the index of the first periodic face pair in the list, last-index is the last one, periodic-zone is the zone ID of the periodic face zone, and shadow-zone is the zone ID of the corresponding shadow face zone. These are in hexadecimal format. The indices in the section body (f*) refer to the faces on each of the periodic boundaries (in hexadecimal), the indices being offsets into the list of faces for the grid. Note that first-index and last-index do not refer to face indices; they refer to indices in the list of periodic pairs. A partial example of such a section follows. (18 (1 2b a c) ( 12 1f 13 21 ad 1c2 . . . ))

Cells Index: Scheme symbol: C macro: Status:

12 xf-cell XF CELL required

The declaration section for cells is similar to that for nodes. (12 (zone-id first-index last-index type element-type)) Again, zone-id is zero to indicate that it is a declaration of the total number of cells. If last-index is zero, then there are no cells in the grid. This is useful when the file contains only a surface mesh to alert FLUENT that it cannot be used. In a declaration section, the type is ignored, and is usually given as zero, while the element-type is ignored completely. For example,

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(12 (0 1 3e3 0)) states that there are 3e3 (hexadecimal) = 995 cells in the grid. This declaration section is required and must precede the regular cell sections. The element-type in a regular cell section header indicates the type of cells in the section, as follows: element-type 0 1 2 3 4 5 6

description nodes/cell mixed triangular 3 tetrahedral 4 quadrilateral 4 hexahedral 8 pyramid 5 wedge 6

faces/cell 3 4 4 6 5 5

Regular cell sections have no body, but they have a header of the same format where first-index and last-index indicate the range for the particular zone, type indicates whether the cell zone is an active zone (solid or fluid), or inactive zone (currently only parent cells resulting from hanging node adaption). Active zones are represented with type=1, while inactive zones are represented with type=32. Note that in past versions of FLUENT, a distinction was made used between solid and fluid zones. This is now determined by properties (i.e., material type). A type of zero indicates a dead zone and will be skipped by FLUENT. If a zone is of mixed type (element-type=0), it will have a body that lists the element type of each cell. For example, (12 (9 1 3d 0 0)( 1 1 1 3 3 1 1 3 1 . . . )) states that there are 3d (hexadecimal) = 61 cells in cell zone 9, of which the first 3 are triangles, the next 2 are quadrilaterals, and so on.

Faces Index: Scheme symbol: C macro: Status:


13 xf-face XF FACE required

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The face section has a header with the same format as that for cells (but with a section index of 13). (13 (zone-id first-index last-index type element-type)) Again, a zone-id of zero indicates a declaration section with no body, and element-type indicates the type of faces in that zone. The body of a regular face section contains the grid connectivity, and each line appears as follows: n0 n1 n2 cr cl where n* are the defining nodes (vertices) of the face, and c* are the adjacent cells. This is an example of the triangular face format; the actual number of nodes depends on the element type. The ordering of the cell indices is important. The first cell, cr, is the cell on the right side of the face and cl is the cell on the left side. Handedness is determined by the right-hand rule: if you curl the fingers of your right hand in the order of the nodes, your thumb will point to the right side of the face. In 2D grids, the kˆ vector pointing outside the grid plane is used to determine the right-hand-side cell (cr) from kˆ × rˆ. If there is no adjacent cell, then either cr or cl is zero. (All cells, faces, and nodes have positive indices.) For files containing only a boundary mesh, both these values are zero. If it is a two-dimensional grid, n2 is omitted. If the face zone is of mixed type (element-type = 0), the body of the section will include the face type and will appear as follows: type v0 v1 v2 c0 c1 where type is the type of face, as defined in the following table: element-type 0 2 3 4

face type nodes/face mixed linear 2 triangular 3 quadrilateral 4

The current valid boundary condition types are defined in the following table:

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bc name interior wall pressure-inlet, inlet-vent, intake-fan pressure-outlet, exhaust-fan, outlet-vent symmetry periodic-shadow pressure-far-field velocity-inlet periodic fan, porous-jump, radiator mass-flow-inlet interface parent (hanging node) outflow axis

bc id 2 3 4 5 7 8 9 10 12 14 20 24 31 36 37

For non-conformal grid interfaces, the faces resulting from the intersection of the nonconformal grids are placed in a separate face zone. A factor of 1000 is added to the type of these sections, e.g., 1003 is a wall zone.

Face Tree Index: Scheme symbol: C macro: Status:

59 xf-face-tree XF FACE TREE only for grids with hanging-node adaption

This section indicates the face hierarchy of the grid containing hanging nodes. The format of the section is as follows: (59 (face-id0 face-id1 parent-zone-id child-zone-id) ( number-of-kids kid-id-0 kid-id-1 ... kid-id-n . . . )) where face-id0 is the index of the first parent face in the section, face-id1 is the index of the last parent face in the section, parent-zone-id is the ID of the zone containing the parent faces, child-zone-id is the ID of the zone containing the children faces, number-of-kids is the number of children of the parent face, and kid-id-n are the face IDs of the children. These are in hexadecimal format.


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Cell Tree Index: Scheme symbol: C macro: Status:

58 xf-cell-tree XF CELL TREE only for grids with hanging-node adaption

This section indicates the cell hierarchy of the grid containing hanging nodes. The format of the section is as follows: (58 (cell-id0 cell-id1 parent-zone-id child-zone-id) ( number-of-kids kid-id-0 kid-id-1 ... kid-id-n . . . )) where cell-id0 is the index of the first parent cell in the section, cell-id1 is the index of the last parent cell in the section, parent-zone-id is the ID of the zone containing the parent cells, child-zone-id is the ID of the zone containing the children cells, number-of-kids is the number of children of the parent cell, and kid-id-n are the cell IDs of the children. These are in hexadecimal format.

Interface Face Parents Index: Scheme symbol: C macro: Status:

61 xf-face-parents XF FACE PARENTS only for grids with non-conformal interfaces

This section indicates the relationship between the intersection faces and original faces. The intersection faces (children) are produced from intersecting two non-conformal surfaces (parents) and are some fraction of the original face. Each child will refer to at least one parent. The format of the section is as follows: (61 (face-id0 face-id1) ( parent-id-0 parent-id-1 . . . ))

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where face-id0 is the index of the first child face in the section, face-id1 is the index of the last child face in the section, parent-id-0 is the index of the right-side parent face, and parent-id-1 is the index of the left-side parent face. These are in hexadecimal format. If you read a non-conformal grid from FLUENT into TGrid, TGrid will skip this section, so it will not maintain all the information necessary to preserve the non-conformal interface. When you read the grid back into FLUENT, you will need to recreate the interface.

Example Files Example 1 Figure 3.18.1 illustrates a simple quadrilateral mesh with no periodic boundaries or hanging nodes.

bn8

bf8

bf9

c1

bn5

bf3

bn2

f1

bn1

bf7

c2

bf4

bn4

f2

bn3

bf6

c3

bf5

bn7

bf10

bn6

Figure 3.18.1: Quadrilateral Mesh

The following describes this mesh:

(0 "Grid:") (0 "Dimensions:") (2 2) (12 (0 1 3 0)) (13 (0 1 a 0)) (10 (0 1 8 0 2)) (12 (7 1 3 1 3)) (13 (2 1 2 2 2)( 1 2 1 2


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3 4 2 3)) (13 5 1 1 3 3 6

(3 3 5 3 2)( 1 0 2 0 3 0))

(13 7 4 4 2 2 8

(4 6 8 3 2)( 3 0 2 0 1 0))

(13 (5 9 9 a 2)( 8 5 1 0)) (13 (6 a a 24 2)( 6 7 3 0)) (10 (1 1 8 1 2) ( 1.00000000e+00 1.00000000e+00 2.00000000e+00 2.00000000e+00 0.00000000e+00 3.00000000e+00 3.00000000e+00 0.00000000e+00

0.00000000e+00 1.00000000e+00 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00))

Example 2 Figure 3.18.2 illustrates a simple quadrilateral mesh with periodic boundaries but no hanging nodes. In this example, bf9 and bf10 are faces on the periodic zones. The following describes this mesh: (0 "Dimensions:") (2 2) (0 "Grid:") (12 (0 1 3 0))

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bn8

bf8

bf9

c1

bn5

bf3

bn2

f1

bn1

bf7

c2

bf4

bn4

f2

bn3

bf6

c3

bf5

bn7

bf10

bn6

Figure 3.18.2: Quadrilateral Mesh with Periodic Boundaries

(13 (0 1 a 0)) (10 (0 1 8 0 2)) (12 (7 1 3 1 3)) (13 (2 1 2 2 2)( 1 2 1 2 3 4 2 3)) (13 5 1 1 3 3 6

(3 3 5 3 2)( 1 0 2 0 3 0))

(13 7 4 4 2 2 8

(4 6 8 3 2)( 3 0 2 0 1 0))

(13 (5 9 9 c 2)( 8 5 1 0)) (13 (1 a a 8 2)( 6 7 3 0)) (18 (1 1 5 1)( 9 a)) (10 (1 1 8 1 2)( 1.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00


3-45


2.00000000e+00 2.00000000e+00 0.00000000e+00 3.00000000e+00 3.00000000e+00 0.00000000e+00

0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00))

Example 3 Figure 3.18.3 illustrates a simple quadrilateral mesh with hanging nodes.

bn13

bf15

bn7

bf14

bn8 bf12 bn2 bf13 bn12 f6

bf16

bn10

f5

c1

bf8

bn6

c2

bf9

n5

c6 f4

f7

c5

f1 c3 f2

bf17

f3 c4

bf18

bn3

n1

bn9 bf11 bn4 bf10 bn11

Figure 3.18.3: Quadrilateral Mesh with Hanging Nodes

The following describes this mesh:

(0 "Grid:") (0 "Dimensions:") (2 2) (12 (0 1 7 0)) (13 (0 1 16 0)) (10 (0 1 d 0 2)) (12 (7 1 6 1 3)) (12 (1 7 7 20 3)) (58 (7 7 1 7)( 4 6 5 4 3)) (13 (2 1 7 2 2)( 1 2 6 3

3-46



1 1 1 6 5 9

3 4 5 7 8 5

3 4 5 1 2 2

4 5 6 2 6 5))

(13 a 6 6 9 4 b 9 4

(3 8 b 3 2)( 1 0 2 0 4 0 5 0))

(13 2 8 c 2 8 7 7 d

(4 c f 3 2)( 6 0 3 0 2 0 1 0))

(13 (5 10 10 a 2)( d a 1 0)) (13 (6 11 12 24 2)( 3 c 3 0 b 3 4 0)) (13 (b 13 13 1f 2)( c 8 7 0)) (13 (a 14 14 1f 2)( b c 7 0)) (13 (9 15 15 1f 2)( 9 b 7 0)) (13 (8 16 16 1f 2)( 9 8 2 7)) (59 (13 13 b 4)( 2 d c)) (59 (14 14 a 6)( 2 12 11))


3-47


(59 (15 15 9 3)( 2 b a)) (59 (16 16 8 2)( 2 7 6)) (10 (1 1 d 1 2) ( 2.50000000e+00 2.50000000e+00 3.00000000e+00 2.50000000e+00 2.00000000e+00 1.00000000e+00 1.00000000e+00 2.00000000e+00 2.00000000e+00 0.00000000e+00 3.00000000e+00 3.00000000e+00 0.00000000e+00

3.18.3

5.00000000e-01 1.00000000e+00 5.00000000e-01 0.00000000e+00 5.00000000e-01 0.00000000e+00 1.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00))

Other (Non-Grid) Case Sections

The following sections store boundary conditions, material properties, and solver control settings.

Zone Index: Scheme symbol: C macro: Status:

39 (45) xf-rp-tv XF RP TV required

There is typically one zone section for each zone referenced by the grid. Although some grid zones may not have corresponding zone sections, there cannot be more than one zone section for each zone. A zone section has the following form: (39 (zone-id zone-type zone-name)( (condition1 . value1)

3-48



(condition2 . value2) (condition3 . value3) . . . )) Grid generators and other preprocessors need only provide the section header and leave the list of conditions empty, as in (39 (zone-id zone-type zone-name)()) The empty parentheses at the end are required. The solver adds conditions as appropriate, depending on the zone type. When only zone-id, zone-type, and zone-name are specified, the index 45 is preferred for a zone section. However, the index 39 must be used if boundary conditions are present, because any and all remaining information in a section of index 45 after zone-id, zone-type, and zone-name will be ignored. Here the zone-id is in decimal format. This is in contrast to the use of hexadecimal in the grid sections. The zone-type is one of the following: axis exhaust fan fan fluid inlet vent intake fan interface interior mass-flow-inlet outlet vent outflow periodic porous-jump pressure-far-field pressure-inlet pressure-outlet radiator shadow solid symmetry velocity-inlet wall


3-49


The interior, fan, porous-jump, and radiator types can be assigned only to zones of faces inside the domain. The interior type is used for the faces within a cell zone; the others are for interior faces that form infinitely thin surfaces within the domain. FLUENT allows the wall type to be assigned to face zones both on the inside and on the boundaries of the domain. Some zone types are valid only for certain types of grid components. For example, cell (element) zones can be assigned only one of the following types: fluid solid All of the other types listed above can be used only for boundary (face) zones. The zone-name is a user-specified label for the zone. It must be a valid Scheme symbol1 and is written without quotes. The rules for a valid zone-name (Scheme symbol) are as follows: • The first character must be a lowercase letter2 or a special-initial. • Each subsequent character must be a lowercase letter, a special-initial, a digit, or a special-subsequent. where a special-initial character is one of the following: ! $ % & * / : < = > ? ~ _ ^ and a special-subsequent is one of the following: . + Examples of valid zone names are inlet-port/cold!, eggs/easy, and e=m*c^2. Below are some examples of zone sections produced by grid generators and preprocessors. (39 (1 fluid fuel)()) (39 (8 pressure-inlet pressure-inlet-8)()) (39 (2 wall wing-skin)()) (39 (3 symmetry mid-plane)()) 1

See Revised(4) Report on the Algorithmic Language Scheme, William Clinger and Jonathan Rees (Editors), 2 November 1991, Section 7.1.1. 2 The Standard actually only requires that case be insignificant; the Fluent Inc. implementation accomplishes this by converting all uppercase input to lowercase.

3-50



Partitions Index: Scheme symbol: C macro: Status:

40 xf-partition XF PARTITION only for partitioned grids

This section indicates each cell’s partition. The format of the section is as follows: (40 (zone-id first-index last-index partition-count)( p1 p2 p3 . . . pn )) p1 is the partition of the cell whose ID is first-index, p2 is the partition of the cell whose ID is first-index+1, etc., and pn is the partition of the cell whose ID is last-index. Partition IDs must be between 0 and partition-count−1, where partition-count is the total number of partitions.

3.18.4

Data Sections

The following sections store iterations, residuals, and data field values.

Grid Size Index: Scheme symbol: C macro: Status:

33 xf-grid-size XF GRID SIZE optional

This section indicates the number of cells, faces, and nodes in the grid that corresponds to the data in the file. This information is used to check that the data and grid match. The format is (33 (n-elements n-faces n-nodes)) where the integers are written in decimal.


3-51


Data Field Index: Scheme symbol: C macro: Status:

300 xf-rf-seg-data XF RF SEG DATA required

This section lists a flow field solution variable for a cell or face zone. The data are stored in the same order as the cells or faces in the case file. Separate sections are written out for each variable for each face or cell zone on which the variable is stored. The format is (300 (sub-section-id zone-id n-phases first-id last-id) ( data for cell or face with data-for-cell-or-face with .. data-for-cell-or-face with ))

size n-time-levels id = first-id id = first-id+1 id = last-id

where sub-section-id is a (decimal) integer that identifies the variable field (e.g., 1 for pressure, 2 for velocity). The complete list of these is available in the header file (xfile.h), which is located in the following directory in your installation area: /Fluent.Inc/fluent6.x/client/src/xfile.h zone-id is the ID number of the cell or face zone and matches the ID used in case file. size denotes the length of the variable vector (1 for a scalar, 2 or 3 for a vector, equal to the number of species for variables defined for each species). n-time-levels and n-phases currently are not used. A sample data file section for the velocity field in a cell zone for a steady-state, singlephase, 2D problem is shown below: (300 (2 16 2 0 0 17 100) (8.08462024e-01 8.11823010e-02 8.78750622e-01 3.15509699e-02 1.06139672e+00 -3.74040119e-02 ... 1.33301604e+00 -5.04243895e-02 6.21703446e-01 -2.46118382e-02 4.41687912e-01 -1.27046436e-01 1.03528820e-01 -1.01711005e-01 )) The variables that are listed in the data file depend on the models active at the time the file is written. Variables that are required by the solver based on the current model

3-52



settings but are missing from the data file are set to their default values when the data file is read. Any extra variables that are present in the data file but are not relevant according to current model settings are ignored.

Residuals Index: Scheme symbol: C macro: Status:

301 xf-rf-seg-residuals XF RF SEG RESIDUALS optional

This section lists the values of the residuals for a particular data field variable at each iteration: (301 (n residual-subsection-id size)( r1 r2 . . . rn )) where n is the number of residuals and size is the length of the variable vector (1 for a scalar, 2 or 3 for a vector, equal to the number of species for variables defined for each species). The residual-subsection-id is an integer (decimal) indicating the equation for which the residual is stored in the section, according to the C constants defined in a header file (xfile.h) available in your installation area, as noted in Section 3.18.2. The equations for which residuals are listed in the data file depend on the models active at the time the file is written. If the residual history is missing from the data file for a currently active equation, it is initialized with zeros.


3-53


3-54


Chapter 4.

Unit Systems

This chapter describes the units used in FLUENT and how you can control them. Information is organized into the following sections: • Section 4.1: Restrictions on Units • Section 4.2: Units in Grid Files • Section 4.3: Built-In Unit Systems in FLUENT • Section 4.4: Customizing Units FLUENT allows you to work in any unit system, including inconsistent units. Thus, for example, you may work in British units with heat input in Watts or you may work in SI units with length defined in inches. This is accomplished by providing FLUENT with a correct set of conversion factors between the units you want to use and the standard SI unit system that is used internally by the solver. FLUENT uses these conversion factors for input and output, internally storing all parameters and performing all calculations in SI units. Both solvers always prompt you for the units required for all dimensional inputs. Units can be altered part-way through a problem setup and/or after you have completed your calculation. If you have input some parameters in SI units and then you switch to British, all of your previous inputs (and the default prompts) are converted to the new unit system. If you have completed a simulation in SI units but you would like to report the results in any other units, you can alter the unit system and FLUENT will convert all of the problem data to the new unit system when results are displayed. As noted above, all problem inputs and results are stored in SI units internally. This means that the parameters stored in the case and data files are in SI units. FLUENT simply converts these values to your unit system at the interface level.


4-1

Unit Systems

4.1

Restrictions on Units

It is important to note that the units for some inputs in FLUENT are different from the units used for the rest of the problem setup. • You must always define the following in SI units, regardless of the unit system you are using: – boundary profiles (see Section 6.26) – source terms (see Section 6.28) – custom field functions (see Section 29.5) – data in externally-created XY plot files (see Section 27.8.3) – user-defined functions (See the separate UDF Manual for details about userdefined functions.) • If you define a material property by specifying a temperature-dependent polynomial or piecewise-polynomial function, remember that temperature in the function is always in units of Kelvin or Rankine. If you are using Celsius or Kelvin as your temperature unit, then polynomial coefficient values must be entered in terms of Kelvin; if you are using Fahrenheit or Rankine as the temperature unit, values must be entered in terms of Rankine. See Section 7.1.3 for information about temperature-dependent material properties.

4.2

Units in Grid Files

Some grid generators allow you to define a set of units for the mesh dimensions. However, when you read the grid into FLUENT, it is always assumed that the unit of length is meters. If this is not true, you will need to scale the grid, as described in Section 5.7.1.

4-2


4.3 Built-In Unit Systems in FLUENT

4.3

Built-In Unit Systems in FLUENT

FLUENT provides four built-in unit systems: British, SI, CGS, and “default.” You can convert all units from one system to another in the Set Units panel (Figure 4.3.1), using the buttons under the Set All To heading. Define −→Units...

Figure 4.3.1: The Set Units Panel To choose the English Engineering standard for all units, click on the british button; to select the International System of units (SI) standard for all units, click on the si button; to choose the CGS (centimeter-gram-second) standard for all units, click on the cgs button; and to return to the “default” system, click on the default button. The default system of units is like SI, but uses degrees instead of radians for angles. Clicking on one of the buttons under Set All To will immediately change the unit system. You can then close the panel if you are not interested in customizing any units. Changing the unit system in the Set Units panel causes all future inputs that have units to be based on the newly selected unit system.


4-3

Unit Systems

4.4

Customizing Units

If you would like a mixed unit system, or any unit system different from the four supplied by FLUENT (and described in Section 4.3), you can use the Set Units panel (Figure 4.3.1) to select an available unit or specify your own unit name and conversion factor for each quantity.

Listing Current Units Before customizing units for one or more quantities, you may want to list the current units. You can do this by clicking on the List button at the bottom of the Set Units panel. FLUENT will print out a list (in the text window) containing all quantities and their current units, conversion factors, and offsets.

Changing the Units for a Quantity FLUENT will allow you to modify the units for individual quantities. This is useful for problems in which you want to use one of the built-in unit systems, but you want to change the units for one quantity (or for a few). For example, you may want to use SI units for your problem, but the dimensions of the geometry are given in inches. You can select the SI unit system, and then change the unit of length from meters to inches. To change the units for a particular quantity, you will follow these two steps: 1. Select the quantity in the Quantities list (they are arranged in alphabetical order). 2. Choose a new unit from those that are available in the Units list. For the example cited above, you would choose length in the Quantities list, and then select in in the Units list. The Factor will automatically be updated to show 0.0254 meters/inch. (See Figure 4.3.1.) If there were a non-zero offset for the new unit, the Offset field would also be updated. For example, if you were using SI units but wanted to define temperature in Celsius instead of Kelvin, you would select temperature in the Quantities list and c in the Units list. The Factor would change to 1, and the Offset would change to 273.15. Once you have selected the quantity and the new unit, no further action is needed, unless you wish to change the units for another quantity by following the same procedure.

Defining a New Unit To create a new unit to be used for a particular quantity, you will follow the procedure below: 1. In the Set Units panel, select the quantity in the Quantities list.

4-4


4.4 Customizing Units

2. Click on the New... button and the Define Unit panel (Figure 4.4.1) will open. In this panel, the selected quantity will be shown in the Quantity field.

Figure 4.4.1: The Define Unit Panel

3. Enter the name of your new unit in the Unit field, the conversion factor in the Factor field, and the offset in the Offset field. 4. Click on OK in the Define Unit panel, and the new unit will appear in the Set Units panel. For example, if you want to use hours as the unit of time, select time in the Quantities list in the Set Units panel and click on the New... button. In the resulting Define Unit panel, enter hr for the Unit and 3600 for the Factor, as in Figure 4.4.1. Then click on OK. The new unit hr will appear in the Units list in the Set Units panel, and it will be selected. Determining the Conversion Factor The conversion factor you specify (Factor in the Define Unit panel) tells FLUENT the number to multiply by to obtain the SI unit value from your customized unit value. Thus the conversion factor should have the form SI units/custom units. For example, if you want the unit of length to be inches, you should input a conversion factor of 0.0254 meters/inch. If you want the unit of velocity to be feet/min, you can determine the conversion factor by using the following equation: x

ft 0.3048 m min m × × =y min ft 60 s s

(4.4-1)

You should input a conversion factor of 0.0051, which is equal to 0.3048/60.


4-5

Unit Systems

4-6


Chapter 5.

Reading and Manipulating Grids

FLUENT can import many different types of grids from various sources. You can modify the grid by translating or scaling node coordinates, partitioning the cells for parallel processing, reordering the cells in the domain to decrease bandwidth, and merging or separating zones. You can also obtain diagnostic information on the grid, including memory usage and simplex, topological, and domain information. You can find out the number of nodes, faces, and cells in the grid, determine the minimum and maximum cell volumes in the domain, and check for the proper numbers of nodes and faces per cell. These and other capabilities are described in the following sections. • Section 5.1: Grid Topologies • Section 5.2: Grid Requirements and Considerations • Section 5.3: Grid Import • Section 5.4: Non-Conformal Grids • Section 5.5: Checking the Grid • Section 5.6: Reporting Grid Statistics • Section 5.7: Modifying the Grid See Chapter 25 for information about adapting the grid based on solution data and related functions, and Section 30.4 for details on partitioning the grid for parallel processing.


5-1


5.1

Grid Topologies

Since FLUENT is an unstructured solver, it uses internal data structures to assign an order to the cells, faces, and grid points in a mesh and to maintain contact between adjacent cells. It does not, therefore, require i,j,k indexing to locate neighboring cells. This gives you the flexibility to use the grid topology that is best for your problem, since the solver does not force an overall structure or topology on the grid. In 2D, quadrilateral and triangular cells are accepted, and in 3D, hexahedral, tetrahedral, pyramid, and wedge cells can be used. (Figure 5.1.1 depicts each of these cell types.) Both single-block and multi-block structured meshes are acceptable, as well as hybrid meshes containing quadrilateral and triangular cells or hexahedral, tetrahedral, pyramid, and wedge cells. In addition, FLUENT also accepts grids with hanging nodes (i.e., nodes on edges and faces that are not vertices of all the cells sharing those edges or faces). See Section 25.2.2 for details. Grids with non-conformal boundaries (i.e., grids with multiple subdomains in which the grid node locations at the internal subdomain boundaries are not identical) are also acceptable. See Section 5.4 for details. Some examples of grids that are valid for FLUENT are presented in Section 5.1.1. Section 5.1.2 explains how to choose the grid type that is best suited for your problem.

5.1.1

Examples of Acceptable Grid Topologies

As mentioned above, FLUENT can solve problems on a wide variety of grids. Figures 5.1.2–5.1.12 show examples of grids that are valid for FLUENT. O-type grids, grids with zero-thickness walls, C-type grids, conformal block-structured grids, multiblock structured grids, non-conformal grids, and unstructured triangular, tetrahedral, quadrilateral, and hexahedral grids are all acceptable. Note that while FLUENT does not require a cyclic branch cut in an O-type grid, it will accept a grid that contains one.

5.1.2

Choosing the Appropriate Grid Type

FLUENT can use grids comprised of triangular or quadrilateral cells (or a combination of the two) in 2D, and tetrahedral, hexahedral, pyramid, or wedge cells (or a combination of these) in 3D. The choice of which mesh type to use will depend on your application. When choosing your mesh type, you should consider the following issues: • Setup time • Computational expense • Numerical diffusion To clarify the trade-offs inherent in your choice of mesh type, these issues are discussed further.

5-2


5.1 Grid Topologies

2D Cell Types

Triangle

Quadrilateral

3D Cell Types

Tetrahedron

Hexahedron

Prism/Wedge

Pyramid

Figure 5.1.1: Cell Types


5-3


Figure 5.1.2: Structured Quadrilateral Grid for an Airfoil

Figure 5.1.3: Unstructured Quadrilateral Grid

5-4


5.1 Grid Topologies

Figure 5.1.4: Multiblock Structured Quadrilateral Grid

Figure 5.1.5: O-Type Structured Quadrilateral Grid


5-5


Figure 5.1.6: Parachute Modeled With Zero-Thickness Wall

Branch Cut

Figure 5.1.7: C-Type Structured Quadrilateral Grid

5-6


5.1 Grid Topologies

Figure 5.1.8: 3D Multiblock Structured Grid

Figure 5.1.9: Unstructured Triangular Grid for an Airfoil


5-7


Figure 5.1.10: Unstructured Tetrahedral Grid

Figure 5.1.11: Hybrid Triangular/Quadrilateral Grid with Hanging Nodes

5-8


5.1 Grid Topologies

Figure 5.1.12: Non-Conformal Hybrid Grid for a Rotor-Stator Geometry

Setup Time Many flow problems solved in engineering practice involve complex geometries. The creation of structured or block-structured grids (consisting of quadrilateral or hexahedral elements) for such problems can be extremely time-consuming, if not impossible. Setup time for complex geometries is, therefore, the major motivation for using unstructured grids employing triangular or tetrahedral cells. If your geometry is relatively simple, however, there may be no clear saving in setup time with either approach. If you already have a mesh created for a structured code such as FLUENT 4, it would clearly save you time to use this mesh in FLUENT rather than regenerate it. This might be a strong motivation for using quadrilateral or hexahedral cells in your FLUENT simulation. Note that FLUENT has a range of filters that allow you to import structured meshes from other codes, including FLUENT 4 (see Section 5.3).

Computational Expense When geometries are complex or the range of length scales of the flow is large, a triangular/tetrahedral mesh can often be created with far fewer cells than the equivalent mesh consisting of quadrilateral/hexahedral elements. This is because a triangular/tetrahedral mesh allows cells to be clustered in selected regions of the flow domain, whereas structured quadrilateral/hexahedral meshes will generally force cells to be placed in regions where they are not needed. Unstructured quadrilateral/hexahedral meshes offer many of the advantages of triangular/tetrahedral meshes for moderately-complex geometries.


5-9


One characteristic of quadrilateral/hexahedral elements that might make them more economical in some situations is that they permit a much larger aspect ratio than triangular/tetrahedral cells. A large aspect ratio in a triangular/tetrahedral cell will invariably affect the skewness of the cell, which is undesirable as it may impede accuracy and convergence. Therefore, if you have a relatively simple geometry in which the flow conforms well to the shape of the geometry, such as a long thin duct, you can use a mesh of highaspect-ratio quadrilateral/hexahedral cells. The mesh is likely to have far fewer cells than if you use triangular/tetrahedral cells.

Numerical Diffusion A dominant source of error in multidimensional situations is numerical diffusion, also termed false diffusion. (The term “false diffusion” is used because the diffusion is not a real phenomenon, yet its effect on a flow calculation is analogous to that of increasing the real diffusion coefficient.) The following points can be made about numerical diffusion: • Numerical diffusion is most noticeable when the real diffusion is small, that is, when the situation is convection-dominated. • All practical numerical schemes for solving fluid flow contain a finite amount of numerical diffusion. This is because numerical diffusion arises from truncation errors that are a consequence of representing the fluid flow equations in discrete form. • The second-order discretization scheme used in FLUENT can help reduce the effects of numerical diffusion on the solution. • The amount of numerical diffusion is inversely related to the resolution of the mesh. Therefore, one way of dealing with numerical diffusion is to refine the mesh. • Numerical diffusion is minimized when the flow is aligned with the mesh. The last point is the most relevant to the choice of the grid. It is clear that if you use a triangular/tetrahedral mesh the flow can never be aligned with the grid. On the other hand, if you use a quadrilateral/hexahedral mesh this situation might occur, but not for complex flows. It is only in a simple flow, such as the flow through a long duct, in which you can rely on a quadrilateral/hexahedral mesh to minimize numerical diffusion. In such situations, there might be some advantage to using a quadrilateral/hexahedral mesh, since you will be able to get a better solution with fewer cells than if you were using a triangular/tetrahedral mesh.

5-10


5.2 Grid Requirements and Considerations

5.2

Grid Requirements and Considerations

This section contains information about special geometry/grid requirements and general comments on mesh quality.

5.2.1

Geometry/Grid Requirements

You should be aware of the following geometry setup and grid construction requirements at the beginning of your problem setup: • Axisymmetric geometries must be defined such that the axis of rotation is the x axis of the Cartesian coordinates used to define the geometry (Figure 5.2.1).

y

x

C L

Figure 5.2.1: Setup of Axisymmetric Geometries with the x Axis as the Centerline

• FLUENT allows you to set up periodic boundaries using either conformal or nonconformal periodic zones. For conformal periodic boundaries, the periodic zones must have identical grids. The conformal periodic boundaries can be created in GAMBIT or TGrid when you are generating the volume mesh. (See the GAMBIT Modeling Guide or the TGrid User’s Guide for more information about creating periodic boundaries in GAMBIT or TGrid.) Alternatively, you can create the conformal periodic boundaries in FLUENT using the make-periodic text command (see Section 5.7.5 for details). Although GAMBIT and TGrid can produce true periodic boundaries, most CAD packages do not. If your mesh was created in such a package, you can create the periodic boundaries using the non-conformal periodic option in FLUENT (see Section 5.7.5 for details). This option, however, is recommended only for periodic zones that are planar.


5-11


5.2.2

Mesh Quality

The quality of the mesh plays a significant role in the accuracy and stability of the numerical computation. The attributes associated with mesh quality are node point distribution, smoothness, and skewness.

Node Density and Clustering Since you are discretely defining a continuous domain, the degree to which the salient features of the flow (such as shear layers, separated regions, shock waves, boundary layers, and mixing zones) are resolved depends on the density and distribution of nodes in the mesh. In many cases, poor resolution in critical regions can dramatically alter the flow characteristics. For example, the prediction of separation due to an adverse pressure gradient depends heavily on the resolution of the boundary layer upstream of the point of separation. Resolution of the boundary layer (i.e., mesh spacing near walls) also plays a significant role in the accuracy of the computed wall shear stress and heat transfer coefficient. This is particularly true in laminar flows where the grid adjacent to the wall should obey yp where

yp u∞ ν x

r

u∞ νx

≤

1

(5.2-1)

= distance to the wall from the adjacent cell centroid = free-stream velocity = kinematic viscosity of the fluid = distance along the wall from the starting point of the boundary layer

Equation 5.2-1 is based upon the Blasius solution for laminar flow over a flat plate at zero incidence [226]. Proper resolution of the mesh for turbulent flows is also very important. Due to the strong interaction of the mean flow and turbulence, the numerical results for turbulent flows tend to be more susceptible to grid dependency than those for laminar flows. In the near-wall region, different mesh resolutions are required depending on the near-wall model being used. See Section 10.9 for detailed guidelines. In general, no flow passage should be represented by fewer than 5 cells. Most cases will require many more cells to adequately resolve the passage. In regions of large gradients, as in shear layers or mixing zones, the grid should be fine enough to minimize the change in the flow variables from cell to cell. Unfortunately, it is usually very difficult to determine in advance the locations of important flow features. Moreover, the grid resolution in most complicated three-dimensional flow fields will be constrained by CPU time and computer resource limitations (i.e., memory and disk space). Although accuracy increases with larger grids, the CPU and memory requirements to compute the solution and postprocess the results also increase. Solution-adaptive grid refinement can be used to increase and/or

5-12


5.2 Grid Requirements and Considerations

decrease grid density based on the evolving flow field, and thus provides the potential for more economical use of grid points (and, hence, reduced time and resource requirements). See Chapter 25 for more information on solution adaption.

Smoothness Rapid changes in cell volume between adjacent cells translate into larger truncation errors. Truncation error is the difference between the partial derivatives in the governing equations and their discrete approximations. FLUENT provides the capability to improve the smoothness by refining the mesh based on the change in cell volume or the gradient of cell volume. See Sections 25.4 and 25.8 for more information on refining the grid based on change in cell volume.

Cell Shape The shape of the cell (including its skewness and aspect ratio) also has a significant impact on the accuracy of the numerical solution. Skewness can be defined as the difference between the cell’s shape and the shape of an equilateral cell of equivalent volume. Highly skewed cells can decrease accuracy and destabilize the solution. For example, optimal quadrilateral meshes will have vertex angles close to 90 degrees, while triangular meshes should preferably have angles of close to 60 degrees and have all angles less than 90 degrees. Aspect ratio is a measure of the stretching of the cell. As discussed in Section 5.1.2, for highly anisotropic flows, extreme aspect ratios may yield accurate results with fewer cells. However, a general rule of thumb is to avoid aspect ratios in excess of 5:1.

Flow-Field Dependency The effect of resolution, smoothness and cell shape on the accuracy and stability of the solution process is strongly dependent on the flow field being simulated. For example, very skewed cells can be tolerated in benign flow regions, but can be very damaging in regions with strong flow gradients. Since the locations of strong flow gradients generally cannot be determined a priori, you should strive to achieve a high-quality mesh over the entire flow domain.


5-13


5.3

Grid Import

Since FLUENT can handle a number of different grid topologies, there are many sources from which you can obtain a grid to be used in your simulation. You can generate a grid using GAMBIT, TGrid, GeoMesh, preBFC, ICEMCFD, I-DEAS, NASTRAN, PATRAN, ARIES, ANSYS, or other preprocessors, or use the grid contained in a FLUENT/UNS, RAMPANT, or FLUENT 4 case file. You can also prepare multiple mesh files and combine them to create a single mesh.

5.3.1

GAMBIT Grid Files

You can use GAMBIT to create 2D and 3D structured/unstructured/hybrid grids. To create any of these meshes for FLUENT, follow the procedure described in the GAMBIT Modeling Guide, and export your mesh in FLUENT 5/6 format. All such meshes can be imported directly into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.

5.3.2

GeoMesh Grid Files

You can use GeoMesh to create complete 2D quadrilateral or triangular grids, 3D hexahedral grids, and triangular surface grids for 3D tetrahedral grids. To create any of these meshes for FLUENT, follow the procedure described in the GeoMesh User’s Guide. To complete the generation of a 3D tetrahedral mesh, you must read the surface mesh into TGrid and generate the volume mesh there. All other meshes, however, can be imported directly into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.

5.3.3

TGrid Grid Files

You can use TGrid to create 2D and 3D unstructured triangular/tetrahedral grids from boundary or surface grids. Follow the meshing procedure described in the TGrid User’s Guide, and save your mesh using the File/Write/Mesh... menu item. To import the grid into FLUENT, use the File/Read/Case... menu item, as described in Section 3.2.

5.3.4

preBFC Grid Files

You can use preBFC to create two different types of grids for FLUENT: structured quadrilateral/hexahedral and unstructured triangular/tetrahedral. The procedure for generating and importing each is outlined below.

Structured Grid Files To generate a structured 2D or 3D grid, follow the procedure described in the preBFC User’s Guide (Chapters 6 and 7). The resulting grid will contain quadrilateral (2D) or

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5.3 Grid Import

hexahedral (3D) elements. Remember to specify no more than 70 wall zones and no more than 35 inlet zones. To import the grid, use the File/Import/preBFC Structured Mesh... menu item, as described in Section 3.2.4. To manually convert a file in preBFC format to a mesh file suitable for FLUENT, enter the following command: utility fl42seg input-filename output-filename The output file produced can be read into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.

Unstructured Triangular and Tetrahedral Grid Files To generate an unstructured 2D grid, follow the procedure described in the preBFC User’s Guide (Chapter 8), and save your mesh file in the RAMPANT format using the MESH-RAMPANT/TGRID command. Note that the current FLUENT format is the same as the RAMPANT format. The resulting grid will contain triangular elements. To import the grid, use the File/Read/Case... menu item, as described in Section 3.2. To generate a 3D unstructured tetrahedral grid, follow the procedure described in Chapter 8 of the preBFC User’s Guide for generating a surface mesh. You will then read the surface mesh into TGrid, and complete the grid generation there. See Section 5.3.3 for information about TGrid grid files.

5.3.5

ICEMCFD Grid Files

You can use ICEMCFD to create structured grids in FLUENT 4 format and unstructured grids in RAMPANT format. To import a FLUENT 4 grid, follow the instructions in Section 5.3.8. To import a RAMPANT grid, use the File/Read/Case... menu item, as described in Section 3.2. Note that the current FLUENT format is the same as the RAMPANT format; it is not the same as the FLUENT 4 format. After reading a triangular or tetrahedral ICEMCFD volume mesh, you should perform smoothing and swapping (as described in Section 25.12) to improve its quality.

5.3.6

Grid Files from Third-Party CAD Packages

FLUENT can import grid files from a number of third-party CAD packages, including I-DEAS, NASTRAN, PATRAN, and ANSYS.


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I-DEAS Universal Files There are three different ways in which you can import an I-DEAS Universal file into FLUENT: 1. You can generate an I-DEAS surface or volume mesh containing triangular, quadrilateral, tetrahedral, wedge and/or hexahedral elements, and import it into TGrid using the commands described in the TGrid User’s Guide and adhering to the restrictions described in Appendix B of the TGrid User’s Guide. In TGrid, complete the grid generation (if necessary) and then follow the instructions in Section 5.3.3. 2. You can generate an I-DEAS volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements, and import it directly using the File/Import/IDEAS Universal... menu item, as described in Section 3.2.6. 3. You can generate an I-DEAS volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements, and then use the filter fe2ram to convert the Universal file to the format used by FLUENT. To convert an input file in I-DEAS Universal format to an output file in FLUENT format, follow the instructions on page 5-20. After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2. Recognized I-DEAS Datasets The following Universal file datasets are recognized by the FLUENT grid import utility: Node Coordinates dataset number 15, 781, 2411 Elements dataset number 71, 780, 2412 Permanent Groups dataset number 752, 2417, 2429, 2430, 2432, 2435 For 2D volume grids, the elements must exist in a constant z plane. Note that mesh area/mesh volume datasets are not recognized. This implies that writing multiple mesh areas/mesh volumes to a single Universal file may confuse FLUENT. Grouping Nodes to Create Face Zones Nodes are grouped in I-DEAS using the Group command to create boundary face zones. In FLUENT, boundary conditions are applied to each zone. Faces that contain the nodes in a group are gathered into a single zone. It is important not to group nodes of internal faces with nodes of boundary faces. One technique is to generate groups automatically based on curves or mesh areas—i.e., every curve or mesh area will be a different zone in FLUENT. You may also create the groups manually, generating groups consisting of all nodes related to a given curve (2D) or mesh area (3D).

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5.3 Grid Import

Grouping Elements to Create Cell Zones Elements in I-DEAS are grouped using the Group command to create the multiple cell zones. All elements grouped together are placed in a single cell zone in FLUENT. If the elements are not grouped, FLUENT will place all the cells into a single zone. Deleting Duplicate Nodes I-DEAS may generate duplicate or coincident nodes in the process of creating elements. These nodes must be removed in I-DEAS before writing the universal file for import into FLUENT.

NASTRAN Files There are three different ways in which you can import a NASTRAN file into FLUENT: 1. You can generate a NASTRAN surface or volume mesh containing triangular, quadrilateral, tetrahedral, wedge, and/or hexahedral elements, and import it into TGrid using the commands described in the TGrid User’s Guide and adhering to the restrictions described in Appendix B of the TGrid User’s Guide. In TGrid, complete the grid generation (if necessary) and then follow the instructions in Section 5.3.3. 2. You can generate a NASTRAN volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements, and import it directly using the File/Import/NASTRAN... menu item, as described in Section 3.2.7. 3. You can generate a NASTRAN volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements, and then use the filter fe2ram to convert the NASTRAN file to the format used by FLUENT. To convert an input file in NASTRAN format to an output file in FLUENT format, follow the instructions on page 5-20. After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2. After reading a triangular or tetrahedral NASTRAN volume mesh using method 2 or 3 above, you should perform smoothing and swapping (as described in Section 25.12) to improve its quality. Recognized NASTRAN Bulk Data Entries The following NASTRAN file datasets are recognized by the FLUENT grid import utility: GRID single-precision node coordinates GRID* double-precision node coordinates


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CBAR line elements CTETRA, CTRIA3 tetrahedral and triangular elements CHEXA, CQUAD4, CPENTA hexahedral, quadrilateral, and wedge elements For 2D volume grids, the elements must exist in a constant z plane. Deleting Duplicate Nodes NASTRAN may generate duplicate or coincident nodes in the process of creating elements. These nodes must be removed in NASTRAN before writing the file for import into FLUENT.

PATRAN Neutral Files There are three different ways in which you can import a PATRAN Neutral file into FLUENT. 1. You can generate a PATRAN surface or volume mesh containing triangular, quadrilateral, tetrahedral, wedge, and/or hexahedral elements, and import it into TGrid using the commands described in the TGrid User’s Guide and adhering to the restrictions described in Appendix B of the TGrid User’s Guide. In TGrid, complete the grid generation (if necessary) and then follow the instructions in Section 5.3.3. 2. You can generate a PATRAN volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements (grouping nodes with the same componentgroup name) and import it directly to FLUENT by selecting the File/Import/ PATRAN... menu item, as described in Section 3.2.8. 3. You can generate a PATRAN volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements and then use the filter fe2ram to convert the Neutral file into the format used by FLUENT. To convert an input file in PATRAN Neutral format to an output file in FLUENT format, follow the instructions on page 5-20. After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2. After reading a triangular or tetrahedral PATRAN volume mesh using method 2 or 3 above, you should perform smoothing and swapping (as described in Section 25.12) to improve its quality.

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5.3 Grid Import

Recognized PATRAN Datasets The following PATRAN Neutral file packet types are recognized by the FLUENT grid import utility: Node Data Packet Type 01 Element Data Packet Type 02 Distributed Load Data Packet Type 06 Node Temperature Data Packet Type 10 Name Components Packet Type 21 File Header Packet Type 25 For 2D volume grids, the elements must exist in a constant z plane. Grouping Elements to Create Cell Zones Elements are grouped in PATRAN using the Named Component command to create the multiple cell zones. All elements grouped together are placed in a single cell zone in FLUENT. If the elements are not grouped, FLUENT will place all the cells into a single zone.

ANSYS Files There are three different ways in which you can import an ANSYS file into FLUENT. 1. You can generate a surface or volume mesh containing triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements using ANSYS or ARIES, and import it into TGrid using the commands described in the TGrid User’s Guide and adhering to the restrictions described in Appendix B of the TGrid User’s Guide. In TGrid, complete the grid generation (if necessary) and then follow the instructions in Section 5.3.3. 2. You can generate an ANSYS volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements and import it directly to FLUENT using the File/Import/ANSYS... menu item, as described in Section 3.2.5. 3. You can generate an ANSYS volume mesh with linear triangular, quadrilateral, tetrahedral, wedge, or hexahedral elements and then use the filter fe2ram to convert the ANSYS file into the format used by FLUENT. To convert an input file in ANSYS 5.4 or 5.5 format to an output file in FLUENT format, follow the instructions on page 5-20. After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.


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After reading a triangular or tetrahedral volume mesh using method 2 or 3 above, you should perform smoothing and swapping (as described in Section 25.12) to improve its quality. Recognized ANSYS 5.4 and 5.5 Datasets FLUENT can import mesh files from ANSYS 5.4 and 5.5 (.cdb files), retaining original boundary names. The following ANSYS file datasets are recognized by the FLUENT grid import utility: NBLOCK node block data EBLOCK element block data CMBLOCK element/node grouping The elements must be STIF63 linear shell elements. In addition, if element data without an explicit element ID is used, the filter assumes sequential numbering of the elements when creating the zones.

Using the fe2ram Filter to Convert Files If you choose to convert the CAD file manually before reading it into FLUENT, you can enter the following command: utility fe2ram [dimension] format [zoning] input-file output-file where items enclosed in square brackets are optional. (Do not type the square brackets.) dimension indicates the dimension of the dataset. Replace dimension by -d2 to indicate that the grid is two-dimensional. For a 3D grid, do not enter anything for dimension, because 3D is the default. format indicates the format of the file you wish to convert. Replace format by -tANSYS for an ANSYS file, -tIDEAS for an I-DEAS file, -tNASTRAN for a NASTRAN file, or -tPATRAN for a PATRAN file. To check if conversion from any other CAD packages has been added, type utility fe2ram -cl -help. zoning indicates how zones were identified in the CAD package. Replace zoning by -zID for a grid that was zoned by property IDs, or -zNONE to ignore all zone groupings. For a grid zoned by group, do not enter anything for zoning, because zoning by groups is the default. input-file and output-file are the names of the original file and the file to which you want to write the converted grid information, respectively.

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5.3 Grid Import

For example, if you wanted to convert the 2D I-DEAS volume mesh file sample.unv to an output file called sample.grd, you would enter the following command: utility fe2ram -d2 -tIDEAS sample.unv sample.grd

5.3.7

FLUENT/UNS and RAMPANT Case Files

If you have a FLUENT/UNS 3 or 4 case file or a RAMPANT 2, 3, or 4 case file and you want to run a FLUENT simulation using the same grid, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.4.

5.3.8

FLUENT 4 Case Files

If you have a FLUENT 4 case file and you want to run a FLUENT simulation using the same grid, you can import it into FLUENT using the File/Import/FLUENT 4 Case... menu item, as described in Section 3.5. FLUENT will read grid information and zone types from the FLUENT 4 case file.

! Note that FLUENT 4 may interpret some pressure boundaries differently from the current release of FLUENT. Check the conversion information printed out by FLUENT to see if you need to modify any boundary types. To manually convert an input file in FLUENT 4 format to an output file in the current FLUENT format, enter the following command: utility fl42seg input-filename output-filename After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.

5.3.9

FIDAP Neutral Files

If you have a FIDAP Neutral file and you want to run a FLUENT simulation using the same grid, you can import it using the File/Import/FIDAP... menu item, as described in Section 3.6. FLUENT will read grid information and zone types from the FIDAP file. To manually convert an input file in FIDAP format to an output file in FLUENT format, enter the following command: utility fe2ram [dimension] -tFIDAP7 input-file output-file where the item in square brackets is optional. (Do not type the square brackets.) For a 2D file, replace dimension with -d2. For a 3D file, do not enter anything for dimension, because 3D is the default. After the output file has been written, you can read it into FLUENT using the File/Read/Case... menu item, as described in Section 3.2.


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5.3.10

Reading Multiple Mesh Files

There may be some cases in which you will need to read multiple mesh files (subdomains) to form your computational domain. Some examples are listed below: • If you plan to solve on a multiblock mesh, you can generate each block of the mesh in the grid generator and save it to a separate grid file. • For very complicated geometries, it may be more efficient to save the mesh for each part as a separate grid file. Note that you do not need to ensure that the grid node locations are identical at the boundaries where two separate meshes meet; FLUENT can handle non-conformal grid interfaces. See Section 5.4 for details about non-conformal grid boundaries. The procedure for reading multiple grid files is as follows: 1. Generate the grid for the whole domain in the grid generator, and save each cell zone (or block or part) to a separate grid file for FLUENT.

!

If one (or more) of the grids you wish to import is structured (e.g., a FLUENT 4 grid file), you will need to first convert it to FLUENT format using the fl42seg filter described in Section 5.3.8. 2. Before you start the solver, use either TGrid or the tmerge filter to combine the grids into one grid file. The TGrid method is more convenient, but the tmerge method allows you to rotate, scale, and/or translate the grids before they are merged. • To use TGrid, follow the procedure below: (a) Read all of the grid files into TGrid. When TGrid reads the grid files, it will automatically merge them into a single grid. (b) Save the merged grid file. See the TGrid User’s Guide for information about reading and writing files in TGrid. • To use the tmerge filter, follow the procedure below (before starting FLUENT): (a) For 3D problems, type utility tmerge -3d. For 2D problems, type utility tmerge -2d. (b) When prompted, specify the names of the input files (the separate grid files) and the name of the output file in which to save the complete grid. For each input file, you can specify scaling factors, translation distances, or a rotation angle. In the example below, no scaling, translation, or rotation is performed.

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5.3 Grid Import

user@mymachine:> utility tmerge -2d Starting /Fluent.Inc/utility/tmerge2.1/ultra/tmerge_2d.2.1.13 Append 2D grid files. tmerge2D Fluent Inc, Version 2.1.11 Enter name of grid file (ENTER to continue) : my1.msh x,y scaling factor, eg. 1 1

: 1 1

x,y translation, eg. 0 1

: 0 0

rotation angle (deg), eg. 45

: 0

Enter name of grid file (ENTER to continue) : my2.msh x,y scaling factor, eg. 1 1

: 1 1

x,y translation, eg. 0 1

: 0 0

rotation angle (deg), eg. 45

: 0

Enter name of grid file (ENTER to continue) : Enter name of output file

: final.msh

Reading... node zone: id 1, ib 1, ie 1677, typ 1 node zone: id 2, ib 1678, ie 2169, typ 2 . . . done. Writing... 492 nodes, id 1, ib 1678, ie 2169, type 2. 1677 nodes, id 2, ib 1, ie 1677, type 1. . . . done. Appending done.

In the above example, where no scaling, translation, or rotation is requested, you could simplify the inputs to the following:


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utility tmerge -2d -cl -p my1.msh my2.msh final.msh 3. Read the combined grid file into the solver in the usual manner (using the File/Read/Case... menu item). For a conformal mesh, if you do not want a boundary between the adjacent cell zones, you can use the Fuse Face Zones panel to fuse the “overlapping” boundaries (see Section 5.7.7). The matching faces will be moved to a new zone with a boundary type of interior. If all faces on either or both of the original zones have been moved to the new zone, the original zone(s) will be discarded.

! If you are planning to use sliding meshes, or if you have non-conformal boundaries between adjacent cell zones, you should not fuse the overlapping zones. You must instead change the type of the two overlapping zones to interface (as described in Section 5.4).

5.4

Non-Conformal Grids

In FLUENT it is possible to use a grid composed of cell zones with non-conformal boundaries. That is, the grid node locations do not need to be identical at the boundaries where two subdomains meet. FLUENT handles such meshes using the same technique that is used in the sliding mesh model, although in this situation the meshes do not slide.

5.4.1

Non-Conformal Grid Calculations

To compute the flux across the non-conformal boundary, FLUENT must first compute the intersection between the “interface” zones that comprise the boundary. The resulting intersection produces an interior zone where the two interface zones overlap (see Figure 5.4.1). If one of the interface zones extends beyond the other (as shown in Figure 5.4.2), FLUENT will create one or two additional wall zones for the portion(s) of the boundary where the two interface zones do not overlap.

interface zone 1

interior zone

interface zone 2

Figure 5.4.1: Completely Overlapping Grid Interface Intersection

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5.4 Non-Conformal Grids

interface zone 1

interior zone

interface zone 2

wall zone 1

wall zone 2

Figure 5.4.2: Partially Overlapping Grid Interface Intersection

Principally, fluxes across the grid interface are computed using the faces resulting from the intersection of the two interface zones, rather than from the interface zone faces themselves. In the example shown in Figure 5.4.3, the interface zones are composed of faces A-B and B-C, and faces D-E and E-F. The intersection of these zones produces the faces a-d, d-b, b-e, and e-c. Faces produced in the region where the two cell zones overlap (d-b, b-e, and e-c) are grouped to form an interior zone, while the remaining face (a-d) forms a wall zone. To compute the flux across the interface into cell IV, for example, face D-E is ignored and faces d-b and b-e are used instead, bringing information into cell IV from cells I and III, respectively. cell zone 1

II

I

III A a

B b

d

interface zone 2

interface zone 1

C c

e

D

F

E IV

VI V

cell zone 2

Figure 5.4.3: Two-Dimensional Non-Conformal Grid Interface


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5.4.2

Requirements and Limitations of Non-Conformal Grids

Please note the following requirements and limitations when using non-conformal grids: • The grid interface can be any shape (including a non-planar surface, in 3D), provided that the two interface boundaries are based on the same geometry. If there are sharp features (e.g., 90-degree angles) or curvature in the mesh, it is especially important that both sides of the interface closely follow that feature. For example, consider the case of two concentric circles that define two fluid zones with a circular, non-conformal interface between them, as shown in Figure 5.4.4. Because the node spacing on the interface edge of the outer fluid zone is coarse compared to the radius of curvature, the interface does not closely follow the feature (in this case, the circular edge.)

!

In general, the maximum tolerance between two interfaces should not be larger than their adjacent cell size at that location; i.e., no cell should be completely enclosed between two interfaces.

Figure 5.4.4: A Circular Non-Conformal Interface

• A face zone cannot share a non-conformal interface with more than one other face zone. This is best illustrated by an example, as shown in Figure 5.4.5. Each volume in the figure is meshed separately and does not match node-to-node at the interface. To create the non-conformal interface, you will need to work with three surfaces: one side of the box (rectangle 1) and an end cap from each pipe (circle 1 and circle 2). To create interfaces between rectangle 1 and the two circles, there needs to be one-to-one mapping between each end cap and the side of the box (see Figure 5.4.6). • If you create a single grid with multiple cell zones separated by a non-conformal boundary, you must be sure that each cell zone has a distinct face zone on the non-conformal boundary. The face zones for two adjacent cell zones will have the same position and shape, but one will correspond to one cell zone and one to the other. (Note that it is also possible to create a separate grid file for each of the cell zones, and then merge them as described in Section 5.3.10.)

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rectangle 1 circle 1

circle 2

Figure 5.4.5: Box with Two Pipes Intersecting One Side

Allowed: Divide rectangle 1 into two surfaces rectangle 1a

rectangle 1b

circle 2

circle 1

interface pairings are: rectangle 1a ⇔ circle 2 rectangle 1b ⇔ circle 1

Not allowed: Keeping things as they are Not Valid:

rectangle 1 circle 2

circle 1

rectangle 1 ⇔ circle 2 rectangle 1 ⇔ circle 1

Figure 5.4.6: One-to-One Mapping


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• All periodic zones must be correctly oriented (either rotational or translational) before you create the non-conformal interface. Periodic non-conformal interfaces must overlap exactly; i.e., they need to have the same rotational or translational extent and, in addition, have the same axial extent. This is not true for interfaces in general, where a wall zone is created for non-overlapping regions. • For 3D cases, if the interface is periodic, only one pair of periodic boundaries can neighbor the interface. See also Section 5.4.4 for information about using non-conformal FLUENT/UNS and RAMPANT cases.

5.4.3

Using a Non-Conformal Grid in FLUENT

If your multiple-zone grid includes non-conformal boundaries, you must follow the procedure below (after ensuring that your grid meets all the requirements listed in Section 5.4.2) to ensure that FLUENT can obtain a solution on your mesh: 1. Read the grid into FLUENT. (If you have multiple grid files that have not yet been merged, first follow the instructions in Section 5.3.10 to merge them into a single grid.) 2. After reading in the grid, change the type of each pair of zones that comprises the non-conformal boundary to interface (as described in Section 6.1.3). Define −→Boundary Conditions... 3. Define the non-conformal grid interfaces in the Grid Interfaces panel (Figure 5.4.7). Define −→Grid Interfaces... (a) Enter a name for the interface in the Grid Interface field. (b) Specify the two interface zones that comprise the grid interface by selecting one in the Interface Zone 1 list and one in the Interface Zone 2 list.

!

If one of your interface zones is much smaller than the other, you should specify the smaller zone as Interface Zone 1 to improve the accuracy of the intersection calculation. (c) Set the Interface Type, if appropriate. There are two options: • Enable Periodic for periodic problems. • Enable Coupled if the interface lies between a solid zone and a fluid zone, or if you would like to model a (thermally) coupled wall between two fluid zones using non-conformal interfaces.

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Figure 5.4.7: The Grid Interfaces Panel

(d) Click on Create to create a new grid interface. For all types of interfaces, FLUENT will create boundary zones for the interface (e.g., wall-9, wall-10), which will appear under Boundary Zone 1 and Boundary Zone 2. If you have enabled the Coupled option, FLUENT will also create wall interface zones (e.g., wall-4, wall-4-shadow), which will appear under Interface Wall Zone 1 and Interface Wall Zone 2. (e) If the two interface zones did not overlap entirely, check the boundary zone type of the zone(s) created for the non-overlapping portion(s) of the boundary. If the zone type is not correct, you can use the Boundary Conditions panel to change it. (f) If you have any Coupled-type interfaces, define boundary conditions (if relevant) by updating the interface wall zones in the Boundary Conditions panel. Define −→Boundary Conditions... If you create an incorrect grid interface, you can select it in the Grid Interface list and click on the Delete button to delete it. (Any boundary zones or wall interface zones that were created when the interface was created will also be deleted.) You may then proceed with the problem setup as usual.


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5.4.4

Starting From a FLUENT/UNS or RAMPANT Case

FLUENT/UNS and RAMPANT case files with non-conformal interfaces can be read and used by FLUENT without any changes. However, you may want to recompute the grid interface to take advantage of FLUENT’s improved intersection calculation. You cannot simply delete the original grid interface and recompute it. Instead, you must use the define/grid-interfaces/recreate text command. define −→ grid-interfaces −→recreate When you select this command, FLUENT will recreate all grid interfaces in the domain. You can then continue the problem setup or calculation as usual.

! If you have a FLUENT/UNS or RAMPANT data file for the non-conformal case, you must read it in before you use the recreate command.

5.5

Checking the Grid

The grid checking capability in FLUENT provides domain extents, volume statistics, grid topology and periodic boundary information, verification of simplex counters, and (for axisymmetric cases) node position verification with respect to the x axis. You can obtain this information by selecting the Check menu item in the Grid pull-down menu. Grid −→Check

! It is generally a good idea to check your grid right after reading it into the solver, in order to detect any grid trouble before you get started with the problem setup.

5.5.1

Grid Check Information

The information that FLUENT generates when you use the Check item will appear in the console window. Sample output is shown below:

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5.5 Checking the Grid

Grid Check Domain Extents: x-coordinate: min (m) = 0.000000e+00, max (m) = 6.400001e+01 y-coordinate: min (m) = -4.538534e+00, max (m) = 6.400000e+01 Volume statistics: minimum volume (m3): 2.353664e-05 maximum volume (m3): 7.599501e-03 total volume (m3): 2.341560e+00 minimum 2d volume (m3): 4.027890e-04 maximum 2d volume (m3): 1.230393e-03 Face area statistics: minimum face area (m2): 1.300719e-04 maximum face area (m2): 3.781404e-02 Checking number of nodes per cell. Checking number of faces per cell. Checking thread pointers. Checking number of cells per face. Checking face cells. Checking bridge faces. Checking right-handed cells. Checking face handedness. Checking for nodes that lie below the x-axis. Checking element type consistency. Checking boundary types: Checking face pairs. Checking periodic boundaries. Checking node count. Checking nosolve cell count. Checking nosolve face count. Checking face children. Checking cell children. Checking storage. Done.

The domain extents list the minimum and maximum x, y, and z coordinates in meters. The volume statistics include minimum, maximum, and total cell volume in m3 . A negative value for the minimum volume indicates that one or more cells have improper connectivity. Cells with a negative volume can often be identified using the Iso-Value Adaption capability to mark them for adaption and view them in the graphics window. For more information on creating and viewing isovalue adaption registers, see Section 25.6. You must eliminate these negative volumes before continuing the flow solution process. The topological information to be verified begins with the number of faces and nodes per cell. A triangular cell (2D) should have 3 faces and 3 nodes, a tetrahedral cell (3D) should have 4 faces and 4 nodes, a quadrilateral cell (2D) should have 4 faces and 4


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nodes, and a hexahedral cell (3D) should have 6 faces and 8 nodes. Next, the face handedness for each zone is checked. The zones should contain all righthanded faces. Usually a grid with negative volumes will also have left-handed faces. Again, you cannot obtain a flow solution until you eliminate these connectivity problems. The last topological verification is checking the element-type consistency. If a mesh does not contain mixed elements (quadrilaterals and triangles or hexahedra and tetrahedra), FLUENT will determine that it does not need to keep track of the element types. By doing so, it can eliminate some unnecessary work. For axisymmetric cases, the number of nodes below the x axis is listed. Nodes below the x axis are forbidden for axisymmetric cases, since the axisymmetric cell volumes are created by rotating the 2D cell volume about the x axis; thus nodes below the x axis would create negative volumes. For solution domains with rotationally periodic boundaries, the minimum, maximum, average, and prescribed periodic angles are computed. A common mistake is to specify the angle incorrectly. For domains with translationally periodic boundaries, the boundary information is checked to ensure that the boundaries are truly periodic. Finally, the simplex counters are verified. The actual numbers of nodes, faces, and cells the solver has constructed are compared to the values specified in the corresponding header declarations in the grid file. Any discrepancies are reported.

5.5.2

Repairing Duplicate Shadow Nodes

If the Grid/Check report includes the following message: WARNING: node on face thread 2 has multiple shadows. it indicates the existence of duplicate shadow nodes. This error occurs only in grids with periodic-type walls. You can repair such a grid using the following text command: grid −→ modify-zones −→repair-periodic If the interface is rotational periodic, you will be prompted for the rotation angle.

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5.6 Reporting Grid Statistics

5.6

Reporting Grid Statistics

There are several methods for reporting information about the grid after it has been read into FLUENT. You can report the amount of memory used by the current problem, the grid size, and statistics about the grid partitions. Zone-by-zone counts of cells and faces can also be reported. Information about grid statistics is provided in the following sections: • Section 5.6.1: Grid Size • Section 5.6.2: Memory Usage • Section 5.6.3: Grid Zone Information • Section 5.6.4: Partition Statistics

5.6.1

Grid Size

You can print out the numbers of nodes, faces, cells, and partitions in the grid by selecting the Grid/Info/Size menu item. Grid −→ Info −→Size A partition is a piece of a grid that has been segregated for parallel processing (see Chapter 30). A sample of the resulting output follows: Grid Size Level 0

Cells 7917

Faces 12247

Nodes 4468

Partitions 1

2 cell zones, 11 face zones.

If you are interested in how the cells and faces are divided among the different zones, you can use the Grid/Info/Zones menu item, as described in Section 5.6.3. If you are using the coupled explicit solver, the grid information will be printed for each grid level. The grid levels result from creating coarse grid levels for the FAS multigrid convergence acceleration (see Section 24.5.4). A sample of the resulting output is shown below:


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Grid Size Level 0 1 2 3 4 5

Cells 7917 1347 392 133 50 17

Faces 12247 3658 1217 475 197 78

Nodes 4468 0 0 0 0 0

Partitions 1 1 1 1 1 1

2 cell zones, 11 face zones.

5.6.2

Memory Usage

During a FLUENT session you may want to check the amount of memory used and allocated in the present analysis. FLUENT has a feature that will report the following information: the numbers of nodes, faces, cells, edges, and object pointers (generic pointers for various grid and graphics utilities) that are used and allocated; the amount of array memory (scratch memory used for surfaces) used and allocated; and the amount of memory used by the solver process. You can obtain this information by selecting the Grid/Info/Memory Usage menu item. Grid −→ Info −→Memory Usage The memory information will be different for UNIX and Windows systems.

UNIX Systems On UNIX systems, the process memory information includes the following: • Process Static memory is essentially the size of the code itself. • Process Dynamic memory is the allocated heap memory used to store the grid and solution variables • Process Total memory is the sum of static and dynamic memory.

Windows Systems On Windows systems, the process memory information includes the following: • Process Physical memory is the allocated heap memory currently resident in RAM.

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5.6 Reporting Grid Statistics

• Process Virtual memory is the allocated heap memory currently swapped to the Windows system page file. • Process Total memory is the sum of physical and virtual memory. Note the following: • The memory information does not include the static (code) memory. • In the serial version of FLUENT, the heap memory value includes storage for the solver (grid and solution variables), and Cortex (GUI and graphics memory), since Cortex and the solver are contained in the same process. • In the parallel version, Cortex runs in its own process, so the heap memory value includes storage for the grid and solution variables only. On Windows systems, you can also get more information on the FLUENT process (or processes) by using the Task Manager (see your Windows documentation for details). For the serial version, the process image name will be something like fl542s.exe. For the parallel version, examples of process image names are as follows: cx332.exe (Cortex), fl542.exe (solver host), and fl smpi542.exe (one solver node).

5.6.3

Grid Zone Information

You can print information in the console window about the nodes, faces, and cells in each zone using the Grid/Info/Zones menu item. Grid −→ Info −→Zones The grid zone information includes the total number of nodes and, for each face and cell zone, the number of faces or cells, the cell (and, in 3D, face) type (triangular, quadrilateral, etc.), the boundary condition type, and the zone ID. Sample output is shown below: Zone sizes on domain 1: 21280 hexahedral cells, zone 4. 532 quadrilateral velocity-inlet faces, zone 1. 532 quadrilateral pressure-outlet faces, zone 2. 1040 quadrilateral symmetry faces, zone 3. 1040 quadrilateral symmetry faces, zone 7. 61708 quadrilateral interior faces, zone 5. 1120 quadrilateral wall faces, zone 6. 23493 nodes.


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5.6.4

Partition Statistics

You can print grid partition statistics in the console window by selecting the Grid/Info/Partitions menu item. Grid −→ Info −→Partitions The statistics include the numbers of cells, faces, interfaces, and neighbors of each partition. See Section 30.4.5 for further details, including sample output.

5.7

Modifying the Grid

There are several ways in which you can modify or manipulate the grid after it has been read into FLUENT. You can scale or translate the grid, merge or separate zones, create or slit periodic zones, and fuse boundaries. In addition, you can reorder the cells in the domain to decrease bandwidth. Smoothing and diagonal swapping, which can be used to improve the mesh, are described in Section 25.12. Methods for partitioning grids to be used in a parallel solver are discussed in Section 30.4.

! Whenever you modify the grid, you should be sure to save a new case file (and a data file, if data exist). If you have old data files that you would like to be able to read in again, be sure to retain the original case file as well, as the data in the old data files may not correspond to the new case file. Information about grid manipulation is provided in the following sections: • Section 5.7.1: Scaling the Grid • Section 5.7.2: Translating the Grid • Section 5.7.3: Merging Zones • Section 5.7.4: Separating Zones • Section 5.7.5: Creating Periodic Zones • Section 5.7.6: Slitting Periodic Zones • Section 5.7.7: Fusing Face Zones • Section 5.7.8: Slitting Face Zones • Section 5.7.9: Extruding Face Zones • Section 5.7.10: Reordering the Domain and Zones • Section 5.7.11: Deleting, Deactivating, and Activating Zones

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5.7 Modifying the Grid

5.7.1

Scaling the Grid

Internally, FLUENT stores the computational grid in meters, the SI unit of length. When grid information is read into the solver, it is assumed that the grid was generated in units of meters. If your grid was created using a different unit of length (inches, feet, centimeters, etc.), you must scale the grid to meters. To do this, you can select from a list of common units to convert the grid or you can supply your own custom scale factors. Each node coordinate will be multiplied by the corresponding scale factor. Scaling can also be used to change the physical size of the grid. For instance, you could stretch the grid in the x direction by assigning a scale factor of 2 in the x direction and 1 in the y and z directions. This would double the extent of the grid in the x direction. However, you should use anisotropic scaling with caution, since it will change the aspect ratios of the cells in your grid.

! If you plan to scale the grid in any way, you should do so before you initialize the flow or begin calculations. Any data that exist when you scale the grid will be invalid. You will use the Scale Grid panel (Figure 5.7.1) to scale the grid from a standard unit of measurement or to apply custom scaling factors. Grid −→Scale...

Figure 5.7.1: The Scale Grid Panel

Using the Scale Grid Panel The procedure for scaling the grid is as follows:


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1. Indicate the units in which you created the grid by choosing the appropriate abbreviation for centimeters, millimeters, inches, or feet in the Grid Was Created In drop-down list. The Scale Factors will automatically be set to the correct values (e.g., 0.0254 meters/inch or 0.3048 meters/foot). If you created your grid using units other than those in the list, you can enter the Scale Factors (e.g., the number of meters per yard) manually. 2. Click on the Scale button. The Domain Extents will be updated to show the correct range in meters. If you prefer to use your original unit of length during the FLUENT session, you can follow the procedure described below to change the unit. Changing the Unit of Length As mentioned above in step 2, when you scale the grid you do not change the units; you just convert the original dimensions of your grid points from your original units to meters by multiplying each node coordinate by the specified Scale Factors. If you want to work in your original units, instead of in meters, you can click on the Change Length Units button. This is a shortcut for changing the length unit in the Set Units panel (see Section 4.4). When you click on the Change Length Units button, the Domain Extents will be updated to show the range in your original units. This unit will be used for all future inputs of length quantities. Unscaling the Grid If you use the wrong scale factor, accidentally click the Scale button twice, or wish to undo the scaling for any other reason, you can click on the UnScale button. “Unscaling” simply divides each of the node coordinates by the specified Scale Factors. (Selecting m in the Grid Was Created In list and clicking on Scale will not unscale the grid.) Changing the Physical Size of the Grid You can also use the Scale Grid panel to change the physical size of the grid. For example, if your grid is 5 feet by 8 feet, and you want to model the same geometry with dimensions twice as big (10 × 16), you can enter 2 for the X and Y Scale Factors and click on Scale. The Domain Extents will be updated to show the new range.

5.7.2

Translating the Grid

You can “move” the grid by applying prescribed offsets to the Cartesian coordinates of all the nodes in the grid. This would be necessary for a rotating problem if the grid were set up with the axis of rotation not passing through the origin, or for an axisymmetric problem if the grid were set up with the axis of rotation not coinciding with the x axis. It is also useful if, for example, you want to move the origin to a particular point on an object (such as the leading edge of a flat plate) to make an XY plot have the desired distances on the x axis.

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You can translate grid points in FLUENT using the Translate Grid panel (Figure 5.7.2). Grid −→Translate...

Using the Translate Grid Panel The procedure for translating the grid is as follows: 1. Enter the desired translations in the x, y, and (for 3D) z directions (i.e., the desired delta in the axes origin) in the X, Y, and Z fields under Translation Offsets. You can specify positive or negative real numbers in the current unit of length. 2. Click on the Translate button. The Domain Extents will be updated to display the new extents of the translated grid. (Note that the Domain Extents are purely informational; you cannot edit them manually.)

Figure 5.7.2: The Translate Grid Panel

5.7.3

Merging Zones

To simplify the solution process, you may want to merge zones. Merging zones involves combining multiple zones of similar type into a single zone. Setting boundary conditions and postprocessing may be easier after you have merged similar zones. Zone merging is performed in the Merge Zones panel (Figure 5.7.3). Grid −→Merge...


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Figure 5.7.3: The Merge Zones Panel

When to Merge Zones FLUENT allows you to merge zones of similar type into a single zone. This is not necessary unless the number of zones becomes prohibitive to efficient setup or postprocessing of the numerical analysis. For example, setting the same boundary condition parameters for a large number of zones can be time-consuming and may introduce inconsistencies. In addition, the postprocessing of the data often involves surfaces generated using the zones. A large number of zones often translates into a large number of surfaces that must be selected for the various display options, such as color contouring. Fortunately, surfaces can also be merged (see Section 26.11), minimizing the negative impact of a large number of zones on postprocessing efficiency. Although merging zones can be helpful, there may be cases where you will want to retain a larger number of zones. Since the merging process is not fully reversible, a larger number of zones provides more flexibility in imposing boundary conditions. Although a large number of zones can make selection of surfaces for display tedious, it can also provide more choices for rendering the grid and the flow-field solution. For instance, it can be difficult to render an internal flow-field solution. If the outer domain is composed of several zones, the grids of subsets of these zones can be plotted along with the solution to provide the relationship between the geometry and solution field.

Using the Merge Zones Panel The procedure for merging multiple zones of the same type into a single zone is as follows: 1. Select the zone type in the Multiple Types list. This list contains all the zone types for which there are multiple zones. When you choose a type from this list, the corresponding zones will appear in the Zones of Type list. 2. Select two or more zones in the Zones of Type list.

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3. Click on the Merge button to merge the selected zones.

! Remember to save a new case file (and a data file, if data exist). 5.7.4

Separating Zones

There are several methods available in FLUENT that allow you to separate a single face or cell zone into multiple zones of the same type. If your grid contains a zone that you want to break up into smaller portions, you can make use of these features. For example, if you created a single wall zone when generating the grid for a duct, but you want to specify different temperatures on specific portions of the wall, you will need to break that wall zone into two or more wall zones. If you plan to solve a problem using the sliding mesh model or multiple reference frames, but you forgot to create different fluid zones for the regions moving at different speeds, you will need to separate the fluid zone into two or more fluid zones.

! After performing any of these separations, you should save a new case file. If data exist, they are automatically assigned to the proper zones when separation occurs, so you should also write a new data file. There are four ways to separate face zones and two ways to separate cell zones. The face separation methods will be described first, followed by the cell separation tools. Slitting (decoupling) of periodic zones is discussed in Section 5.7.6. Note that all of the separation methods allow you to report the result of the separation before you commit to performing it.

Separating Face Zones Methods for Separating Face Zones For geometries with sharp corners, it is often easy to separate face zones based on significant angle. Faces with normal vectors that differ by an angle greater than or equal to the specified significant angle will be placed in different zones. For example, if your grid consists of a cube, and all 6 sides of the cube are in a single wall zone, you would specify a significant angle of 89◦ . Since the normal vector for each cube side differs by 90◦ from the normals of its adjacent sides, each of the 6 sides will be placed in a different wall zone. If you have a small face zone and would like to put each face in the zone into its own zone, you can do so by separating the faces based on face. You can also separate face zones based on the marks stored in adaption registers. For example, you can mark cells for adaption based on their location in the domain (region adaption), their boundary closeness (boundary adaption), isovalues of some variable, or any of the other adaption methods discussed in Chapter 25. When you specify which


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register is to be used for the separation of the face zone, all faces of cells that are marked will be placed into a new face zone. (Use the Manage Adaption Registers panel to determine the ID of the register you wish to use.) Finally, you can separate face zones based on contiguous regions. For example, when you use coupled wall boundary conditions you need the faces on the zone to have a consistent orientation. Consistent orientation can only be guaranteed on contiguous regions, so you may need to separate face zones to allow proper boundary condition specification. Inputs for Separating Face Zones To break up a face zone based on angle, face, adaption mark, or region, use the Separate Face Zones panel (Figure 5.7.4). Grid −→ Separate −→Faces...

Figure 5.7.4: The Separate Face Zones Panel

! If you are planning to separate face zones, you should do so before performing any adaptions using the (default) hanging node adaption method. Face zones that contain hanging nodes cannot be separated. The steps for separating faces are as follows: 1. Select the separation method (Angle, Face, Mark, or Region) under Options. 2. Specify the face zone to be separated in the Zones list. 3. If you are separating by face or region, skip to the next step. Otherwise, do one of the following: • If you are separating faces by angle, specify the significant angle in the Angle field.

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• If you are separating faces by mark, select the adaption register to be used in the Registers list. 4. (optional) To check what the result of the separation will be before you actually separate the face zone, click on the Report button. The report will look like this: Zone not separated. 45 faces in contiguous region 0 30 faces in contiguous region 1 11 faces in contiguous region 2 14 faces in contiguous region 3 Separates zone 4 into 4 zone(s).

5. To separate the face zone, click on the Separate button. FLUENT will print the following information: 45 faces in contiguous region 0 30 faces in contiguous region 1 11 faces in contiguous region 2 14 faces in contiguous region 3 Separates zone 4 into 4 zone(s). Updating zone information ... created zone wall-4:001 created zone wall-4:002 created zone wall-4:010 done.

! When you separate the face zone by adaption mark, you may sometimes find that a face of a corner cell will be placed in the wrong face zone. You can usually correct this problem by performing an additional separation, based on angle, to move the offending face to a new zone. You can then merge this new zone with the zone in which you want the face to be placed, as described in Section 5.7.3.

Separating Cell Zones Methods for Separating Cell Zones If you have two or more enclosed cell regions sharing internal boundaries (as shown in Figure 5.7.5), but all of the cells are contained in a single cell zone, you can separate the cells into distinct zones using the separation-by-region method. Note that if the shared


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internal boundary is of type interior, you must change it to another double-sided face zone type (fan, radiator, etc.) prior to performing the separation.

zone 1

zone 2

Figure 5.7.5: Cell Zone Separation Based on Region You can also separate cell zones based on the marks stored in adaption registers. You can mark cells for adaption using any of the adaption methods discussed in Chapter 25 (e.g., you can mark cells with a certain isovalue range or cells inside or outside a specified region). When you specify which register is to be used for the separation of the cell zone, cells that are marked will be placed into a new cell zone. (Use the Manage Adaption Registers panel to determine the ID of the register you wish to use.) Inputs for Separating Cell Zones To break up a cell zone based on region or adaption mark, use the Separate Cell Zones panel (Figure 5.7.6). Grid −→ Separate −→Cells...

Figure 5.7.6: The Separate Cell Zones Panel

! If you are planning to separate cell zones, you should do so before performing any adaptions using the (default) hanging node adaption method. Cell zones that contain hanging nodes cannot be separated. The steps for separating cells are as follows:

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1. Select the separation method (Mark or Region) under Options. 2. Specify the cell zone to be separated in the Zones list. 3. If you are separating cells by mark, select the adaption register to be used in the Registers list. 4. (optional) To check what the result of the separation will be before you actually separate the cell zone, click on the Report button. The report will look like this: Zone not separated. Separates zone 14 into two zones, with 1275 and 32 cells.

5. To separate the cell zone, click on the Separate button. FLUENT will print the following information: Separates zone 14 into two zones, with 1275 and 32 cells. No faces marked on thread, 2 No faces marked on thread, 3 No faces marked on thread, 1 No faces marked on thread, 5 No faces marked on thread, 7 No faces marked on thread, 8 No faces marked on thread, 9 No faces marked on thread, 61 Separates zone 62 into two zones, with 1763 and 58 faces. All faces marked on thread, 4 No faces marked on thread, 66 Moved 20 faces from face zone 4 to zone 6 Updating zone information ... Moved 32 cells from cell zone 14 to zone 10 created zone interior-4 created zone interior-6 created zone fluid-14:010 done.

As shown in the example above, separation of a cell zone will often result in the separation of face zones as well. When you separate by mark, faces of cells that are moved to a new zone will be placed in a new face zone. When you separate by region, faces of cells that are moved to a new zone will not necessarily be placed in a new face zone.


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If you find that any faces are placed incorrectly, see the comment above, at the end of the inputs for face zone separation.

5.7.5

Creating Periodic Zones

FLUENT allows you to set up periodic boundaries using either conformal or non-conformal periodic zones. You can assign periodicity to your grid by coupling a pair of face zones. If the two zones have identical node and face distributions, you can create a conformal periodic zone. If the two zones are not identical at the boundaries within a specified tolerance, then you can create a non-conformal periodic zone. (See Section 5.4 for more information about non-conformal grids.)

! Remember to save a new case file (and a data file, if data exist) after creating or slitting a periodic boundary.

Creating Conformal Periodic Zones To create conformal periodic boundaries, you will use the make-periodic text command. grid −→ modify-zones −→make-periodic You will need to specify the two face zones that will comprise the periodic pair (you can enter their full names or just their IDs), and indicate whether they are rotationally or translationally periodic. The order in which you specify the periodic zone and its matching shadow zone is not significant.

/grid/modify-zones> mp Periodic zone [()] 1 Shadow zone [()] 4 Rotational periodic? (if no, translational) [yes] n Create periodic zones? [yes] yes computed translation deltas: -2.000000 -2.000000 all 10 faces matched for zones 1 and 4. zone 4 deleted Created periodic zones.

When you create a conformal periodic boundary, the solver will check to see if the faces on the selected zones “match” (i.e., whether or not the nodes on corresponding faces are coincident). The matching tolerance for a face is a fraction of the minimum edge length of the face. If the periodic boundary creation fails, you can change the matching tolerance using the matching-tolerance command, but it should not exceed 0.5 or you may match up the periodic zones incorrectly and corrupt the grid.

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grid −→ modify-zones −→matching-tolerance

Creating Non-Conformal Periodic Zones To create non-conformal periodic boundaries, you need to change the non-conformal periodic zones to interface zones. You will then need to set up the origin as well as the axes of the adjacent cell zone. For example, if interface-15 and interface-2 are the two non-conformal periodic zones, the non-conformal periodic boundaries are set up using the make-periodic command in the define/grid-interfaces text menu. define −→ grid-interfaces −→make-periodic For example:

/define/grid-interfaces> make-periodic Periodic zone [()] interface-15 Shadow zone [()] interface-2 Rotational periodic? (if no, translational) [yes] yes Rotation angle (deg) [0] 40.0 Create periodic zone? [yes] yes grid-interface name [] fan-periodic

5.7.6

Slitting Periodic Zones

If you wish to decouple the zones in a periodic pair, you can use the slit-periodic command. grid −→ modify-zones −→slit-periodic You will specify the periodic zone’s name or ID, and the solver will decouple the two zones in the pair (the periodic zone and its shadow) and change them to two symmetry zones: /grid/modify-zones> sp periodic zone [()] periodic-1 Separated periodic zone.


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5.7.7

Fusing Face Zones

The face fusing utility is a convenient feature that can be used to fuse boundaries (and merge duplicate nodes and faces) created by assembling multiple mesh regions. When the domain is divided into subdomains and the grid is generated separately for each subdomain, you will combine the subdomains into a single file before reading the grid into the solver. (See Section 5.3.10 for details.) This situation could arise if you generate each block of a multiblock grid separately and save it to a separate grid file. Another possible scenario is that you decided, during grid generation, to save the mesh for each part of a complicated geometry as a separate part file. (Note that the grid node locations need not be identical at the boundaries where two subdomains meet; see Section 5.4 for details.) The Fuse Face Zones panel (Figure 5.7.7) allows you to merge the duplicate nodes and delete these artificial internal boundaries. Grid −→Fuse...

Figure 5.7.7: The Fuse Face Zones Panel The boundaries on which the duplicate nodes lie are assigned zone ID numbers (just like any other boundary) when the grid files are combined, as described in Section 5.3.10. You need to keep track of the zone ID numbers when tmerge or TGrid reports its progress or, after the complete grid is read in, display all boundary grid zones and use the mouseprobe button to determine the zone names (see Section 27.3 for information about the mouse button functions).

Inputs for Fusing Face Zones The steps for fusing face zones are as follows: 1. Select the zones to be fused in the Zones list.

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2. Click on the Fuse button to fuse the selected zones. If all of the appropriate faces do not get fused using the default Tolerance, you should increase it and attempt to fuse the zones again. (This tolerance is the same as the matching tolerance discussed in Section 5.7.5.) The Tolerance should not exceed 0.5, or you may fuse the wrong nodes.

! Remember to save a new case file (and a data file, if data exist) after fusing faces. Fusing Zones on Branch Cuts Meshes imported from structured mesh generators or solvers (such as FLUENT 4) can often be O-type or C-type grids with a reentrant branch cut where coincident duplicate nodes lie on a periodic boundary. Since FLUENT uses an unstructured grid representation, there is no reason to retain this artificial internal boundary. (Of course, you can preserve these periodic boundaries and the solution algorithm will solve the problem with periodic boundary conditions.) To fuse this periodic zone with itself, you must first slit the periodic zone, as described in Section 5.7.6. This will create two symmetry zones that you can fuse using the procedure above. Note that if you need to fuse portions of a non-periodic zone with itself, you must use the text command fuse-face-zones. grid −→ modify-zones −→fuse-face-zones This command will prompt you for the name or ID of each zone to be fused. (You will enter the same zone twice.) To change the node tolerance, use the matching-tolerance command.

5.7.8

Slitting Face Zones

The face-zone slitting feature has two uses: • You can slit a single boundary zone of any double-sided type (i.e., any boundary zone that has cells on both sides of it) into two distinct zones. • You can slit a coupled wall zone into two distinct, uncoupled wall zones. When you slit a face zone, the solver will duplicate all faces and nodes, except those nodes that are located at the ends (2D) or edges (3D) of the zone. One set of nodes and faces will belong to one of the resulting boundary zones and the other set will belong to the other zone. The only ill effect of the shared nodes at each end is that you may see some inaccuracies at those points when you graphically display solution data with a slit


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boundary. (Note that if you adapt the boundary after slitting, you will not be able to fuse the boundaries back together again.) Normally, you will not need to manually slit a face zone. Two-sided walls are automatically slit, but remain coupled. (This coupling refers only to the grid; it is independent of thermal coupling.) The adaption process treats these coupled walls just like periodic boundaries; adapting on one wall causes the same adaption on the shadow. If you want to adapt one wall independent of its shadow, you should slit the coupled wall to obtain two distinct walls.

! You should not confuse “slitting” a face zone with “separating” a face zone. When you slit a face zone, additional faces and nodes are created and placed in a new zone. When you separate a face zone, a new zone will be created, but no new faces or nodes are created; the existing faces and nodes are simply redistributed among the zones.

Inputs for Slitting Face Zones If you wish to slit a face zone, you can use the slit-face-zone command. grid −→ modify-zones −→slit-face-zone You will specify the face zone’s name or ID, and the solver will replace the zone with two zones: /grid/modify-zones> slfz face zone id/name [] wall-4 zone 4 deleted face zone 4 created face zone 10 created

! Remember to save a new case file (and a data file, if data exist) after slitting faces. 5.7.9

Extruding Face Zones

The ability to extrude a boundary face zone allows you to extend the solution domain without having to exit the solver. A typical application of the extrusion capability is to extend the solution domain when recirculating flow is impinging on a flow outlet. The current extrusion capability creates prismatic or hexahedral layers based on the shape of the face and normal vectors computed by averaging the face normals to the face zone’s nodes. You can define the extrusion process by specifying a list of displacements (in SI units) or by specifying a total distance (in SI units) and parametric coordinates.

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Specifying Extrusion by Displacement Distances You can specify the extrusion by entering a list of displacement distances (in SI units) using the extrude-face-zone-delta command. grid −→ modify-zones −→extrude-face-zone-delta You will be prompted for the boundary face zone ID or name and a list of displacement distances.

Specifying Extrusion by Parametric Coordinates You can specify the extrusion by specifying a distance (in SI units) and parametric coordinates using the extrude-face-zone-para command grid −→ modify-zones −→extrude-face-zone-para You will be prompted for the boundary face zone ID or name, a total distance, and a list of parametric coordinates. The list of parametric coordinates should begin with 0.0 and end with 1.0. For example, the following list of parametric coordinates would create two equally spaced extrusion layers: 0.0, 0.5, 1.0.

5.7.10

Reordering the Domain and Zones

Reordering the domain can improve the computational performance of the solver by rearranging the nodes, faces, and cells in memory. The Grid/Reorder submenu contains commands for reordering the domain and zones, and also for printing the bandwidth of the present grid partitions. The domain can be reordered to increase memory access efficiency, and the zones can be reordered for user-interface convenience. The bandwidth provides insight into the distribution of the cells in the zones and in memory. To reorder the domain, select the Domain menu item. Grid −→ Reorder −→Domain To reorder the zones, select the Zones menu item. Grid −→ Reorder −→Zones Finally, you can print the bandwidth of the present grid partitions by selecting the Print Bandwidth menu item. This command prints the semi-bandwidth and maximum memory distance for each grid partition. Grid −→ Reorder −→Print Bandwidth

! Remember to save a new case file (and a data file, if data exist) after reordering.


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About Reordering The Reverse Cuthill-McKee algorithm [48] is used in the reordering process to construct a “level tree” initiated from a “seed cell” in the domain. First a cell (called the seed cell) is selected using the algorithm of Gibbs, Poole, and Stockmeyer [84]. Each cell is then assigned to a level based on its distance from the seed cell. These level assignments form the level tree. In general, the faces and cells are reordered so that neighboring cells are near each other in the zone and in memory. Since most of the computational loops are over faces, you would like the two cells in memory cache at the same time to reduce cache and/or disk swapping—i.e., you want the cells near each other in memory to reduce the cost of memory access. The present scheme reorders the faces and cells in the zone, and the nodes, faces, and cells in memory. You may also choose to reorder the zones. The zones are reordered by first sorting on zone type and then on zone ID. Zone reordering is performed simply for user-interface convenience. A typical output produced using the domain reordering is shown below: >> Reordering domain using Reverse Cuthill-McKee method: zones, cells, faces, done. Bandwidth reduction = 809/21 = 38.52 Done.

If you print the bandwidth, you will see a report similar to the following: Maximum cell distance = 21

The bandwidth is the maximum difference between neighboring cells in the zone—i.e., if you numbered each cell in the zone list sequentially and compared the differences between these indices.

5.7.11

Deleting, Deactivating, and Activating Zones

You can permanently delete a cell zone and all associated face zones, or temporarily deactivate zones from your FLUENT case. To permanently delete zones, select them in the Delete Cell Zones panel (Figure 5.7.8), and click Delete. Grid −→ Zone −→Delete... To deactivate zones, select them in the Deactivate Cell Zones panel (Figure 5.7.9), and click Deactivate. Grid −→ Zone −→Deactivate...

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Figure 5.7.8: The Delete Cell Zones Panel

Figure 5.7.9: The Deactivate Cell Zones Panel


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When you deactivate a zone using the Deactivate Cell Zones panel, FLUENT will remove the zone from the grid and from all relevant solver loops. You will then be able to reactivate the zones and recover the last data available for them using the Activate Cell Zones panel (Figure 5.7.10). Grid −→ Zone −→Activate...

Figure 5.7.10: The Activate Cell Zones Panel Note that the Activate Cell Zones panel will only be populated with zones that were previously deactivated.

! Zone deletion, deactivation, and activation are available only for serial cases, and are not available for parallel cases. Deactivation will separate all relevant interior face zones (i.e., fan, interior, porus-jump, or radiator) into wall and wall-shadow pairs. After reactivation, you need to make sure that the boundary conditions for the wall and wall-shadow pairs are restored correctly to what you assigned before deactivating the zones. Note also that if you plan to reactivate them at a later time, you need to make sure that the face zones that are separated during deactivation are not modified. Adaption, however, is supported.

5-54


Chapter 6.

Boundary Conditions

This chapter describes the boundary condition options available in FLUENT. Details regarding the boundary condition inputs you must supply and the internal treatment at boundaries are provided. The information in this chapter is divided into the following sections: • Section 6.1: Overview of Defining Boundary Conditions • Section 6.2: Flow Inlets and Exits • Section 6.3: Pressure Inlet Boundary Conditions • Section 6.4: Velocity Inlet Boundary Conditions • Section 6.5: Mass Flow Inlet Boundary Conditions • Section 6.6: Inlet Vent Boundary Conditions • Section 6.7: Intake Fan Boundary Conditions • Section 6.8: Pressure Outlet Boundary Conditions • Section 6.9: Pressure Far-Field Boundary Conditions • Section 6.10: Outflow Boundary Conditions • Section 6.11: Outlet Vent Boundary Conditions • Section 6.12: Exhaust Fan Boundary Conditions • Section 6.13: Wall Boundary Conditions • Section 6.14: Symmetry Boundary Conditions • Section 6.15: Periodic Boundary Conditions • Section 6.16: Axis Boundary Conditions • Section 6.17: Fluid Conditions • Section 6.18: Solid Conditions • Section 6.19: Porous Media Conditions


6-1

Boundary Conditions

• Section 6.20: Fan Boundary Conditions • Section 6.21: Radiator Boundary Conditions • Section 6.22: Porous Jump Boundary Conditions • Section 6.23: Non-Reflecting Boundary Conditions • Section 6.24: User-Defined Fan Model • Section 6.25: Heat Exchanger Models • Section 6.26: Boundary Profiles • Section 6.27: Fixing the Values of Variables • Section 6.28: Defining Mass, Momentum, Heat, and Other Sources • Section 6.29: Coupling Boundary Conditions with GT-Power • Section 6.30: Coupling Boundary Conditions with WAVE

6.1

Overview of Defining Boundary Conditions

Boundary conditions specify the flow and thermal variables on the boundaries of your physical model. They are, therefore, a critical component of your FLUENT simulations and it is important that they are specified appropriately.

6.1.1

Available Boundary Types

The boundary types available in FLUENT are classified as follows: • Flow inlet and exit boundaries: pressure inlet, velocity inlet, mass flow inlet, inlet vent, intake fan, pressure outlet, pressure far-field, outflow, outlet vent, exhaust fan • Wall, repeating, and pole boundaries: wall, symmetry, periodic, axis • Internal cell zones: fluid, solid (porous is a type of fluid zone) • Internal face boundaries: fan, radiator, porous jump, wall, interior (The internal face boundary conditions are defined on cell faces, which means that they do not have a finite thickness and they provide a means of introducing a step change in flow properties. These boundary conditions are used to implement physical models representing fans, thin porous membranes, and radiators. The “interior” type of internal face zone does not require any input from you.)

6-2


6.1 Overview of Defining Boundary Conditions

In this chapter, the boundary conditions listed above will be described, and an explanation of how to set them and when they are most appropriately used will be provided. Note that while periodic boundaries are described in Section 6.15, additional information about modeling fully-developed periodic flows is provided in Section 8.3.

6.1.2

The Boundary Conditions Panel

The Boundary Conditions panel (Figure 6.1.1) allows you to change the boundary zone type for a given zone and open other panels to set the boundary condition parameters for each zone. Define −→Boundary Conditions...

Figure 6.1.1: The Boundary Conditions Panel Sections 6.1.3–6.1.6 explain how to perform these operations with the Boundary Conditions panel, and how to use the mouse and the graphics display in conjunction with the panel.

6.1.3

Changing Boundary Zone Types

Before you set any boundary conditions, you should check the zone types of all boundary zones and change any if necessary. For example, if your grid includes a pressure inlet, but you want to use a velocity inlet instead, you will need to change the pressure-inlet zone to a velocity-inlet zone. The steps for changing a zone type are as follows: 1. In the Boundary Conditions panel, select the zone to be changed in the Zone list.


6-3

Boundary Conditions

2. Choose the correct zone type in the Type list. 3. Confirm the change when prompted by the Question dialog box.

Once you have confirmed the change, the zone type will be changed, the name will change automatically (if the original name was the default name for that zone—see Section 6.1.7), and the panel for setting conditions for the zone will open automatically.

! Note that you cannot use this method to change zone types to or from the periodic type, since additional restrictions exist for this boundary type. Section 5.7.5 explains how to create and uncouple periodic zones.

! If you are using one of the general multiphase models (VOF, mixture, or Eulerian), the procedure for changing types is slightly different. See Section 22.6.16 for details.

Categories of Zone Types You should be aware that you can only change boundary types within each category listed in Table 6.1.1. (Note that a double-sided face zone is a zone that separates two different cell zones or regions.) Table 6.1.1: Zone Types Listed by Category Category Zone Types Faces axis, outflow, mass flow inlet, pressure farfield, pressure inlet, pressure outlet, symmetry, velocity inlet, wall, inlet vent, intake fan, outlet vent, exhaust fan Double-Sided Faces fan, interior, porous jump, radiator, wall Periodic periodic Cells fluid, solid (porous is a type of fluid cell)

6.1.4

Setting Boundary Conditions

In FLUENT, boundary conditions are associated with zones, not with individual faces or cells. If you want to combine two or more zones that will have the same boundary conditions, see Section 5.7.3 for information about merging zones.

6-4



To set boundary conditions for a particular zone, perform one of the following sequences: 1. Choose the zone in the Boundary Conditions panel’s Zone list. 2. Click on the Set... button. or 1. Choose the zone in the Zone list. 2. Click on the selected zone type in the Type list. or 1. Double-click on the zone in the Zone list. The panel for the selected boundary zone will open, and you can specify the appropriate boundary conditions.

! If you are using one of the general multiphase models (VOF, mixture, or Eulerian), the procedure for setting boundary conditions is slightly different from that described above. See Section 22.6.16 for details.

6.1.5

Copying Boundary Conditions

You can copy boundary conditions from one zone to other zones of the same type. If, for example, you have several wall zones in your model and they all have the same boundary conditions, you can set the conditions for one wall, and then simply copy them to the others. The procedure for copying boundary conditions is as follows: 1. In the Boundary Conditions panel, click the Copy... button. This will open the Copy BCs panel (Figure 6.1.2). 2. In the From Zone list, select the zone that has the conditions you want to copy. 3. In the To Zones list, select the zone or zones to which you want to copy the conditions. 4. Click Copy. FLUENT will set all of the boundary conditions for the zones selected in the To Zones list to be the same as the conditions for the zone selected in the From Zone list. (You cannot copy a subset of the conditions, such as only the thermal conditions.)


6-5

Boundary Conditions

Figure 6.1.2: The Copy BCs Panel

Note that you cannot copy conditions from external walls to internal (i.e., two-sided) walls, or vice versa, if the energy equation is being solved, since the thermal conditions for external and internal walls are different.

! If you are using one of the general multiphase models (VOF, mixture, or Eulerian), the procedure for copying boundary conditions is slightly different. See Section 22.6.16 for details.

6.1.6

Selecting Boundary Zones in the Graphics Display

Whenever you need to select a zone in the Boundary Conditions panel, you can use the mouse in the graphics window to choose the appropriate zone. This feature is particularly useful if you are setting up a problem for the first time, or if you have two or more zones of the same type and you want to determine the zone IDs (i.e., figure out which zone is which). To use this feature, do the following: 1. Display the grid using the Grid Display panel. 2. Use the mouse probe button (the right button, by default—see Section 27.3 to modify the mouse button functions) to click on a boundary zone in the graphics window. The zone you select in the graphics display will automatically be selected in the Zone list in the Boundary Conditions panel, and its name and ID will be printed in the console window.

6.1.7

Changing Boundary Zone Names

The default name for a zone is its type plus an ID number (e.g., pressure-inlet-7). In some cases, you may want to assign more descriptive names to the boundary zones. If you

6-6



have two pressure-inlet zones, for example, you might want to rename them small-inlet and large-inlet. (Changing the name of a zone will not change its type. Instructions for changing a zone’s type are provided in Section 6.1.3.) To rename a zone, follow these steps: 1. Select the zone to be renamed in the Zones list in the Boundary Conditions panel. 2. Click Set... to open the panel for the selected zone. 3. Enter a new name under Zone Name. 4. Click the OK button. Note that if you specify a new name for a zone and then change its type, the name you specified will be retained; the automatic name change that accompanies a change in type occurs only if the name of the zone is its type plus its ID.

6.1.8

Defining Non-Uniform Boundary Conditions

Most conditions at each type of boundary zone can be defined as profile functions instead of constant values. You can use a profile contained in an externally generated boundary profile file, or a function that you create using a user-defined function (UDF). Boundary condition profiles are described in Section 6.26, and user-defined functions are described in the separate UDF Manual.

6.1.9

Defining Transient Boundary Conditions

There are two ways you can specify transient boundary conditions: • transient profile with a format similar to the standard boundary profiles described in Section 6.26 • transient profile in a tabular format

! For both methods, the boundary condition will vary only in time; it must be spatially uniform.

Standard Transient Profiles The format of the standard transient profile file (based on the profiles described in Section 6.26) is


6-7

Boundary Conditions

((profile-name transient n periodic?) (field_name-1 a1 a2 a3 .... an) (field_name-2 b1 b2 b3 .... bn) . . . . (field_name-r r1 r2 r3 .... rn)) One of the field names should be used for the time field, and the time field section must be in ascending order. The periodic? entry indicates whether or not the profile is time-periodic. Set it to 1 for a time-periodic profile, or 0 if the profile is not time-periodic. An example is shown below: ((sampleprofile transient 3 1) (time 1 2 3 ) (u 10 20 30 ) )

! All quantities, including coordinate values, must be specified in SI units because FLUENT does not perform unit conversion when reading profile files. Also, boundary profile names must have all lowercase letters (e.g., name). Uppercase letters in boundary profile names are not acceptable. You can read this file into FLUENT using the Boundary Profiles panel or the File/Read/Profile... menu item. Define −→Profiles... File −→ Read −→Profile... See Section 6.26.3 for details.

Tabular Transient Profiles The format of the tabular transient profile file is

6-8



profile-name n_field n_data periodic? field-name-1 field-name-2 field-name-3 .... field-name-n_field v-1-1 v-2-1 ... ... ... ... v-n_field-1 v-1-2 v-2-2 ... ... ... ... v-n_field-2 . . . . . v-1-n_data v-2-n_data ... ... ... ... v-n_field-n_data One of the field-names should be used for the time field, and the time field section must be in ascending order. The periodic? entry indicates whether or not the profile is time-periodic. Set it to 1 for a time-periodic profile, or 0 if the profile is not time-periodic. An example is shown below: sampletabprofile 2 3 1 time u 1 10 2 20 3 30 This file defines the same transient profile as the standard profile example above.

! All quantities, including coordinate values, must be specified in SI units because FLUENT does not perform unit conversion when reading profile files. Also, boundary profile names must have all lowercase letters (e.g., name). Uppercase letters in boundary profile names are not acceptable. You can read this file into FLUENT using the read-transient-table text command. file −→read-transient-table

6.1.10

Saving and Reusing Boundary Conditions

You can save boundary conditions to a file so that you can use them to specify the same conditions for a different case, as described in Section 3.10.


6-9

Boundary Conditions

6.2

Flow Inlets and Exits

FLUENT has a wide range of boundary conditions that permit flow to enter and exit the solution domain. To help you select the most appropriate boundary condition for your application, this section includes descriptions of how each type of condition is used, and what information is needed for each one. Recommendations for determining inlet values of the turbulence parameters are also provided.

6.2.1

Using Flow Boundary Conditions

This section provides an overview of flow boundaries in FLUENT and how to use them. FLUENT provides 10 types of boundary zone types for the specification of flow inlets and exits: velocity inlet, pressure inlet, mass flow inlet, pressure outlet, pressure far-field, outflow, inlet vent, intake fan, outlet vent, and exhaust fan. The inlet and exit boundary condition options in FLUENT are as follows: • Velocity inlet boundary conditions are used to define the velocity and scalar properties of the flow at inlet boundaries. • Pressure inlet boundary conditions are used to define the total pressure and other scalar quantities at flow inlets. • Mass flow inlet boundary conditions are used in compressible flows to prescribe a mass flow rate at an inlet. It is not necessary to use mass flow inlets in incompressible flows because when density is constant, velocity inlet boundary conditions will fix the mass flow. • Pressure outlet boundary conditions are used to define the static pressure at flow outlets (and also other scalar variables, in case of backflow). The use of a pressure outlet boundary condition instead of an outflow condition often results in a better rate of convergence when backflow occurs during iteration. • Pressure far-field boundary conditions are used to model a free-stream compressible flow at infinity, with free-stream Mach number and static conditions specified. This boundary type is available only for compressible flows. • Outflow boundary conditions are used to model flow exits where the details of the flow velocity and pressure are not known prior to solution of the flow problem. They are appropriate where the exit flow is close to a fully developed condition, as the outflow boundary condition assumes a zero normal gradient for all flow variables except pressure. They are not appropriate for compressible flow calculations. • Inlet vent boundary conditions are used to model an inlet vent with a specified loss coefficient, flow direction, and ambient (inlet) total pressure and temperature.

6-10


6.2 Flow Inlets and Exits

• Intake fan boundary conditions are used to model an external intake fan with a specified pressure jump, flow direction, and ambient (intake) total pressure and temperature. • Outlet vent boundary conditions are used to model an outlet vent with a specified loss coefficient and ambient (discharge) static pressure and temperature. • Exhaust fan boundary conditions are used to model an external exhaust fan with a specified pressure jump and ambient (discharge) static pressure.

6.2.2

Determining Turbulence Parameters

When the flow enters the domain at an inlet, outlet, or far-field boundary, FLUENT requires specification of transported turbulence quantities. This section describes which quantities are needed for specific turbulence models and how they must be specified. It also provides guidelines for the most appropriate way of determining the inflow boundary values.

Specification of Turbulence Quantities Using Profiles If it is important to accurately represent a boundary layer or fully-developed turbulent flow at the inlet, you should ideally set the turbulence quantities by creating a boundary profile file (see Section 6.26) from experimental data or empirical formulas. If you have an analytical description of the profile, rather than data points, you can either use this analytical description to create a boundary profile file, or create a user-defined function to provide the inlet boundary information. (See the separate UDF Manual for information on user-defined functions.) Once you have created the profile function, you can use it as described below: • Spalart-Allmaras model: Choose Turbulent Viscosity or Turbulent Viscosity Ratio in the Turbulence Specification Method drop-down list and select the appropriate profile name in the drop-down list next to Turbulent Viscosity or Turbulent Viscosity Ratio. FLUENT computes the boundary value for the modified turbulent viscosity, ν˜, by combining µt /µ with the appropriate values of density and molecular viscosity. • k- models: Choose K and Epsilon in the Turbulence Specification Method drop-down list and select the appropriate profile names in the drop-down lists next to Turb. Kinetic Energy and Turb. Dissipation Rate. • k-ω models: Choose K and Omega in the Turbulence Specification Method drop-down list and select the appropriate profile names in the drop-down lists next to Turb. Kinetic Energy and Spec. Dissipation Rate.


6-11

Boundary Conditions

• Reynolds stress model: Choose K and Epsilon in the Turbulence Specification Method drop-down list and select the appropriate profile names in the drop-down lists next to Turb. Kinetic Energy and Turb. Dissipation Rate. Choose Reynolds-Stress Components in the Reynolds-Stress Specification Method drop-down list and select the appropriate profile name in the drop-down list next to each of the individual Reynolds-stress components.

Uniform Specification of Turbulence Quantities In some situations, it is appropriate to specify a uniform value of the turbulence quantity at the boundary where inflow occurs. Examples are fluid entering a duct, far-field boundaries, or even fully-developed duct flows where accurate profiles of turbulence quantities are unknown. In most turbulent flows, higher levels of turbulence are generated within shear layers than enter the domain at flow boundaries, making the result of the calculation relatively insensitive to the inflow boundary values. Nevertheless, caution must be used to ensure that boundary values are not so unphysical as to contaminate your solution or impede convergence. This is particularly true of external flows where unphysically large values of effective viscosity in the free stream can “swamp” the boundary layers. You can use the turbulence specification methods described above to enter uniform constant values instead of profiles. Alternatively, you can specify the turbulence quantities in terms of more convenient quantities such as turbulence intensity, turbulent viscosity ratio, hydraulic diameter, and turbulence length scale. These quantities are discussed further in the following sections. Turbulence Intensity The turbulence intensity, I, is defined as the ratio of the root-mean-square of the velocity fluctuations, u0 , to the mean flow velocity, uavg . A turbulence intensity of 1% or less is generally considered low and turbulence intensities greater than 10% are considered high. Ideally, you will have a good estimate of the turbulence intensity at the inlet boundary from external, measured data. For example, if you are simulating a wind-tunnel experiment, the turbulence intensity in the free stream is usually available from the tunnel characteristics. In modern low-turbulence wind tunnels, the free-stream turbulence intensity may be as low as 0.05%. For internal flows, the turbulence intensity at the inlets is totally dependent on the upstream history of the flow. If the flow upstream is under-developed and undisturbed, you can use a low turbulence intensity. If the flow is fully developed, the turbulence intensity may be as high as a few percent. The turbulence intensity at the core of a fully-developed duct flow can be estimated from the following formula derived from an empirical correlation for pipe flows:

6-12



I≡

u0 = 0.16(ReDH )−1/8 uavg

(6.2-1)

At a Reynolds number of 50,000, for example, the turbulence intensity will be 4%, according to this formula. Turbulence Length Scale and Hydraulic Diameter The turbulence length scale, `, is a physical quantity related to the size of the large eddies that contain the energy in turbulent flows. In fully-developed duct flows, ` is restricted by the size of the duct, since the turbulent eddies cannot be larger than the duct. An approximate relationship between ` and the physical size of the duct is ` = 0.07L

(6.2-2)

where L is the relevant dimension of the duct. The factor of 0.07 is based on the maximum value of the mixing length in fully-developed turbulent pipe flow, where L is the diameter of the pipe. In a channel of non-circular cross-section, you can base L on the hydraulic diameter. If the turbulence derives its characteristic length from an obstacle in the flow, such as a perforated plate, it is more appropriate to base the turbulence length scale on the characteristic length of the obstacle rather than on the duct size. It should be noted that the relationship of Equation 6.2-2, which relates a physical dimension (L) to the turbulence length scale (`), is not necessarily applicable to all situations. For most cases, however, it is a suitable approximation. Guidelines for choosing the characteristic length L or the turbulence length scale ` for selected flow types are listed below: • For fully-developed internal flows, choose the Intensity and Hydraulic Diameter specification method and specify the hydraulic diameter L = DH in the Hydraulic Diameter field. • For flows downstream of turning vanes, perforated plates, etc., choose the Intensity and Hydraulic Diameter method and specify the characteristic length of the flow opening for L in the Hydraulic Diameter field. • For wall-bounded flows in which the inlets involve a turbulent boundary layer, choose the Intensity and Length Scale method and use the boundary-layer thickness, δ99 , to compute the turbulence length scale, `, from ` = 0.4δ99 . Enter this value for ` in the Turbulence Length Scale field.


6-13

Boundary Conditions

Turbulent Viscosity Ratio The turbulent viscosity ratio, µt /µ, is directly proportional to the turbulent Reynolds number (Ret ≡ k 2 /(ν)). Ret is large (on the order of 100 to 1000) in high-Reynoldsnumber boundary layers, shear layers, and fully-developed duct flows. However, at the free-stream boundaries of most external flows, µt /µ is fairly small. Typically, the turbulence parameters are set so that 1 < µt /µ < 10. To specify quantities in terms of the turbulent viscosity ratio, you can choose Turbulent Viscosity Ratio (for the Spalart-Allmaras model) or Intensity and Viscosity Ratio (for the k- models, the k-ω models, or the RSM).

Relationships for Deriving Turbulence Quantities To obtain the values of transported turbulence quantities from more convenient quantities such as I, L, or µt /µ, you must typically resort to an empirical relation. Several useful relations, most of which are used within FLUENT, are presented below. Estimating Modified Turbulent Viscosity from Turbulence Intensity and Length Scale To obtain the modified turbulent viscosity, ν˜, for the Spalart-Allmaras model from the turbulence intensity, I, and length scale, `, the following equation can be used:

ν˜ =

s

3 uavg I ` 2

(6.2-3)

This formula is used in FLUENT if you select the Intensity and Hydraulic Diameter specification method with the Spalart-Allmaras model. ` is obtained from Equation 6.2-2. Estimating Turbulent Kinetic Energy from Turbulence Intensity The relationship between the turbulent kinetic energy, k, and turbulence intensity, I, is 3 k = (uavg I)2 2

(6.2-4)

where uavg is the mean flow velocity. This relationship is used in FLUENT whenever the Intensity and Hydraulic Diameter, Intensity and Length Scale, or Intensity and Viscosity Ratio method is used instead of specifying explicit values for k and .

6-14



Estimating Turbulent Dissipation Rate from a Length Scale If you know the turbulence length scale, `, you can determine from the relationship = Cµ3/4

k 3/2 `

(6.2-5)

where Cµ is an empirical constant specified in the turbulence model (approximately 0.09). The determination of ` was discussed previously. This relationship is used in FLUENT whenever the Intensity and Hydraulic Diameter or Intensity and Length Scale method is used instead of specifying explicit values for k and . Estimating Turbulent Dissipation Rate from Turbulent Viscosity Ratio The value of can be obtained from the turbulent viscosity ratio µt /µ and k using the following relationship: k2 = ρCµ µ

µt µ

!−1

(6.2-6)

where Cµ is an empirical constant specified in the turbulence model (approximately 0.09). This relationship is used in FLUENT whenever the Intensity and Viscosity Ratio method is used instead of specifying explicit values for k and . Estimating Turbulent Dissipation Rate for Decaying Turbulence If you are simulating a wind-tunnel situation in which the model is mounted in the test section downstream of a grid and/or wire mesh screens, you can choose a value of such that ≈

∆kU∞ L∞

(6.2-7)

where ∆k is the approximate decay of k you wish to have across the flow domain (say, 10% of the inlet value of k), U∞ is the free-stream velocity, and L∞ is the streamwise length of the flow domain. Equation 6.2-7 is a linear approximation to the power-law decay observed in high-Reynolds-number isotropic turbulence. Its basis is the exact equation for k in decaying turbulence, U ∂k/∂x = −. If you use this method to estimate , you should also check the resulting turbulent viscosity ratio µt /µ to make sure that it is not too large, using Equation 6.2-6.


6-15

Boundary Conditions

Although this method is not used internally by FLUENT, you can use it to derive a constant free-stream value of that you can then specify directly by choosing K and Epsilon in the Turbulence Specification Method drop-down list. In this situation, you will typically determine k from I using Equation 6.2-4. Estimating Specific Dissipation Rate from a Length Scale If you know the turbulence length scale, `, you can determine ω from the relationship

ω=

k 1/2

(6.2-8)

1/4

Cµ `

where Cµ is an empirical constant specified in the turbulence model (approximately 0.09). The determination of ` was discussed previously. This relationship is used in FLUENT whenever the Intensity and Hydraulic Diameter or Intensity and Length Scale method is used instead of specifying explicit values for k and ω. Estimating Specific Dissipation Rate from Turbulent Viscosity Ratio The value of ω can be obtained from the turbulent viscosity ratio µt /µ and k using the following relationship: k ω=ρ µ

µt µ

!−1

(6.2-9)

This relationship is used in FLUENT whenever the Intensity and Viscosity Ratio method is used instead of specifying explicit values for k and ω. Estimating Reynolds Stress Components from Turbulent Kinetic Energy When the RSM is used, if you do not specify the values of the Reynolds stresses explicitly at the inlet using the Reynolds-Stress Components option in the Reynolds-Stress Specification Method drop-down list, they are approximately determined from the specified values of k. The turbulence is assumed to be isotropic such that u0i u0j = 0

(6.2-10)

2 u0α u0α = k 3

(6.2-11)

and

6-16


6.3 Pressure Inlet Boundary Conditions

(no summation over the index α). FLUENT will use this method if you select K or Turbulence Intensity in the Reynolds-Stress Specification Method drop-down list.

Specifying Inlet Turbulence for LES The turbulence intensity value specified at a velocity inlet for LES, as described in Section 10.10.2, is used to randomly perturb the instantaneous velocity field at the inlet. It does not specify a modeled turbulence quantity. Instead, the stochastic components of the flow at the inlet boundary are accounted for by superposing random perturbations on individual velocity components as described in Section 10.7.3.

6.3

Pressure Inlet Boundary Conditions

Pressure inlet boundary conditions are used to define the fluid pressure at flow inlets, along with all other scalar properties of the flow. They are suitable for both incompressible and compressible flow calculations. Pressure inlet boundary conditions can be used when the inlet pressure is known but the flow rate and/or velocity is not known. This situation may arise in many practical situations, including buoyancy-driven flows. Pressure inlet boundary conditions can also be used to define a “free” boundary in an external or unconfined flow. You can find the following information about pressure inlet boundary conditions in this section: • Section 6.3.1: Inputs at Pressure Inlet Boundaries • Section 6.3.2: Default Settings at Pressure Inlet Boundaries • Section 6.3.3: Calculation Procedure at Pressure Inlet Boundaries For an overview of flow boundaries, see Section 6.2.

6.3.1

Inputs at Pressure Inlet Boundaries

Summary You will enter the following information for a pressure inlet boundary: • Total (stagnation) pressure • Total (stagnation) temperature • Flow direction


6-17

Boundary Conditions

• Static pressure • Turbulence parameters (for turbulent calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) • Progress variable (for premixed or partially premixed combustion calculations) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for general multiphase calculations) All values are entered in the Pressure Inlet panel (Figure 6.3.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.3.1: The Pressure Inlet Panel

6-18



Pressure Inputs and Hydrostatic Head The pressure field (p0s ) and your pressure inputs (p0s or p00 ) include the hydrostatic head, ρ0 gx. That is, the pressure in FLUENT is defined as p0s = ps − ρ0 gx

(6.3-1)

∂p0s ∂ps = − ρ0 g ∂x ∂x

(6.3-2)

or

This definition allows the hydrostatic head to be taken into the body force term, (ρ−ρ0 )g, and excluded from the pressure calculation when the density is uniform. Thus your inputs of pressure should not include hydrostatic pressure differences, and reports of pressure (p0s ) will not show any influence of the hydrostatic pressure. See Section 11.5 for information about buoyancy-driven (natural-convection) flows.

Defining Total Pressure and Temperature Enter the value for total pressure in the Gauge Total Pressure field in the Pressure Inlet panel. Total temperature is set in the Total Temperature field. Remember that the total pressure value is the gauge pressure with respect to the operating pressure defined in the Operating Conditions panel. Total pressure for an incompressible fluid is defined as 1 p0 = ps + ρ|~v |2 2

(6.3-3)

and for a compressible fluid as

p0 = ps where

p0 ps M γ

γ−1 2 1+ M 2

γ/(γ−1)

(6.3-4)

= total pressure = static pressure = Mach number = ratio of specific heats (cp /cv )

If you are modeling axisymmetric swirl, ~v in Equation 6.3-3 will include the swirl component. If the adjacent cell zone is moving (i.e., if you are using a rotating reference frame, multiple reference frames, a mixing plane, or sliding meshes) and you are using the


6-19

Boundary Conditions

segregated solver, the velocity in Equation 6.3-3 (or the Mach number in Equation 6.3-4) will be absolute or relative to the grid velocity, depending on whether or not the Absolute velocity formulation is enabled in the Solver panel. For the coupled solvers, the velocity in Equation 6.3-3 (or the Mach number in Equation 6.3-4) is always in the absolute frame.

Defining the Flow Direction You can define the flow direction at a pressure inlet explicitly, or you can define the flow to be normal to the boundary. If you choose to specify the direction vector, you can set either the (Cartesian) x, y, and z components, or the (cylindrical) radial, tangential, and axial components. For moving zone problems calculated using the segregated solver, the flow direction will be absolute or relative to the grid velocity, depending on whether or not the Absolute velocity formulation is enabled in the Solver panel. For the coupled solvers, the flow direction will always be in the absolute frame. The procedure for defining the flow direction is as follows, referring to Figure 6.3.1: 1. Choose which method you will use to specify the flow direction by selecting Direction Vector or Normal to Boundary in the Direction Specification Method drop-down list. 2. If you selected Normal to Boundary in step 1 and you are modeling axisymmetric swirl, enter the appropriate value for the Tangential-Component of Flow Direction. If you chose Normal to Boundary and your geometry is 3D or 2D without axisymmetric swirl, there are no additional inputs for flow direction. 3. If you chose in step 1 to specify the direction vector, and your geometry is 3D, you will next choose the coordinate system in which you will define the vector components. Choose Cartesian (X, Y, Z), Cylindrical (Radial, Tangential, Axial), or Local Cylindrical (Radial, Tangential, Axial) in the Coordinate System drop-down list. • The Cartesian coordinate system is based on the Cartesian coordinate system used by the geometry. • The Cylindrical coordinate system uses the axial, radial, and tangential components based on the following coordinate systems: – For problems involving a single cell zone, the coordinate system is defined by the rotation axis and origin specified in the Fluid panel. – For problems involving multiple zones (e.g., multiple reference frames or sliding meshes), the coordinate system is defined by the rotation axis specified in the Fluid (or Solid) panel for the fluid (or solid) zone that is adjacent to the inlet.

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For all of the above definitions of the cylindrical coordinate system, positive radial velocities point radially out from the rotation axis, positive axial velocities are in the direction of the rotation axis vector, and positive tangential velocities are based on the right-hand rule using the positive rotation axis (see Figure 6.3.2). axial tangential

radial tangential

radial rotation axis

rotation axis origin

radial

rotation axis

axial tangential (swirl)

Figure 6.3.2: Cylindrical Velocity Components in 3D, 2D, and Axisymmetric Domains • The Local Cylindrical coordinate system allows you to define a coordinate system specifically for the inlet. When you use the local cylindrical option, you will define the coordinate system right here in the Pressure Inlet panel. The local cylindrical coordinate system is useful if you have several inlets with different rotation axes. 4. If you chose in step 1 to specify the direction vector, define the vector components as follows: • If your geometry is 2D non-axisymmetric, or you chose in step 3 to input Cartesian vector components, enter the appropriate values for X, Y, and (in 3D) Z-Component of Flow Direction. • If your geometry is 2D axisymmetric, or you chose in step 3 to input Cylindrical components, enter the appropriate values for Axial, Radial, and (if you are modeling axisymmetric swirl or using cylindrical coordinates) TangentialComponent of Flow Direction. • If you are using Local Cylindrical coordinates, enter the appropriate values for Axial, Radial, and Tangential-Component of Flow Direction, and then specify the X, Y, and Z-Component of Axis Direction and the X, Y, and Z-Coordinate of Axis Origin. Figure 6.3.2 shows the vector components for these different coordinate systems.


6-21

Boundary Conditions

Defining Static Pressure The static pressure (termed the Supersonic/Initial Gauge Pressure) must be specified if the inlet flow is supersonic or if you plan to initialize the solution based on the pressure inlet boundary conditions. Solution initialization is discussed in Section 24.13. Remember that the static pressure value you enter is relative to the operating pressure set in the Operating Conditions panel. Note the comments in Section 6.3.1 regarding hydrostatic pressure. The Supersonic/Initial Gauge Pressure is ignored by FLUENT whenever the flow is subsonic, in which case it is calculated from the specified stagnation quantities. If you choose to initialize the solution based on the pressure-inlet conditions, the Supersonic/Initial Gauge Pressure will be used in conjunction with the specified stagnation pressure to compute initial values according to the isentropic relations (for compressible flow) or Bernoulli’s equation (for incompressible flow). Therefore, for a sub-sonic inlet it should generally be set based on a reasonable estimate of the inlet Mach number (for compressible flow) or inlet velocity (for incompressible flow).

Defining Turbulence Parameters For turbulent calculations, there are several ways in which you can define the turbulence parameters. Instructions for deciding which method to use and determining appropriate values for these inputs are provided in Section 6.2.2. Turbulence modeling in general is described in Chapter 10.

Defining Radiation Parameters If you are using the P-1 radiation model, the DTRM, the DO model, or the surface-tosurface model, you will set the Internal Emissivity and (optionally) Black Body Temperature. See Section 11.3.16 for details. (The Rosseland radiation model does not require any boundary condition inputs.)

Defining Species Mass Fractions If you are modeling species transport, you will set the species mass fractions under Species Mass Fractions. For details, see Section 13.1.5.

Defining Non-Premixed Combustion Parameters If you are using the non-premixed or partially premixed combustion model, you will set the Mean Mixture Fraction and Mixture Fraction Variance (and the Secondary Mean Mixture Fraction and Secondary Mixture Fraction Variance, if you are using two mixture fractions), as described in Section 14.3.3.

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Defining Premixed Combustion Boundary Conditions If you are using the premixed or partially premixed combustion model, you will set the Progress Variable, as described in Section 15.3.5.

Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the pressure inlet. See Section 21.10 for details.

Defining Multiphase Boundary Conditions If you are using the VOF, mixture, or Eulerian model for multiphase flow, you will need to specify volume fractions for secondary phases and (for some models) additional parameters. See Section 22.6.16 for details.

6.3.2

Default Settings at Pressure Inlet Boundaries

Default settings (in SI) for pressure inlet boundary conditions are as follows: Gauge Total Pressure Supersonic/Initial Gauge Pressure Total Temperature X-Component of Flow Direction Y-Component of Flow Direction Z-Component of Flow Direction Turb. Kinetic Energy Turb. Dissipation Rate

6.3.3

0 0 300 1 0 0 1 1

Calculation Procedure at Pressure Inlet Boundaries

The treatment of pressure inlet boundary conditions by FLUENT can be described as a loss-free transition from stagnation conditions to the inlet conditions. For incompressible flows, this is accomplished by application of the Bernoulli equation at the inlet boundary. In compressible flows, the equivalent isentropic flow relations for an ideal gas are used.

Incompressible Flow Calculations at Pressure Inlet Boundaries When flow enters through a pressure inlet boundary, FLUENT uses the boundary condition pressure you input as the total pressure of the fluid at the inlet plane, p0 . In incompressible flow, the inlet total pressure and the static pressure, ps , are related to the inlet velocity via Bernoulli’s equation:


6-23

Boundary Conditions

1 p0 = ps + ρv 2 2

(6.3-5)

With the resulting velocity magnitude and the flow direction vector you assigned at the inlet, the velocity components can be computed. The inlet mass flow rate and fluxes of momentum, energy, and species can then be computed as outlined in Section 6.4.3. For incompressible flows, density at the inlet plane is either constant or calculated as a function of temperature and/or species mass fractions, where the mass fractions are the values you entered as an inlet condition. If flow exits through a pressure inlet, the total pressure specified is used as the static pressure. For incompressible flows, total temperature is equal to static temperature.

Compressible Flow Calculations at Pressure Inlet Boundaries In compressible flows, isentropic relations for an ideal gas are applied to relate total pressure, static pressure, and velocity at a pressure inlet boundary. Your input of total pressure, p00 , at the inlet and the static pressure, p0s , in the adjacent fluid cell are thus related as p00 + pop γ−1 2 = 1+ M 0 ps + pop 2

γ/(γ−1)

(6.3-6)

where M≡

v v =√ c γRTs

(6.3-7)

c = the speed of sound, and γ = cp /cv . Note that the operating pressure, pop , appears in Equation 6.3-6 because your boundary condition inputs are in terms of pressure relative to the operating pressure. Given p00 and p0s , Equations 6.3-6 and 6.3-7 are used to compute the velocity magnitude of the fluid at the inlet plane. Individual velocity components at the inlet are then derived using the direction vector components. For compressible flow, the density at the inlet plane is defined by the ideal gas law in the form p0s + pop ρ= RTs

(6.3-8)

The specific gas constant, R, is computed from the species mass fractions, Yi , that you defined as boundary conditions at the pressure inlet boundary. The static temperature at the inlet, Ts , is computed from your input of total temperature, T0 , as

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6.4 Velocity Inlet Boundary Conditions

T0 γ−1 2 =1+ M Ts 2

6.4

(6.3-9)

Velocity Inlet Boundary Conditions

Velocity inlet boundary conditions are used to define the flow velocity, along with all relevant scalar properties of the flow, at flow inlets. The total (or stagnation) properties of the flow are not fixed, so they will rise to whatever value is necessary to provide the prescribed velocity distribution.

! This boundary condition is intended for incompressible flows, and its use in compressible flows will lead to a nonphysical result because it allows stagnation conditions to float to any level. You should also be careful not to place a velocity inlet too close to a solid obstruction, since this could cause the inflow stagnation properties to become highly non-uniform. In special instances, a velocity inlet may be used in FLUENT to define the flow velocity at flow exits. (The scalar inputs are not used in such cases.) In such cases you must ensure that overall continuity is maintained in the domain. You can find the following information about velocity inlet boundary conditions in this section: • Section 6.4.1: Inputs at Velocity Inlet Boundaries • Section 6.4.2: Default Settings at Velocity Inlet Boundaries • Section 6.4.3: Calculation Procedure at Velocity Inlet Boundaries For an overview of flow boundaries, see Section 6.2.

6.4.1

Inputs at Velocity Inlet Boundaries

Summary You will enter the following information for a velocity inlet boundary: • Velocity magnitude and direction or velocity components • Swirl velocity (for 2D axisymmetric problems with swirl) • Temperature (for energy calculations) • Outflow gauge pressure (for calculations with the coupled solvers) • Turbulence parameters (for turbulent calculations)


6-25

Boundary Conditions

• Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) • Progress variable (for premixed or partially premixed combustion calculations) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for general multiphase calculations) All values are entered in the Velocity Inlet panel (Figure 6.4.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.4.1: The Velocity Inlet Panel

Defining the Velocity You can define the inflow velocity by specifying the velocity magnitude and direction, the velocity components, or the velocity magnitude normal to the boundary. If the cell zone

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adjacent to the velocity inlet is moving (i.e., if you are using a rotating reference frame, multiple reference frames, or sliding meshes), you can specify either relative or absolute velocities. For axisymmetric problems with swirl in FLUENT, you will also specify the swirl velocity. The procedure for defining the inflow velocity is as follows: 1. Choose which method you will use to specify the flow direction by selecting Magnitude and Direction, Components, or Magnitude, Normal to Boundary in the Velocity Specification Method drop-down list. 2. If the cell zone adjacent to the velocity inlet is moving, you can choose to specify relative or absolute velocities by selecting Relative to Adjacent Cell Zone or Absolute in the Reference Frame drop-down list. If the adjacent cell zone is not moving, Absolute and Relative to Adjacent Cell Zone will be equivalent, so you need not visit the list. 3. If you are going to set the velocity magnitude and direction or the velocity components, and your geometry is 3D, you will next choose the coordinate system in which you will define the vector or velocity components. Choose Cartesian (X, Y, Z), Cylindrical (Radial, Tangential, Axial), or Local Cylindrical (Radial, Tangential, Axial) in the Coordinate System drop-down list. See Section 6.3.1 for information about Cartesian, cylindrical, and local cylindrical coordinate systems. 4. Set the appropriate velocity parameters, as described below for each specification method. Setting the Velocity Magnitude and Direction If you selected Magnitude and Direction as the Velocity Specification Method in step 1 above, you will enter the magnitude of the velocity vector at the inflow boundary (the Velocity Magnitude) and the direction of the vector: • If your geometry is 2D non-axisymmetric, or you chose in step 3 to use the Cartesian coordinate system, you will define the X, Y, and (in 3D) Z-Component of Flow Direction. • If your geometry is 2D axisymmetric, or you chose in step 3 to use a Cylindrical coordinate system, enter the appropriate values of Radial, Axial, and (if you are modeling axisymmetric swirl or using cylindrical coordinates) Tangential-Component of Flow Direction. • If you chose in step 3 to use a Local Cylindrical coordinate system, enter the appropriate values for Axial, Radial, and Tangential-Component of Flow Direction, and then specify the X, Y, and Z-Component of Axis Direction and the X, Y, and Z-Coordinate of Axis Origin.


6-27

Boundary Conditions

Figure 6.3.2 shows the vector components for these different coordinate systems. Setting the Velocity Magnitude Normal to the Boundary If you selected Magnitude, Normal to Boundary as the Velocity Specification Method in step 1 above, you will enter the magnitude of the velocity vector at the inflow boundary (the Velocity Magnitude). If you are modeling 2D axisymmetric swirl, you will also enter the Tangential-Component of Flow Direction. Setting the Velocity Components If you selected Components as the Velocity Specification Method in step 1 above, you will enter the components of the velocity vector at the inflow boundary as follows: • If your geometry is 2D non-axisymmetric, or you chose in step 3 to use the Cartesian coordinate system, you will define the X, Y, and (in 3D) Z-Velocity. • If your geometry is 2D axisymmetric without swirl, you will set the Radial and Axial-Velocity. • If your model is 2D axisymmetric with swirl, you will set the Axial, Radial, and Swirl-Velocity, and (optionally) the Swirl Angular Velocity, as described below. • If you chose in step 3 to use a Cylindrical coordinate system, you will set the Radial, Tangential, and Axial-Velocity, and (optionally) the Angular Velocity, as described below. • If you chose in step 3 to use a Local Cylindrical coordinate system, you will set the Radial, Tangential, and Axial-Velocity, and (optionally) the Angular Velocity, as described below, and then specify the X, Y, and Z-Component of Axis Direction and the X, Y, and Z-Coordinate of Axis Origin.

! Remember that positive values for x, y, and z velocities indicate flow in the positive x, y, and z directions. If flow enters the domain in the negative x direction, for example, you will need to specify a negative value for the x velocity. The same holds true for the radial, tangential, and axial velocities. Positive radial velocities point radially out from the axis, positive axial velocities are in the direction of the axis vector, and positive tangential velocities are based on the right-hand rule using the positive axis. Setting the Angular Velocity If you chose Components as the Velocity Specification Method in step 1 above, and you are modeling axisymmetric swirl, you can specify the inlet Swirl Angular Velocity Ω in addition to the Swirl-Velocity. Similarly, if you chose Components as the Velocity Specification

6-28



Method and you chose in step 3 to use a Cylindrical or Local Cylindrical coordinate system, you can specify the inlet Angular Velocity Ω in addition to the Tangential-Velocity. If you specify Ω, vθ is computed for each ell as Ωr, where r is the radial coordinate in the coordinate system defined by the rotation axis and origin. If you specify both the Swirl-Velocity and the Swirl Angular Velocity, or the Tangential-Velocity nd the Angular Velocity, FLUENT will add vθ and Ωr to get the swirl or tangential velocity at each cell.

Defining the Temperature For calculations in which the energy equation is being solved, you will set the static temperature of the flow at the velocity inlet boundary in the Temperature field.

Defining Outflow Gauge Pressure If you are using one of the coupled solvers, you can specify an Outflow Gauge Pressure for a velocity nlet boundary. If the flow exits the domain at any face on the boundary, that face will be treated as a pressure outlet with the pressure prescribed in the Outflow Gauge Pressure field.

Defining Turbulence Parameters For turbulent calculations, there are several ways in which you can efine the turbulence parameters. Instructions for deciding which method to use and determining appropriate values for these inputs are provided in Section 6.2.2. Turbulence modeling in general is described in Chapter 10.

Defining Radiation Parameters If you are using the P-1 radiation model, the DTRM, he DO model, or the surface-tosurface model, you will set the Internal Emissivity and (optionally) Black Body Temperature. See Section 11.3.16 for details. (The Rosseland radiation model does not require any boundary condition inputs.)


Defining Non-Premixed Combustion Parameters If you are using the non-premixed or partially premixed combustion model, you will set the Mean Mixture Fraction and Mixture Fraction Variance (and the Secondary Mean Mixture


6-29

Boundary Conditions

Fraction and Secondary Mixture Fraction Variance, if you are using two mixture fractions), as described in Section 14.3.3.


Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the velocity inlet. See Section 21.10 for details.


6.4.2

Default Settings at Velocity Inlet Boundaries

Default settings (in SI) for velocity inlet boundary conditions are as follows: Temperature Velocity Magnitude X-Component of Flow Direction Y-Component of Flow Direction Z-Component of Flow Direction X-Velocity Y-Velocity Z-Velocity Turb. Kinetic Energy Turb. Dissipation Rate Outflow Gauge Pressure

6.4.3

300 0 1 0 0 0 0 0 1 1 0

Calculation Procedure at Velocity Inlet Boundaries

FLUENT uses your boundary condition inputs at velocity inlets to compute the mass flow into the domain through the inlet and to compute the fluxes of momentum, energy, and species through the inlet. This section describes these calculations for the case of flow entering the domain through the velocity inlet boundary and for the less common case of flow exiting the domain through the velocity inlet boundary.

6-30



Treatment of Velocity Inlet Conditions at Flow Inlets When your velocity inlet boundary condition defines flow entering the physical domain of the model, FLUENT uses both the velocity components and the scalar quantities that you defined as boundary conditions to compute the inlet mass flow rate, momentum fluxes, and fluxes of energy and chemical species. The mass flow rate entering a fluid cell adjacent to a velocity inlet boundary is computed as m ˙ =

Z

~ ρ~v · dA

(6.4-1)

Note that only the velocity component normal to the control volume face contributes to the inlet mass flow rate.

Treatment of Velocity Inlet Conditions at Flow Exits Sometimes a velocity inlet boundary is used where flow exits the physical domain. This approach might be used, for example, when the flow rate through one exit of the domain is known or is to be imposed on the model.

! In such cases you must ensure that overall continuity is maintained in the domain. In the segregated solver, when flow exits the domain through a velocity inlet boundary FLUENT uses the boundary condition value for the velocity component normal to the exit flow area. It does not use any other boundary conditions that you have input. Instead, all flow conditions except the normal velocity component are assumed to be those of the upstream cell. In the coupled solvers, if the flow exits the domain at any face on the boundary, that face will be treated as a pressure outlet with the pressure prescribed in the Outflow Gauge Pressure field.

Density Calculation Density at the inlet plane is either constant or calculated as a function of temperature, pressure, and/or species mass fractions, where the mass fractions are the values you entered as an inlet condition.


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Boundary Conditions

6.5

Mass Flow Inlet Boundary Conditions

Mass flow boundary conditions can be used in FLUENT to provide a prescribed mass flow rate or mass flux distribution at an inlet. Physically, specifying the mass flux permits the total pressure to vary in response to the interior solution. This is in contrast to the pressure inlet boundary condition (see Section 6.3), where the total pressure is fixed while the mass flux varies. A mass flow inlet is often used when it is more important to match a prescribed mass flow rate than to match the total pressure of the inflow stream. An example is the case of a small cooling jet that is bled into the main flow at a fixed mass flow rate, while the velocity of the main flow is governed primarily by a (different) pressure inlet/outlet boundary condition pair.

! The adjustment of inlet total pressure might result in a slower convergence, so if both the pressure inlet boundary condition and the mass flow inlet boundary condition are acceptable choices, you should choose the former.

! It is not necessary to use mass flow inlets in incompressible flows because when density is constant, velocity inlet boundary conditions will fix the mass flow. You can find the following information about mass flow inlet boundary conditions in this section: • Section 6.5.1: Inputs at Mass Flow Inlet Boundaries • Section 6.5.2: Default Settings at Mass Flow Inlet Boundaries • Section 6.5.3: Calculation Procedure at Mass Flow Inlet Boundaries For an overview of flow boundaries, see Section 6.2.

6.5.1

Inputs at Mass Flow Inlet Boundaries

Summary You will enter the following information for a mass flow inlet boundary: • Mass flow rate, mass flux, or (primarily for the mixing plane model) mass flux with average mass flux • Total (stagnation) temperature • Static pressure • Flow direction

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6.5 Mass Flow Inlet Boundary Conditions

• Turbulence parameters (for turbulent calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) • Progress variable (for premixed or partially premixed combustion calculations) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for general multiphase calculations) All values are entered in the Mass-Flow Inlet panel (Figure 6.5.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Defining the Mass Flow Rate or Mass Flux You can specify the mass flow rate through the inlet zone and have FLUENT convert this value to mass flux, or specify the mass flux directly. For cases where the mass flux varies across the boundary, you can also specify an average mass flux; see below for more information about this specification method. If you set the mass flow rate, it will be converted internally to a uniform mass flux over the zone by dividing the flow rate by the area of the zone. You can define the mass flux (but not the mass flow rate) using a boundary profile or a user-defined function. The inputs for mass flow rate or flux are as follows: 1. Choose the method you will use to specify the mass flow by selecting Mass Flow Rate, Mass Flux, or Mass Flux with Average Mass Flux in the Mass Flow Specification Method drop-down list. 2. If you selected Mass Flow Rate (the default), set the prescribed mass flow rate in the Mass Flow-Rate field.

!

Note that for axisymmetric problems, this mass flow rate is the flow rate through the entire (2π-radian) domain, not through a 1-radian slice. If you selected Mass Flux, set the prescribed mass flux in the Mass Flux field.

!

Note that for axisymmetric problems, this mass flux is the flux through a 1-radian slice of the domain. If you selected Mass Flux with Average Mass Flux, set the prescribed mass flux and average mass flux in the Mass Flux and Average Mass Flux fields.


6-33

Boundary Conditions

Figure 6.5.1: The Mass-Flow Inlet Panel

6-34



!

Note that for axisymmetric problems, this mass flux is the flux through a 1-radian slice of the domain.

More About Mass Flux and Average Mass Flux As noted above, you can specify an average mass flux with the mass flux. If, for example, you specify a mass flux profile such that the average mass flux integrated over the zone area is 4.7, but you actually want to have a total mass flux of 5, you can keep the profile unchanged, and specify an average mass flux of 5. FLUENT will maintain the profile shape but adjust the values so that the resulting mass flux across the boundary is 5. The mass flux with average mass flux specification method is also used by the mixing plane model described in Section 9.4. If the mass flow inlet boundary is going to represent one of the mixing planes, then you do not need to specify the mass flux or flow rate; you can keep the default Mass Flow-Rate of 1. When you create the mixing plane later on in the problem setup, FLUENT will automatically select the Mass Flux with Average Mass Flux method in the Mass-Flow Inlet panel and set the Average Mass Flux to the value obtained by integrating the mass flux profile for the upstream zone. This will ensure that mass is conserved between the upstream zone and the downstream (mass flow inlet) zone.

Defining the Total Temperature Enter the value for the total (stagnation) temperature of the inflow stream in the Total Temperature field in the Mass-Flow Inlet panel.

Defining Static Pressure The static pressure (termed the Supersonic/Initial Gauge Pressure) must be specified if the inlet flow is supersonic or if you plan to initialize the solution based on the pressure inlet boundary conditions. Solution initialization is discussed in Section 24.13. The Supersonic/Initial Gauge Pressure is ignored by FLUENT whenever the flow is subsonic. If you choose to initialize the flow based on the mass flow inlet conditions, the Supersonic/Initial Gauge Pressure will be used in conjunction with the specified stagnation quantities to compute initial values according to isentropic relations. Remember that the static pressure value you enter is relative to the operating pressure set in the Operating Conditions panel. Note the comments in Section 6.3.1 regarding hydrostatic pressure.

Defining the Flow Direction You can define the flow direction at a mass flow inlet explicitly, or you can define the flow to be normal to the boundary.


6-35

Boundary Conditions

You will have the option to specify the flow direction either in the absolute or relative reference frame, when the cell zone adjacent to the mass-flow inlet is moving. If the cell zone adjacent to the mass-flow inlet is not moving, both formulations are equivalent. The procedure for defining the flow direction is as follows, referring to Figure 6.5.1: 1. Choose which method you will use to specify the flow direction by selecting Direction Vector or Normal to Boundary in the Direction Specification Method drop-down list. 2. If you selected Normal to Boundary, there are no additional inputs for flow direction.

!

Note that if you are modeling axisymmetric swirl, the flow direction will be normal to the boundary; i.e., there will be no swirl component at the boundary for axisymmetric swirl. 3. If the cell zone adjacent to the mass-flow inlet is moving, choose Absolute (the default) or Relative in the Reference Frame drop-down list.

!

These options are equivalent when the cell zone next to the mass-flow inlet is stationary. 4. If you selected Direction Vector and your geometry is 2D, go to the next step. If your geometry is 3D, you will next choose the coordinate system in which you will define the flow direction components. Choose Cartesian (X, Y, Z), Cylindrical (Radial, Tangential, Axial), or Local Cylindrical (Radial, Tangential, Axial) in the Coordinate System drop-down list. See Section 6.3.1 for information about Cartesian, cylindrical, and local cylindrical coordinate systems. 5. If you selected Direction Vector, set the vector components as follows: • If your geometry is 2D non-axisymmetric, or you chose to use a 3D Cartesian coordinate system, enter the appropriate values for X, Y, and (in 3D) Z-Component of Flow Direction. • If your geometry is 2D axisymmetric, or you chose to use a 3D Cylindrical coordinate system, enter the appropriate values for Axial, Radial, and (if you are modeling swirl or using cylindrical coordinates) Tangential-Component of Flow Direction. • If you chose to use a 3D Local Cylindrical coordinate system, enter the appropriate values for Axial, Radial, and Tangential-Component of Flow Direction, and then specify the X, Y, and Z-Component of Axis Direction and the X, Y, and Z-Coordinate of Axis Origin. Figure 6.3.2 shows the vector components for these different coordinate systems.

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Defining Turbulence Parameters For turbulent calculations, there are several ways in which you can define the turbulence parameters. Instructions for deciding which method to use and determining appropriate values for these inputs are provided in Section 6.2.2. Turbulence modeling is described in Chapter 10.



Defining Non-Premixed Combustion Parameters If you are using the non-premixed or partially premixed combustion model, you will set the Mean Mixture Fraction and Mixture Fraction Variance (and the Secondary Mean Mixture Fraction and Secondary Mixture Fraction Variance, if you are using two mixture fractions), as described in Section 14.3.3.


Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the mass flow inlet. See Section 21.10 for details.



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Boundary Conditions

6.5.2

Default Settings at Mass Flow Inlet Boundaries

Default settings (in SI) for mass flow inlet boundary conditions are as follows: Mass Flow-Rate Total Temperature Supersonic/Initial Gauge Pressure X-Component of Flow Direction Y-Component of Flow Direction Z-Component of Flow Direction Turb. Kinetic Energy Turb. Dissipation Rate

6.5.3

1 300 0 1 0 0 1 1

Calculation Procedure at Mass Flow Inlet Boundaries

When mass flow boundary conditions are used for an inlet zone, a velocity is computed for each face in that zone, and this velocity is used to compute the fluxes of all relevant solution variables into the domain. With each iteration, the computed velocity is adjusted so that the correct mass flow value is maintained. To compute this velocity, your inputs for mass flow rate, flow direction, static pressure, and total temperature are used. There are two ways to specify the mass flow rate. The first is to specify the total mass flow rate, m, ˙ for the inlet. The second is to specify the mass flux, ρvn (mass flow rate per unit area). If a total mass flow rate is specified, FLUENT converts it internally to a uniform mass flux by dividing the mass flow rate by the total inlet area: ρvn =

m ˙ A

(6.5-1)

If the direct mass flux specification option is used, the mass flux can be varied over the boundary by using profile files or user-defined functions. If the average mass flux is also specified (either explicitly by you or automatically by FLUENT), it is used to correct the specified mass flux profile, as described earlier in this section. Once the value of ρvn at a given face has been determined, the density, ρ, at the face must be determined in order to find the normal velocity, vn . The manner in which the density is obtained depends upon whether the fluid is modeled as an ideal gas or not. Each of these cases is examined below.

Flow Calculations at Mass Flow Boundaries for Ideal Gases If the fluid is an ideal gas, the static temperature and static pressure are required to compute the density:

6-38



p = ρRT

(6.5-2)

If the inlet is supersonic, the static pressure used is the value that has been set as a boundary condition. If the inlet is subsonic, the static pressure is extrapolated from the cells inside the inlet face. The static temperature at the inlet is computed from the total enthalpy, which is determined from the total temperature that has been set as a boundary condition. The total enthalpy is given by 1 h0 (T0 ) = h(T ) + v 2 2

(6.5-3)

where the velocity is related to the mass flow rate given by Equation 6.5-1. Using Equation 6.5-2 to relate density to the (known) static pressure and (unknown) temperature, Equation 6.5-3 can be solved to obtain the static temperature.

Flow Calculations at Mass Flow Boundaries for Incompressible Flows When you are modeling incompressible flows, the static temperature is nearly the same as the total temperature. The density at the inlet is either constant or readily computed as a function of the temperature and (optionally) the species mass fractions. The velocity is then computed using Equation 6.5-1.

Flux Calculations at Mass Flow Boundaries To compute the fluxes of all variables at the inlet, the flux velocity, vn , is used along with the inlet value of the variable in question. For example, the flux of mass is ρvn , and the flux of turbulence kinetic energy is ρkvn . These fluxes are used as boundary conditions for the corresponding conservation equations during the course of the solution.


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Boundary Conditions

6.6

Inlet Vent Boundary Conditions

Inlet vent boundary conditions are used to model an inlet vent with a specified loss coefficient, flow direction, and ambient (inlet) pressure and temperature.

6.6.1

Inputs at Inlet Vent Boundaries

You will enter the following information for an inlet vent boundary: • Total (stagnation) pressure • Total (stagnation) temperature • Flow direction • Static pressure • Turbulence parameters (for turbulent calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) • Progress variable (for premixed or partially premixed combustion calculations) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for general multiphase calculations) • Loss coefficient All values are entered in the Inlet Vent panel (Figure 6.6.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). The first 11 items listed above are specified in the same way that they are specified at pressure inlet boundaries. See Section 6.3.1 for details. Specification of the loss coefficient is described here.

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6.6 Inlet Vent Boundary Conditions

Figure 6.6.1: The Inlet Vent Panel

Specifying the Loss Coefficient An inlet vent is considered to be infinitely thin, and the pressure drop through the vent is assumed to be proportional to the dynamic head of the fluid, with an empirically determined loss coefficient that you supply. That is, the pressure drop, ∆p, varies with the normal component of velocity through the vent, v, as follows: 1 ∆p = kL ρv 2 2

(6.6-1)

where ρ is the fluid density, and kL is the non-dimensional loss coefficient.

! ∆p is the pressure drop in the direction of the flow; therefore the vent will appear as a resistance even in the case of backflow. You can define the Loss-Coefficient across the vent as a constant, polynomial, piecewiselinear, or piecewise-polynomial function of the normal velocity. The panels for defining


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Boundary Conditions

these functions are the same as those used for defining temperature-dependent properties. See Section 7.1.3 for details.

6.7

Intake Fan Boundary Conditions

Intake fan boundary conditions are used to model an external intake fan with a specified pressure jump, flow direction, and ambient (intake) pressure and temperature.

6.7.1

Inputs at Intake Fan Boundaries

You will enter the following information for an intake fan boundary: • Total (stagnation) pressure • Total (stagnation) temperature • Flow direction • Static pressure • Turbulence parameters (for turbulent calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) • Progress variable (for premixed or partially premixed combustion calculations) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for general multiphase calculations) • Pressure jump All values are entered in the Intake Fan panel (shown in Figure 6.7.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). The first 11 items listed above are specified in the same way that they are specified at pressure inlet boundaries. See Section 6.3.1 for details. Specification of the pressure jump is described here.

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6.7 Intake Fan Boundary Conditions

Figure 6.7.1: The Intake Fan Panel

Specifying the Pressure Jump An intake fan is considered to be infinitely thin, and the discontinuous pressure rise across it is specified as a function of the velocity through the fan. In the case of reversed flow, the fan is treated like an outlet vent with a loss coefficient of unity. You can define the Pressure-Jump across the fan as a constant, polynomial, piecewise-linear, or piecewise-polynomial function of the normal velocity. The panels for defining these functions are the same as those used for defining temperature-dependent properties. See Section 7.1.3 for details.


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Boundary Conditions

6.8

Pressure Outlet Boundary Conditions

Pressure outlet boundary conditions require the specification of a static (gauge) pressure at the outlet boundary. The value of static pressure specified is used only while the flow is subsonic. Should the flow become locally supersonic, the specified pressure is no longer used; pressure will be extrapolated from the flow in the interior. All other flow quantities are extrapolated from the interior. A set of “backflow” conditions is also specified to be used if the flow reverses direction at the pressure outlet boundary during the solution process. Convergence difficulties will be minimized if you specify realistic values for the backflow quantities. FLUENT also provides an option to use a radial equilibrium outlet boundary condition (see Section 6.8.1 for details), and an option to specify a target mass flow rate for pressure outlets (see Section 6.8.3 for details). You can find the following information about pressure outlet boundary conditions in this section: • Section 6.8.1: Inputs at Pressure Outlet Boundaries • Section 6.8.2: Default Settings at Pressure Outlet Boundaries • Section 6.8.3: Calculation Procedure at Pressure Outlet Boundaries For an overview of flow boundaries, see Section 6.2.

6.8.1

Inputs at Pressure Outlet Boundaries

Summary You will enter the following information for a pressure outlet boundary: • Static pressure • Backflow conditions – Total (stagnation) temperature (for energy calculations) – Backflow direction specification method – Turbulence parameters (for turbulent calculations) – Chemical species mass fractions (for species calculations) – Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) – Progress variable (for premixed or partially premixed combustion calculations)

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6.8 Pressure Outlet Boundary Conditions

– Multiphase boundary conditions (for general multiphase calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Discrete phase boundary conditions (for discrete phase calculations) All values are entered in the Pressure Outlet panel (Figure 6.8.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.8.1: The Pressure Outlet Panel

Defining Static Pressure To set the static pressure at the pressure outlet boundary, enter the appropriate value for Gauge Pressure in the Pressure Outlet panel. This value will be used for subsonic flow only. Should the flow become locally supersonic, the pressure will be extrapolated from the upstream conditions.


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Boundary Conditions

Remember that the static pressure value you enter is relative to the operating pressure set in the Operating Conditions panel. Note the comments in Section 6.3.1 regarding hydrostatic pressure. FLUENT also provides an option to use a radial equilibrium outlet boundary condition. To enable this option, turn on Radial Equilibrium Pressure Distribution. When this feature is active, the specified gauge pressure applies only to the position of minimum radius (relative to the axis of rotation) at the boundary. The static pressure on the rest of the zone is calculated from the assumption that radial velocity is negligible, so that the pressure gradient is given by ∂p ρv 2 = θ ∂r r

(6.8-1)

where r is the distance from the axis of rotation and vθ is the tangential velocity. Note that this boundary condition can be used even if the rotational velocity is zero. For example, it could be applied to the calculation of the flow through an annulus containing guide vanes.

! Note that the radial equilibrium outlet condition is available only for 3D and axisymmetric swirl calculations.

Defining Backflow Conditions Backflow properties consistent with the models you are using will appear in the Pressure Outlet panel. The specified values will be used only if flow is pulled in through the outlet. • The Backflow Total Temperature should be set for problems involving energy calculation. • When the direction of the backflow re-entering the computational domain is known, and deemed to be relevant to the flow field solution, you can specify it choosing one of the options available in the Backflow Direction Specification Method drop-down list. The default value for this field is Normal to Boundary, and requires no further input. If you choose Direction Vector, the panel will expand to show the inputs for the components of the direction vector for the backflow, and if you are running the 3D version of FLUENT, the Coordinate System drop-down list. If you choose From Neighboring Cell, FLUENT will determine the direction of the backflow using the direction of the flow in the cell layer adjacent to the pressure outlet. • For turbulent calculations, there are several ways in which you can define the turbulence parameters. Instructions for deciding which method to use and determining appropriate values for these inputs are provided in Section 6.2.2. Turbulence modeling in general is described in Chapter 10.

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• If you are modeling species transport, you will set the backflow species mass fractions under Species Mass Fractions. For details, see Section 13.1.5. • If you are modeling combustion using the non-premixed or partially premixed combustion model, you will set the backflow mixture fraction and variance values. See Section 14.3.3 for details. • If you are modeling combustion using the premixed or partially premixed combustion model, you will set the backflow Progress Variable value. See Section 15.3.5 for details. • If you are using the VOF, mixture, or Eulerian model for multiphase flow, you will need to specify volume fractions for secondary phases and (for some models) additional parameters. See Section 22.6.16 for details. • If backflow occurs, the pressure you specified as the Gauge Pressure will be used as total pressure, so you need not specify a backflow pressure value explicitly. The flow direction in this case will be normal to the boundary. If the cell zone adjacent to the pressure outlet is moving (i.e., if you are using a rotating reference frame, multiple reference frames, mixing planes, or sliding meshes) and you are using the segregated solver, the velocity in the dynamic contribution to total pressure (see Equation 6.3-3) will be absolute or relative to the motion of the cell zone, depending on whether or not the Absolute velocity formulation is enabled in the Solver panel. For the coupled solvers, the velocity in Equation 6.3-3 (or the Mach number in Equation 6.3-4) is always in the absolute frame.

! Even if no backflow is expected in the converged solution, you should always set realistic values to minimize convergence difficulties in the event that backflow does occur during the calculation.


Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the pressure outlet. See Section 21.10 for details.


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Boundary Conditions

6.8.2

Default Settings at Pressure Outlet Boundaries

Default settings (in SI) for pressure outlet boundary conditions are as follows: Gauge Pressure 0 Backflow Total Temperature 300 Backflow Turb. Kinetic Energy 1 Backflow Turb. Dissipation Rate 1

6.8.3

Calculation Procedure at Pressure Outlet Boundaries

At pressure outlets, FLUENT uses the boundary condition pressure you input as the static pressure of the fluid at the outlet plane, ps , and extrapolates all other conditions from the interior of the domain.

Target Mass Flow Rate Option Using the text interface, the target mass flow rate option can be turned on for a pressure outlet boundary. This option allows you to specify a target mass flow rate. The target rate is achieved by adjusting the pressure value at the pressure outlet up and down at every iteration according to one of two methods until the target mass flow rate is obtained. Method 1 (the default method) This method is suited for turbomachinery applications, and it consists of three steps: First Step: loop over the faces of the pressure outlet boundary and calculate a meanstatic-pressure. This is used as a first value for the static pressure. Second Step: starting with the static pressure value obtained in the first step, loop over the faces of pressure outlet boundary and calculate the corresponding mass flow rate. Use the difference between the obtained mass flow rate and the target mass flow rate to obtain a pressure difference to adjust the static pressure. Repeat this process until the calculated mass flow matches the desired mass flow rate (within a tolerance). Third Step: impose the mean static pressure obtained from the loop in the second step on the boundary, using under-relaxation based on the previous value. Method 2 This method is more suited for adjusting the pressure outlet boundary for manifolds with multiple exits to obtain a desired target mass flow rate, and consists of two steps: First Step: loop over the pressure outlet boundary faces to calculate the mean static pressure and the mass flow rate.

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Second Step: use the required mass flow rate (the target mass flow rate), the current computed mass flow rate, and mean static pressure in Bernoulli’s equation to obtain a new mean static pressure value, applying under-relaxation to keep the solution stable. There are two steps needed to activate the target mass flow rate (TMR) option, accessed from the target-mass-flow-rate-settings text menu: define −→ boundary-conditions −→target-mass-flow-rate-settings To turn on the target mass flow rate option, enter yes at the enable? text command. The target-mass-flow-rate-settings menu will expand to include the set method and verbosity? options. Then, you will select which pressure outlets will use the target mass flow rate and the values of the target mass flow rates. Obtain a list of the pressure outlets in your geometry: define −→ boundary-conditions −→pressure-outlet Select the pressure outlets for which you want to activate the target mass flow rate option (by entering the corresponding names at the prompt), and set the options for the target mass flow rate: specify targeted mass-flow rate Enter yes or no. targeted mass-flow Enter the desired value.


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Boundary Conditions

6.9

Pressure Far-Field Boundary Conditions

Pressure far-field conditions are used in FLUENT to model a free-stream condition at infinity, with free-stream Mach number and static conditions being specified. The pressure far-field boundary condition is often called a characteristic boundary condition, since it uses characteristic information (Riemann invariants) to determine the flow variables at the boundaries.

! This boundary condition is applicable only when the density is calculated using the ideal-gas law (see Section 7.2). Using it for other flows is not permitted. To effectively approximate true infinite-extent conditions, you must place the far-field boundary far enough from the object of interest. For example, in lifting airfoil calculations, it is not uncommon for the far-field boundary to be a circle with a radius of 20 chord lengths. You can find the following information about pressure far-field boundary conditions in this section: • Section 6.9.1: Inputs at Pressure Far-Field Boundaries • Section 6.9.2: Default Settings at Pressure Far-Field Boundaries • Section 6.9.3: Calculation Procedure at Pressure Far-Field Boundaries For an overview of flow boundaries, see Section 6.2.

6.9.1

Inputs at Pressure Far-Field Boundaries

Summary You will enter the following information for a pressure far-field boundary: • Static pressure • Mach number • Temperature • Flow direction • Turbulence parameters (for turbulent calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Chemical species mass fractions (for species calculations) • Discrete phase boundary conditions (for discrete phase calculations)

6-50


6.9 Pressure Far-Field Boundary Conditions

All values are entered in the Pressure Far-Field panel (Figure 6.9.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.9.1: The Pressure Far-Field Panel

Defining Static Pressure, Mach Number, and Static Temperature To set the static pressure and temperature at the far-field boundary, enter the appropriate values for Gauge Pressure and Temperature in the Pressure Far-Field panel. You will also set the Mach Number there. The Mach number can be subsonic, sonic, or supersonic.

Defining the Flow Direction You can define the flow direction at a pressure far-field boundary by setting the components of the direction vector. If your geometry is 2D non-axisymmetric or 3D, enter the appropriate values for X, Y, and (in 3D) Z-Component of Flow Direction in the Pressure Far-Field panel. If your geometry is 2D axisymmetric, enter the appropriate values for Axial, Radial, and (if you are modeling axisymmetric swirl) Tangential-Component of Flow Direction.


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Boundary Conditions

Defining Turbulence Parameters For turbulent calculations, there are several ways in which you can define the turbulence parameters. Instructions for deciding which method to use and determining appropriate values for these inputs are provided in Section 6.2.2. Turbulence modeling is described in Chapter 10.

Defining Radiation Parameters If you are using the P-1 radiation model, the DTRM, the DO model, or the surface-tosurface model, you will set the Internal Emissivity and (optionally) Black Body Temperature. See Section 11.3.16 for details.

Defining Species Transport Parameters If you are modeling species transport, you will set the species mass fractions under Species Mass Fractions. See Section 13.1.5 for details.

Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the pressure far-field boundary. See Section 21.10 for details.

6.9.2

Default Settings at Pressure Far-Field Boundaries

Default settings (in SI) for pressure far-field boundary conditions are as follows: Gauge Pressure Mach Number Temperature X-Component of Flow Direction Y-Component of Flow Direction Z-Component of Flow Direction Turb. Kinetic Energy Turb. Dissipation Rate

6.9.3

0 0.6 300 1 0 0 1 1

Calculation Procedure at Pressure Far-Field Boundaries

The pressure far-field boundary condition is a non-reflecting boundary condition based on the introduction of Riemann invariants (i.e., characteristic variables) for a one-dimensional flow normal to the boundary. For flow that is subsonic there are two Riemann invariants, corresponding to incoming and outgoing waves:

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6.9 Pressure Far-Field Boundary Conditions

R∞ = vn∞ −

Ri = vni +

2c∞ γ−1

2ci γ−1

(6.9-1)

(6.9-2)

where vn is the velocity magnitude normal to the boundary, c is the local speed of sound and γ is the ratio of specific heats (ideal gas). The subscript ∞ refers to conditions being applied at infinity (the boundary conditions), and the subscript i refers to conditions in the interior of the domain (i.e., in the cell adjacent to the boundary face). These two invariants can be added and subtracted to give the following two equations: 1 vn = (Ri + R∞ ) 2 c=

γ−1 (Ri − R∞ ) 4

(6.9-3)

(6.9-4)

where vn and c become the values of normal velocity and sound speed applied on the boundary. At a face through which flow exits, the tangential velocity components and entropy are extrapolated from the interior; at an inflow face, these are specified as having free-stream values. Using the values for vn , c, tangential velocity components, and entropy the values of density, velocity, temperature, and pressure at the boundary face can be calculated.


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Boundary Conditions

6.10

Outflow Boundary Conditions

Outflow boundary conditions in FLUENT are used to model flow exits where the details of the flow velocity and pressure are not known prior to solution of the flow problem. You do not define any conditions at outflow boundaries (unless you are modeling radiative heat transfer, a discrete phase of particles, or split mass flow): FLUENT extrapolates the required information from the interior. It is important, however, to understand the limitations of this boundary type.

! Note that outflow boundaries cannot be used in the following cases: • if a problem includes pressure inlet boundaries; use pressure outlet boundary conditions (see Section 6.8) instead • if you are modeling compressible flow • if you are modeling unsteady flows with varying density, even if the flow is incompressible You can find the following information about outflow boundary conditions in this section: • Section 6.10.1: FLUENT’s Treatment at Outflow Boundaries • Section 6.10.2: Using Outflow Boundaries • Section 6.10.3: Mass Flow Split Boundary Conditions • Section 6.10.4: Other Inputs at Outflow Boundaries For an overview of flow boundaries, see Section 6.2.

6.10.1

FLUENT’s Treatment at Outflow Boundaries

The boundary conditions used by FLUENT at outflow boundaries are as follows: • A zero diffusion flux for all flow variables • An overall mass balance correction The zero diffusion flux condition applied at outflow cells means that the conditions of the outflow plane are extrapolated from within the domain and have no impact on the upstream flow. The extrapolation procedure used by FLUENT updates the outflow velocity and pressure in a manner that is consistent with a fully-developed flow assumption, as noted below, when there is no area change at the outflow boundary.

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6.10 Outflow Boundary Conditions

The zero diffusion flux condition applied by FLUENT at outflow boundaries is approached physically in fully-developed flows. Fully-developed flows are flows in which the flow velocity profile (and/or profiles of other properties such as temperature) is unchanging in the flow direction. It is important to note that gradients in the cross-stream direction may exist at an outflow boundary. Only the diffusion fluxes in the direction normal to the exit plane are assumed to be zero.

6.10.2

Using Outflow Boundaries

As noted in Section 6.10.1, the outflow boundary condition is obeyed in fully-developed flows where the diffusion flux for all flow variables in the exit direction are zero. However, you may also define outflow boundaries at physical boundaries where the flow is not fully developed—and you can do so with confidence if the assumption of a zero diffusion flux at the exit is expected to have a small impact on your flow solution. The appropriate placement of an outflow boundary is described by example below. • Outflow boundaries where normal gradients are negligible: Figure 6.10.1 shows a simple two-dimensional flow problem and several possible outflow boundary location choices. Location C shows the outflow boundary located upstream of the plenum exit but in a region of the duct where the flow is fully-developed. At this location, the outflow boundary condition is exactly obeyed. A

B

C

outflow outflow outflow condition condition condition obeyed ill-posed not obeyed

Figure 6.10.1: Choice of the Outflow Boundary Condition Location

• Ill-posed outflow boundaries: Location B in Figure 6.10.1 shows the outflow boundary near the reattachment point of the recirculation in the wake of the backwardfacing step. This choice of outflow boundary condition is ill-posed as the gradients


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Boundary Conditions

normal to the exit plane are quite large at this point and can be expected to have a significant impact on the flow field upstream. Because the outflow boundary condition ignores these axial gradients in the flow, location B is a poor choice for an outflow boundary. The exit location should be moved downstream from the reattachment point. Figure 6.10.1 shows a second ill-posed outflow boundary at location A. Here, the outflow is located where flow is pulled into the FLUENT domain through the outflow boundary. In situations like this the FLUENT calculation typically does not converge and the results of the calculation have no validity. This is because when flow is pulled into the domain through an outflow, the mass flow rate through the domain is “floating” or undefined. In addition, when flow enters the domain through an outflow boundary, the scalar properties of the flow are not defined. For example, the temperature of the flow pulled in through the outflow is not defined. (FLUENT chooses the temperature using the temperature of the fluid adjacent to the outflow, inside the domain.) Thus you should view all calculations that involve flow entering the domain through an outflow boundary with skepticism. For such calculations, pressure outlet boundary conditions (see Section 6.8) are recommended.

!

Note that convergence may be affected if there is recirculation through the outflow boundary at any point during the calculation, even if the final solution is not expected to have any flow reentering the domain. This is particularly true of turbulent flow simulations.

6.10.3

Mass Flow Split Boundary Conditions

In FLUENT, it is possible to use multiple outflow boundaries and specify the fractional flow rate through each boundary. In the Outflow panel, set the Flow Rate Weighting to indicate what portion of the outflow is through the boundary.

Figure 6.10.2: The Outflow Panel

The Flow Rate Weighting is a weighting factor: Flow Rate Weighting specified on boundary percentage flow = through boundary sum of all Flow Rate Weightings

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(6.10-1)


6.10 Outflow Boundary Conditions

By default, the Flow Rate Weighting for all outflow boundaries is set to 1. If the flow is divided equally among all of your outflow boundaries (or if you have just one outflow boundary), you need not change the settings from the default; FLUENT will scale the flow rate fractions to obtain equal fractions through all outflow boundaries. Thus, if you have two outflow boundaries and you want half of the flow to exit through each one, no inputs are required from you. If, however, you want 75% of the flow to exit through one, and 25% through the other, you will need to explicitly specify both Flow Rate Weightings, i.e., 0.75 for one boundary and 0.25 for the other.

! If you specify a Flow Rate Weighting of 0.75 at the first exit and leave the default Flow Rate Weighting (1.0) at the second exit, then the flow through each boundary will be Boundary 1 =

0.75 0.75+1.0

= 0.429 or 42.9%

Boundary 2 =

1.0 0.75+1.0

= 0.571 or 57.1%

6.10.4

Other Inputs at Outflow Boundaries

Radiation Inputs at Outflow Boundaries In general, there are no boundary conditions for you to set at an outflow boundary. If, however, you are using the P-1 radiation model, the DTRM, the DO model, or the surface-to-surface model, you will set the Internal Emissivity and (optionally) Black Body Temperature in the Outflow panel. These parameters are described in Section 11.3.16. The default value for Internal Emissivity is 1 and the default value for Black Body Temperature is 300.

Defining Discrete Phase Boundary Conditions If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the outflow boundary. See Section 21.10 for details.


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Boundary Conditions

6.11

Outlet Vent Boundary Conditions

Outlet vent boundary conditions are used to model an outlet vent with a specified loss coefficient and ambient (discharge) pressure and temperature.

6.11.1

Inputs at Outlet Vent Boundaries

You will enter the following information for an outlet vent boundary: • Static pressure • Backflow conditions – Total (stagnation) temperature (for energy calculations) – Turbulence parameters (for turbulent calculations) – Chemical species mass fractions (for species calculations) – Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) – Progress variable (for premixed or partially premixed combustion calculations) – Multiphase boundary conditions (for general multiphase calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Discrete phase boundary conditions (for discrete phase calculations) • Loss coefficient All values are entered in the Outlet Vent panel (Figure 6.11.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). The first 4 items listed above are specified in the same way that they are specified at pressure outlet boundaries. See Section 6.8.1 for details. Specification of the loss coefficient is described here.

Specifying the Loss Coefficient An outlet vent is considered to be infinitely thin, and the pressure drop through the vent is assumed to be proportional to the dynamic head of the fluid, with an empirically determined loss coefficient which you supply. That is, the pressure drop, ∆p, varies with the normal component of velocity through the vent, v, as follows: 1 ∆p = kL ρv 2 2

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(6.11-1)


6.11 Outlet Vent Boundary Conditions

Figure 6.11.1: The Outlet Vent Panel

where ρ is the fluid density, and kL is the nondimensional loss coefficient.

! ∆p is the pressure drop in the direction of the flow; therefore the vent will appear as a resistance even in the case of backflow. You can define a constant, polynomial, piecewise-linear, or piecewise-polynomial function for the Loss-Coefficient across the vent. The panels for defining these functions are the same as those used for defining temperature-dependent properties. See Section 7.1.3 for details.


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Boundary Conditions

6.12

Exhaust Fan Boundary Conditions

Exhaust fan boundary conditions are used to model an external exhaust fan with a specified pressure jump and ambient (discharge) pressure.

6.12.1

Inputs at Exhaust Fan Boundaries

You will enter the following information for an exhaust fan boundary: • Static pressure • Backflow conditions – Total (stagnation) temperature (for energy calculations) – Turbulence parameters (for turbulent calculations) – Chemical species mass fractions (for species calculations) – Mixture fraction and variance (for non-premixed or partially premixed combustion calculations) – Progress variable (for premixed or partially premixed combustion calculations) – Multiphase boundary conditions (for general multiphase calculations) – User-defined scalar boundary conditions (for user-defined scalar calculations) • Radiation parameters (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Discrete phase boundary conditions (for discrete phase calculations) • Pressure jump All values are entered in the Exhaust Fan panel (Figure 6.12.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). The first 4 items listed above are specified in the same way that they are specified at pressure outlet boundaries. See Section 6.8.1 for details. Specification of the pressure jump is described here.

Specifying the Pressure Jump An exhaust fan is considered to be infinitely thin, and the discontinuous pressure rise across it is specified as a function of the local fluid velocity normal to the fan. You can define a constant, polynomial, piecewise-linear, or piecewise-polynomial function for the Pressure-Jump across the fan. The panels for defining these functions are the same as those used for defining temperature-dependent properties. See Section 7.1.3 for details.

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6.12 Exhaust Fan Boundary Conditions

Figure 6.12.1: The Exhaust Fan Panel

! You must be careful to model the exhaust fan so that a pressure rise occurs for forward flow through the fan. In the case of reversed flow, the fan is treated like an inlet vent with a loss coefficient of unity.


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Boundary Conditions

6.13

Wall Boundary Conditions

Wall boundary conditions are used to bound fluid and solid regions. In viscous flows, the no-slip boundary condition is enforced at walls by default, but you can specify a tangential velocity component in terms of the translational or rotational motion of the wall boundary, or model a “slip” wall by specifying shear. (You can also model a slip wall with zero shear using the symmetry boundary type, but using a symmetry boundary will apply symmetry conditions for all equations. See Section 6.14 for details.) The shear stress and heat transfer between the fluid and wall are computed based on the flow details in the local flow field. You can find the following information about wall boundary conditions in this section: • Section 6.13.1: Inputs at Wall Boundaries • Section 6.13.2: Default Settings at Wall Boundaries • Section 6.13.3: Shear-Stress Calculation Procedure at Wall Boundaries • Section 6.13.4: Heat Transfer Calculation Procedure at Wall Boundaries

6.13.1

Inputs at Wall Boundaries

Summary You will enter the following information for a wall boundary: • Thermal boundary conditions (for heat transfer calculations) • Wall motion conditions (for moving or rotating walls) • Shear conditions (for slip walls, optional) • Wall roughness (for turbulent flows, optional) • Species boundary conditions (for species calculations) • Chemical reaction boundary conditions (for surface reactions) • Radiation boundary conditions (for calculations using the P-1 model, the DTRM, the DO model, or the surface-to-surface model) • Discrete phase boundary conditions (for discrete phase calculations) • Multiphase boundary conditions (for VOF calculations, optional)

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6.13 Wall Boundary Conditions

Defining Thermal Boundary Conditions at Walls When you are solving the energy equation, you need to define thermal boundary conditions at wall boundaries. Five types of thermal conditions are available: • Fixed heat flux • Fixed temperature • Convective heat transfer • External radiation heat transfer • Combined external radiation and convection heat transfer If the wall zone is a “two-sided wall” (a wall that forms the interface between two regions, such as the fluid/solid interface for a conjugate heat transfer problem) a subset of these thermal conditions will be available, but you will also be able to choose whether or not the two sides of the wall are “coupled”. See below for details. The inputs for each type of thermal condition are described below. If the wall has a nonzero thickness, you should also set parameters for calculating thin-wall thermal resistance and heat generation in the wall, as described below. You can model conduction within boundary walls and internal (i.e., two-sided) walls of your model. This type of conduction, called shell conduction, allows you to more conveniently model heat conduction on walls where the wall thickness is small with respect to the overall geometry (e.g., finned heat exchangers or sheet metal in automobile underhoods). Meshing these walls with solid cells would lead to high-aspect-ratio meshes and a significant increase in the total number of cells. See below for details about shell conduction. Thermal conditions are entered in the Thermal section of the Wall panel (Figure 6.13.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). To view the thermal conditions, click the Thermal tab. Heat Flux Boundary Conditions For a fixed heat flux condition, choose the Heat Flux option under Thermal Conditions. You will then need to set the appropriate value for the heat flux at the wall surface in the Heat Flux field. You can define an adiabatic wall by setting a zero heat flux condition. This is the default condition for all walls.


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Boundary Conditions

Figure 6.13.1: The Wall Panel (Thermal Section)

Temperature Boundary Conditions To select the fixed temperature condition, choose the Temperature option under Thermal Conditions in the Wall panel. You will need to specify the temperature at the wall surface (Temperature). The heat transfer to the wall is computed using Equation 6.13-8 or Equation 6.13-9. Convective Heat Transfer Boundary Conditions For a convective heat transfer wall boundary, select Convection under Thermal Conditions. Your inputs of Heat Transfer Coefficient and Free Stream Temperature will allow FLUENT to compute the heat transfer to the wall using Equation 6.13-12. External Radiation Boundary Conditions If radiation heat transfer from the exterior of your model is of interest, you can enable the Radiation option in the Wall panel and set the External Emissivity and External Radiation Temperature.

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Combined Convection and External Radiation Boundary Conditions You can choose a thermal condition that combines the convection and radiation boundary conditions by selecting the Mixed option. With this thermal condition, you will need to set the Heat Transfer Coefficient, Free Stream Temperature, External Emissivity, and External Radiation Temperature. Thin-Wall Thermal Resistance Parameters By default, a wall will have a thickness of zero. You can, however, in conjunction with any of the thermal conditions, model a thin layer of material between two zones. For example, you can model the effect of a piece of sheet metal between two fluid zones, a coating on a solid zone, or contact resistance between two solid regions. FLUENT will solve a 1D conduction equation to compute the thermal resistance offered by the wall and the heat generation in the wall. To include these effects in the heat transfer calculation you will need to specify the type of material, the thickness of the wall, and the heat generation rate in the wall. Select the material type in the Material Name drop-down list, and specify the thickness in the Wall Thickness field. If you want to check or modify the properties of the selected material, you can click Edit... to open the Material panel; this panel contains just the properties of the selected material, not the full contents of the standard Materials panel. The thermal resistance of the wall is ∆x/k, where k is the conductivity of the wall material and ∆x is the wall thickness. The thermal boundary condition you set will be specified on the outside of the thin wall, as shown in Figure 6.13.2, where Tb is the fixed Temperature specified at the wall.

! Note that for thin walls, you can specify only a constant thermal conductivity. If you want to use a non-constant thermal conductivity for a wall with non-zero thickness, you should use the shell conduction model (see below for details). Specify the heat generation rate inside the wall in the Heat Generation Rate field. This option is useful if, for example, you are modeling printed circuit boards where you know the electrical power dissipated in the circuits. Thermal Conditions for Two-Sided Walls If the wall zone has a fluid or solid region on each side, it is called a “two-sided wall”. When you read a grid with this type of wall zone into FLUENT, a “shadow” zone will automatically be created so that each side of the wall is a distinct wall zone. In the Wall panel, the shadow zone’s name will be shown in the Shadow Face Zone field. You can choose to specify different thermal conditions on each zone, or to couple the two zones: • To couple the two sides of the wall, select the Coupled option under Thermal Conditions. (This option will appear in the Wall panel only when the wall is a two-sided


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Boundary Conditions

outer surface

thin wall

Tb

fluid or solid cells

inner surface

∆x

Figure 6.13.2: Thermal Conditions are Specified on the Outside of a Thin Wall

wall.) No additional thermal boundary conditions are required, because the solver will calculate heat transfer directly from the solution in the adjacent cells. You can, however, specify the material type, wall thickness, and heat generation rate for thin-wall thermal resistance calculations, as described above. Note that the resistance parameters you set for one side of the wall will automatically be assigned to its shadow wall zone. Specifying the heat generation rate inside the wall is useful if, for example, you are modeling printed circuit boards where you know the electrical power dissipated in the circuits but not the heat flux or wall temperature. • To uncouple the two sides of the wall and specify different thermal conditions on each one, choose Temperature or Heat Flux as the thermal condition type. (Convection and Radiation are not applicable for two-sided walls.) The relationship between the wall and its shadow will be retained, so that you can couple them again at a later time, if desired. You will need to set the relevant parameters for the selected thermal condition, as described above. The two uncoupled walls can have different thicknesses, and are effectively insulated from one another. If you specify a non-zero wall thickness for the uncoupled walls, the thermal boundary conditions you set will be specified on the outer sides of the two thin walls, as shown in Figure 6.13.3, where Tb1 is the Temperature (or qb1 is the Heat Flux) specified on one wall and Tb2 is the Temperature (or qb2 is the Heat Flux) specified on the other wall. kw1 and kw2 are the thermal conductivities of the uncoupled thin walls. Note that the gap between the walls in Figure 6.13.3 is not part of the model; it is included in

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the figure only to show where the thermal boundary condition for each uncoupled wall is applied. thin walls

q b1 or Tb1

q b2 or Tb2 fluid or solid cells

fluid or solid cells

k w1

k w2

Figure 6.13.3: Thermal Conditions are Specified on the Outer Sides of the Uncoupled Thin Walls

Shell Conduction in Walls To enable shell conduction for a wall, turn on the Shell Conduction option in the Wall boundary condition panel. When this option is enabled, FLUENT will compute heat conduction within the wall, in addition to conduction across the wall (which is always computed when the energy equation is solved). The Shell Conduction option will appear in the Wall panel for all walls when solution of the energy equation is active. For a boundary wall, the thermal conditions are applied as described above for thin walls.

! You must specify a non-zero Wall Thickness in the Wall panel, because the shell conduction model is relevant only for walls with non-zero thickness.

! Note that the shell conduction model has several limitations: • It is available only in 3D. • It is available only when the segregated solver is used. • It cannot be used with the non-premixed or partially premixed combustion model.


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Boundary Conditions

• It cannot be used with the multiphase mixture, VOF, or Eulerian model. • When used in conjunction with the discrete ordinates (DO) radiation model, shell conducting walls cannot be semi-transparent. • Shell conducting walls cannot be split or merged. If you need to split or merge a shell conducting wall, disable the Shell Conduction option for the wall, perform the split or merge operation, and then enable Shell Conduction for the new wall zones. • The shell conduction model cannot be used on a wall zone that has been adapted. If you want to perform adaption elsewhere in the computational domain, be sure to use the mask register described in Section 25.10.1 to ensure that no adaption is performed on the shell conducting wall. • Fluxes at the ends of a shell conducting wall are not included in the heat balance reports. These fluxes are accounted for correctly in the FLUENT solution, but not in the flux report itself.

Defining Wall Motion Wall boundaries can be either stationary or moving. The stationary boundary condition specifies a fixed wall, whereas the moving boundary condition can be used to specify the translational or rotational velocity of the wall, or the velocity components. Wall motion conditions are entered in the Momentum section of the Wall panel (Figure 6.13.4), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). To view the wall motion conditions, click the Momentum tab. Defining a Stationary Wall For a stationary wall, choose the Stationary Wall option under Wall Motion. Defining Velocity Conditions for Moving Walls If you wish to include tangential motion of the wall in your calculation, you need to define the translational or rotational velocity, or the velocity components. Select the Moving Wall option under Wall Motion. The Wall panel will expand, as shown in Figure 6.13.4, to show the wall velocity conditions. Note that you cannot use the moving wall condition to model problems where the wall has a motion normal to itself. FLUENT will neglect any normal component of wall motion that you specify using the methods below.

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Figure 6.13.4: The Wall Panel for a Moving Wall

Specifying Relative or Absolute Velocity If the cell zone adjacent to the wall is moving (e.g., if you are using a moving reference frame or a sliding mesh), you can choose to specify velocities relative to the zone motion by enabling the Relative to Adjacent Cell Zone option. If you choose to specify relative velocities, a velocity of zero means that the wall is stationary in the relative frame, and therefore moving at the speed of the adjacent cell zone in the absolute frame. If you choose to specify absolute velocities (by enabling the Absolute option), a velocity of zero means that the wall is stationary in the absolute frame, and therefore moving at the speed of the adjacent cell zone—but in the opposite direction—in the relative reference frame.

! If you are using one or more moving reference frames, sliding meshes, or mixing planes, and you want the wall to be fixed in the moving frame, it is recommended that you


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Boundary Conditions

specify relative velocities (the default) rather than absolute velocities. Then, if you modify the speed of the adjacent cell zone, you will not need to make any changes to the wall velocities, as you would if you specified absolute velocities. Note that if the adjacent cell zone is not moving, the absolute and relative options are equivalent. Translational Wall Motion For problems that include linear translational motion of the wall boundary (e.g., a rectangular duct with a moving belt as one wall) you can enable the Translational option and specify the wall’s Speed and Direction (X,Y,Z vector). By default, wall motion is “disabled” by the specification of Translational velocity with a Speed of zero. If you need to define non-linear translational motion, you will need to use the Components option, described below. Rotational Wall Motion For problems that include rotational wall motion you can enable the Rotational option and define the rotational Speed about a specified axis. To define the axis, set the RotationAxis Direction and Rotation-Axis Origin. This axis is independent of the axis of rotation used by the adjacent cell zone, and independent of any other wall rotation axis. For 3D problems, the axis of rotation is the vector passing through the specified RotationAxis Origin and parallel to the vector from (0,0,0) to the (X,Y,Z) point specified under Rotation-Axis Direction. For 2D problems, you will specify only the Rotation-Axis Origin; the axis of rotation is the z-direction vector passing through the specified point. For 2D axisymmetric problems, you will not define the axis: the rotation will always be about the x axis, with the origin at (0,0). Note that the modeling of tangential rotational motion will be correct only if the wall bounds a surface of revolution about the prescribed axis of rotation (e.g., a circle or cylinder). Note also that rotational motion can be specified for a wall in a stationary reference frame. Wall Motion Based on Velocity Components For problems that include linear or non-linear translational motion of the wall boundary you can enable the Components option and specify the X-Velocity, Y-Velocity, and ZVelocity of the wall. You can define non-linear translational motion using a boundary profile or a user-defined function for the X-Velocity, Y-Velocity, and/or Z-Velocity of the wall.

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Wall Motion for Two-Sided Walls As discussed earlier in this section, when you read a grid with a two-sided wall zone (which forms the interface between fluid/solid regions) into FLUENT, a “shadow” zone will automatically be created so that each side of the wall is a distinct wall zone. For two-sided walls, it is possible to specify different motions for the wall and shadow zones, whether or not they are coupled. Note, however, that you cannot specify motion for a wall (or shadow) that is adjacent to a solid zone.

Defining Shear Conditions at Walls Three types of shear conditions are available: • no-slip • specified shear • Marangoni stress Note that all moving walls are no-slip; the other shear conditions are relevant only for stationary walls. The no-slip condition is the default, and it indicates that the fluid sticks to the wall and moves with the same velocity as the wall, if it is moving. The specified shear and Marangoni stress boundary conditions are useful in modeling situations in which the shear stress (rather than the motion of the fluid) is known. Examples of such situations are applied shear stress, slip wall (zero shear stress), and free surface conditions (zero shear stress or shear stress dependent on surface tension gradient). The specified shear boundary condition allows you to specify the x, y, and z components of the shear stress as constant values or boundary profiles. The Marangoni stress boundary condition allows you to specify the gradient of the surface tension with respect to the temperature at this surface. The shear stress is calculated based on the surface gradient of the temperature and the specified surface tension gradient. The Marangoni stress option is available only for calculations in which the energy equation is being solved. Shear conditions are entered in the Momentum section of the Wall panel, which is opened from the Boundary Conditions panel (as described in Section 6.1.4). To view the shear conditions, click the Momentum tab. Modeling No-Slip Walls You can model a no-slip wall by selecting the No Slip option under Shear Condition. This is the default for all walls in viscous flows.


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Specified Shear In addition to the no-slip wall that is the default for viscous flows, you can model a slip wall by specifying zero or non-zero shear. To specify the shear, select the Specified Shear option under Shear Condition (see Figure 6.13.5). You can then enter x, y, and z components of shear under Shear Stress. Wall functions for turbulence are not used with the Specified Shear option.

Figure 6.13.5: The Wall Panel for Specified Shear

Marangoni Stress FLUENT can also model shear stresses caused by the variation of surface tension due to temperature. The shear stress applied at the wall is given by τ=

dσ ∇s T dT

(6.13-1)

where dσ/dT is the surface tension gradient with respect to temperature, and ∇s T is the surface gradient. This shear stress is then applied to the momentum equation.

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To model Marangoni stress for the wall, select the Marangoni Stress option under Shear Condition (see Figure 6.13.6). This option is available only for calculations in which the energy equation is being solved. You can then enter the surface tension gradient (dσ/dT in Equation 6.13-1) in the Surface Tension Gradient field. Wall functions for turbulence are not used with the Marangoni Stress option.

Figure 6.13.6: The Wall Panel for Marangoni Stress

Modeling Wall Roughness Effects in Turbulent Wall-Bounded Flows Fluid flows over rough surfaces are encountered in diverse situations. Examples are, among many others, flows over the surfaces of airplanes, ships, turbomachinery, heat exchangers, and piping systems, and atmospheric boundary layers over terrain of varying roughness. Wall roughness affects drag (resistance) and heat and mass transfer on the walls. If you are modeling a turbulent wall-bounded flow in which the wall roughness effects are considered to be significant, you can include the wall roughness effects through the law-of-the-wall modified for roughness.


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Law-of-the-Wall Modified for Roughness Experiments in roughened pipes and channels indicate that the mean velocity distribution near rough walls, when plotted in the usual semi-logarithmic scale, has the same slope (1/κ) but a different intercept (additive constant B in the log-law). Thus, the law-ofthe-wall for mean velocity modified for roughness has the form u p u∗ 1 ρu∗ yp = ln(E ) − ∆B τw /ρ κ µ

(6.13-2)

where u∗ = Cµ1/4 k 1/2 and ∆B =

1 ln fr κ

(6.13-3)

where fr is a roughness function that quantifies the shift of the intercept due to roughness effects. ∆B depends, in general, on the type (uniform sand, rivets, threads, ribs, mesh-wire, etc.) and size of the roughness. There is no universal roughness function valid for all types of roughness. For a sand-grain roughness and similar types of uniform roughness elements, however, ∆B has been found to be well-correlated with the nondimensional roughness height, Ks+ = ρKs u∗ /µ, where Ks is the physical roughness height and u∗ = Cµ1/4 k 1/2 . Analyses of experimental data show that the roughness function is not a single function of Ks+ , but takes different forms depending on the Ks+ value. It has been observed that there are three distinct regimes: • Hydrodynamically smooth (Ks+ ≤ 2.25) • Transitional (2.25 < Ks+ ≤ 90) • Fully rough (Ks+ > 90) According to the data, roughness effects are negligible in the hydrodynamically smooth regime, but become increasingly important in the transitional regime, and take full effect in the fully rough regime. In FLUENT, the whole roughness regime is subdivided into the three regimes, and the formulas proposed by Cebeci and Bradshaw based on Nikuradse’s data [34] are adopted to compute ∆B for each regime. For the hydrodynamically smooth regime (Ks+ ≤ 2.25): ∆B = 0

(6.13-4)

For the transitional regime (2.25 < Ks+ ≤ 90):

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n o 1 Ks+ − 2.25 ∆B = ln + Cs Ks+ × sin 0.4258(ln Ks+ − 0.811) κ 87.75 "

#

(6.13-5)

where Cs is a roughness constant, and depends on the type of the roughness. In the fully rough regime (Ks+ > 90): ∆B =

1 ln(1 + Cs Ks+ ) κ

(6.13-6)

In the solver, given the roughness parameters, ∆B(Ks+ ) is evaluated using the corresponding formula (Equation 6.13-4, 6.13-5, or 6.13-6). The modified law-of-the-wall in Equation 6.13-2 is then used to evaluate the shear stress at the wall and other wall functions for the mean temperature and turbulent quantities. Setting the Roughness Parameters The roughness parameters are in the Momentum section of the Wall panel (see Figure 6.13.6), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). To view the wall roughness parameters, click the Momentum tab. To model the wall roughness effects, you must specify two roughness parameters: the Roughness Height, Ks , and the Roughness Constant, Cs . The default roughness height (Ks ) is zero, which corresponds to smooth walls. For the roughness to take effect, you must specify a non-zero value for Ks . For a uniform sand-grain roughness, the height of the sand-grain can simply be taken for Ks . For a non-uniform sand-grain, however, the mean diameter (D50 ) would be a more meaningful roughness height. For other types of roughness, an “equivalent” sand-grain roughness height should be used for Ks . Choosing a proper roughness constant (Cs ) is dictated mainly by the type of the given roughness. The default roughness constant (Cs = 0.5) was determined so that, when used with k- turbulence models, it reproduces Nikuradse’s resistance data for pipes roughened with tightly-packed, uniform sand-grain roughness. You may need to adjust the roughness constant when the roughness you want to model departs much from uniform sand-grain. For instance, there is some experimental evidence that, for non-uniform sand-grains, ribs, and wire-mesh roughness, a higher value (Cs = 0.5 ∼ 1.0) is more appropriate. Unfortunately, a clear guideline for choosing Cs for arbitrary types of roughness is not available. Note that it is not physically meaningful to have a mesh size such that the wall-adjacent cell is smaller than the roughness height. For best results, make sure that the distance from the wall to the centroid of the wall-adjacent cell is greater than Ks .


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Defining Species Boundary Conditions for Walls By default, a zero-gradient condition for all species is assumed at walls (except for species that participate in surface reactions), but it is also possible to specify species mass fractions at walls. That is, Dirichlet boundary conditions such as those that are specified at inlets can be used at walls as well. If you wish to retain the default zero-gradient condition for a species, no inputs are required. If you want to specify the mass fraction for a species at the wall, the steps are as follows: 1. Click the Species tab in the Wall panel to view the species boundary conditions for the wall (see Figure 6.13.7). 2. Under Species Boundary Condition, select Specified Mass Fraction (rather than Zero Diffusive Flux) in the drop-down list to the right of the species name. The panel will expand to include space for Species Mass Fractions.

Figure 6.13.7: The Wall Panel for Species Boundary Condition Input

3. Under Species Mass Fractions, specify the mass fraction for the species.

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The boundary condition type for each species is specified separately, so you can choose to use different methods for different species. If you are modeling species transport with reactions, you can, alternatively, enable a reaction mechanism at a wall by turning on the Reaction option and selecting an available mechanism from the Reaction Mechanisms drop-down list. See Section 13.1.4 more information about defining reaction mechanisms.

Defining Reaction Boundary Conditions for Walls If you have enabled the modeling of wall surface reactions in the Species Model panel, you can indicate whether or not surface reactions should be activated for the wall. In the Species section of the Wall panel (Figure 6.13.7), turn the Surface Reactions option on or off. Note that a zero-gradient condition is assumed at the wall for species that do not participate in any surface reactions.

Defining Radiation Boundary Conditions for Walls If you are using the P-1 radiation model, the DTRM, the DO model, or the surface-tosurface model, you will need to set the emissivity of the wall (Internal Emissivity) in the Radiation section of the Wall panel. If you are using the Rosseland model you do not need to set the emissivity, because FLUENT assumes the emissivity is 1. If you are using the DO model you will also need to define the wall as diffuse, specular, or semi-transparent. See Section 11.3.16 for details.

Defining Discrete Phase Boundary Conditions for Walls If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the wall in the DPM section of the Wall panel. See Section 21.10 for details.

Defining Multiphase Boundary Conditions for Walls If you are using the VOF model and you are modeling wall adhesion, you can specify the contact angle for each pair of phases at the wall in the Momentum section of the Wall panel. See Section 22.6.16 for details.

Defining Boundary Conditions for User-Defined Scalars If you are using any user-defined scalars in your simulation, you can specify boundary conditions for them in the UDS section of the Wall panel. See the separate UDF Manual for details about user-defined scalars.


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6.13.2

Default Settings at Wall Boundaries

The default thermal boundary condition is a fixed heat flux of zero. Walls are, by default, not moving.

6.13.3

Shear-Stress Calculation Procedure at Wall Boundaries

For no-slip wall conditions, FLUENT uses the properties of the flow adjacent to the wall/fluid boundary to predict the shear stress on the fluid at the wall. In laminar flows this calculation simply depends on the velocity gradient at the wall, while in turbulent flows one of the approaches described in Section 10.8 is used. For specified-shear walls, FLUENT will compute the tangential velocity at the boundary. If you are modeling inviscid flow with FLUENT, all walls use a slip condition, so they are frictionless and exert no shear stress on the adjacent fluid.

Shear-Stress Calculation in Laminar Flow In a laminar flow, the wall shear stress is defined by the normal velocity gradient at the wall as τw = µ

∂v ∂n

(6.13-7)

When there is a steep velocity gradient at the wall, you must be sure that the grid is sufficiently fine to accurately resolve the boundary layer. Guidelines for the appropriate placement of the near-wall node in laminar flows are provided in Section 5.2.2.

Shear-Stress Calculation in Turbulent Flows Wall treatments for turbulent flows are described in Section 10.8.

6.13.4

Heat Transfer Calculations at Wall Boundaries

Temperature Boundary Conditions When a fixed temperature condition is applied at the wall, the heat flux to the wall from a fluid cell is computed as q = hf (Tw − Tf ) + qrad

(6.13-8)

where

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hf Tw Tf qrad

= = = =

fluid-side local heat transfer coefficient wall surface temperature local fluid temperature radiative heat flux

Note that the fluid-side heat transfer coefficient is computed based on the local flow-field conditions (e.g., turbulence level, temperature, and velocity profiles), as described by Equations 6.13-15 and 10.8-5. Heat transfer to the wall boundary from a solid cell is computed as q=

ks (Tw − Ts ) + qrad ∆n

(6.13-9)

where ks Ts ∆n

= thermal conductivity of the solid = local solid temperature = distance between wall surface and the solid cell center

Heat Flux Boundary Conditions When you define a heat flux boundary condition at a wall, you specify the heat flux at the wall surface. FLUENT uses Equation 6.13-8 and your input of heat flux to determine the wall surface temperature adjacent to a fluid cell as Tw =

q − qrad + Tf hf

(6.13-10)

where, as noted above, the fluid-side heat transfer coefficient is computed based on the local flow-field conditions. When the wall borders a solid region, the wall surface temperature is computed as Tw =

(q − qrad )∆n + Ts ks

(6.13-11)

Convective Heat Transfer Boundary Conditions When you specify a convective heat transfer coefficient boundary condition at a wall, FLUENT uses your inputs of the external heat transfer coefficient and external heat sink temperature to compute the heat flux to the wall as

q = hf (Tw − Tf ) + qrad = hext (Text − Tw )


(6.13-12)

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where hext Text qrad

= = =

external heat transfer coefficient defined by you external heat-sink temperature defined by you radiative heat flux

Equation 6.13-12 assumes a wall of zero thickness.

External Radiation Boundary Conditions When the external radiation boundary condition is used in FLUENT, the heat flux to the wall is computed as

q = hf (Tw − Tf ) + qrad 4 = ext σ(T∞ − Tw4 )

(6.13-13)

where ext σ Tw T∞ qrad

= = = =

emissivity of the external wall surface defined by you Stefan-Boltzmann constant surface temperature of the wall temperature of the radiation source or sink on the exterior of the domain, defined by you = radiative heat flux to the wall from within the domain

Equation 6.13-13 assumes a wall of zero thickness.

Combined External Convection and Radiation Boundary Conditions When you choose the combined external heat transfer condition, the heat flux to the wall is computed as

q = hf (Tw − Tf ) + qrad 4 = hext (Text − Tw ) + ext σ(T∞ − Tw4 )

(6.13-14)

where the variables are as defined above. Equation 6.13-14 assumes a wall of zero thickness.

Calculation of the Fluid-Side Heat Transfer Coefficient In laminar flows, the fluid side heat transfer at walls is computed using Fourier’s law applied at the walls. FLUENT uses its discrete form:

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6.14 Symmetry Boundary Conditions

q = kf

∂T ∂n

!

(6.13-15)

wall

where n is the local coordinate normal to the wall. For turbulent flows, FLUENT uses the law-of-the-wall for temperature derived using the analogy between heat and momentum transfer [141]. See Section 10.8.2 for details.

6.14

Symmetry Boundary Conditions

Symmetry boundary conditions are used when the physical geometry of interest, and the expected pattern of the flow/thermal solution, have mirror symmetry. They can also be used to model zero-shear slip walls in viscous flows. This section describes the treatment of the flow at symmetry planes and provides examples of the use of symmetry. You do not define any boundary conditions at symmetry boundaries, but you must take care to correctly define your symmetry boundary locations.

! At the centerline of an axisymmetric geometry, you should use the axis boundary type rather than the symmetry boundary type, as illustrated in Figure 6.16.1. See Section 6.16 for details.

6.14.1

Examples of Symmetry Boundaries

Symmetry boundaries are used to reduce the extent of your computational model to a symmetric subsection of the overall physical system. Figures 6.14.1 and 6.14.2 illustrate two examples of symmetry boundary conditions used in this way.

symmetry planes

Figure 6.14.1: Use of Symmetry to Model One Quarter of a 3D Duct

Figure 6.14.3 illustrates two problems in which a symmetry plane would be inappropriate. In both examples, the problem geometry is symmetric but the flow itself does not obey the symmetry boundary conditions. In the first example, buoyancy creates an asymmetric


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Boundary Conditions

2 symmetry planes (model includes a 90° sector)

Figure 6.14.2: Use of Symmetry to Model One Quarter of a Circular Cross-Section

flow. In the second, swirl in the flow creates a flow normal to the would-be symmetry plane. Note that this second example should be handled using rotationally periodic boundaries (as illustrated in Figure 6.15.1).

6.14.2

Calculation Procedure at Symmetry Boundaries

FLUENT assumes a zero flux of all quantities across a symmetry boundary. There is no convective flux across a symmetry plane: the normal velocity component at the symmetry plane is thus zero. There is no diffusion flux across a symmetry plane: the normal gradients of all flow variables are thus zero at the symmetry plane. The symmetry boundary condition can therefore be summarized as follows: • Zero normal velocity at a symmetry plane • Zero normal gradients of all variables at a symmetry plane As stated above, these conditions determine a zero flux across the symmetry plane, which is required by the definition of symmetry. Since the shear stress is zero at a symmetry boundary, it can also be interpreted as a “slip” wall when used in viscous flow calculations.

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6.14 Symmetry Boundary Conditions

cold hot fluid rises

g

hot

cold

not a plane of symmetry

not a plane of symmetry

Figure 6.14.3: Inappropriate Use of Symmetry


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6.15

Periodic Boundary Conditions

Periodic boundary conditions are used when the physical geometry of interest and the expected pattern of the flow/thermal solution have a periodically repeating nature. Two types of periodic conditions are available in FLUENT. The first type does not allow a pressure drop across the periodic planes. (Note to FLUENT 4 users: This type of periodic boundary is referred to as a “cyclic” boundary in FLUENT 4.) The second type allows a pressure drop to occur across translationally periodic boundaries, enabling you to model “fully-developed” periodic flow. (In FLUENT 4 this is a “periodic” boundary.) This section discusses the no-pressure-drop periodic boundary condition. A complete description of the fully-developed periodic flow modeling capability is provided in Section 8.3. You can find the following information about periodic boundary conditions in this section: • Section 6.15.1: Examples of Periodic Boundaries • Section 6.15.2: Inputs for Periodic Boundaries • Section 6.15.3: Default Settings at Periodic Boundaries • Section 6.15.4: Calculation Procedure at Periodic Boundaries

6.15.1

Examples of Periodic Boundaries

Periodic boundary conditions are used when the flows across two opposite planes in your computational model are identical. Figure 6.15.1 illustrates a typical application of periodic boundary conditions. In this example the flow entering the computational model through one periodic plane is identical to the flow exiting the domain through the opposite periodic plane. Periodic planes are always used in pairs as illustrated in this example.

6.15.2

Inputs for Periodic Boundaries

For a periodic boundary without any pressure drop, there is only one input you need to consider: whether the geometry is rotationally or translationally periodic. (Additional inputs are required for a periodic flow with a periodic pressure drop. See Section 8.3.) Rotationally periodic boundaries are boundaries that form an included angle about the centerline of a rotationally symmetric geometry. Figure 6.15.1 illustrates rotational periodicity. Translationally periodic boundaries are boundaries that form periodic planes in a rectilinear geometry. Figure 6.15.2 illustrates translationally periodic boundaries. You will specify translational or rotational periodicity for a periodic boundary in the Periodic panel (Figure 6.15.3), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

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6.15 Periodic Boundary Conditions 4 tangential inlets

periodic boundaries

Figure 6.15.1: Use of Periodic Boundaries to Define Swirling Flow in a Cylindrical Vessel

(There will be an additional item in the Periodic panel for the coupled solvers, which allows you to specify the periodic pressure jump. See Section 8.3 for details.) If the domain is rotationally periodic, select Rotational as the Periodic Type; if it is translationally periodic, select Translational. For rotationally periodic domains, the solver will automatically compute the angle through which the periodic zone is rotated. The axis used for this rotation is the axis of rotation specified for the adjacent cell zone. Note that there is no need for the adjacent cell zone to be moving for you to use a rotationally periodic boundary. You could, for example, model pipe flow in 3D using a nonrotating reference frame with a pie-slice of the pipe; the sides of the slice would require rotational periodicity. You can use the Grid/Check menu item (see Section 5.5) to compute and display the minimum, maximum, and average rotational angles of all faces on periodic boundaries. If the difference between the minimum, maximum, and average values is not negligible, then there is a problem with the grid: the grid geometry is not periodic about the specified axis.

6.15.3

Default Settings at Periodic Boundaries

By default, all periodic boundaries are translational.

6.15.4

Calculation Procedure at Periodic Boundaries

FLUENT treats the flow at a periodic boundary as though the opposing periodic plane is a direct neighbor to the cells adjacent to the first periodic boundary. Thus, when calculating the flow through the periodic boundary adjacent to a fluid cell, the flow conditions at the fluid cell adjacent to the opposite periodic plane are used.


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Boundary Conditions

(a) Physical Domain

periodic boundary

periodic boundary (b) Modeled Domain

Figure 6.15.2: Example of Translational Periodicity

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6.16 Axis Boundary Conditions

Figure 6.15.3: The Periodic Panel

6.16

Axis Boundary Conditions

The axis boundary type must be used as the centerline of an axisymmetric geometry (see Figure 6.16.1). It can also be used for the centerline of a cylindrical-polar quadrilateral or hexahedral grid (e.g., a grid created for a structured-grid code such as FLUENT 4). You do not need to define any boundary conditions at axis boundaries.

axis

Figure 6.16.1: Use of an Axis Boundary as the Centerline in an Axisymmetric Geometry

Calculation Procedure at Axis Boundaries To determine the appropriate physical value for a particular variable at a point on the axis, FLUENT uses the cell value in the adjacent cell.


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6.17

Fluid Conditions

A fluid zone is a group of cells for which all active equations are solved. The only required input for a fluid zone is the type of fluid material. You must indicate which material the fluid zone contains so that the appropriate material properties will be used.

! If you are modeling species transport and/or combustion, you will not select a material here; the mixture material is specified in the Species Model panel when you enable the model. Similarly, you will not specify the materials for a multiphase flow here; you will choose them when you define the phases, as described in Section 22.6.9. Optional inputs allow you to set sources or fixed values of mass, momentum, heat/temperature, turbulence, species, and other scalar quantities. You can also define motion for the fluid zone. If there are rotationally periodic boundaries adjacent to the fluid zone, you will need to specify the rotation axis. If you are modeling turbulence using one of the k- models, the k-ω model, or the Spalart-Allmaras model, you can choose to define the fluid zone as a laminar flow region. If you are modeling radiation using the DO model, you can specify whether or not the fluid participates in radiation.

! For information about porous zones, see Section 6.19. 6.17.1

Inputs for Fluid Zones

You will set all fluid conditions in the Fluid panel (Figure 6.17.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Defining the Fluid Material To define the material contained in the fluid zone, select the appropriate item in the Material Name drop-down list. This list will contain all fluid materials that have been defined (or loaded from the materials database) in the Materials panel. If you want to check or modify the properties of the selected material, you can click Edit... to open the Material panel; this panel contains just the properties of the selected material, not the full contents of the standard Materials panel.

! If you are modeling species transport or multiphase flow, the Material Name list will not appear in the Fluid panel. For species calculations, the mixture material for all fluid zones will be the material you specified in the Species Model panel. For multiphase flows, the materials are specified when you define the phases, as described in Section 22.6.9.

Defining Sources If you wish to define a source of heat, mass, momentum, turbulence, species, or other scalar quantity within the fluid zone, you can do so by enabling the Source Terms option. See Section 6.28 for details.

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6.17 Fluid Conditions

Figure 6.17.1: The Fluid Panel

Defining Fixed Values If you wish to fix the value of one or more variables in the fluid zone, rather than computing them during the calculation, you can do so by enabling the Fixed Values option. See Section 6.27 for details.

Specifying a Laminar Zone When you are calculating a turbulent flow using one of the k- models, the k-ω model, or the Spalart-Allmaras model, it is possible to “turn off” turbulence modeling (i.e., disable turbulence production and turbulent viscosity, but transport the turbulence quantities) in a specific fluid zone. This is useful if you know that the flow in a certain region is laminar. For example, if you know the location of the transition point on an airfoil, you can create a laminar/turbulent transition boundary where the laminar cell zone borders the turbulent cell zone. This feature allows you to model turbulent transition on the airfoil. To disable turbulence modeling in a fluid zone, turn on the Laminar Zone option in the Fluid panel.


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Boundary Conditions

Specifying a Reaction Mechanism If you are modeling species transport with reactions, you can enable a reaction mechanism in a fluid zone by turning on the Reaction option and selecting an available mechanism from the Reaction Mechanisms drop-down list. See Section 13.1.4 more information about defining reaction mechanisms.

Specifying the Rotation Axis If there are rotationally periodic boundaries adjacent to the fluid zone or if the zone is rotating, you must specify the rotation axis. To define the axis, set the Rotation-Axis Direction and Rotation-Axis Origin. This axis is independent of the axis of rotation used by any adjacent wall zones or any other cell zones. For 3D problems, the axis of rotation is the vector from the Rotation-Axis Origin in the direction of the vector given by your Rotation-Axis Direction inputs. For 2D non-axisymmetric problems, you will specify only the Rotation-Axis Origin; the axis of rotation is the z-direction vector passing through the specified point. (The z direction is normal to the plane of your geometry so that rotation occurs in the plane.) For 2D axisymmetric problems, you will not define the axis: the rotation will always be about the x axis, with the origin at (0,0).

Defining Zone Motion To define zone motion for a rotating or translating reference frame, select Moving Reference Frame in the Motion Type drop-down list (visible if you scroll down using the scroll bar to the right of the Rotation-Axis Origin and Direction) and then set the appropriate parameters in the expanded portion of the panel. To define zone motion for a sliding mesh, select Moving Mesh in the Motion Type dropdown list and then set the appropriate parameters in the expanded portion of the panel. See Section 9.5 for details. For problems that include linear, translational motion of the fluid zone, specify the Translational Velocity by setting the X, Y, and Z components. For problems that include rotational motion, specify the rotational Speed under Rotational Velocity. The rotation axis is defined as described above. See Chapter 9 for details about modeling flows in moving reference frames.

Defining Radiation Parameters If you are using the DO radiation model, you can specify whether or not the fluid zone participates in radiation using the Participates in Radiation option. See Section 11.3.16 for details.

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6.18 Solid Conditions

6.18

Solid Conditions

A “solid” zone is a group of cells for which only a heat conduction problem is solved; no flow equations are solved. The material being treated as a solid may actually be a fluid, but it is assumed that no convection is taking place. The only required input for a solid zone is the type of solid material. You must indicate which material the solid zone contains so that the appropriate material properties will be used. Optional inputs allow you to set a volumetric heat generation rate (heat source) or a fixed value of temperature. You can also define motion for the solid zone. If there are rotationally periodic boundaries adjacent to the solid zone, you will need to specify the rotation axis. If you are modeling radiation using the DO model, you can specify whether or not the solid material participates in radiation.

6.18.1

Inputs for Solid Zones

You will set all solid conditions in the Solid panel (Figure 6.18.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.18.1: The Solid Panel

Defining the Solid Material To define the material contained in the solid zone, select the appropriate item in the Material Name drop-down list. This list will contain all solid materials that have been defined (or loaded from the materials database) in the Materials panel. If you want to


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check or modify the properties of the selected material, you can click Edit... to open the Material panel; this panel contains just the properties of the selected material, not the full contents of the standard Materials panel.

Defining a Heat Source If you wish to define a source of heat within the solid zone, you can do so by enabling the Source Terms option. See Section 6.28 for details.

Defining a Fixed Temperature If you wish to fix the value of temperature in the solid zone, rather than computing it during the calculation, you can do so by enabling the Fixed Values option. See Section 6.27 for details.

Specifying the Rotation Axis If there are rotationally periodic boundaries adjacent to the solid zone or if the zone is rotating, you must specify the rotation axis. To define the axis, set the Rotation-Axis Direction and Rotation-Axis Origin. This axis is independent of the axis of rotation used by any adjacent wall zones or any other cell zones. For 3D problems, the axis of rotation is the vector from the Rotation-Axis Origin in the direction of the vector given by your Rotation-Axis Direction inputs. For 2D non-axisymmetric problems, you will specify only the Rotation-Axis Origin; the axis of rotation is the z-direction vector passing through the specified point. (The z direction is normal to the plane of your geometry so that rotation occurs in the plane.) For 2D axisymmetric problems, you will not define the axis: the rotation will always be about the x axis, with the origin at (0,0).

Defining Zone Motion To define zone motion for a rotating or translating reference frame, select Moving Reference Frame in the Motion Type drop-down list and then set the appropriate parameters in the expanded portion of the panel. To define zone motion for a sliding mesh, select Moving Mesh in the Motion Type dropdown list and then set the appropriate parameters in the expanded portion of the panel. See Section 9.5 for details. For problems that include linear, translational motion of the fluid zone, specify the Translational Velocity by setting the X, Y, and Z components. For problems that include rotational motion, specify the rotational Speed under Rotational Velocity. The rotation axis is defined as described above. See Chapter 9 for details about modeling flows in moving reference frames.

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6.19 Porous Media Conditions

Defining Radiation Parameters If you are using the DO radiation model, you can specify whether or not the solid material participates in radiation using the Participates in Radiation option. See Section 11.3.16 for details.

6.19

Porous Media Conditions

The porous media model can be used for a wide variety of problems, including flows through packed beds, filter papers, perforated plates, flow distributors, and tube banks. When you use this model, you define a cell zone in which the porous media model is applied and the pressure loss in the flow is determined via your inputs as described in Section 6.19.2. Heat transfer through the medium can also be represented, subject to the assumption of thermal equilibrium between the medium and the fluid flow, as described in Section 6.19.3. A 1D simplification of the porous media model, termed the “porous jump,” can be used to model a thin membrane with known velocity/pressure-drop characteristics. The porous jump model is applied to a face zone, not to a cell zone, and should be used (instead of the full porous media model) whenever possible because it is more robust and yields better convergence. See Section 6.22 for details. You can find information about modeling porous media in the following sections: • Section 6.19.1: Limitations and Assumptions of the Porous Media Model • Section 6.19.2: Momentum Equations for Porous Media • Section 6.19.3: Treatment of the Energy Equation in Porous Media • Section 6.19.4: Treatment of Turbulence in Porous Media • Section 6.19.5: Effect of Porosity on Transient Scalar Equations • Section 6.19.6: User Inputs for Porous Media • Section 6.19.7: Modeling Porous Media Based on Physical Velocity • Section 6.19.8: Solution Strategies for Porous Media • Section 6.19.9: Postprocessing for Porous Media


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6.19.1

Limitations and Assumptions of the Porous Media Model

The porous media model incorporates an empirically determined flow resistance in a region of your model defined as “porous”. In essence, the porous media model is nothing more than an added momentum sink in the governing momentum equations. As such, the following modeling assumptions and limitations should be readily recognized: • Since the volume blockage that is physically present is not represented in the model, by default FLUENT uses and reports a superficial velocity inside the porous medium, based on the volumetric flow rate, to ensure continuity of the velocity vectors across the porous medium interface. As a more accurate alternative, you can instruct FLUENT to use the true (physical) velocity inside the porous medium. See Section 6.19.7 for details. • The effect of the porous medium on the turbulence field is only approximated. See Section 6.19.4 for details. • When applying the porous media model in a moving reference frame, use the relative reference frame rather than the absolute reference frame to obtain the correct source terms.

6.19.2

Momentum Equations for Porous Media

Porous media are modeled by the addition of a momentum source term to the standard fluid flow equations. The source term is composed of two parts: a viscous loss term (Darcy, the first term on the right-hand side of Equation 6.19-1 ), and an inertial loss term (the second term on the right-hand side of Equation 6.19-1) 

3 X



3 X

1 Si = −  Dij µvj + Cij ρvmag vj  2 j=1 j=1

(6.19-1)

where Si is the source term for the ith (x, y, or z) momentum equation, and D and C are prescribed matrices. This momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity (or velocity squared) in the cell. To recover the case of simple homogeneous porous media µ 1 Si = − vi + C2 ρvmag vi α 2

(6.19-2)

where α is the permeability and C2 is the inertial resistance factor, simply specify D and C as diagonal matrices with 1/α and C2 , respectively, on the diagonals (and zero for the other elements).

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FLUENT also allows the source term to be modeled as a power law of the velocity magnitude: Si = −C0 |v|C1 = −C0 |v|(C1 −1) vi

(6.19-3)

where C0 and C1 are user-defined empirical coefficients.

! In the power-law model, the pressure drop is isotropic and the units for C0 are SI. Darcy’s Law in Porous Media In laminar flows through porous media, the pressure drop is typically proportional to velocity and the constant C2 can be considered to be zero. Ignoring convective acceleration and diffusion, the porous media model then reduces to Darcy’s Law: µ ∇p = − ~v α

(6.19-4)

The pressure drop that FLUENT computes in each of the three (x,y,z) coordinate directions within the porous region is then

∆px =

3 X µ

vj ∆nx

3 X µ

vj ∆ny

3 X µ

vj ∆nz

j=1

∆py =

j=1

∆pz =

j=1

αxj

αyj

αzj

(6.19-5)

where 1/αij are the entries in the matrix D in Equation 6.19-1, vj are the velocity components in the x, y, and z directions, and ∆nx , ∆ny , and ∆nz are the thicknesses of the medium in the x, y, and z directions. Here, the thickness of the medium (∆nx , ∆ny , or ∆nz ) is the actual thickness of the porous region in your model. Thus if the thicknesses used in your model differ from the actual thicknesses, you must make the adjustments in your inputs for 1/αij .

Inertial Losses in Porous Media At high flow velocities, the constant C2 in Equation 6.19-1 provides a correction for inertial losses in the porous medium. This constant can be viewed as a loss coefficient


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Boundary Conditions

per unit length along the flow direction, thereby allowing the pressure drop to be specified as a function of dynamic head. If you are modeling a perforated plate or tube bank, you can sometimes eliminate the permeability term and use the inertial loss term alone, yielding the following simplified form of the porous media equation:

∇p = −

3 X

j=1

C2ij

1 ρvj vmag 2

(6.19-6)

or when written in terms of the pressure drop in the x, y, z directions:

3 X

∆px ≈

1 C2xj ∆nx ρvj vmag 2 j=1

∆py ≈

3 X

1 C2yj ∆ny ρvj vmag 2 j=1

∆pz ≈

3 X

1 C2zj ∆nz ρvj vmag 2 j=1

(6.19-7)

Again, the thickness of the medium (∆nx , ∆ny , or ∆nz ) is the thickness you have defined in your model.

6.19.3

Treatment of the Energy Equation in Porous Media

FLUENT solves the standard energy transport equation (Equation 11.2-1) in porous media regions with modifications to the conduction flux and the transient terms only. In the porous medium, the conduction flux uses an effective conductivity and the transient term includes the thermal inertia of the solid region on the medium:

"

!

#

X ∂ (γρf Ef + (1 − γ)ρs Es ) + ∇ · (~v (ρf Ef + p)) = ∇ · keff ∇T − hi Ji + (τ · ~v ) + Sfh ∂t i (6.19-8)

where Ef Es γ keff Sfh

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= = = = =

total fluid energy total solid medium energy porosity of the medium effective thermal conductivity of the medium fluid enthalpy source term



Effective Conductivity in the Porous Medium The effective thermal conductivity in the porous medium, keff , is computed by FLUENT as the volume average of the fluid conductivity and the solid conductivity: keff = γkf + (1 − γ)ks

(6.19-9)

where γ kf ks

= porosity of the medium = fluid phase thermal conductivity (including the turbulent contribution, kt ) = solid medium thermal conductivity

The fluid thermal conductivity kf and the solid thermal conductivity ks can be computed via user-defined functions. The anisotropic effective thermal conductivity can also be specified via user-defined functions. In this case, the isotropic contributions from the fluid, γkf , are added to the diagonal elements of the solid anisotropic thermal conductivity matrix.

6.19.4

Treatment of Turbulence in Porous Media

FLUENT will, by default, solve the standard conservation equations for turbulence quantities in the porous medium. In this default approach, therefore, turbulence in the medium is treated as though the solid medium has no effect on the turbulence generation or dissipation rates. This assumption may be reasonable if the medium’s permeability is quite large and the geometric scale of the medium does not interact with the scale of the turbulent eddies. In other instances, however, you may want to suppress the effect of turbulence in the medium. If you are using one of the k- turbulence models, the k-ω model, or the Spalart-Allmaras model, you can suppress the effect of turbulence in a porous region by setting the turbulent contribution to viscosity, µt , equal to zero. When you choose this option, FLUENT will transport the inlet turbulence quantities through the medium, but their effect on the fluid mixing and momentum will be ignored. In addition, the generation of turbulence will be set to zero in the medium. This modeling strategy is enabled by turning on the Laminar Zone option in the Fluid panel. Enabling this option implies that µt is zero and that generation of turbulence will be zero in this porous zone. Disabling the option (the default) implies that turbulence will be computed in the porous region just as in the bulk fluid flow.

6.19.5

Effect of Porosity on Transient Scalar Equations

For transient porous media calculations, the effect of porosity on the time-derivative terms is accounted for in all scalar transport equations and the continuity equation. When the


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Boundary Conditions

effect of porosity is taken into account, the time-derivative term becomes φ is the scalar quantity (k, , etc.) and γ is the porosity.

∂ (γρφ), ∂t

where

The effect of porosity is enabled automatically for transient calculations, and the porosity is set to 1 by default.

6.19.6

User Inputs for Porous Media

When you are modeling a porous region, the only additional inputs for the problem setup are as follows. Optional inputs are indicated as such. 1. Define the porous zone. 2. Define the porous velocity formulation. (optional) 3. Identify the fluid material flowing through the porous medium. 4. Enable reactions for the porous zone, if appropriate, and select the reaction mechanism. 5. Set the viscous resistance coefficients (Dij in Equation 6.19-1, or 1/α in Equation 6.19-2) and the inertial resistance coefficients (Cij in Equation 6.19-1, or C2 in Equation 6.19-2), and define the direction vectors for which they apply. Alternatively, specify the coefficients for the power-law model. 6. Specify the porosity of the porous medium. 7. Select the material contained in the porous medium (required only for models that include heat transfer). 8. Set the volumetric heat generation rate in the solid portion of the porous medium (or any other sources, such as mass or momentum). (optional) 9. Set any fixed values for solution variables in the fluid region (optional). 10. Suppress the turbulent viscosity in the porous region, if appropriate. 11. Specify the rotation axis and/or zone motion, if relevant. Methods for determining the resistance coefficients and/or permeability are presented below. If you choose to use the power-law approximation of the porous-media momentum source term, you will enter the coefficients C0 and C1 in Equation 6.19-3 instead of the resistance coefficients and flow direction. You will set all parameters for the porous medium in the Fluid panel (Figure 6.19.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

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Figure 6.19.1: The Fluid Panel for a Porous Zone

Defining the Porous Zone As mentioned in Section 6.1, a porous zone is modeled as a special type of fluid zone. To indicate that the fluid zone is a porous region, enable the Porous Zone option in the Fluid panel. The panel will expand to show the porous media inputs (as shown in Figure 6.19.1).

Defining the Porous Velocity Formulation The Solver panel contains a Porous Formulation region where you can instruct FLUENT to use either a superficial or physical velocity in the porous medium simulation. By default, the velocity is set to Superficial Velocity. For details about using the Physical Velocity formulation, see Section 6.19.7.


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Boundary Conditions

Defining the Fluid Passing Through the Porous Medium To define the fluid that passes through the porous medium, select the appropriate fluid in the Material Name drop-down list in the Fluid panel. If you want to check or modify the properties of the selected material, you can click Edit... to open the Material panel; this panel contains just the properties of the selected material, not the full contents of the standard Materials panel.

! If you are modeling species transport or multiphase flow, the Material Name list will not appear in the Fluid panel. For species calculations, the mixture material for all fluid/porous zones will be the material you specified in the Species Model panel. For multiphase flows, the materials are specified when you define the phases, as described in Section 22.6.9.

Enabling Reactions in a Porous Zone If you are modeling species transport with reactions, you can enable reactions in a porous zone by turning on the Reaction option in the Fluid panel and selecting a mechanism in the Reaction Mechanism drop-down list. If your mechanism contains wall surface reactions, you will also need to specify a value for the Surface-to-Volume Ratio. This value is the surface area of the pore walls per unit volume ( VA ), and can be thought of as a measure of catalyst loading. With this value, FLUENT can calculate the total surface area on which the reaction takes place in each cell by multiplying VA by the volume of the cell. See Section 13.1.4 for details about defining reaction mechanisms. See Section 13.2 for details about wall surface reactions.

Defining the Viscous and Inertial Resistance Coefficients The viscous and inertial resistance coefficients are both defined in the same manner. The basic approach for defining the coefficients using a Cartesian coordinate system is to define one direction vector in 2D or two direction vectors in 3D, and then specify the viscous and/or inertial resistance coefficients in each direction. In 2D, the second direction, which is not explicitly defined, is normal to the plane defined by the specified direction vector and the z direction vector. In 3D, the third direction is normal to the plane defined by the two specified direction vectors. For a 3D problem, the second direction must be normal to the first. If you fail to specify two normal directions, the solver will ensure that they are normal by ignoring any component of the second direction that is in the first direction. You should therefore be certain that the first direction is correctly specified. You can also define the viscous and/or inertial resistance coefficients in each direction using a user-defined function (UDF). The user-defined options become available in the corresponding drop-down list when the UDF has been created and loaded into FLUENT. Note that the coefficients defined in the UDF must utilize the DEFINE PROPERTY macro.

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For more information on creating and using user-defined function, see the separate UDF Manual. If you are modeling axisymmetric swirling flows, you can specify an additional direction component for the viscous and/or inertial resistance coefficients. This direction component is always tangential to the other two specified directions. This option is available for both coupled and segregated solvers. In 3D, it is also possible to define the coefficients using a conical (or cylindrical) coordinate system, as described below.

! Note that the viscous and inertial resistance coefficients are generally based on the superficial velocity of the fluid in the porous media. The procedure for defining resistance coefficients is as follows: 1. Define the direction vectors. • To use a Cartesian coordinate system, simply specify the Direction-1 Vector and, for 3D, the Direction-2 Vector. Each direction will be that of the vector from (0,0) or (0,0,0) to the specified (X,Y) or (X,Y,Z). (The unspecified direction will be determined as described above.) For some problems in which the principal axes of the porous medium are not aligned with the coordinate axes of the domain, you may not know a priori the direction vectors of the porous medium. In such cases, the plane tool in 3D (or the line tool in 2D) can help you to determine these direction vectors. (a) “Snap” the plane tool (or the line tool) onto the boundary of the porous region. (Follow the instructions in Section 26.6.1 or 26.5.1 for initializing the tool to a position on an existing surface.) (b) Rotate the axes of the tool appropriately until they are aligned with the porous medium. (c) Once the axes are aligned, click on the Update From Plane Tool or Update From Line Tool button in the Fluid panel. FLUENT will automatically set the Direction-1 Vector to the direction of the red arrow of the tool, and (in 3D) the Direction-2 Vector to the direction of the green arrow. • To use a conical coordinate system (e.g., for an annular, conical filter element), follow the steps below. This option is available only in 3D cases. (a) Turn on the Conical option. (b) Specify the Cone Axis Vector and Point on Cone Axis. The direction of the Cone Axis Vector will be that of the vector from (0,0,0) to the specified (X,Y,Z). The Point on Cone Axis will be used by FLUENT to transform the resistances to the Cartesian coordinate system.


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(c) Set the Cone Half Angle (the angle between the cone’s axis and its surface, shown in Figure 6.19.2). To use a cylindrical coordinate system, set the Cone Half Angle to 0.

θ Figure 6.19.2: Cone Half Angle For some problems in which the axis of the conical filter element is not aligned with the coordinate axes of the domain, you may not know a priori the direction vector of the cone axis and coordinates of a point on the cone axis. In such cases, the plane tool can help you to determine the cone axis vector and point coordinates. One method is as follows: (a) Select a boundary zone of the conical filter element that is normal to the cone axis vector in the drop-down list next to the Snap to Zone button. (b) Click on the Snap to Zone button. FLUENT will automatically “snap” the plane tool onto the boundary. It will also set the Cone Axis Vector and the Point on Cone Axis. (Note that you will still have to set the Cone Half Angle yourself.) An alternate method is as follows: (a) “Snap” the plane tool onto the boundary of the porous region. (Follow the instructions in Section 26.6.1 for initializing the tool to a position on an existing surface.) (b) Rotate and translate the axes of the tool appropriately until the red arrow of the tool is pointing in the direction of the cone axis vector and the origin of the tool is on the cone axis (c) Once the axes and origin of the tool are aligned, click on the Update From Plane Tool button in the Fluid panel. FLUENT will automatically set the Cone Axis Vector and the Point on Cone Axis. (Note that you will still have to set the Cone Half Angle yourself.) 2. Under Viscous Resistance, specify the viscous resistance coefficient 1/α in each direction, and under Inertial Resistance, specify the inertial resistance coefficient C2 in each direction. (You will need to scroll down with the scroll bar to view these inputs.) If you are using the Conical specification method, Direction-1 is the cone axis direction, Direction-2 is the normal to the cone surface (radial (r) direction for a cylinder), and Direction-3 is the circumferential (θ) direction. In 3D there are three possible categories of coefficients, and in 2D there are two:

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• In the isotropic case, the resistance coefficients in all directions are the same (e.g., a sponge). For an isotropic case, you must explicitly set the resistance coefficients in each direction to the same value. • When (in 3D) the coefficients in two directions are the same and those in the third direction are different or (in 2D) the coefficients in the two directions are different, you must be careful to specify the coefficients properly for each direction. For example, if you had a porous region consisting of cylindrical straws with small holes in them positioned parallel to the flow direction, the flow would pass easily through the straws, but the flow in the other two directions (through the small holes) would be very little. If you had a plane of flat plates perpendicular to the flow direction, the flow would not pass through them at all; it would instead move in the other two directions. • In 3D the third possible case is one in which all three coefficients are different. For example, if the porous region consisted of a plane of irregularly-spaced objects (e.g., pins), the movement of flow between the blockages would be different in each direction. You would therefore need to specify different coefficients in each direction. (Note the comments in Section 6.19.8 when specifying anisotropic coefficients.) Methods for deriving viscous and inertial loss coefficients are described below. Deriving Porous Media Inputs Based on Superficial Velocity, Using a Known Pressure Loss When you use the porous media model, you must keep in mind that the porous cells in FLUENT are 100% open, and that the values that you specify for 1/αij and/or C2ij must be based on this assumption. Suppose, however, that you know how the pressure drop varies with the velocity through the actual device, which is only partially open to flow. The following exercise is designed to show you how to compute a value for C2 which is appropriate for the FLUENT model. Consider a perforated plate which has 25% area open to flow. The pressure drop through the plate is known to be 0.5 times the dynamic head in the plate. The loss factor, KL , defined as 1 2 ∆p = KL ( ρv25%open ) 2

(6.19-10)

is therefore 0.5, based on the actual fluid velocity in the plate, i.e., the velocity through the 25% open area. To compute an appropriate value for C2 , note that in the FLUENT model: 1. The velocity through the perforated plate assumes that the plate is 100% open.


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Boundary Conditions

2. The loss coefficient must be converted into dynamic head loss per unit length of the porous region. Noting item 1, the first step is to compute an adjusted loss factor, KL0 , which would be based on the velocity of a 100% open area: 1 2 ∆p = KL0 ( ρv100%open ) 2

(6.19-11)

or, noting that for the same flow rate, v25%open = 4 × v100%open ,

KL0 = KL × = 0.5 ×

2 v25%open 2 v100%open

2

4 1

= 8

(6.19-12)

The adjusted loss factor has a value of 8. Noting item 2, you must now convert this into a loss coefficient per unit thickness of the perforated plate. Assume that the plate has a thickness of 1.0 mm (10−3 m). The inertial loss factor would then be KL0 thickness 8 = = 8000 m−1 10−3

C2 =

(6.19-13)

Note that, for anisotropic media, this information must be computed for each of the 2 (or 3) coordinate directions. Using the Ergun Equation to Derive Porous Media Inputs for a Packed Bed As a second example, consider the modeling of a packed bed. In turbulent flows, packed beds are modeled using both a permeability and an inertial loss coefficient. One technique for deriving the appropriate constants involves the use of the Ergun equation [70], a semiempirical correlation applicable over a wide range of Reynolds numbers and for many types of packing: |∆p| 150µ (1 − )2 1.75ρ (1 − ) 2 = v∞ + v∞ 2 3 L Dp Dp 3

(6.19-14)

When modeling laminar flow through a packed bed, the second term in the above equation may be dropped, resulting in the Blake-Kozeny equation [70]:

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|∆p| 150µ (1 − )2 v∞ = L Dp2 3

(6.19-15)

In these equations, µ is the viscosity, Dp is the mean particle diameter, L is the bed depth, and is the void fraction, defined as the volume of voids divided by the volume of the packed bed region. Comparing Equations 6.19-4 and 6.19-6 with 6.19-14, the permeability and inertial loss coefficient in each component direction may be identified as

α=

Dp2 3 150 (1 − )2

(6.19-16)

3.5 (1 − ) Dp 3

(6.19-17)

and C2 =

Using an Empirical Equation to Derive Porous Media Inputs for Turbulent Flow Through a Perforated Plate As a third example we will take the equation of Van Winkle et al. [192, 240] and show how porous media inputs can be calculated for pressure loss through a perforated plate with square-edged holes. The expression, which is claimed by the authors to apply for turbulent flow through square-edged holes on an equilateral triangular spacing, is q

m ˙ = CAf (2ρ∆p)/(1 − (Af /Ap )2 )

(6.19-18)

where m ˙ Af Ap C

= = = =

mass flow rate through the plate the free area or total area of the holes the area of the plate (solid and holes) a coefficient that has been tabulated for various Reynolds-number ranges and for various D/t D/t = the ratio of hole diameter to plate thickness for t/D > 1.6 and for Re > 4000 the coefficient C takes a value of approximately 0.98, where the Reynolds number is based on hole diameter and velocity in the holes. Rearranging Equation 6.19-18, making use of the relationship m ˙ = ρvAp


(6.19-19)

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Boundary Conditions

and dividing by the plate thickness, ∆x = t, we obtain ∆p 1 2 1 (Ap /Af )2 − 1 = ρv ∆x 2 C2 t

(6.19-20)

where v is the superficial velocity (not the velocity in the holes). Comparing with Equation 6.19-6 it is seen that, for the direction normal to the plate, the constant C2 can be calculated from C2 =

1 (Ap /Af )2 − 1 C2 t

(6.19-21)

Using Tabulated Data to Derive Porous Media Inputs for Laminar Flow Through a Fibrous Mat Consider the problem of laminar flow through a mat or filter pad which is made up of randomly-oriented fibers of glass wool. As an alternative to the Blake-Kozeny equation (Equation 6.19-15) we might choose to employ tabulated experimental data. Such data is available for many types of fiber [110]. volume fraction of dimensionless permeability B solid material of glass wool 0.262 0.25 0.258 0.26 0.221 0.40 0.218 0.41 0.172 0.80 where B = α/a2 and a is the fiber diameter. α, for use in Equation 6.19-4, is easily computed for a given fiber diameter and volume fraction. Deriving the Porous Coefficients Based on Experimental Pressure and Velocity Data When you have experimental data for the porous component in the form of pressure drop against velocity through the component, you can extrapolate the data in order to determine the coefficients for the porous media. The following example takes you through the steps of defining the porous media boundary coefficients from such experimental data. If the data is: then an xy curve can be plotted to create a trendline through these points yielding the following equation

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∆p = 0.28296v 2 − 4.33539v

(6.19-22)

where ∆p is the pressure drop and v is the velocity. This equation is equivalent to Equation 6.19-2, i.e., a polynomial in velocity, so taking the curve coefficients: 1 0.28296 = C2 ρ 2

(6.19-23)

with ρ = 1.225 kg/m3 and the inertial resistance factor C2 = 0.462. Likewise, − 4.33539 =

µ α

with µ = 1.7894 × 10−5 and the viscous inertial factor,

(6.19-24) 1 α

= −242282.

! Note that this same technique can be applied to the porous jump boundary condition. In the case of a porous jump, you have to take into account the thickness of the medium ∆m. Your experimental data can be plotted in an xy curve, yielding an equation that is equivalent to Equation 6.22-1. From there, you can determine the permeability α and the pressure jump coefficient C2 .

Using the Power-Law Model If you choose to use the power-law approximation of the porous-media momentum source term (Equation 6.19-3), the only inputs required are the coefficients C0 and C1 . Under Power Law Model in the Fluid panel, enter the values for C0 and C1. Note that the power-law model can be used in conjunction with the Darcy and inertia models. C0 must be in SI units, consistent with the value of C1. Velocity (m/s) 20.0 50.0 80.0 110.0


Pressure Drop (Pa) 78.0 487.0 1432.0 2964.0

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Boundary Conditions

Defining Porosity To define the porosity, scroll down below the resistance inputs in the Fluid panel, and set the Porosity under Fluid Porosity. You can also define the porosity using a user-defined function (UDF). The user-defined option becomes available in the corresponding drop-down list when the UDF has been created and loaded into FLUENT. Note that the porosity defined in the UDF must utilize the DEFINE PROPERTY macro. For more information on creating and using user-defined function, see the separate UDF Manual. The porosity, γ, is the volume fraction of fluid within the porous region (i.e., the open volume fraction of the medium). The porosity is used in the prediction of heat transfer in the medium, as described in Section 6.19.3, and in the time-derivative term in the scalar transport equations for unsteady flow, as described in Section 6.19.5. It also impacts the calculation of reaction source terms and body forces in the medium. These sources will be proportional to the fluid volume in the medium. If you want to represent the medium as completely open (no effect of the solid medium), you should set the porosity equal to 1.0 (the default). When the porosity is equal to 1.0, the solid portion of the medium will have no impact on heat transfer or thermal/reaction source terms in the medium.

Defining the Porous Material If you choose to model heat transfer in the porous medium, you must specify the material contained in the porous medium. To define the material contained in the porous medium, scroll down below the resistance inputs in the Fluid panel, and select the appropriate solid in the Solid Material Name drop-down list under Fluid Porosity. If you want to check or modify the properties of the selected material, you can click Edit... to open the Material panel; this panel contains just the properties of the selected material, not the full contents of the standard Materials panel. In the Material panel, you can define the non-isotropic thermal conductivity of the porous material using a user-defined function (UDF). The user-defined option becomes available in the corresponding drop-down list when the UDF has been created and loaded into FLUENT. Note that the non-isotropic thermal conductivity defined in the UDF must utilize the DEFINE PROPERTY macro. For more information on creating and using userdefined function, see the separate UDF Manual.

Defining Sources If you want to include effects of the heat generated by the porous medium in the energy equation, enable the Source Terms option and set a non-zero Energy source. The solver will compute the heat generated by the porous region by multiplying this value by the total volume of the cells comprising the porous zone. You may also define sources of mass, momentum, turbulence, species, or other scalar quantities, as described in Section 6.28.

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Defining Fixed Values If you want to fix the value of one or more variables in the fluid region of the zone, rather than computing them during the calculation, you can do so by enabling the Fixed Values option. See Section 6.27 for details.

Suppressing the Turbulent Viscosity in the Porous Region As discussed in Section 6.19.4, turbulence will be computed in the porous region just as in the bulk fluid flow. If you are using one of the k- turbulence models, the SpalartAllmaras model, or the k-ω model, and you want to suppress the effect of turbulence in a porous region (so that turbulence generation is zero in the porous zone), turn on the Laminar Zone option in the Fluid panel.

Specifying the Rotation Axis and Defining Zone Motion Inputs for the rotation axis and zone motion are the same as for a standard fluid zone. See Section 6.17.1 for details.

6.19.7

Modeling Porous Media Based on Physical Velocity

As stated in Section 6.19.1, by default FLUENT calculates the superficial velocity based on volumetric flow rate. The superficial velocity in the governing equations can be represented as ~vsuperficial = γ~vphysical

(6.19-25)

where γ is the porosity of the media defined as the ratio of the volume occupied by the fluid to the total volume. The superficial velocity values within the porous region remain the same as those outside of the porous region. This limits the accuracy of the porous model where there should be an increase in velocity throughout the porous region. For more accurate simulations of porous media flows, it becomes necessary to solve for the true, or physical velocity throughout the flowfield, rather than the superficial velocity. FLUENT allows the calculation on the physical velocity using the Porous Formulation region of the Solver panel. By default, the Superficial Velocity option is turned on. Using the physical velocity formulation, and assuming a general scalar φ, the governing equation in an isotropic porous media has the following form: ∂(γρφ) + ∇ · (γρ~v φ) = ∇ · (γΓ∇φ) + γSφ ∂t


(6.19-26)

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Boundary Conditions

Assuming isotropic porosity and single phase flow, the volume-averaged mass and momentum conservation equations are as follows: ∂(γρ) + ∇ · (γρ~v ) = 0 ∂t

(6.19-27)

∂(γρ~v ) ~ f − µ + C2 ρ |~v | ~v + ∇ · (γρ~v~v ) = −γ∇p + ∇ · (γ~τ ) + γ B ∂t α 2

(6.19-28)

The last term in Equation 6.19-28 represents the viscous and inertial drag forces imposed by the pore walls on the fluid.

! Note that even when you solve for the physical velocity in Equation 6.19-28, the two resistance coefficients can still be derived using the superficial velocity as given in Section 6.19.6. FLUENT assumes that the inputs for these resistance coefficients are based upon well-established empirical correlations that are usually based on superficial velocity. Therefore, FLUENT automatically converts the inputs for the resistance coefficients into those that are compatible with the physical velocity formulation.

! Note that the inlet mass flow is also calculated from the superficial velocity. Therefore, for the same mass flow rate at the inlet and the same resistance coefficients, for either the physical or superficial velocity formulation you should obtain the same pressure drop across the porous media zone.

6.19.8

Solution Strategies for Porous Media

In general, you can use the standard solution procedures and solution parameter settings when your FLUENT model includes porous media. You may find, however, that the rate of convergence slows when you define a porous region through which the pressure drop is relatively large in the flow direction (e.g., the permeability, α, is low or the inertial factor, C2 , is large). This slow convergence can occur because the porous media pressure drop appears as a momentum source term—yielding a loss of diagonal dominance—in the matrix of equations solved. The best remedy for poor convergence of a problem involving a porous medium is to supply a good initial guess for the pressure drop across the medium. You can supply this guess by patching a value for the pressure in the fluid cells upstream and/or downstream of the medium, as described in Section 24.13.2. It is important to recall, when patching the pressure, that the pressures you input should be defined as the gauge pressures used by the solver (i.e., relative to the operating pressure defined in the Operating Conditions panel). Another possible way to deal with poor convergence is to temporarily disable the porous media model (by turning off the Porous Zone option in the Fluid panel) and obtain an initial flow field without the effect of the porous region. With the porous media model turned off, FLUENT will treat the porous zone as a fluid zone and calculate the flow field accordingly. Once an initial solution is obtained, or the calculation is proceeding steadily

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to convergence, you can enable the porous media model and continue the calculation with the porous region included. (This method is not recommended for porous media with high resistance.) Simulations involving highly anisotropic porous media may, at times, pose convergence troubles. You can address these issues by limiting the anisotropy of the porous media coefficients (1/αij and C2i,j ) to two or three orders of magnitude. Even if the medium’s resistance in one direction is infinite, you do not need to set the resistance in that direction to be greater than 1000 times the resistance in the primary flow direction.

6.19.9

Postprocessing for Porous Media

The impact of a porous region on the flow field can be determined by examining either velocity components or pressure values. Graphical plots (including XY plots and contour or vector plots) or alphanumeric reports of the following variables/functions may be of interest: • X, Y, Z Velocity (in the Velocity... category) • Static Pressure (in the Pressure... category) These variables are contained in the specified categories of the variable selection dropdown list that appears in postprocessing panels. Note that thermal reporting in the porous region does not reflect the solid medium properties. The reported density, heat capacity, conductivity, and enthalpy in the porous region are those of the fluid and do not include the effect of the solid medium.

! For porous media involving surface reactions, you can display/report the surface reaction rates using the Arrhenius Rate of Reaction-n in the Reactions... category of the variable selection drop-down list.


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Boundary Conditions

6.20

Fan Boundary Conditions

The fan model is a lumped parameter model that can be used to determine the impact of a fan with known characteristics upon some larger flow field. The fan boundary type allows you to input an empirical fan curve which governs the relationship between head (pressure rise) and flow rate (velocity) across a fan element. You can also specify radial and tangential components of the fan swirl velocity. The fan model does not provide an accurate description of the detailed flow through the fan blades. Instead, it predicts the amount of flow through the fan. Fans may be used in conjunction with other flow sources, or as the sole source of flow in a simulation. In the latter case, the system flow rate is determined by the balance between losses in the system and the fan curve. FLUENT also provides a connection for a special user-defined fan model that updates the pressure jump function during the calculation. This feature is described in Section 6.24. You can find the following information about modeling fans in this section: • Section 6.20.1: Fan Equations • Section 6.20.2: User Inputs for Fans • Section 6.20.3: Postprocessing for Fans

6.20.1

Fan Equations

Modeling the Pressure Rise Across the Fan A fan is considered to be infinitely thin, and the discontinuous pressure rise across it is specified as a function of the velocity through the fan. The relationship may be a constant, a polynomial, piecewise-linear, or piecewise-polynomial function, or a userdefined function. In the case of a polynomial, the relationship is of the form

∆p =

N X

fn v n−1

(6.20-1)

n=1

where ∆p is the pressure jump, fn are the pressure-jump polynomial coefficients, and v is the magnitude of the local fluid velocity normal to the fan.

! The velocity v can be either positive or negative. You must be careful to model the fan so that a pressure rise occurs for forward flow through the fan. You can, optionally, use the mass-averaged velocity normal to the fan to determine a single pressure-jump value for all faces in the fan zone.

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6.20 Fan Boundary Conditions

Modeling the Fan Swirl Velocity For three-dimensional problems, the values of the convected tangential and radial velocity fields can be imposed on the fan surface to generate swirl. These velocities can be specified as functions of the radial distance from the fan center. The relationships may be constant or polynomial functions, or user-defined functions.

! You must use SI units for all fan swirl velocity inputs. For the case of polynomial functions, the tangential and radial velocity components can be specified by the following equations:

Uθ =

N X

fn rn ; −1 ≤ N ≤ 6

(6.20-2)

N X

gn rn ; −1 ≤ N ≤ 6

(6.20-3)

n=−1

Ur =

n=−1

where Uθ and Ur are, respectively, the tangential and radial velocities on the fan surface in m/s, fn and gn are the tangential and radial velocity polynomial coefficients, and r is the distance to the fan center.

6.20.2

User Inputs for Fans

Once the fan zone has been identified (in the Boundary Conditions panel), you will set all modeling inputs for the fan in the Fan panel (Figure 6.20.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). Inputs for a fan are as follows: 1. Identify the fan zone. 2. Define the pressure jump across the fan. 3. Define the discrete phase boundary condition for the fan (for discrete phase calculations). 4. Define the swirl velocity, if desired (3D only).

Identifying the Fan Zone Since the fan is considered to be infinitely thin, it must be modeled as the interface between cells, rather than a cell zone. Thus the fan zone is a type of internal face zone (where the faces are line segments in 2D or triangles/quadrilaterals in 3D). If, when you read your grid into FLUENT, the fan zone is identified as an interior zone, use the Boundary


6-113

Boundary Conditions

Figure 6.20.1: The Fan Panel

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Conditions panel (as described in Section 6.1.3) to change the appropriate interior zone to a fan zone. Define −→Boundary Conditions... Once the interior zone has been changed to a fan zone, you can open the Fan panel and specify the pressure jump and, optionally, the swirl velocity.

Defining the Pressure Jump To define the pressure jump, you will specify a polynomial, piecewise-linear, or piecewisepolynomial function of velocity, a user-defined function, or a constant value. You should also check the Zone Average Direction vector to be sure that a pressure rise occurs for forward flow through the fan. The Zone Average Direction, calculated by the solver, is the face-averaged direction vector for the fan zone. If this vector is pointing in the direction you want the fan to blow, do not select Reverse Fan Direction; if it is pointing in the opposite direction, select Reverse Fan Direction. Polynomial, Piecewise-Linear, or Piecewise-Polynomial Function Follow these steps to set a polynomial, piecewise-linear, or piecewise-polynomial function for the pressure jump: 1. Check that the Profile Specification of Pressure-Jump option is off in the Fan panel. 2. Choose polynomial, piecewise-linear, or piecewise-polynomial in the drop-down list to the right of Pressure-Jump. (If the function type you want is already selected, you can click on the Edit... button to open the panel where you will define the function.) 3. In the panel that appears for the definition of the Pressure-Jump function (e.g., Figure 6.20.2), enter the appropriate values. These profile input panels are used the same way as the profile input panels for temperature-dependent properties. See Section 7.1.3 to find out how to use them. 4. Set any of the optional parameters described below. (optional) When you define the pressure jump using any of these types of functions, you can choose to limit the minimum and maximum velocity magnitudes used to calculate the pressure jump. Turning on the Limit Polynomial Velocity Range option allows you to specify minimum and maximum velocity magnitudes. If the calculated normal velocity magnitude exceeds the Max Velocity Magnitude that you specify, the Max Velocity Magnitude value will be used instead. Similarly, if the calculated velocity is less than the specified Min Velocity Magnitude, the Min Velocity Magnitude will be substituted for the calculated value.


6-115

Boundary Conditions

Figure 6.20.2: Polynomial Profile Panel for Pressure-Jump Definition

You also have the option to use the mass-averaged velocity normal to the fan to determine a single pressure-jump value for all faces in the fan zone. Turning on Calculate PressureJump from Average Conditions enables this option. Constant Value To define a constant pressure jump, follow these steps: 1. Turn off the Profile Specification of Pressure-Jump option in the Fan panel. 2. Choose constant in the drop-down list to the right of Pressure-Jump. 3. Enter the value for ∆p in the Pressure-Jump field. You can follow the procedure below, if it is more convenient: 1. Turn on the Profile Specification of Pressure-Jump option. 2. Select constant in the drop-down list below Pressure Jump Profile, and enter the value for ∆p in the Pressure Jump Profile field. User-Defined Function or Boundary Profile For a user-defined pressure-jump function or a function defined in a boundary profile file, you will follow these steps: 1. Turn on the Profile Specification of Pressure-Jump option. 2. Choose the appropriate function in the drop-down list below Pressure Jump Profile. See the separate UDF Manual for information about user-defined functions, and Section 6.26 for details about boundary profile files.

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Example: Determining the Pressure Jump Function This example shows you how to determine the function for the pressure jump. Consider the simple two-dimensional duct flow illustrated in Figure 6.20.3. Air at constant density enters the 2.0 m × 0.4 m duct with a velocity of 15 m/s. Centered in the duct is a fan. Fan

Air

0.4 m 5 m/s

2.0 m

Figure 6.20.3: A Fan Located In a 2D Duct

Assume that the fan characteristics are as follows when the fan is operating at 2000 rpm: Q (m3 /s)

∆p (Pa)

25 20 15 10 5 0

0.0 175 350 525 700 875

where Q is the flow through the fan and ∆p is the pressure rise across the fan. The fan characteristics in this example follow a simple linear relationship between pressure rise and flow rate. To convert this into a relationship between pressure rise and velocity, the cross-sectional area of the fan must be known. In this example, assuming that the duct is 1.0 m deep, this area is 0.4 m2 , so that the corresponding velocity values are as follows: v (m/s) ∆p (Pa) 62.5 50.0 37.5 25.0 12.5 0


0.0 175 350 525 700 875

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Boundary Conditions

The polynomial form of this relationship is the following equation for a line: ∆p = 875 − 14v

(6.20-4)

Defining Discrete Phase Boundary Conditions for the Fan If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the fan. See Section 21.10 for details.

Defining the Fan Swirl Velocity If you want to set tangential and radial velocity fields on the fan surface to generate swirl in a 3D problem, follow these steps: 1. Turn on the Swirl-Velocity Specification option in the Fan panel. 2. Specify the fan’s axis of rotation by defining the axis origin (Fan Origin) and direction vector (Fan Axis). 3. Set the value for the radius of the fan’s hub (Fan Hub Radius). The default is 1 × 10−6 to avoid division by zero in the polynomial. 4. Set the tangential and radial velocity functions as polynomial functions of radial distance, constant values, or user-defined functions.

! You must use SI units for all fan swirl velocity inputs. Polynomial Function To define a polynomial function for tangential or radial velocity, follow the steps below: 1. Check that the Profile Specification of Tangential Velocity or Profile Specification of Radial Velocity option is off in the Fan panel. 2. Enter the coefficients fn in Equation 6.20-2 or gn in Equation 6.20-3 in the Tangentialor Radial-Velocity Polynomial Coefficients field. Enter f−1 first, then f0 , etc. Separate each coefficient by a blank space. Remember that the first coefficient is for 1r .

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Constant Value To define a constant tangential or radial velocity, the steps are as follows: 1. Turn on the Profile Specification of Tangential Velocity or Profile Specification of Radial Velocity option in the Fan panel. 2. Select constant in the drop-down list under Tangential or Radial Velocity Profile. 3. Enter the value for Uθ or Ur in the Tangential or Radial Velocity Profile field. You can follow the procedure below, if it is more convenient: 1. Turn off the Profile Specification of Tangential Velocity or Profile Specification of Radial Velocity option in the Fan panel. 2. Enter the value for Uθ or Ur in the Tangential- or Radial-Velocity Polynomial Coefficients field. User-Defined Function or Boundary Profile For a user-defined tangential or radial velocity function or a function contained in a boundary profile file, follow the procedure below: 1. Turn on the Profile Specification of Tangential or Radial Velocity option. 2. Choose the appropriate function from the drop-down list under Tangential or Radial Velocity Profile. See the separate UDF Manual for information about user-defined functions, and Section 6.26 for details about boundary profile files.

6.20.3

Postprocessing for Fans

Reporting the Pressure Rise Through the Fan You can use the Surface Integrals panel to report the pressure rise through the fan, as described in Section 28.5. There are two steps to this procedure: 1. Create a surface on each side of the fan zone. Use the Transform Surface panel (as described in Section 26.10) to translate the fan zone slightly upstream and slightly downstream to create two new surfaces. 2. In the Surface Integrals panel, report the average Static Pressure just upstream and just downstream of the fan. You can then calculate the pressure rise through the fan.


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Boundary Conditions

Graphical Plots Graphical reports of interest with fans are as follows: • Contours or profiles of Static Pressure and Static Temperature • XY plots of Static Pressure and Static Temperature vs. position Chapter 27 explains how to generate graphical displays of data.

! When generating these plots, be sure to turn off the display of node values so that you can see the different values on each side of the fan. (If you display node values, the cell values on either side of the fan will be averaged to obtain a node value, and you will not see, for example, the pressure jump across the fan.)

6.21

Radiator Boundary Conditions

A lumped-parameter model for a heat exchange element (for example, a radiator or condenser), is available in FLUENT. The radiator boundary type allows you to specify both the pressure drop and heat transfer coefficient as functions of the velocity normal to the radiator. You can find the following information about modeling radiators in this section: • Section 6.21.1: Radiator Equations • Section 6.21.2: User Inputs for Radiators • Section 6.21.3: Postprocessing for Radiators A more detailed heat exchanger model is also available in FLUENT. See Section 6.25 for details.

6.21.1

Radiator Equations

Modeling the Pressure Loss Through a Radiator A radiator is considered to be infinitely thin, and the pressure drop through the radiator is assumed to be proportional to the dynamic head of the fluid, with an empirically determined loss coefficient which you supply. That is, the pressure drop, ∆p, varies with the normal component of velocity through the radiator, v, as follows: 1 ∆p = kL ρv 2 2

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(6.21-1)


6.21 Radiator Boundary Conditions

where ρ is the fluid density, and kL is the non-dimensional loss coefficient, which can be specified as a constant or as a polynomial, piecewise-linear, or piecewise-polynomial function. In the case of a polynomial, the relationship is of the form

kL =

N X

rn v n−1

(6.21-2)

n=1

where rn are polynomial coefficients and v is the magnitude of the local fluid velocity normal to the radiator.

Modeling the Heat Transfer Through a Radiator The heat flux from the radiator to the surrounding fluid is given as q = h(Tair,d − Text )

(6.21-3)

where q is the heat flux, Tair,d is the temperature downstream of the heat exchanger (radiator), and Text is the reference temperature for the liquid. The convective heat transfer coefficient, h, can be specified as a constant or as a polynomial, piecewise-linear, or piecewise-polynomial function. For a polynomial, the relationship is of the form

h=

N X

hn v n ; 0 ≤ N ≤ 7

(6.21-4)

n=0

where hn are polynomial coefficients and v is the magnitude of the local fluid velocity normal to the radiator in m/s. Either the actual heat flux (q) or the heat transfer coefficient and radiator temperature (h, Text ) may be specified. q (either the entered value or the value calculated using Equation 6.21-3) is integrated over the radiator surface area. Calculating the Heat Transfer Coefficient To model the thermal behavior of the radiator, you must supply an expression for the heat transfer coefficient, h, as a function of the fluid velocity through the radiator, v. To obtain this expression, consider the heat balance equation: q=


mc ˙ p ∆T = h(Tair,d − Text ) A

(6.21-5)

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Boundary Conditions

where q m ˙ cp h Text Tair,d A

= = = = = = =

heat flux (W/m2 ) fluid mass flow rate (kg/s) specific heat capacity of fluid (J/kg-K) empirical heat transfer coefficient (W/m2 -K) external temperature (reference temperature for the liquid) (K) temperature downstream from the heat exchanger (K) heat exchanger frontal area (m2 )

Equation 6.21-5 can be rewritten as q=

mc ˙ p (Tair,u − Tair,d ) = h(Tair,d − Text ) A

(6.21-6)

where Tair,u is the upstream air temperature. The heat transfer coefficient, h, can therefore be computed as h=

mc ˙ p (Tair,u − Tair,d ) A(Tair,d − Text )

(6.21-7)

h=

ρvcp (Tair,u − Tair,d ) Tair,d − Text

(6.21-8)

or, in terms of the fluid velocity,

6.21.2

User Inputs for Radiators

Once the radiator zone has been identified (in the Boundary Conditions panel), you will set all modeling inputs for the radiator in the Radiator panel (Figure 6.21.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4). The inputs for a radiator are as follows: 1. Identify the radiator zone. 2. Define the pressure loss coefficient. 3. Define either the heat flux or the heat transfer coefficient and radiator temperature. 4. Define the discrete phase boundary condition for the radiator (for discrete phase calculations).

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Figure 6.21.1: The Radiator Panel

Identifying the Radiator Zone Since the radiator is considered to be infinitely thin, it must be modeled as the interface between cells, rather than a cell zone. Thus the radiator zone is a type of internal face zone (where the faces are line segments in 2D or triangles/quadrilaterals in 3D). If, when you read your grid into FLUENT, the radiator zone is identified as an interior zone, use the Boundary Conditions panel (as described in Section 6.1.3) to change the appropriate interior zone to a radiator zone. Define −→Boundary Conditions... Once the interior zone has been changed to a radiator zone, you can open the Radiator panel and specify the loss coefficient and heat flux information.

Defining the Pressure Loss Coefficient Function To define the pressure loss coefficient kL you can specify a polynomial, piecewise-linear, or piecewise-polynomial function of velocity, or a constant value. Polynomial, Piecewise-Linear, or Piecewise-Polynomial Function Follow these steps to set a polynomial, piecewise-linear, or piecewise-polynomial function for the pressure loss coefficient: 1. Choose polynomial, piecewise-linear, or piecewise-polynomial in the drop-down list to the right of Loss-Coefficient. (If the function type you want is already selected, you can click on the Edit... button to open the panel where you will define the function.)


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Boundary Conditions

2. In the panel that appears for the definition of the Loss-Coefficient function (e.g., Figure 6.21.2), enter the appropriate values. These profile input panels are used the same way as the profile input panels for temperature-dependent properties. See Section 7.1.3 to find out how to use them.

Figure 6.21.2: Polynomial Profile Panel for Loss-Coefficient Definition

Constant Value To define a constant loss coefficient, follow these steps: 1. Choose constant in the Loss-Coefficient drop-down list. 2. Enter the value for kL in the Loss-Coefficient field. Example: Calculating the Loss Coefficient This example shows you how to determine the loss coefficient function. Consider the simple two-dimensional duct flow of air through a water-cooled radiator, shown in Figure 6.21.3. The radiator characteristics must be known empirically. For this case, assume that the radiator to be modeled yields the test data shown in Table 6.21.1, which was taken with a waterside flow rate of 7 kg/min and an inlet water temperature of 400.0 K. To compute the loss coefficient, it is helpful to construct a table with values of the dynamic head, 1 ρv 2 , as a function of pressure drop, ∆p, and the ratio of these two values, kL (from 2 Equation 6.21-1). (The air density, defined in Figure 6.21.3, is 1.0 kg/m3 .) The reduced data are shown in Table 6.21.2 below. The loss coefficient is a linear function of the velocity, decreasing as the velocity increases. The form of this relationship is

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T = 300 K

AIR

➯

0.5 m

T = 300 K U = 8 m/s

RADIATOR, T = 400 K 2.0 m

Figure 6.21.3: A Simple Duct with a Radiator

Table 6.21.1: Airside Radiator Data Velocity (m/s) 5.0 10.0 15.0

Upstream Temp (K) 300.0 300.0 300.0

Downstream Temp (K) 330.0 322.5 320.0

Pressure Drop (Pa) 75.0 250.0 450.0

Table 6.21.2: Reduced Radiator Data v (m/s) 5.0 10.0 15.0


1 ρv 2 2

(Pa) 12.5 50.0 112.5

∆p (Pa) 75.0 250.0 450.0

kL 6.0 5.0 4.0

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Boundary Conditions

kL = 7.0 − 0.2v

(6.21-9)

where v is now the absolute value of the velocity through the radiator.

Defining the Heat Flux Parameters As mentioned in Section 6.21.1, you can either define the actual heat flux (q) in the Heat Flux field, or set the heat transfer coefficient and radiator temperature (h, Text ). All inputs are in the Radiator panel. To define the actual heat flux, specify a Temperature of 0, and set the constant Heat Flux value. To define the radiator temperature, enter the value for Text in the Temperature field. To define the heat transfer coefficient, you can specify a polynomial, piecewise-linear, or piecewise-polynomial function of velocity, or a constant value. Polynomial, Piecewise-Linear, or Piecewise-Polynomial Function Follow these steps to set a polynomial, piecewise-linear, or piecewise-polynomial function for the heat transfer coefficient: 1. Choose polynomial, piecewise-linear, or piecewise-polynomial in the drop-down list to the right of Heat-Transfer-Coefficient. (If the function type you want is already selected, you can click on the Edit... button to open the panel where you will define the function.) 2. In the panel that appears for the definition of the Heat-Transfer-Coefficient function, enter the appropriate values. These profile input panels are used the same way as the profile input panels for temperature-dependent properties. See Section 7.1.3 to find out how to use them. Constant Value To define a constant heat transfer coefficient, follow these steps: 1. Choose constant in the Heat-Transfer-Coefficient drop-down list. 2. Enter the value for h in the Heat-Transfer-Coefficient field.

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Example: Determining the Heat Transfer Coefficient Function This example shows you how to determine the function for the heat transfer coefficient. Consider the simple two-dimensional duct flow of air through a water-cooled radiator, shown in Figure 6.21.3. The data supplied in Table 6.21.1 along with values for the air density (1.0 kg/m3 ) and specific heat (1000 J/kg-K) can be used to obtain the following values for the heat transfer coefficient h: Velocity (m/s)

h (W/m2 -K)

5.0 10.0 15.0

2142.9 2903.2 3750.0

The heat transfer coefficient obeys a second-order polynomial relationship (fit to the points in the table above) with the velocity, which is of the form h = 1469.1 + 126.11v + 1.73v 2

(6.21-10)

Note that the velocity v is assumed to be the absolute value of the velocity passing through the radiator.

Defining Discrete Phase Boundary Conditions for the Radiator If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the radiator. See Section 21.10 for details.

6.21.3

Postprocessing for Radiators

Reporting the Radiator Pressure Drop You can use the Surface Integrals panel to report the pressure drop across the radiator, as described in Section 28.5. There are two steps to this procedure: 1. Create a surface on each side of the radiator zone. Use the Transform Surface panel (as described in Section 26.10) to translate the radiator zone slightly upstream and slightly downstream to create two new surfaces. 2. In the Surface Integrals panel, report the average Static Pressure just upstream and just downstream of the radiator. You can then calculate the pressure drop across the radiator.


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Boundary Conditions

To check this value against the expected value based on Equation 6.21-1, you can use the Surface Integrals panel to report the average normal velocity through the radiator. (If the radiator is not aligned with the x, y, or z axis, you will need to use the Custom Field Function Calculator panel to generate a function for the velocity normal to the radiator.) Once you have the average normal velocity, you can use Equation 6.21-2 to determine the loss coefficient and then Equation 6.21-1 to calculate the expected pressure loss.

Reporting Heat Transfer in the Radiator To determine the temperature rise across the radiator, follow the procedure outlined above for the pressure drop to generate surfaces upstream and downstream of the radiator. Then use the Surface Integrals panel (as for the pressure drop report) to report the average Static Temperature on each surface. You can then calculate the temperature rise across the radiator.

Graphical Plots Graphical reports of interest with radiators are as follows: • Contours or profiles of Static Pressure and Static Temperature • XY plots of Static Pressure and Static Temperature vs. position. Chapter 27 explains how to generate graphical displays of data.

! When generating these plots, be sure to turn off the display of node values so that you can see the different values on each side of the radiator. (If you display node values, the cell values on either side of the radiator will be averaged to obtain a node value, and you will not see, for example, the pressure loss across the radiator.)

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6.22 Porous Jump Boundary Conditions

6.22

Porous Jump Boundary Conditions

Porous jump conditions are used to model a thin “membrane” that has known velocity/pressuredrop characteristics. It is essentially a 1D simplification of the porous media model available for cell zones. Examples of uses for the porous jump condition include modeling pressure drops through screens and filters, and modeling radiators when you are not concerned with heat transfer. This simpler model should be used whenever possible (instead of the full porous media model) because it is more robust and yields better convergence. The thin porous medium has a finite thickness over which the pressure change is defined as a combination of Darcy’s Law and an additional inertial loss term: ∆p = −

1 µ v + C2 ρv 2 ∆m α 2

(6.22-1)

where µ is the laminar fluid viscosity, α is the permeability of the medium, C2 is the pressure-jump coefficient, v is the velocity normal to the porous face, and ∆m is the thickness of the medium. Appropriate values for α and C2 can be calculated using the techniques described in Section 6.19.6.

User Inputs for the Porous Jump Model Once the porous jump zone has been identified (in the Boundary Conditions panel), you will set all modeling inputs for the porous jump in the Porous Jump panel (Figure 6.22.1), which is opened from the Boundary Conditions panel (as described in Section 6.1.4).

Figure 6.22.1: The Porous Jump Panel The inputs required for the porous jump model are as follows: 1. Identify the porous-jump zone. 2. Set the Face Permeability of the medium (α in Equation 6.22-1).


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Boundary Conditions

3. Set the Porous Medium Thickness (∆m). 4. Set the Pressure-Jump Coefficient (C2 ). 5. Define the discrete phase boundary condition for the porous jump (for discrete phase calculations). Identifying the Porous Jump Zone Since the porous jump model is a 1D simplification of the porous media model, the porous-jump zone must be modeled as the interface between cells, rather than a cell zone. Thus the porous-jump zone is a type of internal face zone (where the faces are line segments in 2D or triangles/quadrilaterals in 3D). If the porous-jump zone is not identified as such by default when you read in the grid (i.e., if it is identified as another type of internal face zone), you can use the Boundary Conditions panel to change the appropriate face zone to a porous-jump zone. Define −→Boundary Conditions... The procedure for changing a zone’s type is described in Section 6.1.3. Once the zone has been changed to a porous jump, you can open the Porous Jump panel (as described in Section 6.1.4) and specify the porous jump parameters listed above. Defining Discrete Phase Boundary Conditions for the Porous Jump If you are modeling a discrete phase of particles, you can set the fate of particle trajectories at the porous jump. See Section 21.10 for details.

Postprocessing for the Porous Jump Postprocessing suggestions for a problem that includes a porous jump are the same as for porous media problems. See Section 6.19.9.

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6.23 Non-Reflecting Boundary Conditions

6.23

Non-Reflecting Boundary Conditions

Information about non-reflecting boundary conditions (NRBCs) is provided in the following sections. • Section 6.23.1: Overview and Limitations • Section 6.23.2: Theory • Section 6.23.3: Using the Non-Reflecting Boundary Conditions

6.23.1


The standard pressure boundary conditions for compressible flow fix specific flow variables at the boundary (e.g., static pressure at an outlet boundary). As a result, pressure waves incident on the boundary will reflect in an unphysical manner, leading to local errors. The effects are more pronounced for internal flow problems where boundaries are usually close to geometry inside the domain, such as compressor or turbine blade rows. The non-reflecting boundary conditions (NRBCs) permit waves to “pass” through the boundaries without spurious reflections. The method used in FLUENT is based on the Fourier transformation of solution variables at the non-reflecting boundary [88]. Similar implementations have been investigated by other authors [168, 221]. In the method used by FLUENT, the solution is rearranged as a sum of terms corresponding to different frequencies, and their contributions are calculated independently. While the method was originally designed for axial turbomachinery, it has been extended for use with radial turbomachinery.

Limitations Note the following limitations of NRBCs: • NRBCs can be used only with the coupled solvers (explicit or implicit). • The current implementation applies to steady compressible flows, with the density calculated using the ideal gas law. • Inlet and outlet boundary conditions must be pressure inlets and outlets only.

!

Note that the pressure inlet boundaries must be set to the cylindrical coordinate flow specification method when NRBCs are used. • Quad-mapped (structured) surface meshes must be used for inflow and outflow boundaries in a 3D geometry (i.e., triangular or quad-paved surface meshes are not allowed). See Figures 6.23.1 and 6.23.2 for examples. Note that you may use unstructured meshes in 2D geometries (Figure 6.23.3), and away from the inlet and outlet boundaries in 3D geometries.


6-131

Boundary Conditions

• The NRBC method used in FLUENT is based on quasi-3D analysis. The method developed for 2D NRBC [88] has been extended for use on 3D geometries [221] by decoupling the tangential flow variations from the radial variations. This approximation works best for geometries with a blade pitch that is small compared to the radius of the geometry.

Figure 6.23.1: Mesh and Prescribed Boundary Conditions in a 3D Axial Flow Problem

6.23.2

Theory

The non-reflecting boundary conditions (NRBCs) are based on Fourier decomposition of solutions to the linearized Euler equations. The solution at the inlet and outlet boundaries is circumferentially decomposed into Fourier modes, with the 0th mode representing the average boundary value (which is to be imposed as a user input), and higher harmonics that are modified to eliminate reflections [221].

Equations in Characteristic Variable Form In order to treat individual waves, the linearized Euler equations are transformed to characteristic variable (Ci ) form. If we first consider the 1D form of the linearized Euler equations, it can be shown that the characteristic variables Ci are related to the solution variables as follows: ˜ = T −1 C Q

6-132

(6.23-1)



Figure 6.23.2: Mesh and Prescribed Boundary Conditions in a 3D Radial Flow Problem

where    ρ˜           u ˜  a 

˜ = u˜t , T −1 Q      u˜r        p˜ 



   =   

− a12 0 0 0 0

0 0 1 ρ a

0 0

0 0 0 1 ρ a

0

1 2a2 1 2 ρ a

1 2a2 1 2 ρ a

0 0

0 0

1 2

1 2



   C1           C   2

    , C = C3        C4         C  5

where a is the average acoustic speed along a boundary zone, ρ˜, uã , u˜t , u˜r , and p˜ represent perturbations from a uniform condition (e.g., ρ˜ = ρ − ρ, p˜ = p − p, etc.). Note that the analysis is performed using the cylindrical coordinate system. All overlined (averaged) flow field variables (e.g., ρ, a) are intended to be averaged along the pitchwise direction. In quasi-3D approaches [88, 168, 221], a procedure is developed to determine the changes in the characteristic variables, denoted by δCi , at the boundaries such that waves will not reflect. These changes in characteristic variables are determined as follows: δC = T δQ

(6.23-2)

where


6-133

Boundary Conditions

Figure 6.23.3: Mesh and Prescribed Boundary Conditions in a 2D Case

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    δC 1           δC 2  



   δC = δC3 , T =          δC    4    δC  5

0 0 0 −a2 0 0 ρa 0 0 0 0 ρa 0 ρa 0 0 0 −ρ a 0 0

1 0 0 1 1



    δρ           δu a  

    , δQ = δut        δur        δp  

The changes to the outgoing characteristics — one characteristic for subsonic inflow (δC5 ), and four characteristics for subsonic outflow (δC1 , δC2 , δC3 , δC4 ) — are determined from extrapolation of the flow field variables using Equation 6.23-2. The changes in the incoming characteristics — four characteristics for subsonic inflow (δC1 , δC2 , δC3 , δC4 ), and one characteristic for subsonic outflow (δC5 ) — are split into two components: average change along the boundary (δC i ), and local changes in the characteristic variable due to harmonic variation along the boundary (δCiL ). The incoming characteristics are therefore given by

δCij = δCioldj + σ δCinewj − δCioldj

δCinewj = δC i + δCiLj

(6.23-3) (6.23-4)

where i = 1, 2, 3, 4 on the inlet boundary or i = 5 on the outlet boundary, and j = 1, ..., N is the grid index in the pitchwise direction including the periodic point once. The underrelaxation factor σ has a default value of 0.75. Note that this method assumes a periodic solution in the pitchwise direction. The flow is decomposed into mean and circumferential components using Fourier decomposition. The 0th Fourier mode corresponds to the average circumferential solution, and is treated according to the standard 1D characteristic theory. The remaining parts of the solution are described by a sum of harmonics, and treated as 2D non-reflecting boundary conditions [88].

Inlet Boundary For subsonic inflow, there is one outgoing characteristic (δC5 ) determined from Equation 6.23-2, and four incoming characteristics (δC1 , δC2 , δC3 , δC4 ) calculated using Equation 6.23-3. The average changes in the incoming characteristics are computed from the requirement that the entropy (s), radial and tangential flow angles (αr and αt ), and stagnation enthalpy (h0 ) are specified. Note that in FLUENT you can specify p0 and T0 at the inlet, from which sin and h0in are easily obtained. This is equivalent to forcing the following four residuals to be zero:

R1 = p (s − sin )


(6.23-5)

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Boundary Conditions

R2 = ρ a (ut − ua tan αt ) R3 = ρ a (ur − ua tan αr )

R4 = ρ h0 − h0in

(6.23-6) (6.23-7)

(6.23-8)

where sin = γ ln (T0in ) − (γ − 1) ln (p0in )

(6.23-9)

h0in = cp T0in

(6.23-10)

The average characteristic is then obtained from residual linearization as follows (see also Figure 6.23.4 for an illustration of the definitions for the prescribed inlet angles):   δC 1        



 δC 2 =   δC 3         δC 4 

−1

0

tan αt (1−γ)M tan αr (γ−1)M 2 (γ−1)M

M1 M Mt M

−Mt M

0 tan αt

M2 M 2 MMr

tan αt t 2M M

0 tan αt M − tan αr M −2 M

  R1       R2    R   3    

(6.23-11)

R4

where

ua a ut = a ur = a

Ma =

(6.23-12)

Mt

(6.23-13)

Mr

(6.23-14)

and M = 1 + Ma − Mt tan αt + Mr tan αr

(6.23-15)

M1 = −1 − Ma − Mr tan αr

(6.23-16)

M2 = −1 − Ma − Mt tan αt

(6.23-17)

where |v| =

6-136

q

u2t + u2r + u2a

(6.23-18)



radial

ur v αr

ut

ua

axial

αt theta

Figure 6.23.4: Prescribed Inlet Angles ut |v| ur = |v| ua = |v|

et =

(6.23-19)

er

(6.23-20)

ea

(6.23-21)

et ea er tan αr = ea tan αt =

(6.23-22) (6.23-23)

To address the local characteristic changes at each j grid point along the inflow boundary, the following relations are developed [88, 221]: δC1Lj = p (sj − s) δC2Lj = C20 j − ρa utj − ut

δC3Lj = −ρa urj − ur δC4Lj =

−2

(1+Maj )

1 δC1Lj γ−1

(6.23-24)

+ Mtj δC2Lj + Mrj δC3Lj + ρ h0j − h0

Note that the relation for the first and fourth local characteristics force the local entropy and stagnation enthalpy to match their average steady-state values. The characteristic variable C20 j is computed from the inverse discrete Fourier transform of the second characteristic. The discrete Fourier transform of the second characteristic in turn is related to the discrete Fourier transform of the fifth characteristic. Hence, the characteristic variable C20 j is computed along the pitch as follows:


6-137

Boundary Conditions

C20 j



N 2

−1

X θj − θ1 = 2<  Cˆ2n exp i2πn 

θN − θ1

n=1

 !  

(6.23-25)

The Fourier coefficients C20 n are related to a set of equidistant distributed characteristic variables C5∗j by the following [168]:

Cˆ2n =

 N  ut + B X jn  ∗   − C exp −i2π   N (a + ua ) j=1 5j N      ut + B    − C5j

β>0 (6.23-26) β0 q −sign (ut ) |β| β < 0

(6.23-27)

β = a2 − u2a − u2t

(6.23-28)

and

The set of equidistributed characteristic variables C5∗j is computed from arbitrary distributed C5j by using a cubic spline for interpolation, where

C5j = −ρ a uaj − ua + (pj − p)

(6.23-29)

For supersonic inflow the user-prescribed static pressure (psin ) along with total pressure (p0in ) and total temperature (T0in ) are sufficient for determining the flow condition at the inlet.

Outlet Boundary For subsonic outflow, there are four outgoing characteristics (δC1 , δC2 , δC3 , and δC4 ) calculated using Equation 6.23-2, and one incoming characteristic (δC5 ) determined from Equation 6.23-3. The average change in the incoming fifth characteristic is given by δC 5 = −2 (p − pout )

(6.23-30)

where p is the current averaged pressure at the exit plane and pout is the desirable average exit pressure (this value is specified by you for single-blade calculations or obtained from

6-138



the assigned profile for mixing-plane calculations). The local changes (δC5Lj ) are given by

δC5Lj = C50 j + ρ a uaj − ua − (pj − p)

(6.23-31)

0

The characteristic variable C5j is computed along the pitch as follows:

C50 j



N 2

−1

θj − θ1 X ˆ = 2<  C5n exp i2πn

θN − θ1

n=1

 !  

(6.23-32)

The Fourier coefficients Cˆ5n are related to two sets of equidistant distributed characteristic variables (C2∗j and C4∗j , respectively) and given by the following [168]:

Cˆ5n =

 N N  A2 X jn A4 X jn  ∗ ∗  C2j exp i2π − C4j exp i2π  

N

    

N

j=1

N

N

j=1

A2 C2j − A4 C4j

β>0 (6.23-33) β output_profile

integer npmax parameter (npmax = 900) integer inp ! input: number of profile points integer iptype ! input: profile type (0=radial, 1=point) real ir(npmax) ! input: radial positions real ip(npmax) ! input: pressure real idp(npmax) ! input: pressure-jump real iva(npmax) ! input: axial velocity

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6.24 User-Defined Fan Model

real ivr(npmax) ! input: radial velocity real ivt(npmax) ! input: tangential velocity character*80 zoneid integer rfanprof ! function to read a profile file integer status c status = rfanprof(npmax,zoneid,iptype, $ inp,ir,ip,idp,iva,ivr,ivt) if (status.ne.0) then write(*,*) ’error reading input profile file’ else do 10 i = 1, inp idp(i) = 200.0 - 10.0*iva(i) ivt(i) = 20.0*ir(i) ivr(i) = 0.0 10 continue call wfanprof(6,zoneid,iptype,inp,ir,idp,ivr,ivt) endif stop end

After the variable declarations, which have comments on the right, the subroutine rfanprof is called to read the profile file, and pass the current values of the relevant variables (as defined in the declaration list) to fantest. A loop is done on the number of points in the profile to compute new values for: • idp, the pressure jump across the fan, which in this example is a function of the axial velocity, iva • ivt, the swirling or tangential velocity, which in this example is proportional to the radial position, ir • ivr, the radial velocity, which in this example is set to zero After the loop, a new profile is written by the subroutine wfanprof, shown below. (For more information on profile file formats, see Section 6.26.2.) subroutine wfanprof(unit,zoneid,ptype,n,r,dp,vr,vt) c c c c

writes a FLUENT profile file for input by the user fan model integer unit character*80 zoneid


! output unit number

6-145

Boundary Conditions

integer ptype integer n real r(n) real dp(n) real vr(n) real vt(n) character*6 typenam

! ! ! ! ! !

profile type (0=radial, 1=point) number of points radial position pressure jump radial velocity tangential velocity

if (ptype.eq.0) then typenam = ’radial’ else typenam = ’point’ endif write(unit,*) ’((’, zoneid(1:index(zoneid,’\0’)-1), ’ ’, $ typenam, n, ’)’ write(unit,*) ’(r’ write(unit,100) r write(unit,*) ’)’ write(unit,*) ’(pressure-jump’ write(unit,100) dp write(unit,*) ’)’ write(unit,*) ’(radial-velocity’ write(unit,100) vr write(unit,*) ’)’ write(unit,*) ’(tangential-velocity’ write(unit,100) vt write(unit,*) ’)’ 100

format(5(e15.8,1x)) return end

This subroutine will write a profile file in either radial or point format, based on your input for the integer ptype. (See Section 6.26 for more details on the types of profile files that are available.) The names that you use for the various profiles are arbitrary. Once you have initialized the profile files, the names you use in wfanprof will appear as profile names in the Fan panel.

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Initializing the Flow Field and Profile Files The next step in the setup of the user-defined fan is to initialize (create) the profile files that will be used. To do this, first initialize the flow field with the Solution Initialization panel (using the velocity inlet conditions, for example), and then type the command (update-user-fans) in the console window. (The parentheses are part of the command, and must be typed in.) This will create the profile names that are given in the subroutine wfanprof.

Selecting the Profiles Once the profile names have been established, you will need to visit the Fan panel (Figure 6.24.3) to complete the problem setup. (See Section 6.20 for general information on using the Fan panel.)

Figure 6.24.3: The Fan Panel


6-147

Boundary Conditions

At this time, the Fan Axis, Fan Origin, and Fan Hub Radius can be entered, along with the choice of profiles for the calculation of pressure jump, tangential velocity, and radial velocity. With the profile options enabled, you can select the names of the profiles from the drop-down lists. In the panel above, the selected profiles are named fan-8-pressurejump, fan-8-tangential-velocity, and fan-8-radial-velocity, corresponding to the names that were used in the subroutine wfanprof.

Performing the Calculation The solution is now ready to run. As it begins to converge, the report in the console window shows that the profile files are being written and read every 10 iterations: iter continuity x-velocity y-velocity z-velocity k 1 residual normalization factors changed (continuity 1 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 ! 2 residual normalization factors changed (continuity 2 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 9.4933e-01 3 6.8870e-01 7.2663e-01 7.3802e-01 7.5822e-01 6.1033e-01 . . . . . . . . . . . . . . . . . . 9 2.1779e-01 9.8139e-02 3.0497e-01 2.9609e-01 2.8612e-01 Writing "fan-8-out.prof"... Done. Reading "fan-8-in.prof"... !

Reading profile file... 10 "fan-8" radial-profile points, r, pressure-jump, radial-velocity, tangential-velocity. Done. 10 1.7612e-01 7.4618e-02 2.5194e-01 2.4538e-01 2.4569e-01 11 1.6895e-01 8.3699e-02 2.0316e-01 2.0280e-01 2.1169e-01 . . . . . . . . . . . .

The file fan-8-out.prof is written out by FLUENT and read by the executable fantest. It contains values for pressure, pressure jump, axial velocity, radial velocity, and tangential velocity at 20 radial locations at the site of the fan. The file fan-8-in.prof is generated by fantest and contains updated values for pressure jump and radial and tangential velocity only. It is therefore a smaller file than fan-8-out.prof. The prefix for these files takes its name from the fan zone with which the profiles are associated. An example of the profile file fan-8-in.prof is shown below. This represents the last profile file to be written by fantest during the convergence history.

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((fan-8 radial 10) (r 0.24295786E-01 0.33130988E-01 0.68471842E-01 0.77307090E-01 ) (pressure-jump 0.10182057E+03 0.98394081E+02 0.98020668E+02 0.98138817E+02 ) (radial-velocity 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00 ) (tangential-velocity 0.48591572E+00 0.66261977E+00 0.13694369E+01 0.15461419E+01 )

0.41966137E-01 0.86142287E-01

0.50801374E-01 0.94963484E-01

0.59636571E-01 0.95353782E-01

0.97748657E+02 0.98264198E+02

0.97787750E+02 0.98469681E+02

0.97905228E+02 0.98478783E+02

0.00000000E+00 0.00000000E+00

0.00000000E+00 0.00000000E+00

0.00000000E+00 0.00000000E+00

0.83932275E+00 0.17228458E+01

0.10160275E+01 0.18992697E+01

0.11927314E+01 0.19070756E+01

Results A plot of the transverse velocity components at the site of the fan is shown in Figure 6.24.4. As expected, there is no radial component, and the tangential (swirling) component increases with radius.

1.04e+01 1.00e+01 9.60e+00 9.20e+00 8.79e+00 8.38e+00 7.97e+00 7.56e+00 7.15e+00 6.75e+00

Y X

Z

6.34e+00


Figure 6.24.4: Transverse Velocities at the Site of the Fan

As a final check on the result, an XY plot of the static pressure as a function of x position is shown (Figure 6.24.5). This XY plot is made on a line at y=0.05 m, or at about half the radius of the duct. According to the input file shown above, the pressure jump at the site of the fan should be approximately 97.8 Pa/m. Examination of the figure supports this finding.


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Boundary Conditions

y=.05 1.00e+01 0.00e+00 -1.00e+01 -2.00e+01 -3.00e+01 -4.00e+01

Static Pressure (pascal)

-5.00e+01 -6.00e+01 -7.00e+01 -8.00e+01 -9.00e+01 -1.00e+02 -0.4

Y X

-0.2

Z

0

0.2

0.4

0.6

0.8

1

Position (m)

Static Pressure

Figure 6.24.5: Static Pressure Jump Across the Fan

6.25

Heat Exchanger Models

Many engineering systems, including power plants, climate control, and engine cooling systems typically contain tubular heat exchangers. However, for most engineering problems, it is impractical to model individual fins and tubes of a heat exchanger core. In principle, heat exchanger cores introduce a pressure drop to the gas stream and transfer heat to a second fluid, referred to here as the coolant. In FLUENT, lumped-parameter models are used to account for the pressure loss and coolant heat rejection. FLUENT provides two heat exchanger models: the simple effectiveness model and the number-of-transfer-units (NTU) model. The models can be used to compute coolant inlet temperature for a fixed heat rejection or total heat rejection for a fixed coolant inlet temperature. For the simple effectiveness model, the coolant fluid may be single-phase or two-phase. The following sections contain information about the heat exchanger models: • Section 6.25.1: Overview and Restrictions of the Heat Exchanger Models • Section 6.25.2: Heat Exchanger Model Theory • Section 6.25.3: Using the Heat Exchanger Model • Section 6.25.4: Using the Heat Exchanger Group • Section 6.25.5: Postprocessing for the Heat Exchanger Model

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6.25 Heat Exchanger Models

6.25.1

Overview and Restrictions of the Heat Exchanger Models

Overview In a typical heat exchanger core, the coolant temperature is stratified in the direction of coolant flow. As a result, heat rejection is not constant over the entire core. In FLUENT, the fluid zone representing the heat exchanger core is subdivided into macroscopic cells or macros along the coolant path (see Figure 6.25.1). The coolant inlet temperature to each macro is computed and then subsequently used to compute the heat rejection from each macro. This approach provides a realistic heat rejection distribution over the heat exchanger core. To use the heat exchanger models, you must define one or more fluid zone(s) to represent the heat exchanger core. Typically, the fluid zone is sized to the dimension of the core itself. As part of the setup procedure, you will define the coolant path, the number of macros, and the physical properties and operating conditions of the core (pressure drop parameters, heat exchanger effectiveness, coolant flow rate, etc.). You can also combine several fluid zones as a single heat exchanger group. In this situation each fluid zone acts as a separate heat exchanger core, and the coolant mass flow rate of the heat exchanger group is divided among the zones in the ratio of the respective volumes. For the purpose of coolant flow, heat exchanger groups can also be connected in series. In addition, a heat exchanger group can have a coolant pressure drop (e.g., for pressure dependent properties) and an auxiliary coolant stream entering or leaving it. For more information of heat exchanger groups, see Section 6.25.4. The heat exchanger models were designed for “compact” heat exchangers, implying that the gas side flow is unidirectional. The coolant is assumed to flow through a large number of parallel tubes, which can optionally double back in a serpentine pattern to create a number of “passes”. You can independently choose the principal coolant flow direction, the pass-to-pass direction and the external gas flow direction.

Restrictions The following restrictions are made for the heat exchanger models: • The core must be approximately rectangular in shape. • The gas streamwise direction (see Equation 6.25-1) must be aligned with one of the three orthogonal axes defined by the rectangular core. • Flow acceleration effects are neglected in calculating the pressure loss coefficient. • For the simple effectiveness model, the gas capacity rate must be less than the coolant capacity rate. • Coolant phase change cannot be modeled using the NTU model.


6-151

Boundary Conditions

Coolant Passage

Macro 0

Macro 1

Macro 2

Macro 21

Macro 2 2

Macro 23

Macro 3

Macro 4

Macro 5

Macro 18

Macro 19

Macro 20

Macro 6

Macro 7

Macro 8

Macro 15

Macro 16

Macro 17

Macro 9

Macro 10

Macro 11

Macro 12

Macro 13

Macro 14

Figure 6.25.1: Core Discretized Into 3 × 4×2 Macros

6.25.2

Heat Exchanger Model Theory

In FLUENT, the heat exchanger core is treated as a fluid zone with momentum and heat transfer. Pressure loss is modeled as a momentum sink in the momentum equation, and heat transfer is modeled as a heat source in the energy equation. FLUENT provides two heat exchanger models: the default NTU model and the simple effectiveness model. The simple effectiveness model interpolates the effectiveness from the velocity vs. effectiveness curve that you provide. For the NTU Model, FLUENT calculates the effectiveness, , from the equation for the number of transfer units, Ntu , based on the scaled value of Ntu for each macro. The NTU model relies on a mass flow rate vs. Ntu curve that you provide for the heat-exchanger zone so that FLUENT can calculate Ntu for macros based on their size and mass flow rate. The NTU model provides the following features: • checks heat capacity for both the gas and the coolant and takes the lesser of the two for the calculation of heat transfer • can be used to model heat transfer to the gas from the coolant and vice-versa • can be used to model gas side reverse flow • can be used with variable density of gas • can be used in either the serial or parallel FLUENT solvers

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The simple effectiveness model provides the following features: • can be used to model heat transfer from the coolant to the fluid • coolant properties can be a function of pressure and temperature, thus allowing phase change of coolant • can be used by serial as well as parallel solvers • can be used to make a network of heat exchangers using a heat exchanger group (Section 6.25.4)

Streamwise Pressure Drop In both heat exchanger models, pressure loss is modeled using the porous media model in FLUENT. The streamwise pressure drop can be expressed as 1 ∆p = f ρm UA2 min 2

(6.25-1)

where ∆p f ρm UAmin

= = = =

streamwise pressure drop streamwise pressure loss coefficient mean gas density gas velocity at the minimum flow area

The pressure loss coefficient is computed from f = (Kc + 1 − σ 2 ) − (1 − σ 2 − Ke )

νe νe A νm +2 − 1 + fc νi νi Ac νi

(6.25-2)

where σ Kc Ke A Ac fc νe νi νm

= = = = = = = = =

minimum flow to face area ratio entrance loss coefficient exit loss coefficient gas-side surface area minimum cross-sectional flow area core friction factor specific volume at the exit specific volume at the inlet mean specific volume ≡ 12 (νe + νi )

You will need to specify these parameters when you set up the heat exchanger model. These parameters are used to set up large resistances in the two non-streamwise directions, effectively forcing the gas flow through the core to be unidirectional.


6-153

Boundary Conditions

In Equation 6.25-2, the core friction factor is defined as fc = aRebmin

(6.25-3)

where a b Remin

= core friction coefficient = core friction exponent = Reynolds number for velocity at the minimum flow area

You will need to specify the core friction coefficient and exponent when you set up either of the heat exchanger models. The Reynolds number in Equation 6.25-3 is defined as Remin =

ρm UAmin Dh µm

(6.25-4)

where ρm µm Dh UAmin

= = = =

mean gas density mean gas viscosity hydraulic diameter gas velocity at the minimum flow area

For a heat exchanger core, the hydraulic diameter can be defined as Ac Dh = 4L A

(6.25-5)

Note that UAmin can be calculated from UAmin =

U σ

(6.25-6)

where U is the gas velocity and σ is the minimum flow to face area ratio.

Heat Transfer Effectiveness For the simple effectiveness model, the heat-exchanger effectiveness, , is defined as the ratio of actual rate of heat transfer from the hot to cold fluid to the maximum possible rate of heat transfer. The maximum possible heat transfer is given by qmax = Cmin (Tin,hot − Tin,cold )

(6.25-7)

where Tin,hot and Tin,cold are the inlet temperatures of the hot and cold fluids and

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Cmin = min[(mc ˙ p )hot , (mc ˙ p )cold ]

(6.25-8)

Thus, the actual rate of heat transfer, q, is defined as q = Cmin (Tin,hot − Tin,cold )

(6.25-9)

The value of depends on the heat exchanger geometry and flow pattern (parallel flow, counter flow, cross flow, etc.). Though the effectiveness is defined for a complete heat exchanger, it can be applied to a small portion of the heat exchanger represented by a computational cell. For the NTU model, FLUENT calculates the effectiveness from the ratio of heat capacity and the number of transfer units using the relation 1 0.22 0.78 (1 − e−Cr Ntu ) = 1 − exp − Ntu Cr

(6.25-10)

where Cr is the ratio of Cmin to Cmax . Ntu should be specified for various gas flow rates (for a single coolant flow rate) as an input to the model. This Ntu for the heat exchanger is scaled for each macro in the ratio of their areas. For each macro, the gas inlet temperature is calculated using the mass average of the incoming gas temperatures at the boundaries. This automatically takes into account any reverse flow of the gas at the boundaries.

Heat Rejection Heat rejection is computed for each cell within a macro and added as a source term to the energy equation for the gas flow. Note that heat rejection from the coolant to gas can be either positive or negative. For the simple effectiveness model, the heat transfer for a given cell is computed from qcell = (mc ˙ p )g (Tin,coolant − Tcell )

(6.25-11)

where (mc ˙ p )g Tin,coolant Tcell


= heat exchanger effectiveness = gas capacity rate (flow rate × specific heat) = coolant inlet temperature of macro containing the cell = cell temperature

6-155

Boundary Conditions

For the simple effectiveness model, the heat rejection from a macro is calculated by summing the heat transfer of all the cells contained within the macro qmacro =

X

qcell

(6.25-12)

all cells in macro

For the NTU model, the heat transfer for a macro is calculated from qmacro = Cmin (Tin,coolant − Tin,gas )

(6.25-13)

where Tin,coolant Tin,gas

= macro effectiveness = macro coolant inlet temperature = macro gas inlet temperature

For the NTU model, the heat transfer for a given cell is computed from qcell = qmacro

Vcell Vmacro

(6.25-14)

For both heat exchanger models, the total heat rejection from the heat exchanger core is computed as the sum of the heat rejection from all the macros: qtotal =

X

qmacro

(6.25-15)

all macros

The coolant inlet temperature to each macro (Tin,coolant in Equations 6.25-11 and 6.25-13) is computed based on the energy balance of the coolant flow. For a given macro, qmacro = (m) ˙ coolant (hout − hin )

(6.25-16)

where hin and hout are the inlet and outlet enthalpies of the coolant in the macro. The coolant outlet temperature from the macro is calculated as

Tout =

    

hout cp,coolant

constant specific heat method (6.25-17)

f (hout , p) UDF method

where f p

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= user-defined function = coolant pressure



The values of hout and Tout then become the inlet conditions to the next macro. The first row of macros (Macros 0, 1, and 2 in Figure 6.25.1) are assumed to be where the coolant enters the heat exchanger core. When fixed total heat rejection from the heat exchanger core is specified, the inlet temperature to the first row of macros is iteratively computed, so that all of the equations are satisfied simultaneously. When a fixed coolant inlet temperature is specified, the heat transfer for the first row of macros are used to calculate their exit enthalpy, which becomes the inlet condition for the next row macros. At the end of each pass the outlet enthalpy of each macro (in the last row) is mass averaged to obtain the inlet condition for the next pass macros.

Heat Exchanger Group Connectivity If the optional heat exchanger group is used, a single heat exchanger may be comprised of multiple fluid zones. In this case, the coolant is assumed to flow through these zones in parallel. Thus, after taking into account any auxiliary stream effects, the coolant inlet mass flow rate is automatically apportioned to each zone in the group as follows:

m ˙i=

!

P

Vi,k m ˙ P P i k Vi,k k

(6.25-18)

where Vi,k refers to the volume of the kth finite volume cell within the ith fluid zone. Within each zone, the coolant flows through each macro in series as usual. At the outlet end of the group, the parallel coolant streams through the individual zones are recombined, and the outlet coolant enthalpy is calculated on a mass-averaged basis: ¯= h

P

m ˙ i hi P ˙i im i

!

(6.25-19)

With user-defined functions, the simple effectiveness model allows you to simulate twophase coolant flows and other complex coolant enthalpy relationships of the form h = h(T, p, x)

(6.25-20)

where p is the absolute pressure and x is the quality (mass fraction of vapor) of a twophase vapor-liquid mixture. When pressure-dependent coolant properties are used, the mean pressure within each macro is calculated and passed to the user-defined function as: 1 ∆p p¯j = pin + j + 2 N


(6.25-21)

6-157

Boundary Conditions

where j pin ∆p N

6.25.3

= = = =

macro row index inlet coolant pressure overall pressure drop across a heat exchanger group number of rows per pass × number of passes.

Using the Heat Exchanger Model

The steps for setting up the heat exchanger models are as follows: 1. Enable the calculation of energy in the Energy panel. Define −→ Models −→Energy... 2. Specify the inputs to the heat exchanger model, using the Heat Exchanger panel (Figure 6.25.2). Define −→ User-Defined −→Heat Exchanger... (a) In the Fluid Zone drop-down list, select the fluid zone representing the heat exchanger core. (b) Specify the Coolant Inlet Direction and the Pass-to-Pass Direction. (c) Define the macro grid using the Number of Passes, the Number of Rows/Pass, and the Number of Cols/Pass fields. (d) Specify the heat exchanger model as either the default NTU Model or the Simple Effectiveness Model. (e) Specify the coolant properties and conditions (Coolant Flow Rate, Inlet Temperature, and Coolant Specific Heat). (f) Specify the pressure-drop parameters and effectiveness of the heat exchanger core using the Heat Exchanger Core Model drop-down list and/or the corresponding Edit... button. (g) Click Apply in the Heat Exchanger panel to save all the settings. (h) Repeat steps (a)–(g) for any other heat exchanger fluid zones. To use multiple fluid zones to define a single heat exchanger, or to connect the coolant flow path among multiple heat exchangers, see Section 6.25.4.

Selecting the Zone for the Heat Exchanger Choose the fluid zone for which you want to define a heat exchanger in the Fluid Zone drop-down list.

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Figure 6.25.2: The Heat Exchanger Panel


6-159

Boundary Conditions

Specifying the Coolant Inlet and Pass-to-Pass Directions To define the coolant direction and flow path, you will specify direction vectors for the Coolant Inlet Direction and the Pass-to-Pass Direction. Figure 6.25.3 shows these directions relative to the macros. For some problems in which the principal axes of the heat exchanger core are not aligned with the coordinate axes of the domain, you may not know the coolant inlet and passto-pass direction vectors a priori. In such cases, you can use the plane tool as follows to help you to determine these direction vectors. 1. “Snap” the plane tool onto the boundary of the heat exchanger core. (Follow the instructions in Section 26.6.1 for initializing the tool to a position on an existing surface.) 2. Translate and rotate the axes of the tool appropriately until they are aligned with the principal directions of the heat exchanger core. The depth direction is determined by the red axis, the height direction by the green axis, and the width direction by the blue axis. 3. Once the axes are aligned, click on the Update From Plane Tool button in the Heat Exchanger panel. The directional vectors will be set automatically. (Note that the Update from Plane Tool button will also set the height, width, and depth of the heat exchanger core.)

Defining the Macros As discussed in Section 6.25.1, the fluid zone representing the heat exchanger core is split into macros. Macros are constructed based on the specified number of passes, the number of macro rows per pass, the number of macro columns per pass, and the corresponding coolant inlet and pass-to-pass directions (see Figure 6.25.3). Macros are numbered from 0 to (n − 1) in the direction of coolant flow, where n is the number of macros. In the Heat Exchanger panel, specify the Number of Passes, the Number of Rows/Pass, and the Number of Cols/Pass. The model will automatically extrude the macros to the depth of the heat exchanger core. Viewing the Macros You can view the coolant path by displaying the macros. To view the macros for your specified Number of Passes, Number of Rows/Pass, and Number of Cols/Pass, click the Apply button at the bottom of the panel. Then click View Passes to display it. The path of the coolant is color-coded in the display: macro 0 is red and macro n − 1 is blue.

! FLUENT can only display macros if the number of macros is less than or equal to 100.

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width Coolant Inlet Direction (1 Macro Column/Pass)

height

(4 Macro Rows/Pass)

Pass-to-Pass Direction (3 Passes)

Figure 6.25.3: 1 × 4×3 Macros


6-161

Boundary Conditions

For some problems, especially complex geometries, you may want to include portions of the computational-domain grid in your macros plot as spatial reference points. For example, you may want to show the location of an inlet and an outlet along with the macros. This is accomplished by turning on the Draw Grid option. The Grid Display panel will appear automatically when you turn on the Draw Grid option, and you can set the grid display parameters there. When you click on View Passes in the Heat Exchanger panel, the grid display, as defined in the Grid Display panel, will be included in the macros plot (see Figure 6.25.4).

5.00e+00

4.00e+00

3.00e+00

2.00e+00

1.00e+00

Y Z

X

0.00e+00 Macros

Figure 6.25.4: Grid Display With Macros

Selecting the Heat Exchanger Model You can specify the model for your heat exchanger by selecting the NTU Model or the Simple Effectiveness Model from the Model Option drop-down list.

Specifying the Coolant Properties and Conditions To define the coolant properties and conditions, you will specify the Coolant Flow Rate (m). ˙ The properties of the coolant can be specified using the Coolant Properties Method drop-down list. You can choose a Constant Specific Heat (cp ) and set the value in the Coolant Specific Heat field below, or as a user-defined function for the enthalpy using the User Defined Enthalpy option and selecting from the Coolant Enthalpy UDF drop-down list.

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• If you want FLUENT to compute the coolant inlet temperature for a specified heat rejection, follow the steps below: 1. Enable the Fixed Heat Rejection option. 2. Specify the Heat Rejection (qtotal in Equation 6.25-15). 3. Specify the Initial Temperature, which will be used by FLUENT as an initial guess for the inlet temperature (Tin in Equations 6.25-11 and 6.25-16). • If you want FLUENT to compute the total heat rejection of the core for a given inlet coolant temperature, follow the steps below: 1. Enable the Fixed Inlet Temperature option. 2. Specify the Inlet Temperature (Tin in Equations 6.25-11 and 6.25-16). • If you enable the User Defined Enthalpy option under the Coolant Properties Method, you must also specify the Inlet Pressure (pin in Equation 6.25-21) and Inlet Quality (x in Equation 6.25-20).

Setting the Pressure-Drop Parameters and Effectiveness The pressure drop parameters and effectiveness define the heat exchanger core model. You can enable this model to calculate porous media parameters by entering the command (set! auto-set-porous? #t) into the FLUENT console window. The porous media inputs are automatically set based on your inputs to the heat exchanger model. There are three ways to specify the heat exchanger core model parameters: • Use the values in FLUENT’s default heat exchanger core model. • Define a new heat exchanger core model with your own values. • Read a heat exchanger core model from an external file. Alternatively, you can explicitly set the porous media parameters by retaining the default value of auto-set-porous?. To do this, follow the procedures described in Section 6.19.6 for the zone(s) declared as a heat exchanger. The models you define will be saved in the case file. Using the Default Heat Exchanger Core Model FLUENT provides a default model for a typical heat exchanger core. To use these values, simply retain the selection of default-model in the Heat Exchanger Core Model drop-down list in the Heat Exchanger panel. (You can view the default parameters in the Heat Exchanger Model panel, as described below.)


6-163

Boundary Conditions

The default-model heat exchanger core model is a list of constant values from the Heat Exchanger Model panel. These constants are used for setting the porous media parameters. Defining a New Heat Exchanger Core Model If you want to define pressure-drop and effectiveness parameters that are different from those in the default heat exchanger core model, you can create a new model. The steps for creating a new model are as follows: 1. Click on the Edit... button to the right of the Heat Exchanger Core Model drop-down list. This will open the Heat Exchanger Model panel (Figure 6.25.5).

Figure 6.25.5: The Heat Exchanger Model Panel

2. Enter the name of your new model in the Name box at the top of the panel. 3. Under Gas-Side Pressure Drop, specify the following parameters used in Equation 6.25-2:

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Min Flow to Face Area Ratio (σ) Entrance Loss Coefficient (Kc ) Exit Loss Coefficient (Ke ) Gas Side Surface Area (A) Min Cross Section Flow Area (Ac ) and the Core Friction Coefficient and Core Friction Exponent (a and b, respectively, in Equation 6.25-3). 4. Under Effectiveness, depending on your choice of heat exchanger model, you can specify the number of points that will be used in the calculation of velocity vs. effectiveness (simple effectiveness model) or the number of points that will be used for the calculation of mass flow rate vs. Ntu (NTU model). For the NTU model: • To specify a constant effectiveness, retain the default Number of Points (1) and specify the value in the NTU field. • To specify a profile for effectiveness, follow the steps below: (a) Specify the Number of Points in your profile. (b) For each Point, enter the Mass Flow Rate and corresponding NTU. For the simple effectiveness model: • To specify a constant effectiveness, retain the default Number of Points (1) and specify the value in the Effectiveness field. • To specify a profile for effectiveness, follow the steps below: (a) Specify the Number of Points in your profile. (b) For each Point, enter the Velocity and corresponding Effectiveness. 5. Click on Change/Create. This will add your new model to the database. Reading Heat Exchanger Parameters from an External File You can read parameters for your heat exchanger core model from an external file. A sample file is shown below: ("modelname" (0.73 0.43 0.053 5.2 0.33 9.1 0.66) ((1 1.0 .6234) (2 2.0 0.5014) (3 3.5 0.3932) (4 5.0 0.3244) (5 6.5 0.2762) (6 8.0 0.2405) (7 10.0 0.2050) (8 12.0 0.1785) (9 15.0 0.1495)))


6-165

Boundary Conditions

The first entry in the file is the name of the model (e.g., modelname). The second set of numbers contains the gas-side pressure drop parameters: (σ Kc Ke A Ac a b) The third entry is a set of points that represent an effectiveness profile (simple effectiveness model) or a mass flow rate vs. Ntu profile (NTU model). Each point in the profile has the following format: Simple effectiveness model: (point

velocity

effectiveness)

NTU model: (point

mass-flow-rate

ntu)

In this sample file, nine points are specified in the effectiveness profile. For either model, local conditions (i.e., mass flow rate or velocity) may fall beyond the range of the user-specified profiles (i.e., mass flow rate vs. Ntu profile or velocity vs. effectiveness profile). When this happens, FLUENT will not extrapolate a new value, but instead uses the extreme value provided as input. For example, when using the NTU model, if the user enters the following mass flow rate vs. Ntu curve: point 0 1

mass-flow-rate (kg/s) 1.0 2.0

ntu 1.01 1.05

and if the local mass flow rate condition is 2.5 kg/s, then FLUENT uses an ntu of 1.05. To read an external heat exchanger file, you will follow these steps: 1. In the Heat Exchanger Model panel, click on the Read... button. 2. In the resulting Select File dialog box, specify the HXC Parameters File name and click OK. FLUENT will read the heat exchanger core model parameters, and add the new model to the database. Viewing the Parameters for an Existing Core Model To view the parameters associated with a heat exchanger core model that you have already defined, select the model name in the Database drop-down list (in the Heat Exchanger Model panel). The values for that model from the database will be displayed in the Heat Exchanger Model panel.

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6.25.4

Using the Heat Exchanger Group

To define a single heat exchanger that uses multiple fluid zones, or to connect the coolant flow path among multiple heat exchangers, you can use heat exchanger groups. To use heat exchanger groups, perform the following steps: 1. Enable the calculation of energy in the Energy panel. Define −→ Models −→Energy... 2. Specify the inputs to the heat exchanger group model, using the Heat Exchanger Group panel (Figure 6.25.6). Define −→ User-Defined −→Heat Exchanger Group... (a) Under Name, enter the name of the heat exchanger group. (b) Under Fluid Zones, select the fluid zones that you want to define in the heat exchanger group. (c) Click on the Model tab. i. In the Model Option drop-down list, select a heat exchanger model and choose from either the default NTU Model or the Simple Effectiveness Model. ii. Under Connectivity, select the Upstream heat exchanger group if such a connection exists. iii. Under Gas Flow Direction, specify the streamwise gas flow direction as either Width, Height, or Depth. iv. In the Heat Exchanger Core Model drop-down list, specify the pressure drop parameters and the effectiveness/Ntu profile of the heat exchanger core. (d) Click on the Geometry tab (Figure 6.25.7). i. Define the macro grid by specifying the Number of Passes, the Number of Rows/Pass, and the Number of Cols/Pass. ii. Specify the Coolant Inlet Direction and Pass-to-Pass Direction. (e) Click on the Coolant tab (Figure 6.25.8). i. Specify the coolant properties and conditions, such as the Specific Heat, the Flow Rate, and the Initial Temperture. (f) If an auxiliary stream is to be modeled, click on the Auxiliary Stream tab (Figure 6.25.9). i. Specify the conditions of the auxiliary coolant (Auxiliary Coolant Flow Rate and Auxiliary Coolant Temperature or Auxiliary Coolant Quality).


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Figure 6.25.6: The Heat Exchanger Group Panel

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Figure 6.25.7: The Heat Exchanger Group Panel - Geometry Tab


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Figure 6.25.8: The Heat Exchanger Group Panel - Coolant Tab

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Figure 6.25.9: The Heat Exchanger Group Panel - Auxiliary Stream Tab


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(g) Click Create or Replace in the Heat Exchanger Group panel to save all the settings. Replace changes the parameters of the already-existing group that is selected in the HX Groups list. 3. If a heat exchanger group is comprised of multiple fluid zones and you wish to override any of the inputs defined in previous step, click on the Set... button to open the Heat Exchanger panel (Figure 6.25.2). Select the particular fluid zone as usual. Notice that the individual heat exchanger inherits the properties of the group by default. You may override any of the following: • macro grid parameters • coolant flow path direction vectors • heat exchanger core model

Selecting the Fluid Zones for the Heat Exchanger Group Select the fluid zones that you want to define in the heat exchanger group in the Fluid Zones drop-down list. The coolant flow in all these zones will be in parallel. Note that one zone cannot be included in more than one heat exchanger group.

Selecting the Upstream Heat Exchanger Group If you want to connect the current group in series with another group, choose the upstream heat exchanger group. Note that any group can have at most one upstream and one downstream group. Also, a group cannot be connected to itself. Select a heat exchanger group from the Upstream drop-down list under Connectivity in the Model tab of the Heat Exchanger Group panel.

! Connecting to an upstream heat exchanger group can be done only while creating a heat exchanger group. The connection will persist even if the connection is later changed and the Replace button is clicked. To change a connection to an upstream heat exchanger group, you need to delete the connecting group and create a new heat exchanger group with the proper connection.

Specifying the Coolant Inlet and Pass-to-Pass Directions The Coolant Inlet Direction and Pass-to-Pass Direction can be specified as directed in Section 6.25.3 in the Heat Exchanger panel. Note that the Update from Plane Tool will set the height, width, and depth as the average of the fluid zones selected in the Fluid Zones.

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Specifying the Coolant Properties The coolant can be specified as having Constant Specific Heat, or a user-defined function can be written to calculate the enthalpy. The function should return the following: • enthalpy for given values of temperature, pressure, and quality • temperature for given values of enthalpy and pressure • specific heat for given values of temperature and pressure The user-defined funtion should be of type DEFINE_SOURCE(udf_name, cell_t c, Thread *t, real d[n], int index). where n in the expression d[n] would be 0 for temperature, 1 for pressure, or 2 for quality. The variable index is 0 for enthalpy, 1 for temperature, or 2 for specific heat. This user-defined function should return real value; /* (temperature or enthalpy or Cp depending on index). */

Specifying Auxiliary Coolant Streams The addition or removal of an auxiliary coolant stream is allowed to any of the heat exchanger groups. Note that auxiliary streams are not allowed for individual zones. You will input the mass flow rate, temperature, and quality of the auxiliary coolant stream. The auxiliary stream has the following assumptions: • The magnitude of a negative auxiliary stream must be less than the primary coolant inlet flow rate of the heat exchanger group. • Added streams will be assumed to have the same fluid properties as the primary inlet coolant.

Initializing the Coolant Temperature When the heat exchanger group is connected to an upstream heat exchanger group, FLUENTwill automatically set the initial guess for coolant inlet temperature, Tin , to be equal to the Tin of the upstream heat exchanger group. Thus the boundary condition Tin for the first heat exchanger group in a connected series will automatically propagate as an initial guess for every other heat exchanger group in the series. However, when it is necessary to further improve convergence properties, you will be allowed to override Tin for


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any connected heat exchanger group by providing a value in the Initial Temperature field. Whenever such an override is supplied, FLUENTwill automatically propagate the new Tin to any heat exchanger groups further downstream in the series. Similarly, every time the Tin boundary condition for the first heat exchanger group is modified, FLUENTwill correspondingly update every downstream heat exchanger group. If you want to impose a non-uniform initialization on the coolant temperature field, first connect the heat exchanger groups and then set Tin for each heat exchanger group in stream-wise order. All heat exchangers included in group must use the fixed Tin option. All heat exchangers within a heat exchanger group must have the same Tin . In other words, no local override of this setting is possible through the Heat Exchanger panel.

6.25.5

Postprocessing for the Heat Exchanger Model

To view the computed values of total heat rejection, outlet temperature, and inlet temperature for your heat exchanger, you can use the following text command: define −→ user-defined −→ heat-exchanger −→heat-exchanger-report When prompted, specify the fluid zone id/name for which you want to report the results. To view the connectivity of the heat exchanger groups, use the text command (report-connectivity)

6.26

Boundary Profiles

FLUENT provides a very flexible boundary profile definition mechanism. This feature allows you to use experimental data, data calculated by an external program, or data written from a previous solution using the Write Profile panel (as described in Section 3.9) as the boundary condition for a variable. Information about boundary profiles is presented in the following subsections: • Section 6.26.1: Boundary Profile Specification Types • Section 6.26.2: Boundary Profile File Format • Section 6.26.3: Using Boundary Profiles • Section 6.26.4: Reorienting Boundary Profiles

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6.26 Boundary Profiles

6.26.1

Boundary Profile Specification Types

Four types of profiles are provided: • Point profiles are specified by an unordered set of n points: (xi , yi , vi ), where 1 ≤ i ≤ n. Profiles written using the Write Profile panel and profiles of experimental data in random order are examples of point profiles. FLUENT will interpolate the point cloud as needed to obtain values at the boundary faces. The interpolation method for unstructured point data is zero order. In other words, for each cell face at the boundary, the solver uses the value from the profile file located closest to the cell. Therefore, if you wish an accurate specification of an inlet profile, your profile file should contain a sufficiently high point density. • Line profiles are specified for 2D problems by an ordered set of n points: (xi , yi , vi ), where 1 ≤ i ≤ n. Zero-order interpolation is performed between the points. An example of a line profile is a profile of data obtained from an external program that calculates a boundary-layer profile. • Mesh profiles are specified for 3D problems by an m by n mesh of points: (xij , yij , zij , vij ), where 1 ≤ i ≤ m and 1 ≤ j ≤ n. Zero-order interpolation is performed between the points. Examples of mesh profiles are profiles of data from a structured mesh solution and experimental data in a regular array. • Radial profiles are specified for 2D and 3D problems by an ordered set of n points: (ri , vi ), where 1 ≤ i ≤ n. The data in a radial profile are a function of radius only. Linear interpolation is performed between the points, which must be sorted in ascending order of the r field. The axis for the cylindrical coordinate system is determined as follows: – For 2D problems, it is the z-direction vector through (0,0). – For 2D axisymmetric problems, it is the x-direction vector through (0,0). – For 3D problems involving a swirling fan, it is the fan axis defined in the Fan panel (unless you are using local cylindrical coordinates at the boundary, as described below). – For 3D problems without a swirling fan, it is the rotation axis of the adjacent fluid zone, as defined in the Fluid panel (unless you are using local cylindrical coordinates at the boundary, as described below). – For 3D problems in which you are using local cylindrical coordinates to specify conditions at the boundary, it is the axis of the specified local coordinate system.


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6.26.2

Boundary Profile File Format

The format of the profile files is fairly simple. The file can contain an arbitrary number of profiles. Each profile consists of a header that specifies the profile name, profile type (point, line, mesh, or radial), and number of defining points, and is followed by an arbitrary number of named “fields”. Some of these fields contain the coordinate points and the rest contain boundary data.

! All quantities, including coordinate values, must be specified in SI units because FLUENT does not perform unit conversion when reading profile files. Parentheses are used to delimit profiles and the fields within the profiles. Any combination of tabs, spaces, and newlines can be used to separate elements.

! In the general format description below, “|” indicates that you should input only one of the items separated by |’s and “...” indicates a continuation of the list. ((profile1-name point|line|radial n) (field1-name a1 a2 ... an) (field2-name b1 b2 ... bn) . . . (fieldf-name f1 f2 ... fn)) ((profile2-name mesh m n) (field1-name a11 a12 ... a21 a22 ... . . . am1 am2 ... . . . (fieldf-name f11 f12 ... f21 f22 ... . . . fm1 fm2 ...

a1n a2n

amn)

f1n f2n

fmn))

Boundary profile names must have all lowercase letters (e.g., name). Uppercase letters in boundary profile names are not acceptable. Each profile of type point, line, and mesh must contain fields with names x, y, and, for 3D, z. Each profile of type radial

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must contain a field with name r. The rest of the names are arbitrary, but must be valid Scheme symbols. For compatibility with old-style profile files, if the profile type is missing, point is assumed.

Example A typical usage of a boundary profile file is to specify the profile of the boundary layer at an inlet. For a compressible flow calculation, this will be done using profiles of total pressure, k, and . For an incompressible flow, it might be preferable to specify the inlet value of streamwise velocity, together with k and . Below is an example of a profile file that does this: ((turb-prof point 8) (x 4.00000E+00 4.00000E+00 4.00000E+00 4.00000E+00 (y 1.06443E-03 3.19485E-03 2.90494E-01 3.31222E-01 (u 5.47866E+00 6.59870E+00 1.01674E+01 1.01656E+01 (tke 4.93228E-01 6.19247E-01 6.89414E-03 6.89666E-03 (eps 1.27713E+02 6.04399E+01 9.78365E-03 9.79056E-03 )

6.26.3

4.00000E+00 4.00000E+00

4.00000E+00 4.00000E+00 )

5.33020E-03 3.84519E-01

7.47418E-03 4.57471E-01 )

7.05731E+00 1.01637E+01

7.40079E+00 1.01616E+01 )

5.32680E-01 6.90015E-03

4.93642E-01 6.90478E-03 )

3.31187E+01 9.80001E-03

2.21535E+01 9.81265E-03 )

Using Boundary Profiles

The procedure for using a boundary profile to define a particular boundary condition is outlined below. 1. Create a file that contains the desired boundary profile, following the format described in Section 6.26.2. 2. Read the boundary profile using the Read... button in the Boundary Profiles panel (Figure 6.26.1) or the File/Read/Profile... menu item. Define −→Profiles... File −→ Read −→Profile...


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3. In the boundary conditions panels (e.g., the Velocity Inlet and Pressure Inlet panels), the fields defined in the profile file (and those defined in any other profile file that you have read in) will appear in the drop-down list to the right of or below each parameter for which profile specification is allowed. To use a particular profile, select it in the list.

! Boundary profiles cannot be used to define volumetric source terms. If you want to define a non-constant source term, you will need to use a user-defined function. For more information on UDFs, refer to the separate UDF Manual. Note that if you use the Boundary Profiles panel to read a file, and a profile in the file has the same name as an existing profile, the old profile will be overwritten.

Checking and Deleting Profiles Each profile file contains one or more profiles, and each profile has one or more fields defined in it. Once you have read in a profile file, you can check which fields are defined in each profile, and you can also delete a particular profile. These tasks are accomplished in the Boundary Profiles panel (Figure 6.26.1). Define −→Profiles...

Figure 6.26.1: The Boundary Profiles Panel To check which fields are defined in a particular profile, select the profile name in the Profile list. The available fields in that file will be displayed in the Fields list. In Figure 6.26.1, the profile fields from the profile file of Section 6.26.2 are shown. To delete a profile, select it in the Profiles list and click on the Delete button. When a profile is deleted, all fields defined in it will be removed from the Fields list.

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Example For the example given in Section 6.26.2, the profiles are used for inlet values of x velocity, turbulent kinetic energy, and turbulent kinetic energy dissipation rate, as illustrated in Figure 6.26.2. (The y velocity is set to a constant value of zero, since it is assumed negligible. However, a profile of y velocity could also be used.)

Figure 6.26.2: Example of Using Profiles as Boundary Conditions

Once the profiles have been specified, the boundary conditions have been saved (OK’d), and the flow solution has been initialized, you can view the inlet profile as follows: • For 2D calculations, open the Solution XY Plot panel. Select the appropriate boundary zone in the Surfaces list, the variable of interest in the Y Axis Function drop-down list, and the desired Plot Direction. Ensure that the Node Values check button is turned on, and then click Plot. You should then see the inlet profile plotted. If the data plotted do not agree with your specified profile, this means that there is an error in the profile file. • For 3D calculations, use the Contours panel to display contours on the appropriate boundary zone surface. The Node Values check button must be turned on in order for you to view the profile data. If the data shown in the contour plot do not agree with your specified profile, this means that there is an error in the profile file.


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6.26.4

Reorienting Boundary Profiles

For 3D cases only, FLUENT allows you to change the orientation of an existing boundary profile so that it can be used at a boundary positioned arbitrarily in space. This allows you, for example, to take experimental data for an inlet with one orientation and apply it to an inlet in your model that has a different spatial orientation. Note that FLUENT assumes that the profile and the boundary are planar.

Steps for Changing the Profile Orientation The procedure for orienting the boundary profile data in the principal directions of a boundary is outlined below: 1. Define and read the boundary profile as described in Section 6.26.3. 2. In the Boundary Profiles panel, select the profile in the Profile list, and then click on the Orient... button. This will open the Orient Profile panel (Figure 6.26.3). 3. In the Orient Profile panel, enter the name of the new profile you want to create in the New Profile box 4. Specify the number of fields you want to create using the up/down arrows next to the New Fields box. The number of new fields is equal to the number of vectors and scalars to be defined plus 1 (for the coordinates). 5. Define the coordinate field. (a) Enter the names of the three coordinates (x, y, z) in the first row under New Field Names.

!

Ensure that the coordinates are named x, y, and z only. Do not use any other names or upper case letters in this field. (b) Select the appropriate local coordinate fields for x, y, and z from the dropdown lists under Compute From.... (A selection of 0 indicates that the coordinate does not exist in the original profile; i.e., the original profile was defined in 2D.) 6. Define the vector fields in the new profile. (a) Enter the names of the 3 components in the directions of the coordinate axes of the boundary under New Field Names.

!

Do not use upper case letters in these fields. (b) Select the names of the 3 components of the vector in the local x, y, and z directions of the boundary profile from the drop-down lists under Compute From....

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Figure 6.26.3: The Orient Profile Panel


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7. Define the scalar fields in the new profile. (a) Enter the name of the scalar in the first column under New Field Names.

!

Do not use upper case letters in these fields. (b) Click on the button under Treat as Scalar Quantity in the same row. (c) Select the name of the scalar in the corresponding drop-down list under Compute From.... 8. Under Orient To..., specify the coordinates of the origin of the local coordinate system in the Center field. 9. Under Orient To..., specify the directional vectors (x,y,z) for the X’-, Y’-, and Z’-axis. The X’-, Y’-, and Z’-axis are the directional vectors of the major axis, the minor axis, and the normal to the boundary. Each direction will be that of the vector from (0,0,0) to the specified (x,y,z). For some problems in which the X’-, Y’- and Z’- directions are not aligned with the coordinate axes of the domain, you may not know a priori the directional vectors. In such cases, the plane tool can help you to determine these directional vectors and the coordinates of the Center (origin): (a) “Snap” the plane tool onto the boundary. (Follow the instructions in Section 26.6.1 for initializing the tool to a position on an existing surface.) (b) Translate and rotate the axes of the tool appropriately until the axes are aligned with the principal directions of the boundary and the origin of the tool is on the centroid of the boundary. (c) Click on the Update From Plane Tool button in the Orient Profile panel. FLUENT will automatically set the Center to the origin of the plane tool axes, the X’-axis to the direction of the green arrow of the tool, the Y’-axis to the direction of the blue arrow of the tool, and the Z’-axis to the direction of the red arrow of the tool. 10. Click the Create button in the Orient Profile panel, and your new profile will be created. Its name (which you entered in the New Profile box) will now appear in the Boundary Profiles panel and will be available for use at the desired boundary.

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6.27 Fixing the Values of Variables

6.27

Fixing the Values of Variables

The option to fix values of variables in FLUENT allows you to set the value of one or more variables in a fluid or solid zone, essentially setting a boundary condition for the variables within the cells of the zone. When a variable is fixed in a given cell, the transport equation for that variable is not solved in the cell (and the cell is not included when the residual sum is computed for that variable). The fixed value is used for the calculation of face fluxes between the cell and its neighbors. The result is a smooth transition between the fixed value of a variable and the values at the neighboring cells.

! You can fix values for velocity components, temperature, and species mass fractions only if you are using the segregated solver.

6.27.1

Overview of Fixing the Value of a Variable

The ability to fix the value of a variable has a wide range of applications. The velocity fixing method is often used to model the flow in stirred tanks. This approach provides an alternative to the use of a rotating reference frame (solution in the reference frame of the blade) and can be used to model baffled tanks. In both 2D and 3D geometries, a fluid cell zone may be used in the impeller regions, and velocity components can be fixed based on measured data. Although the actual impeller geometry can be modeled and the flow pattern calculated using the sliding mesh model, experimental data for the velocity profile in the outflow region are available for many impeller types. If you do not need to know the details of the flow around the blades for your problem, you can model the impeller by fixing the experimentally-obtained liquid velocities in its outflow zone. The velocities in the rest of the vessel can then be calculated using this fixed velocity profile as a boundary condition. Figure 6.27.1 shows an example of how this method is used to model the flow pattern created by a disk-turbine in an axisymmetric stirred vessel.

Variables That Can Be Fixed The variables that can be fixed include velocity components (segregated solver only), turbulence quantities, temperature (segregated solver only), enthalpy, species mass fractions (segregated solver only), and user-defined scalars. For turbulence quantities, different values can be set depending on your choice of turbulence model. You can fix the value of the temperature in a fluid or solid zone if you are solving the energy equation. If you are using the non-premixed combustion model, you can fix the enthalpy in a fluid zone. If you have more than one species in your model, you can specify fixed values for the species mass fractions for each individual species except the last one you defined. See the separate UDF Manual for details about defining user-defined scalars. If you are using the Eulerian multiphase model, you can fix the values of velocity components and (depending on which multiphase turbulence model you are using) turbulence


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Figure 6.27.1: Fixing Values for the Flow in a Stirred Tank

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6.27 Fixing the Values of Variables

quantities on a per-phase basis. See Section 22.6.16 for details about setting boundary conditions for Eulerian multiphase calculations.

6.27.2

Procedure for Fixing Values of Variables in a Zone

To fix the values of one or more variables in a cell zone, follow these steps (remembering to use only SI units): 1. In the Fluid panel or Solid panel, turn on the Fixed Values option. 2. Fix the values for the appropriate variables, noting the comments below. • To specify a constant value for a variable, choose constant in the drop-down list next to the relevant field and then enter the constant value in the field. • To specify a non-constant value for a variable, you can use a boundary profile (see Section 6.26) or a user-defined function for a boundary profile (see the separate UDF Manual). Select the appropriate profile or UDF in the dropdown list next to the relevant field. If you specify a radial-type boundary profile (see Section 6.26.1) for temperature, enthalpy, species mass fractions, or turbulence quantities for the k-, Spalart-Allmaras, or k-ω model, the local coordinate system upon which the radial profile is based is defined by the Rotation-Axis Origin and Rotation-Axis Direction for the fluid zone. See Section 6.17.1 for information about setting these parameters. (Note that it is acceptable to specify the rotation axis and direction for a non-rotating zone. This will not cause the zone to rotate; it will not rotate unless it has been explicitly defined as a moving zone.) • If you do not want to fix the value for a variable, choose (or keep) none in the drop-down list next to the relevant field. This is the default for all variables.

Fixing Velocity Components To fix the velocity components, you can specify X, Y, and (in 3D) Z Velocity values, or, for axisymmetric cases, Axial, Radial, and (for axisymmetric swirl) Swirl Velocity values. The units for a fixed velocity are m/s. For 3D cases, you can choose to specify cylindrical velocity components instead of Cartesian components. Turn on the Local Coordinate System For Fixed Velocities option, and then specify the Axial, Radial, and/or Tangential Velocity values. The local coordinate system is defined by the Rotation-Axis Origin and Rotation-Axis Direction for the fluid zone. See Section 6.17.1 for information about setting these parameters. (Note that it is acceptable to specify the rotation axis and direction for a non-rotating zone. This will not cause the zone to rotate; it will not rotate unless it has been explicitly defined as a moving zone.)

! You can fix values for velocity components only if you are using the segregated solver.


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Fixing Temperature and Enthalpy If you are solving the energy equation, you can fix the temperature in a zone by specifying the value of the Temperature. The units for a fixed temperature are K. If you are using the non-premixed combustion model, you can fix the enthalpy in a zone by specifying the value of the Enthalpy. The units for a fixed enthalpy are m2 /s2 . If you specify a radial-type boundary profile (see Section 6.26.1) for temperature or enthalpy, the local coordinate system upon which the radial profile is based is defined by the Rotation-Axis Origin and Rotation-Axis Direction for the fluid zone. See above for details.

! You can fix the value of temperature only if you are using the segregated solver. Fixing Species Mass Fractions If you are using the species transport model, you can fix the values of the species mass fractions for individual species. FLUENT allows you to fix the species mass fraction for each species (e.g., h2, o2) except the last one you defined. If you specify a radial-type boundary profile (see Section 6.26.1) for a species mass fraction, the local coordinate system upon which the radial profile is based is defined by the Rotation-Axis Origin and Rotation-Axis Direction for the fluid zone. See above for details.

! You can fix values for species mass fractions only if you are using the segregated solver. Fixing Turbulence Quantities To fix the values of k and in the k- equations, specify the Turbulence Kinetic Energy and Turbulence Dissipation Rate values. The units for k are m2 /s2 and those for are m2 /s3 . To fix the value of the modified turbulent viscosity (˜ ν ) for the Spalart-Allmaras model, specify the Modified Turbulent Viscosity value. The units for the modified turbulent viscosity are m2 /s. To fix the values of k and ω in the k-ω equations, specify the Turbulence Kinetic Energy and Specific Dissipation Rate values. The units for k are m2 /s2 and those for ω are 1/s. To fix the value of k, , or the Reynolds stresses in the RSM transport equations, specify the Turbulence Kinetic Energy, Turbulence Dissipation Rate, UU Reynolds Stress, VV Reynolds Stress, WW Reynolds Stress, UV Reynolds Stress, VW Reynolds Stress, and/or UW Reynolds Stress. The units for k and the Reynolds stresses are m2 /s2 , and those for are m2 /s3 . If you specify a radial-type boundary profile (see Section 6.26.1) for k, , ω, or ν˜, the local coordinate system upon which the radial profile is based is defined by the Rotation-Axis

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6.28 Defining Mass, Momentum, Energy, and Other Sources

Origin and Rotation-Axis Direction for the fluid zone. See above for details. Note that you cannot specify radial-type profiles for the Reynolds stresses.

Fixing User-Defined Scalars To fix the value of a user-defined scalar, specify the User defined scalar-n value. (There will be one for each user-defined scalar you have defined.) The units for a user-defined scalar will be the appropriate SI units for the scalar quantity. See the separate UDF Manual for information on user-defined scalars.

6.28

Defining Mass, Momentum, Energy, and Other Sources

You can define volumetric sources of mass (for single or multiple species), momentum, energy, turbulence, and other scalar quantities in a fluid zone, or a source of energy for a solid zone. This feature is useful when you want to input a known value for these sources. (For more complicated sources with functional dependency, you can create a user-defined function as described in the separate UDF Manual.) To add source terms to a cell or group of cells, you must place the cell(s) in a separate zone. The sources are then applied to that cell zone. Typical uses for this feature are listed below: • A flow source that cannot be represented by an inlet, e.g., due to an issue of scale. If you need to model an inlet that is smaller than a cell, you can place the cell where the tiny “inlet” is located in its own fluid zone and then define the mass, momentum, and energy sources in that cell zone. For the example shown in Figure 6.28.1, you ˙ j ˙ ˙ should set a mass source of m = ρj AVj vj and a momentum source of mv = mv , where V V V V is the cell volume. • Heat release due to a source (e.g., fire) that is not explicitly defined in your model. For this case, you can place the cell(s) into which the heat is originally released in its own fluid zone and then define the energy source in that cell zone. • An energy source in a solid zone, for conjugate heat transfer applications. For this case, you can place the cell(s) into which the heat is originally released in its own solid zone and then define the energy source in that cell zone. • A species source due to a reaction that is not explicitly included in the model. In the above example of simulating a fire, you might need to define a source for a species representing smoke generation.

! Note that if you define a mass source for a cell zone, you should also define a momentum source and, if appropriate for your model, energy and turbulence sources. If you define only a mass source, that mass enters the domain with no momentum or thermal heat. The mass will therefore have to be accelerated and heated by the flow and, consequently, there may be a drop in velocity or temperature. This drop may or may not be perceptible,


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v

j

Aj

Figure 6.28.1: Defining a Source for a Tiny Inlet

depending on the size of the source. (Note that defining only a momentum, energy, or turbulence source is acceptable.)

Sign Conventions and Units All positive source terms indicate sources, and all negative source terms indicate sinks. All sources must be specified in SI units.

6.28.1

Procedure for Defining Sources

To define one or more source terms for a zone, follow these steps (remembering to use only SI units): 1. In the Fluid panel or Solid panel, turn on the Source Terms option. 2. Set the appropriate source terms, noting the comments below. • To specify a constant source, choose constant in the drop-down list next to the source term field and then enter the constant value in the field. • To specify a temperature-dependent or other functional source, you can use a user-defined function (see the separate UDF Manual). Select the appropriate UDF in the drop-down list next to the relevant field. • If you do not want to specify a source term for a variable, choose (or keep) none in the drop-down list next to the relevant field. This is the default for all variables. • Remember that you should not define just a mass source without defining the other sources, as described above.

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• Since the sources you specify are defined per unit volume, to determine the appropriate value of your source term you will often need to first determine the volume of the cell(s) in the zone for which you are defining the source. To do this, you can use the Volume Integrals panel.

Mass Sources If you have only one species in your problem, you can simply define a Mass source for that species. The units for the mass source are kg/m3 -s. In the continuity equation (Equation 8.2-1), the defined mass source will appear in the Sm term. If you have more than one species, you can specify mass sources for each individual species. There will be a total Mass source term as well as a source term listed explicitly for each species (e.g., h2, o2) except the last one you defined. If the total of all species mass sources (including the last one) is 0, then you should specify a value of 0 for the Mass source, and also specify the values of the non-zero individual species mass sources. Since you cannot specify the mass source for the last species explicitly, FLUENT will compute it by subtracting the sum of all other species mass sources from the specified total Mass source. For example, if the mass source for hydrogen in a hydrogen-air mixture is 0.01, the mass source for oxygen is 0.02, and the mass source for nitrogen (the last species) is 0.015, you will specify a value of 0.01 in the h2 field, a value of 0.02 in the o2 field, and a value of 0.045 in the Mass field. This concept also applies within each cell if you use user-defined functions for species mass sources. The units for the species mass sources are kg/m3 -s. In the conservation equation for a chemical species (Equation 13.1-1), the defined mass source will appear in the Si term.

Momentum Sources To define a source of momentum, specify the X Momentum, Y Momentum, and/or Z Momentum term. The units for the momentum source are N/m3 . In the momentum equation (Equation 8.2-3), the defined momentum source will appear in the F~ term.

Energy Sources To define a source of energy, specify an Energy term. The units for the energy source are W/m3 . In the energy equation (Equation 11.2-1), the defined energy source will appear in the Sh term.


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Boundary Conditions

Turbulence Sources Turbulence Sources for the k- Model To define a source of k or in the k- equations, specify the Turbulence Kinetic Energy or Turbulence Dissipation Rate term. The units for the k source are kg/m-s3 and those for are kg/m-s4 . The defined k source will appear in the Sk term on the right-hand side of the turbulent kinetic energy equation (e.g., Equation 10.4-1). The defined source will appear in the S term on the right-hand side of the turbulent dissipation rate equation (e.g., Equation 10.4-2). Turbulence Sources for the Spalart-Allmaras Model To define a source of modified turbulent viscosity, specify the Modified Turbulent Viscosity term. The units for the modified turbulent viscosity source are kg/m-s2 . In the transport equation for the Spalart-Allmaras model (Equation 10.3-1), the defined modified turbulent viscosity source will appear in the Sν˜ term. Turbulence Sources for the k-ω Model To define a source of k or ω in the k-ω equations, specify the Turbulence Kinetic Energy or Specific Dissipation Rate term. The units for the k source are kg/m-s3 and those for ω are kg/m3 -s2 . The defined k source will appear in the Sk term on the right-hand side of the turbulent kinetic energy equation (Equation 10.5-1). The defined ω source will appear in the Sω term on the right-hand side of the specific turbulent dissipation rate equation (Equation 10.5-2). Turbulence Sources for the Reynolds Stress Model To define a source of k, , or the Reynolds stresses in the RSM transport equations, specify the Turbulence Kinetic Energy, Turbulence Dissipation Rate, UU Reynolds Stress, VV Reynolds Stress, WW Reynolds Stress, UV Reynolds Stress, VW Reynolds Stress, and/or UW Reynolds Stress terms. The units for the k source and the sources of Reynolds stress are kg/m-s3 , and those for are kg/m-s4 . The defined Reynolds stress sources will appear in the Suser term on the right-hand side of the Reynolds stress transport equation (Equation 10.6-1). The defined k source will appear in the Sk term on the right-hand side of Equation 10.6-23. The defined will appear in the S term on the right-hand side of Equation 10.6-26.

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Mean Mixture Fraction and Variance Sources To define a source of the mean mixture fraction or its variance for the non-premixed combustion model, specify the Mean Mixture Fraction or Mixture Fraction Variance term. The units for the mean mixture fraction source are kg/m3 -s, and those for the mixture fraction variance source are kg/m3 -s. The defined mean mixture fraction source will appear in the Suser term in the transport equation for the mixture fraction (Equation 14.1-4). The defined mixture fraction variance source will appear in the Suser term in the transport equation for the mixture fraction variance (Equation 14.1-5). If you are using the two-mixture-fraction approach, you can also specify sources of the Secondary Mean Mixture Fraction and Secondary Mixture Fraction Variance.

P-1 Radiation Sources To define a source for the P-1 radiation model, specify the P1 term. The units for the radiation source are W/m3 , and the defined source will appear in the SG term in Equation 11.3-12. Note that, if the source term you are defining represents a transfer from internal energy to radiative energy (e.g., absorption or emission), you will need to specify an Energy source of the same magnitude as the P1 source, but with the opposite sign, in order to ensure overall energy conservation.

Progress Variable Sources To define a source of the progress variable for the premixed combustion model, specify the Progress Variable term. The units for the progress variable source are kg/m3 -s, and the defined source will appear in the ρSc term in Equation 15.2-1.

NO, HCN, and NH3 Sources for the NOx Model To define a source of NO, HCN, or NH3 for the NOx model, specify the no, hcn, or nh3 term. The units for these sources are kg/m3 -s, and the defined sources will appear in the SNO , SHCN , and SNH3 terms of Equations 18.1-1, 18.1-2, and 18.1-3.

User-Defined Scalar Sources To define a source for a user-defined scalar transport equation, specify the User defined scalar-n term. (There will be one for each user-defined scalar you have defined.) The units for a user-defined scalar source will be the appropriate SI units for the scalar quantity. The source will appear in the Sφi term of the scalar transport equation. See the separate UDF Manual for information on user-defined scalars.


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Boundary Conditions

6.29

Coupling Boundary Conditions with GT-Power

GT-Power users can define time-dependent boundary conditions in FLUENT based on information from GT-Power. During the FLUENT simulation, FLUENT and GT-Power are coupled together and information about the boundary conditions at each time step is transferred between them.

6.29.1

Requirements and Restrictions

Note the following requirements and restrictions for the GT-Power coupling: • The flow must be unsteady. • The compressible ideal gas law must be used for density. • Each boundary zone for which you plan to define conditions using GT-Power must be a flow boundary of one of the following types: – velocity inlet – mass flow inlet – pressure inlet – pressure outlet Also, a maximum of 20 boundary zones can be coupled to GT-Power. • If a mass flow inlet or pressure inlet is coupled to GT-Power, you must select Normal to Boundary as the Direction Specification Method in the Mass-Flow Inlet or Pressure Inlet panel. For a velocity inlet, you must select Magnitude, Normal to Boundary as the Velocity Specification Method in the Velocity Inlet panel. • Boundary conditions for the following variables can be obtained from GT-Power: – velocity – temperature – pressure – density – species mass fractions – k and (Note that it is recommended that you define these conditions in FLUENT yourself, rather than using the data provided by GT-Power, since the GT-Power values are based on a 1D model.) • Make sure that the material properties you set in FLUENT are the same as those used in GT-Power, so that the boundary conditions will be valid for your coupled simulation.

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6.29 Coupling Boundary Conditions with GT-Power

• If your model includes species, make sure that the name of each species in GT-Power corresponds to the Chemical Formula for that species material in the Materials panel. Also, recall that FLUENT can handle a maximum of 50 species. • You can install the GT-Power libraries in a directory other than the default location. If the GT-Power libraries are loaded into a non-default location, you need to set the following environment variables: – GTIHOME - the top level GTI installation directory where GT-Power is installed – FLUENT GTIVERSION - the current version of the GTI installation (i.e., version 5.1.0 or version 5.2.0)

!

GTI is not backwards compatible.

6.29.2

User Inputs

The procedure for setting up the GT-Power coupling in FLUENT is presented below. 1. Read in the mesh file and define the models, materials, and boundary zone types (but not the actual boundary conditions), noting the requirements and restrictions listed in Section 6.29.1. 2. Specify the location of the GT-Power data and have FLUENT use them to generate user-defined functions for the relevant boundary conditions (using the 1D Simulation Library panel, shown in Figure 6.29.1). Define −→ User-Defined −→1D Coupling...

Figure 6.29.1: The 1D Simulation Library Panel

(a) Select GTpower in the 1D Library drop-down list. (b) Specify the name of the GT-Power input file in the 1D Input File Name field. (c) Click the Start button.


6-193

Boundary Conditions

When you click Start, GT-Power will start up and FLUENT user-defined functions for each boundary in the input file will be generated. 3. Set boundary conditions for all zones. For flow boundaries for which you are using GT-Power data, select the appropriate UDFs as the conditions.

!

Note that you must select the same UDF for all conditions at a particular boundary zone (as shown, for example, in Figure 6.29.2); this UDF contains all of the conditions at that boundary.

Figure 6.29.2: Using GT-Power Data for Boundary Conditions

4. If you plan to continue the simulation at a later time, starting from the final data file of the current simulation, specify how often you want to have the case and data files saved automatically. File −→ Write −→Autosave...

6-194


6.30 Coupling Boundary Conditions with WAVE

!

When FLUENT saves a data file at the specified automatic save interval, it will also save a restart file for GT-Power. This is the only way to save a GT-Power restart file; if you use the File/Write/Data... menu item to save a data file manually, the restart file will not be created. To use a GT-Power restart file to restart a FLUENT calculation, you must edit the GT-Power input data file. See the GT-Power User’s Guide for instructions. 5. Continue the problem setup and calculate a solution in the usual manner.

6.30

Coupling Boundary Conditions with WAVE

WAVE users can define time-dependent boundary conditions in FLUENT based on information from WAVE. During the FLUENT simulation, FLUENT and WAVE are coupled together and information about the boundary conditions at each time step is transferred between them.

6.30.1

Requirements and Restrictions

Note the following requirements and restrictions for the WAVE coupling: • WAVE needs to be installed and licensed. • WAVE is not supported on Windows. • There are always five species that must be modeled in FLUENT just as they are defined in WAVE (F1, F2, F3, F4, and F5). It is recommended that realistic material properties be assigned to each of the five species. • The flow must be unsteady. • The compressible ideal gas law must be used for density. • Each boundary zone for which you plan to define conditions using WAVE must be a flow boundary of one of the following types: – velocity inlet – mass flow inlet – pressure inlet – pressure outlet Also, a maximum of 20 boundary zones can be coupled to WAVE. • If a mass flow inlet or pressure inlet is coupled to WAVE, you must select Normal to Boundary as the Direction Specification Method in the Mass-Flow Inlet or Pressure Inlet panel. For a velocity inlet, you must select Magnitude, Normal to Boundary as the Velocity Specification Method in the Velocity Inlet panel.


6-195

Boundary Conditions

• Boundary conditions for the following variables can be obtained from WAVE: – velocity – temperature – pressure – density – species mass fractions – k and (Note that you are required to define these conditions in FLUENT yourself, since WAVE does not calculate them.) • Make sure that the material properties you set in FLUENT are the same as those used in WAVE, so that the boundary conditions will be valid for your coupled simulation. • If your model includes species, make sure that the name of each species in WAVE corresponds to the Chemical Formula for that species material in the Materials panel. Also, recall that FLUENT can handle a maximum of 50 species.

6.30.2

User Inputs

The procedure for setting up the WAVE coupling in FLUENT is presented below. 1. Read in the mesh file and define the models, materials, and boundary zone types. 2. Specify the location of the WAVE data and have FLUENT use them to generate user-defined functions for the relevant boundary conditions (using the 1D Simulation Library panel, shown in Figure 6.30.1). Define −→ User-Defined −→1D Coupling...

Figure 6.30.1: The 1D Simulation Library Panel with WAVE Selected

(a) Select WAVE in the 1D Library drop-down list.

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6.30 Coupling Boundary Conditions with WAVE

(b) Specify the name of the WAVE input file in the 1D Input File Name field. (c) Click the Start button. When you click Start, WAVE will start up and FLUENT user-defined functions for each boundary in the input file will be generated. 3. Set boundary conditions for all zones. For flow boundaries for which you are using WAVE data, select the appropriate UDFs as the conditions.

!

Note that you must select the same UDF for all conditions at a particular boundary zone (as shown, for example, in Figure 6.30.2); this UDF contains all of the conditions at that boundary.

Figure 6.30.2: Using WAVE Data for Boundary Conditions

4. If you plan to continue the simulation at a later time, restarting from the final data file of the current simulation, you need to instruct both FLUENTand WAVE how


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Boundary Conditions

often that you want to automatically save your data. You should instruct FLUENT to automatically save case and data files at specified intervals using the autosave feature. File −→ Write −→Autosave... In addition, you should instruct WAVE as to how often it should generate its own restart files. See the WAVE User’s Guide for instructions on this feature.

!

To use the restart feature, the time interval for writing data files must be set to the same value in both FLUENT and WAVE. For example, if FLUENT has set the autosave feature to 100, then WAVE must also set the resart file write frequency to 100 as well. 5. Continue the problem setup and calculate a solution in the usual manner.

6-198


Chapter 7.

Physical Properties

This chapter describes the physical equations used to compute material properties and the procedures you can use for each property input. Each property is described in detail in the following sections. If you are using one of the general multiphase models (VOF, mixture, or Eulerian), see Section 22.6.8 for information about how to define the individual phases, including their material properties. • Section 7.1: Setting Physical Properties • Section 7.2: Density • Section 7.3: Viscosity • Section 7.4: Thermal Conductivity • Section 7.5: Specific Heat Capacity • Section 7.6: Radiation Properties • Section 7.7: Mass Diffusion Coefficients • Section 7.8: Standard State Enthalpies • Section 7.9: Standard State Entropies • Section 7.10: Molecular Heat Transfer Coefficient • Section 7.11: Kinetic Theory Parameters • Section 7.12: Operating Pressure • Section 7.13: Reference Pressure Location • Section 7.14: Real Gas Models


7-1

Physical Properties

7.1

Setting Physical Properties

An important step in the setup of your model is the definition of the physical properties of the material. Material properties are defined in the Materials panel, which allows you to input values for the properties that are relevant to the problem scope you have defined in the Models panels. These properties may include the following: • Density and/or molecular weights • Viscosity • Heat capacity • Thermal conductivity • Mass diffusion coefficients • Standard state enthalpies • Kinetic theory parameters Properties may be temperature- and/or composition-dependent, with temperature dependence based on a polynomial, piecewise-linear, or piecewise-polynomial function and individual component properties either defined by you or computed via kinetic theory. The Materials panel will show the properties that need to be defined for the active physical models. Note that, if any property you define requires the energy equation to be solved (e.g., ideal gas law for density, temperature-dependent profile for viscosity), FLUENT will automatically activate the energy equation for you. You will then need to define thermal boundary conditions and other parameters yourself.

Physical Properties for Solid Materials For solid materials, only density, thermal conductivity, and heat capacity are defined (unless you are modeling semi-transparent media, in which case radiation properties are also defined). You can specify a constant value, a temperature-dependent function, or a user-defined function for thermal conductivity; a constant value or temperaturedependent function for heat capacity; and a constant value for density. If you are using the segregated solver, density and heat capacity for a solid material are not required unless you are modeling unsteady flow or moving solid zones. Heat capacity will appear in the list of solid properties for steady flows as well, but the value will be used just for postprocessing enthalpy; it will not be used in the calculation.

7-2


7.1 Setting Physical Properties

7.1.1

Material Types

In FLUENT, physical properties of fluids and solids are associated with named “materials,” and these materials are then assigned as boundary conditions for zones. When you model species transport, you will define a “mixture” material, consisting of the various species involved in the problem. Properties will be defined for the mixture, as well as for the constituent species, which are fluid materials. (The mixture material concept is discussed in detail in Section 13.1.2.) Additional material types are available for the discrete-phase model, as described in Section 21.11.2. Materials can be defined from scratch, or they can be downloaded from a global (sitewide) database and edited. See Section 7.1.4 for information about modifying your site-wide material property database.

! All the materials that exist in your local materials list will be saved in the case file (when you write one). Your materials will be available to you if you read this case file into a new solver session.

7.1.2

Using the Materials Panel

The Materials panel (Figure 7.1.1) allows you to create new materials, copy materials from the global database, and modify material properties. Define −→Materials... These generic functions are described here in this section, and the inputs for temperaturedependent properties are explained in Section 7.1.3. The specific inputs for each material property are discussed in the remaining sections of this chapter. By default, your local materials list (i.e., in the solver session) will include a single fluid material (air) and a single solid material (aluminum). If the fluid involved in your problem is air, you may use the default properties for air or modify the properties. If the fluid in your problem is water, for example, you can either copy water from the global database or create a new “water” material from scratch. If you copy water from the database, you can still make modifications to the properties of your local copy of water. Mixture materials will not exist in your local list unless you have enabled species transport (see Chapter 13). Similarly, inert, droplet, and combusting particle materials will not be available unless you have created a discrete phase injection of these particle types (see Chapter 21). When a mixture material is copied from the database, all of its constituent fluid materials (species) will automatically be copied over as well.

Modifying Properties of an Existing Material Probably the most common operation you will perform with the Materials panel is the modification of properties for an existing material. The steps for this procedure are as follows:


7-3

Physical Properties

Figure 7.1.1: The Materials Panel

1. Select the type of material (fluid, solid, etc.) in the Material Type drop-down list. 2. Choose the material for which you want to modify properties in the Fluid Materials drop-down list, Solid Materials list, or other similarly-named list. (The list’s name will be the same as the material type you selected in step 1.) 3. Make the desired changes to the properties contained in the Properties area. If there are many properties listed, you may use the scroll bar to the right of the Properties area to scroll through the listed items. 4. Click on the Change/Create button to change the properties of the selected material to your new property settings. To change the properties of an additional material, repeat the process described above. Remember to click the Change/Create button after making the changes to each material’s properties.

7-4



Renaming an Existing Material Each material is identified by a name and a chemical formula (if one exists). You can change a material’s name, but you should not change its chemical formula (unless you are creating a new material, as described later in this section). The steps for changing a material’s name are as follows: 1. Select the type of material (fluid, solid, etc.) in the Material Type drop-down list. 2. Choose the material for which you want to modify properties in the Fluid Materials drop-down list, Solid Materials list, or other similarly-named list. (The list’s name will be the same as the material type you selected in step 1.) 3. Enter the new name in the Name field at the top of the panel. 4. Click on the Change/Create button. A Question dialog box will appear, asking you if the original material should be overwritten. Since you are simply renaming the original material, you can click Yes to overwrite it. (If you were creating a new material, as described later in this section, you would click on No to retain the original material.) To rename another material, repeat the process described above. Remember to click the Change/Create button after changing each material’s name.

Copying a Material from the Database The global (site-wide) materials database contains many commonly used fluid, solid, and mixture materials, with property data from several different sources [164, 217, 290]. If you wish to use one of these materials in your problem, you can simply copy it from the database to your local materials list. The procedure for copying a material is detailed below: 1. Click on the Database... button in the Materials panel to open the Database Materials panel (Figure 7.1.2). 2. Select the type of material (fluid, solid, etc.) in the Material Type drop-down list. 3. In the Fluid Materials list, Solid Materials list, or other similarly-named list (the list’s name will be the same as the material type you selected in step 2), choose the material you wish to copy. Its properties will be displayed in the Properties area. 4. If you want to check the material’s properties, you can use the scroll bar to the right of the Properties area to scroll through the listed items. For some properties, temperature-dependent functions are available in addition to the constant values. You can select one of the function types in the drop-down list to the right of


7-5

Physical Properties

Figure 7.1.2: The Database Materials Panel

the property and the relevant parameters will be displayed. You cannot edit these values, but the panels in which they are displayed function in the same way as those that you use for setting temperature-dependent property functions, as described in Section 7.1.3. 5. Click on the Copy button. The properties will be downloaded from the database into your local list, and your own copy of the properties will now be displayed in the Materials panel. 6. Repeat the process to copy another material, or close the Database Materials panel. Once you have copied a material from the database, you may modify its properties or change its name, as described earlier in this section. The original material in the database will not be affected by any changes you make to your local copy of the material.

7-6



Creating a New Material If the material you want to use is not available in the database, you can easily create a new material for your local list. The steps for creating a new material are listed below: 1. Select the new material’s type (fluid, solid, etc.) in the Material Type drop-down list. (It does not matter which material is selected in the Fluid Materials, Solid Materials, or other similarly-named list.) 2. Enter the new material’s name in the Name field. 3. Set the material’s properties in the Properties area. If there are many properties listed, you may use the scroll bar to the right of the Properties area to scroll through the listed items. 4. Click on the Change/Create button. A Question dialog box will appear, asking you if the original material should be overwritten. Click on No to retain the original material and add your new material to the list. A panel will appear asking you to enter the chemical formula of your new material. Enter the formula if it is known, and click on OK; otherwise, leave the formula blank and click on OK. The Materials panel will be updated to show the new material name and chemical formula in the Fluid Materials list (or Solid Materials or other similarly-named list).

Saving Materials and Properties All the materials—and properties—in your local list are saved in the case file when it is written. If you read this case file into a new solver session, all of your materials and properties will be available for use in the new session.

Deleting a Material If there are materials in your local materials list that you no longer need, you can easily delete them by following these steps: 1. Select the type of material (fluid, solid, etc.) in the Material Type drop-down list. 2. Choose the material to be deleted in the Fluid Materials drop-down list, Solid Materials list, or other similarly-named list. (The list’s name will be the same as the material type you selected in step 1.) 3. Click on the Delete button. Deleting materials from your local list will have no effect on the materials contained in the global database.


7-7

Physical Properties

Changing the Order of the Materials List By default, the materials in your local list and those in the database are listed alphabetically by name (e.g., air, atomic-oxygen (o), carbon-dioxide (co2)). If you prefer to list them alphabetically by chemical formula, select the Chemical Formula option under Order Materials By. The example materials listed above will now be ordered as follows: air, co2 (carbon-dioxide), o (atomic-oxygen). To change back to the alphabetical listing by name, choose the Name option under Order Materials By. Note that you may specify the ordering method separately for the Materials and Database Materials panels. For example, you can order the database materials by chemical formula and the local materials list by name. Each panel has its own Order Materials By options.

7.1.3

Defining Properties Using Temperature-Dependent Functions

Material properties can be defined as functions of temperature. For most properties, you can define a polynomial, piecewise-linear, or piecewise-polynomial function of temperature: • polynomial: φ(T ) = A1 + A2 T + A3 T 2 + ...

(7.1-1)

• piecewise-linear: φ(T ) = φn +

φn+1 − φn (T − Tn ) Tn+1 − Tn

(7.1-2)

where 1 ≤ n ≤ N and N is the number of segments • piecewise-polynomial:

for Tmin,1 < T < Tmax,1 : φ(T ) = A1 + A2 T + A3 T 2 + ... for Tmin,2 < T < Tmax,2 : φ(T ) = B1 + B2 T + B3 T 2 + ...

(7.1-3)

In the equations above, φ is the property.

! If you define a polynomial or piecewise-polynomial function of temperature, note that temperature in the function is always in units of Kelvin or Rankine. If you are using Celsius or Kelvin as your temperature unit, then polynomial coefficient values must be entered in terms of Kelvin; if you are using Fahrenheit or Rankine as the temperature unit, values must be entered in terms of Rankine.

7-8



Some properties have additional functions available, and for some only a subset of these three functions can be used. See the section on the property in question to determine which temperature-dependent functions you can use. This section will describe the inputs required for definition of polynomial, piecewiselinear, and piecewise-polynomial functions.

Inputs for Polynomial Functions To define a polynomial function of temperature for a material property, follow these steps: 1. In the Materials panel, choose polynomial in the drop-down list to the right of the property name (e.g., Density). The Polynomial Profile panel (Figure 7.1.3) will open automatically. (Since this is a modal panel, the solver will not allow you to do anything else until you perform the steps below.)

Figure 7.1.3: The Polynomial Profile Panel

2. Specify the number of Coefficients. (Up to 8 coefficients are available.) The number of coefficients defines the order of the polynomial. The default of 1 defines a polynomial of order 0: the property will be constant and equal to the single coefficient A1 ; an input of 2 defines a polynomial of order 1: the property will vary linearly with temperature; etc. 3. Define the coefficients. Coefficients 1, 2, 3,... correspond to A1 ,A2 , A3 ,... in Equation 7.1-1. The panel in Figure 7.1.3 shows the inputs for the following function: ρ(T ) = 1000 − 0.02T

(7.1-4)

! Note the restriction on the units for temperature, as described above.


7-9

Physical Properties

Inputs for Piecewise-Linear Functions To define a piecewise-linear function of temperature for a material property, follow these steps: 1. In the Materials panel, choose piecewise-linear in the drop-down list to the right of the property name (e.g., Viscosity). The Piecewise-Linear Profile panel (Figure 7.1.4) will open automatically. (Since this is a modal panel, the solver will not allow you to do anything else until you perform the steps below.)

Figure 7.1.4: The Piecewise-Linear Profile Panel

2. Set the number of Points defining the piecewise distribution. 3. Under Data Points, enter the data pairs for each point. First enter the independent and dependent variable values for Point 1, then increase the Point number and enter the appropriate values for each additional pair of variables. The pairs of points must be supplied in the proper order (by increasing value of temperature); the solver will not sort them for you. A maximum of 30 piecewise points can be defined for each property. The panel in Figure 7.1.4 shows the final inputs for the profile depicted in Figure 7.1.5.

!

If the temperature exceeds the maximum Temperature (Tmax ) you have specified for your profile, FLUENT will use the Value corresponding to Tmax . If the temperature falls below the minimum Temperature (Tmin ) you have specified for your profile, FLUENT will use the Value corresponding to Tmin .

Inputs for Piecewise-Polynomial Functions To define a piecewise-polynomial function of temperature for a material property, follow these steps:

7-10



Viscosity, µ × 10 5 (Pa-sec)

3 (440, 2.445 × 10-5 )

•

2

•

-5

(360, 2.117 × 10 ) -5 (300, 1.846 × 10 ) • (250, 1.599 × 10 -5 )

•

1 250

300

350

400

450

Temperature, T (K)

Figure 7.1.5: Piecewise-Linear Definition of Viscosity as µ(T )

1. In the Materials panel, choose piecewise-polynomial in the drop-down list to the right of the property name (e.g., Cp). The Piecewise Polynomial Profile panel (Figure 7.1.6) will open automatically. (Since this is a modal panel, the solver will not allow you to do anything else until you perform the steps below.)

Figure 7.1.6: The Piecewise Polynomial Profile Panel

2. Specify the number of Ranges. For the example of Equation 7.1-5, two ranges of temperatures are defined:


7-11

Physical Properties

cp (T ) =

  for 300 < T < 1000 :    −3 2 −6 3 −10 4   T  429.929 + 1.874T − 1.966 × 10 T + 1.297 × 10 T − 4.000 × 10    for 1000 < T < 5000 :    

841.377 + 0.593T − 2.415 × 10−4 T 2 + 4.523 × 10−8 T 3 − 3.153 × 10−12 T 4 (7.1-5)

You may define up to three ranges. The ranges must be supplied in the proper order (by increasing value of temperature); the solver will not sort them for you. 3. For the first range (Range = 1), specify the Minimum and Maximum temperatures, and the number of Coefficients. (Up to eight coefficients are available.) The number of coefficients defines the order of the polynomial. The default of 1 defines a polynomial of order 0: the property will be constant and equal to the single coefficient A1 ; an input of 2 defines a polynomial of order 1: the property will vary linearly with temperature; etc. 4. Define the coefficients. Coefficients 1, 2, 3,... correspond to A1 ,A2 , A3 ,... in Equation 7.1-3. The panel in Figure 7.1.6 shows the inputs for the first range of Equation 7.1-5. 5. Increase the value of Range and enter the Minimum and Maximum temperatures, number of Coefficients, and the Coefficients (B1 ,B2 , B3 ,...) for the next range. Repeat if there is a third range.

! Note the restriction on the units for temperature, as described above. Checking and Modifying Existing Profiles If you want to check or change the coefficients, data pairs, or ranges for a previouslydefined profile, click on the Edit... button to the right of the property name. The appropriate panel will open, and you can check or modify the inputs as desired.

! In the Database Materials panel, you cannot edit the profiles, but you can examine them by clicking on the View... button (instead of the Edit... button.)

7.1.4

Customizing the Materials Database

The materials database is located in the following file: ⇓

path/Fluent.Inc/fluent6.x/cortex/lib/propdb.scm

7-12



where path is the directory in which you have installed FLUENT and the variable x corresponds to your release version, e.g., 1 for fluent6.1. If you wish to enhance the materials database to include additional materials that you use frequently, you can follow the procedure below: 1. Copy the file propdb.scm from the directory listed above to your working directory. 2. Using a text editor, add the desired material(s) following the format for the other materials. You may want to copy an existing material that is similar to the one you want to add, and then change its name and properties. The entries for air and aluminum are shown below as examples: (air fluid (chemical-formula . #f) (density (constant . 1.225) (premixed-combustion 1.225 300)) (specific-heat (constant . 1006.43)) (thermal-conductivity (constant . 0.0242)) (viscosity (constant . 1.7894e-05) (sutherland 1.7894e-05 273.11 110.56) (power-law 1.7894e-05 273.11 0.666)) (molecular-weight (constant . 28.966)) ) (aluminum (solid) (chemical-formula . al) (density (constant . 2719)) (specific-heat (constant . 871)) (thermal-conductivity (constant . 202.4)) (formation-entropy (constant . 164448.08)) ) When you next load the materials database in a FLUENT session started in the working directory, FLUENT will load your modified propdb.scm, rather than the original database, and your custom materials will be available in the Database Materials panel. If you want to make the modified database available to others at your site, you can put your customized propdb.scm file in the cortex/lib directory, replacing the default database. Before doing so, you should save the original propdb.scm file provided by Fluent Inc. to a different name (e.g., propdb.scm.orig) in case you need it at a later time.


7-13

Physical Properties

7.2

Density

FLUENT provides several options for definition of the fluid density: • constant density • temperature- and/or composition-dependent density Each of these input options and the governing physical models are detailed in this section. In all cases, you will define the Density in the Materials panel. Define −→Materials...

7.2.1

Defining Density for Various Flow Regimes

The selection of density in FLUENT is very important. You should set the density relationship based on your flow regime. • For compressible flows, the ideal gas law is the appropriate density relationship. • For incompressible flows, you may choose one of the following methods: – Constant density should be used if you do not want density to be a function of temperature. – The incompressible ideal gas law should be used when pressure variations are small enough that the flow is fully incompressible but you wish to use the ideal gas law to express the relationship between density and temperature (e.g., for a natural convection problem). – Density as a polynomial, piecewise-linear, or piecewise-polynomial function of temperature is appropriate when the density is a function of temperature only, as in a natural convection problem. – The Boussinesq model can be used for natural convection problems involving small changes in temperature.

Mixing Density Relationships in Multiple-Zone Models If your model has multiple fluid zones that use different materials, you should be aware of the following: • For calculations with the segregated solver that do not use one of the general multiphase models, the compressible ideal gas law cannot be mixed with any other density methods. This means that if the compressible ideal gas law is used for one material, it must be used for all materials. This restriction does not apply to the coupled solvers.

7-14


7.2 Density

• There is only one specified operating pressure and one specified operating temperature. This means that if you are using the ideal gas law for more than one material, they will share the same operating pressure; and if you are using the Boussinesq model for more than one material, they will share the same operating temperature.

7.2.2

Input of Constant Density

If you want to define the density of your fluid as a constant, check that constant is selected in the drop-down list to the right of Density in the Materials panel, and enter the value of density for the material. For the default fluid (air), the density is 1.225 kg/m3 .

7.2.3

Inputs for the Boussinesq Approximation

To enable the Boussinesq approximation for density, choose boussinesq from the dropdown list to the right of Density in the Materials panel and specify a constant value for Density. You will also need to set the Thermal Expansion Coefficient, as well as relevant operating conditions, as described in Section 11.5.3.

7.2.4

Density as a Profile Function of Temperature

If you are modeling a problem that involves heat transfer, you can define the density as a function of temperature. Three types of functions are available: • piecewise-linear: ρ(T ) = ρn +

ρn+1 − ρn (T − Tn ) Tn+1 − Tn

(7.2-1)

• piecewise-polynomial: for Tmin,1 < T < Tmax,1 : ρ(T ) = A1 + A2 T + A3 T 2 + ... for Tmin,2 < T < Tmax,2 : ρ(T ) = B1 + B2 T + B3 T 2 + ...

(7.2-2) (7.2-3)

• polynomial: ρ(T ) = A1 + A2 T + A3 T 2 + ...

(7.2-4)

For one of the these methods, select piecewise-linear, piecewise-polynomial, or polynomial in the drop-down list to the right of Density. You can input the data pairs (Tn , ρn ), ranges and coefficients, or coefficients that describe these functions using the Materials panel, as described in Section 7.1.3.


7-15

Physical Properties

7.2.5

Incompressible Ideal Gas Law

In FLUENT, if you choose to define the density using the ideal gas law for an incompressible flow, the solver will compute the density as ρ=

pop R T Mw

(7.2-5)

where R is the universal gas constant, Mw is the molecular weight of the gas, and pop is defined by you as the Operating Pressure in the Operating Conditions panel. In this form, the density depends only on the operating pressure and not on the local relative pressure field.

Density Inputs for the Incompressible Ideal Gas Law Inputs for the incompressible ideal gas law are as follows: 1. Enable the ideal gas law for an incompressible fluid by choosing incompressible-idealgas from the drop-down list to the right of Density in the Materials panel. You must specify the incompressible ideal gas law individually for each material that you want to use it for. See Section 7.2.7 for information on specifying the incompressible ideal gas law for mixtures. 2. Set the operating pressure by defining the Operating Pressure in the Operating Conditions panel. Define −→Operating Conditions...

!

The input of the operating pressure is of great importance when you are computing density with the ideal gas law. See Section 7.12 for recommendations on setting appropriate values for the operating pressure. Operating pressure is, by default, set to 101325 Pa. 3. Set the molecular weight of the homogeneous or single-component fluid (if no chemical species transport equations are to be solved), or the molecular weights of each fluid material (species) in a multicomponent mixture. For each fluid material, enter the value of the Molecular Weight in the Materials panel.

7.2.6

Ideal Gas Law for Compressible Flows

For compressible flows, the gas law has the following form: ρ=

7-16

pop + p R T Mw

(7.2-6)


7.2 Density

where p is the local relative (or gauge) pressure predicted by FLUENT and pop is defined by you as the Operating Pressure in the Operating Conditions panel.

Density Inputs for the Ideal Gas Law for Compressible Flows Inputs for the ideal gas law are as follows: 1. Enable the ideal gas law for a compressible fluid by choosing ideal-gas from the drop-down list to the right of Density in the Materials panel. You must specify the ideal gas law individually for each material that you want to use it for. See Section 7.2.7 for information on specifying the ideal gas law for mixtures. 2. Set the operating pressure by defining the Operating Pressure in the Operating Conditions panel. Define −→Operating Conditions...

!

The input of the operating pressure is of great importance when you are computing density with the ideal gas law. Equation 7.2-6 notes that the operating pressure is added to the relative pressure field computed by the solver, yielding the absolute static pressure. See Section 7.12 for recommendations on setting appropriate values for the operating pressure. Operating pressure is, by default, set to 101325 Pa. 3. Set the molecular weight of the homogeneous or single-component fluid (if no chemical species transport equations are to be solved), or the molecular weights of each fluid material (species) in a multicomponent mixture. For each fluid material, enter the value of the Molecular Weight in the Materials panel.

7.2.7

Composition-Dependent Density for Multicomponent Mixtures

If you are solving species transport equations, you will need to set properties for the mixture material and for the constituent fluids (species), as described in detail in Section 13.1.4. To define a composition-dependent density for a mixture, follow these steps: 1. Select the density method: • For non-ideal-gas mixtures, select the volume-weighted-mixing-law method for the mixture material in the drop-down list to the right of Density in the Materials panel. • If you are modeling compressible flow, select ideal-gas for the mixture material in the drop-down list to the right of Density in the Materials panel.


7-17

Physical Properties

• If you are modeling incompressible flow using the ideal gas law, select incompressible-ideal-gas for the mixture material in the drop-down list to the right of Density in the Materials panel. • If you have a user-defined function that you want to use to model the density, you can choose either the user-defined method or the user-defined-mixing-law method for the mixture material in the drop-down list. The only difference between the user-defined-mixing-law and the user-defined option for specifying density, viscosity and thermal conductivity of mixture materials, is that with the user-defined-mixing-law option, the individual properties of the species materials can also be specified. (Note that only the constant, the polynomial methods and the user-defined methods are available.) 2. Click on Change/Create. 3. If you selected volume-weighted-mixing-law, define the density for each of the fluid materials that comprise the mixture. You may define constant or (if applicable) temperature-dependent densities for the individual species. 4. If you selected user-defined-mixing-law, define the density for each of the fluid materials that comprise the mixture. You may define constant, or (if applicable) temperature-dependent densities, or user-defined densities for the individual species. For more information on defining properties with user-defined functions, see the separate UDF Manual . If you are modeling a non-ideal-gas mixture, FLUENT will compute the mixture density as 1 ρ = P Yi

(7.2-7)

i ρi

where Yi is the mass fraction and ρi is the density of species i. For compressible flows, the gas law has the following form: ρ=

pop + p P i RT i MYw,i

(7.2-8)

where p is the local relative (or gauge) pressure predicted by FLUENT, R is the universal gas constant, Yi is the mass fraction of species i, Mw,i is the molecular weight of species i, and pop is defined by you as the Operating Pressure in the Operating Conditions panel. In FLUENT, if you choose to define the density using the ideal gas law for an incompressible flow, the solver will compute the density as

7-18


7.3 Viscosity

ρ=

pop RT

Yi i Mw,i

P

(7.2-9)

where R is the universal gas constant, Yi is the mass fraction of species i, Mw,i is the molecular weight of species i, and pop is defined by you as the Operating Pressure in the Operating Conditions panel. In this form, the density depends only on the operating pressure and not on the local relative pressure field.

7.3

Viscosity

FLUENT provides several options for definition of the fluid viscosity: • Constant viscosity • Temperature- and/or composition-dependent viscosity • Kinetic theory • Non-Newtonian viscosity • User-defined function Each of these input options and the governing physical models are detailed in this section. (User-defined functions are described in the separate UDF Manual.) In all cases, you will define the Viscosity in the Materials panel. Define −→Materials... Viscosities are input as dynamic viscosity (µ) in units of kg/m-s in SI units or lbm /ft-s in British units. FLUENT does not ask for input of the kinematic viscosity (ν).

7.3.1

Input of Constant Viscosity

If you want to define the viscosity of your fluid as a constant, check that constant is selected in the drop-down list to the right of Viscosity in the Materials panel, and enter the value of viscosity for the fluid. For the default fluid (air), the viscosity is 1.7894 × 10−5 kg/m-s.

7.3.2

Viscosity as a Function of Temperature

If you are modeling a problem that involves heat transfer, you can define the viscosity as a function of temperature. Five types of functions are available:


7-19

Physical Properties

• piecewise-linear: µ(T ) = µn +

µn+1 − µn (T − Tn ) Tn+1 − Tn

(7.3-1)

• piecewise-polynomial:

for Tmin,1 < T < Tmax,1 : µ(T ) = A1 + A2 T + A3 T 2 + ... for Tmin,2 < T < Tmax,2 : µ(T ) = B1 + B2 T + B3 T 2 + ...

(7.3-2) (7.3-3)

• polynomial: µ(T ) = A1 + A2 T + A3 T 2 + ...

(7.3-4)

• Sutherland’s law (described below) • Power law (described below)

! Note that the power law described below is different from the non-Newtonian power law described in Section 7.3.5. For one of the first three, select piecewise-linear, piecewise-polynomial, polynomial in the drop-down list to the right of Viscosity, and then input the data pairs (Tn , µn ), ranges and coefficients, or coefficients that describe these functions using the Materials panel, as described in Section 7.1.3. For Sutherland’s law or the power law, choose sutherland or power-law in the drop-down list and enter the parameters as described below.

Sutherland Viscosity Law Sutherland’s viscosity law resulted from a kinetic theory by Sutherland (1893) using an idealized intermolecular-force potential. The formula is specified using two or three coefficients. Sutherland’s law with two coefficients has the form

µ=

C1 T 3/2 T + C2

(7.3-5)

where µ is the viscosity in kg/m-s, T is the static temperature in K, and C1 and C2 are the coefficients. For air at moderate temperatures and pressures, C1 = 1.458 × 10−6 kg/m-s-K1/2 , and C2 = 110.4 K. Sutherland’s law with three coefficients has the form

7-20


7.3 Viscosity

µ = µ0

T T0

3/2

T0 + S T +S

(7.3-6)

where µ is the viscosity in kg/m-s, T is the static temperature in K, µ0 is a reference value in kg/m-s, T0 is a reference temperature in K, and S is an effective temperature in K, called the Sutherland constant, which is characteristic of the gas. For air at moderate temperatures and pressures, µ0 = 1.7894×10−5 kg/m-s, T0 = 273.11 K, and S = 110.56 K. Inputs for Sutherland’s Law To use Sutherland’s law, choose sutherland in the drop-down list to the right of Viscosity. The Sutherland Law panel will open, and you can enter the coefficients as follows: 1. Select the Two Coefficient Method or the Three Coefficient Method.

!

Note that you must use SI units if you choose the two-coefficient method. 2. For the Two Coefficient Method, set C1 and C2. For the Three Coefficient Method, set the Reference Viscosity µ0 , the Reference Temperature T0 , and the Effective Temperature S.

Power-Law Viscosity Law Another common approximation for the viscosity of dilute gases is the power-law form. For dilute gases at moderate temperatures, this form is considered to be slightly less accurate than Sutherland’s law. A power-law viscosity law with two coefficients has the form µ = BT n

(7.3-7)

where µ is the viscosity in kg/m-s, T is the static temperature in K, and B is a dimensional coefficient. For air at moderate temperatures and pressures, B = 4.093 × 10−7 , and n = 2/3. A power-law viscosity law with three coefficients has the form µ = µ0

T T0

n

(7.3-8)

where µ is the viscosity in kg/m-s, T is the static temperature in K, T0 is a reference value in K, µ0 is a reference value in kg/m-s. For air at moderate temperatures and pressures, µ0 = 1.716 × 10−5 kg/m-s, T0 = 273 K, and n = 2/3.

! The non-Newtonian power law for viscosity is described in Section 7.3.5.


7-21

Physical Properties

Inputs for the Power Law To use the power law, choose power-law in the drop-down list to the right of Viscosity. The Power Law panel will open, and you can enter the coefficients as follows: 1. Select the Two Coefficient Method or the Three Coefficient Method.

!

Note that you must use SI units if you choose the two-coefficient method. 2. For the Two Coefficient Method, set B and the Temperature Exponent n. For the Three Coefficient Method, set the Reference Viscosity µ0 , the Reference Temperature T0 , and the Temperature Exponent n.

7.3.3

Defining the Viscosity Using Kinetic Theory

If you are using the gas law (as described in Section 7.2), you have the option to define the fluid viscosity using kinetic theory as √ −6

µ = 2.67 × 10

Mw T σ 2 Ωµ

(7.3-9)

where µ is in units of kg/m-s, T is in units of Kelvin, σ is in units of Angstroms, and Ωµ = Ωµ (T ∗ ) where T∗ =

T (/kB )

(7.3-10)

The Lennard-Jones parameters, σ and /kB , are inputs to the kinetic theory calculation that you supply by selecting kinetic-theory from the drop-down list to the right of Viscosity in the Materials panel. The solver will use these kinetic theory inputs in Equation 7.3-9 to compute the fluid viscosity. See Section 7.11 for details about these inputs.

7.3.4

Composition-Dependent Viscosity for Multicomponent Mixtures

If you are modeling a flow that includes more than one chemical species (multicomponent flow), you have the option to define a composition-dependent viscosity. (Note that you can also define the viscosity of the mixture as a constant value or a function of temperature.) To define a composition-dependent viscosity for a mixture, follow these steps:

7-22


7.3 Viscosity

1. For the mixture material, choose mass-weighted-mixing-law or, if you are using the ideal gas law for density, ideal-gas-mixing-law in the drop-down list to the right of Viscosity. If you have a user-defined function that you want to use to model the viscosity, you can choose either the user-defined method or the user-defined-mixinglaw method for the mixture material in the drop-down list. 2. Click Change/Create. 3. Define the viscosity for each of the fluid materials that comprise the mixture. You may define constant or (if applicable) temperature-dependent viscosities for the individual species. You may also use kinetic theory for the individual viscosities, or specify a non-Newtonian viscosity, if applicable. 4. If you selected user-defined-mixing-law, define the viscosity for each of the fluid materials that comprise the mixture. You may define constant, or (if applicable) temperature-dependent viscosities, or user-defined viscosities for the individual species. For more information on defining properties with user-defined functions, see the separate UDF Manual . The only difference between the user-defined-mixing-law and the user-defined option for specifying density, viscosity and thermal conductivity of mixture materials, is that with the user-defined-mixing-law option, the individual properties of the species materials can also be specified. (Note that only the constant, the polynomial methods and the user-defined methods are available.) If you are using the ideal gas law, the solver will compute the mixture viscosity based on kinetic theory as Xi µi j Xi φij

X

µ=

(7.3-11)

P

i

where

1+

φij =

µi µj

1/2

h

8 1+

Mw,j Mw,i

Mw,i Mw,j

1/4 2

i1/2

(7.3-12)

and Xi is the mole fraction of species i. For non-ideal gas mixtures, the mixture viscosity is computed based on a simple mass fraction average of the pure species viscosities: µ=

X

Yi µi

(7.3-13)

i


7-23

Physical Properties

7.3.5

Viscosity for Non-Newtonian Fluids

For incompressible Newtonian fluids, the shear stress is proportional to the rate-ofdeformation tensor D: τ = µD

(7.3-14)

where D is defined by

D=

∂ui ∂uj + ∂xi ∂xj

!

(7.3-15)

and µ is the viscosity, which is independent of D. For some non-Newtonian fluids, the shear stress can similarly be written in terms of a non-Newtonian viscosity η:

τ =η D D

(7.3-16)

In general, η is a function of all three invariants of the rate-of-deformation tensor D. However, in the non-Newtonian models available in FLUENT, η is considered to be a function of the shear rate γ˙ only. γ˙ is related to the second invariant of D and is defined as γ˙ =

q

D:D

(7.3-17)

FLUENT provides four options for modeling non-Newtonian flows: • Power law • Carreau model for pseudo-plastics • Cross model • Herschel-Bulkley model for Bingham plastics

! Note that the non-Newtonian power law described below is different from the power law described in Section 7.3.2. Appropriate values for the input parameters for these models can be found in the literature (e.g., [264]).

7-24


7.3 Viscosity

Power Law for Non-Newtonian Viscosity If you choose non-newtonian-power-law in the drop-down list to the right of Viscosity, non-Newtonian flow will be modeled according to the following power law for the nonNewtonian viscosity: η = k γ˙ n−1 eT0 /T

(7.3-18)

FLUENT allows you to place upper and lower limits on the power law function, yielding the following equation: ηmin < η = k γ˙ n−1 eT0 /T < ηmax

(7.3-19)

where k, n, T0 , ηmin , and ηmax are input parameters. k is a measure of the average viscosity of the fluid (the consistency index); n is a measure of the deviation of the fluid from Newtonian (the power-law index), as described below; T0 is the reference temperature; and ηmin and ηmax are, respectively, the lower and upper limits of the power law. If the viscosity computed from the power law is less than ηmin , the value of ηmin will be used instead. Similarly, if the computed viscosity is greater than ηmax , the value of ηmax will be used instead. Figure 7.3.1 shows how viscosity is limited by ηmin and ηmax at low and high shear rates.

η max log η

η min .

log γ Figure 7.3.1: Variation of Viscosity with Shear Rate According to the Non-Newtonian Power Law The value of n determines the class of the fluid: n=1 → n>1 → n τ0 , the material flows as a power-law fluid. The Herschel-Bulkley model combines the effects of Bingham and power-law behavior in a fluid. For low strain rates (γ˙ < τ0 /µ0 ), the “rigid” material acts like a very viscous


7-27

Physical Properties

fluid with viscosity µ0 . As the strain rate increases and the yield stress threshold, τ0 , is passed, the fluid behavior is described by a power law. η=

τ0 + k[γ˙ n − (τ0 /µ0 )n ] γ˙

(7.3-23)

where k is the consistency factor, and n is the power-law index. Figure 7.3.3 shows how shear stress (τ ) varies with shear rate (γ) ˙ for the Herschel-Bulkley model. n>1 Bingham (n=1) 0 define/user-defined/real-gas/nist-real-gas-model use real gas? [no]

yes

The list of available pure-fluid materials you can select from will be displayed: CO2.fld R11.fld R113.fld R114.fld R115.fld R116.fld R12.fld

R123.fld R124.fld R125.fld R13.fld R134a.fld R14.fld R141b.fld

R142b.fld R143a.fld R152a.fld R22.fld R227ea.fld R23.fld R236ea.fld

R236fa.fld R245ca.fld R245fa.fld R32.fld R41.fld RC318.fld ammonia.fld

butane.fld ethane.fld isobutan.fld propane.fld propylen.fld

2. Select a pure-fluid material from the REFPROP database list:

select real-gas data file [""] "R125.fld"

!

You must enter the complete name of the material (including the .fld suffix) contained within quotes (" "). Upon selection of a valid material (e.g., R125.fld), FLUENT will load data for that material from a library of pure fluids supported by the REFPROP database, and report that it is opening the shared library (librealgas.so) where the compiled REFPROP database source code is located.

/usr/local/Fluent.Inc/fluent6.1/realgas/lib/R125.fld Opening "/usr/local/Fluent.Inc/fluent6.1/realgas/ ultra/librealgas.so"... Setting material "air" to a real-gas... matl name: "R125" : "pentafluoroethane" : "354-33-6" Mol Wt : 120.022 Critical properties: Temperature : 339.33 (K) Pressure : 3.629e+06 (Pa) Density : 4.75996 (mol/L) 571.3 (kg/m^3)

! Once the real gas model is activated, any information for a fluid that is displayed in the Materials panel is ignored by FLUENT.

7-58


7.14 Real Gas Models

Writing Your Case File When you save your completed NIST real gas model to a case file, the linkage to the shared library containing REFPROP will be saved to the case file, along with property data for the material you selected. Consequently, whenever you read your case file in a later session, FLUENT will report this information to the console during the read process. Postprocessing All postprocessing functions properly report and display the current thermodynamic and transport properties of the real gas. The thermodynamic and transport properties controlled by the REFPROP database include the following: • density • enthalpy • entropy • gas constant • molecular viscosity • sound speed • specific heat • thermal conductivity • any quantities that are derived from the properties listed above (e.g., total quantities, ratio of specific heats)

7.14.2

The User-Defined Real Gas Model

Overview and Limitations of the User-Defined Real Gas Model The user-defined real gas model (UDRGM) has been developed for the FLUENT coupled solvers to allow you to write your own custom real gas model to fit your particular modeling needs. The UDRGM requires a library of functions written in the C programing language. Moreover, there are certain coding requirements that need to be followed when writing these functions. Sample real gas function libraries are provided to assist you in writing your own UDRGM. When UDRGM functions are compiled, they will be grouped in a shared library which later will be loaded and linked with the FLUENT executable. The procedure for using the UDRGM is defined below:


7-59

Physical Properties

1. Define the real gas equation of state and all related thermodynamic and transport property equations. 2. Create a C source code file that conforms to the format defined in this section. 3. Start FLUENT and set up your case file in the usual way. 4. Compile your UDRGM C library and build a shared library file (you can use the available compiled UDF utilities in either the graphical user interface or the text command interface) 5. Load your newly created UDRGM library via the text command menu using the define −→ user-defined −→real-gas text command. Upon activating the UDRGM, the function library will now supply the fluid material properties for your case. 6. Run your calculation The following limitations exist for the UDRGM: • The user-defined real gas model can only be used with the coupled solvers. • The user-defined real gas model assumes that the fluid material is a homogeneous, compressible substance (i.e., multiphase behavior is not taken into account).

Writing the UDRGM C Function Library Creating a UDRGM C function library is reasonably straightforward; however, your code must make use of specific function names and macros, which will be described in detail below. The basic library requirements are as follows: • The code must contain the udf.h file inclusion directive at the beginning of the source code. This allows the definitions for DEFINE macros and other FLUENT functions to be accessible during the compilation process. • The code must include at least one of the UDF’s DEFINE functions (i.e. DEFINE ON DEMAND) to be able to use the compiled UDFs utility (see the sample UDRGM codes provided below). • Any values that are passed to the solver by the UDRGM or returned by the solver to the UDRGM are assumed to be in SI units.

7-60



• You must use the principle set of functions listed below in your UDRGM library. These functions are the mechanism by which your thermodynamic property data are transferred to the FLUENT solver. Note that ANYNAME can be any string of alphanumeric characters, and allows you to provide unique names to your library functions. Below, the UDRGM function names and argument lists are listed, followed by a short description of the function. Function inputs from the FLUENT solver consist of one or more of the following variables: T p ρ Yi []

= = = =

Temperature, K Pressure, Pa Density, kg/m3 Species mass fraction

! Yi [] is inactive at this time, and exists in the argument list for future use. Currently, it has a value of 1.0. void ANYNAME error(int err, char *f, char *msg) prints error messages. void ANYNAME Setup(Domain *domain, char *filename, int (*messagefunc) (char *format, ...), void (*errorfunc)(char *format, ...)) performs model setup and initialization. Can be used to read data and parameters related to your UDRGM. double ANYNAME density(double T, double P, double yi[]) returns the value of density as a function of temperature and pressure. This is your equation of state.

!

Since this function is called numerous times during each solver iteration, it is important to make this function as numerically efficient as possible. double ANYNAME specific heat(double T, double Rho, double yi[]) returns the real gas specific heat at constant pressure as a function of temperature and density. double ANYNAME enthalpy(double T, double Rho, double yi[]) returns the enthalpy as a function of temperature and density. double ANYNAME entropy(double T, double Rho, double yi[]) returns the entropy as a function of temperature and density. double ANYNAME mw(double yi[]) returns the fluid molecular weight. double ANYNAME speed of sound(double T, double Rho, double yi[]) returns the value of speed of sound as a function of temperature and density. double ANYNAME viscosity(double T, double Rho, double yi[]) returns the value of dynamic viscosity as a function of temperature and density.


7-61

Physical Properties

double ANYNAME thermal conductivity(double T, double Rho, double yi[]) returns the value of thermal conductivity as a function of temperature and density. double ANYNAME rho t(double T, double Rho, double yi[]) returns the value of at constant pressure as a function of temperature and density.

dρ dT

double ANYNAME rho p(double T, double Rho, double yi[]) returns the value of at constant temperature as function of temperature and density.

dρ dp

double ANYNAME enthalpy t(double T, double Rho, double yi[]) returns the value dh of dT at constant pressure as function of temperature and density. double ANYNAME enthalpy p(double T, double Rho, double yi[]) returns the value of dh at constant temperature as function of temperature and density. dp At the end of the code you must define a structure of type RGAS Function whose members are pointers to the principle functions listed above. The structure is of type RGAS Function and its name is RealGasFunctionList.

! It is imperative that the sequence of function pointers shown below be followed. Otherwise, your real gas model will not load properly into the FLUENT code. UDF_EXPORT RGAS_Functions RealGasFunctionList = { ANYNAME_Setup, /* Setup initialize */ ANYNAME_density, /* density */ ANYNAME_enthalpy, /* enthalpy */ ANYNAME_entropy, /* entropy */ ANYNAME_specific_heat, /* specific_heat */ ANYNAME_mw, /* molecular_weight */ ANYNAME_speed_of_sound, /* speed_of_sound */ ANYNAME_viscosity, /* viscosity */ ANYNAME_thermal_conductivity, /* thermal_conductivity */ ANYNAME_rho_t, /* drho/dT |const p */ ANYNAME_rho_p, /* drho/dp |const T */ ANYNAME_enthalpy_t, /* dh/dT |const p */ ANYNAME_enthalpy_p /* dh/dp |const T */ };

Compiling Your UDRGM C Functions and Building a Shared Library File This section presents the steps you will need to follow to compile your UDRGM C code and build a shared library file. This process requires the use of a C compiler. Most UNIX

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operating systems provide a C compiler as a standard feature. If you are using a PC, you will need to ensure that a C++ compiler is installed before you can proceed (e.g., Microsoft Visual C++, v6.0 or higher). To use the UDRGM you will need to first build the UDRGM library by compiling your UDRGM C code and then loading the library into the FLUENT code. The UDRGM shared library is built in the same way that the FLUENT executable itself is built. Internally, a script called Makefile is used to invoke the system C compiler to build an object code library that contains the native machine language translation of your higher-level C source code. This shared library is then loaded into FLUENT (either at runtime or automatically when a case file is read) by a process called dynamic loading. The object libraries are specific to the computer architecture being used, as well as to the particular version of the FLUENT executable being run. The libraries must, therefore, be rebuilt any time FLUENT is upgraded, when the computer’s operating system level changes, or when the job is run on a different type of computer. The general procedure for compiling UDRGM C code is as follows: • Place the UDRGM C code in your working directory, i.e., where your case file resides. • Launch FLUENT. • Read your case file into FLUENT. • You can now compile your UDRGM C code and build a shared library file using either the graphical interface or the text command interface.

! To build UDRGM library you will use the compiled UDF utilities. However, you will not use the UDF utilities to load the library. A separate loading area for the UDRGM library will be used. Compiling the UDRGM Using the Graphical Interface Please refer to the separate UDF Manual for information on compiled UDFs and building libraries using the FLUENT graphical user intergace. If the build is successful, then the compiled library will be placed in the appropriate architecture directory (e.g., ntx86/2d). By default the library name is libudf.so (libudf.dll on Windows). Compiling the UDRGM Using the Text Interface The UDRGM library can be compiled in the text command interface as follows:


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Physical Properties

• Select the menu item define −→ user-defined −→compiled-functions. • Select the compile option. • Enter the compiled UDF library name.

!

The name given here is the name of the directory where the shared library (e.g., libudf) will reside. For example, if you hit then a directory should exist with the name libudf, and this directory will contain library file called libudf. If, however, you type a new library name such as myrealgas, then a directory called myrealgas will be created and it will contain the library libudf. • Continue on with the procedure when prompted. • Enter the C source file names.

!

Ideally you should place all of your functions into a single file. However, you can split them into separate files if desired. • Enter the header file names, if applicable. If you do not have an extra header file then hit when prompted. FLUENT will then start compiling the UDRGM C code and put it in the appropriate architecture directory. Example: > define/user-defined/compiled-functions load OR compile ? [load]> compile Compiled UDF library name: ["libudf"]

my_lib

Make sure that UDF source files are in the directory that contains your case and data files. If you have an existing libudf directory, please remove this directory to ensure that latest files are used. Continue?[yes] Give C-Source file names: First file name: [""] my_c_file.c Next

file name: [""]

Give header file names: First file name: [""]

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my_header_file.h



Loading the UDRGM Shared Library File To load the UDRGM library: • Go to the following menu item in the text command interface. define −→ user-defined −→real-gas • Select user-defined-real-gas-model. • Turn on the real gas model. use real gas? [no]

yes

FLUENT will ask for the location of the user-defined real gas library. You can enter either the name of the directory where the UDRGM shared library is called or the entire path to the UDRGM shared library. If the loading of the UDRGM library is successful you will see a message similar to the following: Opening Library Setting Loading

user-defined realgas library "RealgasLibraryname"... "RealgasDirName/lnx86/2d/libudf.so" opened material "air" to a real-gas... Real-RealGasPrefexLable Library:

UDRGM Example: Ideal Gas Equation of State This section describes an example of a user-defined real gas model. You can use this example as the basis for your own UDRGM code. In this simple example, the standard ideal gas equation of state is used in the UDRGM. p T Cp H S ρ c R

= = = = = = = =

pressure temperature specific heat enthalpy entropy density speed of sound universal gas constant/molecular weight

The ideal gas equation of state can be written in terms of pressure and temperature as ρ=


p RT

(7.14-1)

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Physical Properties

The specific heat is defined to be constant Cp = 1006.42. The enthalpy is, therefore, defined as H = Cp T

(7.14-2)

and entropy is given by T S = Cp log Tref

pref + R log p

!

(7.14-3)

where Tref = 288.15 K and pref = 101325 Pa The speed of sound is simply defined as

c=

s

T Cp

R (Cp − R)

(7.14-4)

1 RT

(7.14-5)

The density derivatives are: dρ dp dρ dT

!

!

=

T

=−

p

p ρ = − RT 2 T

(7.14-6)

The enthalpy derivatives are: dH dT dH dp

! T

!

= Cp

(7.14-7)

p

"

#

Cp p dρ = 1− =0 ρR ρ dp

(7.14-8)

When you activate the real gas model and load the library successfully into FLUENT, you will be using the equation of state and other fluid properties from this library rather than the one built into the FLUENT code, therefore, the access to the Materials panel will be restricted. Ideal Gas UDRGM Code Listing /**********************************************************************/ /* User Defined Real Gas Model : */ /* For Ideal Gas Equation of State */

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/* */ /**********************************************************************/ #include "udf.h" #include "stdio.h" #include "ctype.h" #include "stdarg.h" #define MW 28.966 /* molec. wt. for single gas (Kg/Kmol) */ #define RGAS (UNIVERSAL_GAS_CONSTANT/MW) static int (*usersMessage)(char *,...); static void (*usersError)(char *,...);

DEFINE_ON_DEMAND(I_do_nothing) { /* This is a dummy function to allow us to use */ /* the Compiled UDFs utility */ }

void IDEAL_error(int err, char *f, char *msg) { if (err) usersError("IDEAL_error (%d) from function: %s\n%s\n",err,f,msg); } void IDEAL_Setup(Domain *domain, char *filename, int (*messagefunc)(char *format, ...), void (*errorfunc)(char *format, ...)) { /* Use this function for any initialization or model setups*/ usersMessage = messagefunc; usersError = errorfunc; usersMessage("\nLoading Real-Ideal Library: %s\n", filename); } double IDEAL_density(double Temp, double press, double yi[]) { double r = press/(RGAS*Temp); /* Density at Temp & press */ return r;


/* (Kg/m^3) */

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Physical Properties

} double IDEAL_specific_heat(double Temp, double density, double yi[]) { double cp=1006.43; return cp;

/* (J/Kg/K) */

} double IDEAL_enthalpy(double Temp, double density, double yi[]) { double h=Temp*IDEAL_specific_heat(Temp, density, yi); return h;

/* (J/Kg) */

} #define TDatum 288.15 #define PDatum 1.01325e5 double IDEAL_entropy(double Temp, double density, double yi[]) { double s=IDEAL_specific_heat(Temp,density,yi)*log(Temp/TDatum)+ RGAS*log(PDatum/(RGAS*Temp*density)); return s; /* (J/Kg/K) */ } double IDEAL_mw(double yi[]) { return MW; }

/* (Kg/Kmol) */

double IDEAL_speed_of_sound(double Temp, double density, double yi[]) { double cp=IDEAL_specific_heat(Temp,density,yi); return sqrt(Temp*cp*RGAS/(cp-RGAS));

/* m/s */

} double IDEAL_viscosity(double Temp, double density, double yi[]) { double mu=1.7894e-05; return mu;

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/* (Kg/m/s) */



} double IDEAL_thermal_conductivity(double Temp, double density, double yi[]) { double ktc=0.0242; return ktc;

/* W/m/K */

} double IDEAL_rho_t(double Temp, double density, double yi[]) { /* derivative of rho wrt. Temp at constant p */ double rho_t=-density/Temp; return rho_t;

/* (Kg/m^3/K) */

} double IDEAL_rho_p(double Temp, double density, double yi[]) { /* derivative of rho wrt. pressure at constant T */ double rho_p=1.0/(RGAS*Temp); return rho_p;

/* (Kg/m^3/Pa) */

} double IDEAL_enthalpy_t(double Temp, double density, double yi[]) { /* derivative of enthalpy wrt. Temp at constant p */ return IDEAL_specific_heat(Temp, density, yi); } double IDEAL_enthalpy_p(double Temp, double density, double yi[]) { /* derivative of enthalpy wrt. pressure at constant T */ /* general form dh/dp|T = (1/rho)*[ 1 + (T/rho)*drho/dT|p] */ /* but for ideal gas dh/dp = 0 */ return 0.0 ; } UDF_EXPORT RGAS_Functions RealGasFunctionList = { IDEAL_Setup, /* initialize


*/

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Physical Properties

IDEAL_density, /* density */ IDEAL_enthalpy, /* enthalpy */ IDEAL_entropy, /* entropy */ IDEAL_specific_heat, /* specific_heat */ IDEAL_mw, /* molecular_weight */ IDEAL_speed_of_sound, /* speed_of_sound */ IDEAL_viscosity, /* viscosity */ IDEAL_thermal_conductivity, /* thermal_conductivity */ IDEAL_rho_t, /* drho/dT |const p */ IDEAL_rho_p, /* drho/dp |const T */ IDEAL_enthalpy_t, /* dh/dT |const p */ IDEAL_enthalpy_p /* dh/dp |const T */ }; /**************************************************************/

UDRGM Example: Redlich-Kwong Equation of State This section describes another example of a user-defined real gas model. You can use this example as the basis for your own UDRGM code. In this example, the Redlich-Kwong equation of state is used in the UDRGM. This section summarizes the equations used in developing the UDRGM for the RedlichKwong equation of state. The model is based on a modified form of the Redlich-Kwong equation of state described in [4]. The equations used in this UDRGM will be listed in the sections below. The following nomenclature applies to this section: a(T ) c Cp H n p R T S V ρ

= = = = = = = = = = =

Redlich-Kwong temperature function speed of sound specific heat enthalpy exponent in function a(T ) pressure universal gas constant/molecular weight temperature entropy specific volume density

The superscript 0 designates a reference state, and the subscript c designates a critical point property.

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Specific Volume and Density The Redlich-Kwong equation of state can be written in the following form: p= where

RT a(T ) − ˜ (V − b) V (V + b0 )

1 Tc V = , a(T ) = ρ T

b0 = 0.08664

n

(7.14-9)

, a0 = 0.42747

R2 Tc2 , pc

RTc RTc + b0 − Vc , ˜b = b0 − c0 , c0 = pc pc + Vc (Vac0+b0 )

Since the real gas model in FLUENTrequires a function for density as a function of pressure and temperature, Equation 7.14-9 must be solved for the specific volume (from which the density can be easily obtained). For convenience, Equation 7.14-9 can be written as a cubic equation for specific volume as follows: V 3 + a1 V 2 + a2 V + a3 = 0 where

(7.14-10)

RT RT b0 a(T ) a(T ) ˜b a1 = −(c + ), a2 = − ˜bb0 + − , a3 = − p p p p !

Equation 7.14-10 is solved using a standard algorithm for cubic equations (see [253] for details). In the UDRGM code, the cubic solution is coded to minimize the number of floating point operations. This is critical for optimal performance, since this function gets called numerous times during an iteration cycle. It should be noted that the value of the exponent, n, in the function a(T ) will depend on the substance. A table of values can be found in [4] for some common substances. Alternatively, [4] states that values of n are well correlated by the empirical equation n = 0.4986 + 1.1735ω + 0.475ω 2

(7.14-11)

where ω is the acentric factor, defined as !

pv (T ) ω = − log − 1.0 pc

(7.14-12)

In the above equation, pv (T ) is the saturated vapor pressure evaluated at temperature T = 0.7Tc .


7-71

Physical Properties

Derivatives of Specific Volume and Density The derivatives of specific volume with respect to temperature and pressure can be easily determined from Equation 7.14-9 using implicit differentiation. The results are presented below:

where (a1 )0p =

∂V ∂p

!

∂V ∂T

!

= −

(a1 )0p V 2 + (a2 )0p + (a3 )0p 3V 2 + 2a1 V + a2

(7.14-13)

= −

(a1 )0T V 2 + (a2 )0T + (a3 )0T 3V 2 + 2a1 V + a2

(7.14-14)

T

p

RT RT b0 − a(T ) a(T ) ˜b 0 0 , (a ) = , (a ) = 2 3 p p p2 p2 p2

−Rb0 + R (a1 )0T = − , (a2 )0T = p p

da(T ) dT

, (a3 )0T =

da(T ) ˜b da(T ) a(T ) , = −n dT p dT T

The derivatives of density can be obtained from the above using the relations ∂ρ ∂p

!

∂ρ ∂T

= −ρ

2

T

!

2

= −ρ

p

∂V ∂p

!

∂V ∂T

!

(7.14-15)

T

(7.14-16)

p

Specific Heat and Enthalpy Following [4], enthalpy for a real gas can be written a(T ) V + b0 H = H (T ) + pV − RT − (1 + n) ln b0 V 0

!

(7.14-17)

where H 0 (T ) is the enthalpy function for a thermally perfect gas (i.e., enthalpy is a function of temperature alone). In the present case, we employ a fourth-order polynomial for the specific heat for a thermally perfect gas [176] Cp0 (T ) = C1 + C2 T + C3 T 2 + C4 T 3 + C5 T 4

(7.14-18)

and obtain the enthalpy from the basic relation

7-72



0

H (T ) =

Z

T

T0

Cp0 (T )dT

(7.14-19)

The result is 1 1 1 1 H 0 (T ) = C1 T + C2 T 2 + C3 T 3 + C4 T 4 + C5 T 5 − H 0 (T 0 ) 2 3 4 5

(7.14-20)

Note that H 0 (T 0 ) is the enthalpy at a reference state (p0 , T 0 ), which can be chosen arbitrarily. The specific heat for the real gas can be obtained by differentiating Equation 7.14-17 with respect to temperature (at constant pressure):

Cp =

∂H ∂T

!

(7.14-21)

p

The result is

Cp = Cp0 (T ) + pV

∂V ∂T

! p

−R−

da(T ) (1 + n) V + b0 ln dT b0 V

!

+ a(T )(1 + n)

∂V ∂T

p

V (V + b0 ) (7.14-22)

Finally, the derivative of enthalpy with respect to pressure (at constant temperature) can be obtained using the following thermodynamic relation [176]: ∂H ∂p

!

∂V ∂T

=V −T

T

!

(7.14-23)

p

Entropy Following [4], the entropy can be expressed in the form V − ˜b S = S 0 (T, p0 ) + R ln + V0 !

da(T ) dT

b0

V + b0 ln V

!

(7.14-24)

where the superscript 0 again refers to a reference state where the ideal gas law is applicable. For an ideal gas at a fixed reference pressure, p0 , the entropy is given by S 0 (T, p0 ) = S(T 0 , p0 ) +


Z

T

T0

Cp0 (T ) dT T

(7.14-25)

7-73

Physical Properties

Note that the pressure term is zero since the entropy is evaluated at the reference pressure. Using the polynomial expression for specific heat, Equation 7.14-18, Equation 7.14-25 becomes

1 1 1 S 0 (T, p0 ) = S(T 0 , p0 ) + C1 ln(T ) + C2 T + C3 T 2 + C4 T 3 + C5 T 4 − f (T 0 ) (7.14-26) 2 3 4 where f (T 0 ) is a constant, which can be absorbed into the reference entropy S(T 0 , p0 ). Speed of Sound The speed of sound for a real gas can be determined from the thermodynamic relation 2

c =

∂p ∂ρ

!

=−

p

Cp CV

V2

∂V ∂p

(7.14-27) T

Noting that v u u c=Vu t

Cp R − Cp

!

1

∂V ∂p

(7.14-28) T

Viscosity and Thermal Conductivity The dynamic viscosity of a gas or vapor can be estimated using the following formula from [39]: µ(T ) = 6.3 ×

M 0.5 p0.6666 c 107 w 0.1666 Tc

Tr1.5 Tr + 0.8

!

(7.14-29)

Here, Tr is the reduced temperature Tr =

T Tc

(7.14-30)

and Mw is the molecular weight of the gas. This formula neglects the effect of pressure on viscosity, which usually becomes significant only at very high pressures. Knowing the viscosity, the thermal conductivity can be estimated using the Euckun formula [66]: 5 k = µ Cp + R 4

7-74

(7.14-31)



It should be noted that both Equation 7.14-29 and 7.14-31 are simple relations, and therefore may not provide satisfactory values of viscosity and thermal conductivity for certain applications. You are encouraged to modify these functions in the UDRGM source code if alternate formulae are available for a given gas. Using the Redlich-Kwong Real Gas UDRGM Using the Redlich-Kwong Real Gas UDRGM simply requires the modification of the top block of #define macros to provide the appropriate parameters for a given substance. An example listing for hydrogen is given below. The parameters required are: MWT = Molecular weight of the substance PCRIT = Critical pressure (Pa) TCRIT = Critical temperature (K) ZCRIT = Critical compressibility factor VCRIT = Critical specific volume (m3 /kg) NRK = Exponent of a(T ) function CC1, CC2, CC3, CC4, CC5 = Coefficients of Cp (T ) polynomial curve fit P REF = Reference pressure (Pa) T REF = Reference temperature (K) The coefficients for the ideal gas specific heat polynomial were obtained from [176] (coefficients for other substances are also provided in [176]). Once the source listing is modified, the UDRGM C code can be recompiled and loaded into FLUENT in the manner described earlier. /* The variables below need to be set for a particular gas */ /* Hydrogen */ /* REAL GAS EQUATION OF STATE MODEL - BASIC VARIABLES */ /* ALL VARIABLES ARE IN SI UNITS! */ #define RGASU UNIVERSAL_GAS_CONSTANT #define PI 3.141592654 #define #define #define #define #define #define

MWT PCRIT TCRIT ZCRIT VCRIT NRK

2.0159 1.2838e6 32.938 0.304 3.188788e-2 0.310

/* IDEAL GAS SPECIFIC HEAT CURVE FIT */


7-75

Physical Properties

#define #define #define #define #define

CC1 CC2 CC3 CC4 CC5

12594.6 11.02903 -2.134119e-2 2.274608e-5 -7.465296e-9

/* REFERENCE STATE */ #define P_REF 101325 #define T_REF 288.15

Redlich-Kwong Real Gas UDRGM Code Listing /**************************************************************/ /* User-Defined Function: Redlich-Kwong Equation of State */ /* for Real Gas Modeling */ /* */ /* Author: Frank Kelecy */ /* Date: August 2002 */ /* Version: 1.0 */ /* */ /* This implementation is completely general. */ /* version here is for STEAM. */ /* */ /**************************************************************/ #include #include #include #include

"udf.h" "stdio.h" "ctype.h" "stdarg.h"

/* The variables below need to be set for a particular gas */ /* Hydrogen */ /* REAL GAS EQUATION OF STATE MODEL - BASIC VARIABLES */ #define RGASU UNIVERSAL_GAS_CONSTANT #define PI 3.141592654 #define #define #define #define #define #define

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MWT PCRIT TCRIT ZCRIT VCRIT NRK

2.0159 1.2838e6 32.938 0.304 3.188788e-2 0.310



/* IDEAL GAS SPECIFIC HEAT CURVE FIT */ #define #define #define #define #define

CC1 CC2 CC3 CC4 CC5

12594.6 11.02903 -2.134119e-2 2.274608e-5 -7.465296e-9

/* REFERENCE STATE */ #define P_REF 101325 #define T_REF 288.15 static int (*usersMessage)(char *,...); static void (*usersError)(char *,...); /* Static variables associated with Redlich-Kwong Model */ static double rgas, a0, b0, c0, bb, cp_int_ref; DEFINE_ON_DEMAND(I_do_nothing) { /* this is a dummy function to allow us */ /* to use the compiled UDFs utility */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_error */ /*------------------------------------------------------------*/ void RKEOS_error(int err, char *f, char *msg) { if (err) usersError("RKEOS_error (%d) from function: %s\n%s\n",err,f,msg); }


7-77

Physical Properties

/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_Setup */ /*------------------------------------------------------------*/ void RKEOS_Setup(Domain *domain, char *filename, void (*messagefunc)(char *format, ...), void (*errorfunc)(char *format, ...)) { rgas = RGASU/MWT; a0 = 0.42747*rgas*rgas*TCRIT*TCRIT/PCRIT; b0 = 0.08664*rgas*TCRIT/PCRIT; c0 = rgas*TCRIT/(PCRIT+a0/(VCRIT*(VCRIT+b0)))+b0-VCRIT; bb = b0-c0; cp_int_ref = CC1*log(T_REF)+T_REF*(CC2+T_REF*(0.5*CC3 +T_REF*(0.333333*CC4+0.25*CC5*T_REF))); usersMessage = messagefunc; usersError = errorfunc; usersMessage("\nLoading Redlich-Kwong Library: %s\n", filename); usersMessage("\nSteam Properties\n"); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_pressure */ /* Returns density given T and density */ /*------------------------------------------------------------*/ double RKEOS_pressure(double temp, double density) { double v = 1./density; double afun = a0*pow(TCRIT/temp,NRK); return rgas*temp/(v-bb)-afun/(v*(v+b0)); }

7-78



/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_spvol */ /* Returns specific volume given T and P */ /*------------------------------------------------------------*/ double RKEOS_spvol(double temp, double press) { double a1,a2,a3; double vv,vv1,vv2,vv3; double qq,qq3,sqq,rr,tt,dd; double afun = a0*pow(TCRIT/temp,NRK); a1 = -(c0+rgas*temp/press); a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a3 = -afun*bb/press; /* Solve cubic equation for specific volume */ qq = (a1*a1-3.*a2)/9.; rr = (2*a1*a1*a1-9.*a1*a2+27.*a3)/54.; qq3 = qq*qq*qq; dd = qq3-rr*rr; /* If dd < 0, then we have one real root */ /* If dd >= 0, then we have three roots -> choose largest root */ if (dd < 0.) { tt = sqrt(-dd)+pow(fabs(rr),0.333333); vv = (tt+qq/tt)-a1/3.; } else { tt = acos(rr/sqrt(qq3)); sqq = sqrt(qq); vv1 = -2.*sqq*cos(tt/3.)-a1/3.; vv2 = -2.*sqq*cos((tt+2.*PI)/3.)-a1/3.; vv3 = -2.*sqq*cos((tt+4.*PI)/3.)-a1/3.; vv = (vv1 > vv2) ? vv1 : vv2; vv = (vv > vv3) ? vv : vv3; } return vv; }


7-79

Physical Properties

/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_density */ /* Returns density given T and P */ /*------------------------------------------------------------*/ double RKEOS_density(double temp, double press, double yi[]) { return 1./RKEOS_spvol(temp, press); /* (Kg/m^3) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_dvdp */ /* Returns dv/dp given T and P */ /*------------------------------------------------------------*/ double RKEOS_dvdp(double temp, double density) { double a1,a2,a1p,a2p,a3p,v,press; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; a1 = -(c0+rgas*temp/press); a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a1p = rgas*temp/(press*press); a2p = a1p*b0-afun/(press*press); a3p = afun*bb/(press*press); return -(a3p+v*(a2p+v*a1p))/(a2+v*(2.*a1+3.*v)); }

7-80



/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_dvdt */ /* Returns dv/dT given T and P */ /*------------------------------------------------------------*/ double RKEOS_dvdt(double temp, double density) { double a1,a2,dadt,a1t,a2t,a3t,v,press; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; dadt = -NRK*afun/temp; a1 = -(c0+rgas*temp/press); a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a1t = -rgas/press; a2t = a1t*b0+dadt/press; a3t = -dadt*bb/press; return -(a3t+v*(a2t+v*a1t))/(a2+v*(2.*a1+3.*v)); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_Cp_ideal_gas */ /* Returns ideal gas specific heat given T */ /*------------------------------------------------------------*/ double RKEOS_Cp_ideal_gas(double temp) { return (CC1+temp*(CC2+temp*(CC3+temp*(CC4+temp*CC5)))); }


7-81

Physical Properties

/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_H_ideal_gas */ /* Returns ideal gas specific enthalpy given T */ /*------------------------------------------------------------*/ double RKEOS_H_ideal_gas(double temp) { return temp*(CC1+temp*(0.5*CC2+temp*(0.333333*CC3 +temp*(0.25*CC4+temp*0.2*CC5)))); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_specific_heat */ /* Returns specific heat given T and rho */ /*------------------------------------------------------------*/ double RKEOS_specific_heat(double temp, double density, double yi[]) { double delta_Cp,press,v,dvdt,dadt; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; dvdt = RKEOS_dvdt(temp, density); dadt = -NRK*afun/temp; delta_Cp = press*dvdt-rgas-dadt*(1+NRK)/b0*log((v+b0)/v) + afun*(1+NRK)*dvdt/(v*(v+b0)); return RKEOS_Cp_ideal_gas(temp)+delta_Cp;

/* (J/Kg/K) */

}

7-82



/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy */ /* Returns specific enthalpy given T and rho */ /*------------------------------------------------------------*/ double RKEOS_enthalpy(double temp, double density, double yi[]) { double delta_h ,press, v; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; delta_h = press*v-rgas*temp-afun*(1+NRK)/b0*log((v+b0)/v); return RKEOS_H_ideal_gas(temp)+delta_h;

/* (J/Kg) */

} /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_entropy */ /* Returns entropy given T and rho */ /*------------------------------------------------------------*/ double RKEOS_entropy(double temp, double density, double yi[]) { double delta_s,v,v0,dadt,cp_integral; double afun = a0*pow(TCRIT/temp,NRK); cp_integral = CC1*log(temp)+temp*(CC2+temp*(0.5*CC3 +temp*(0.333333*CC4+0.25*CC5*temp))) - cp_int_ref; v = 1./density; v0 = rgas*temp/P_REF; dadt = -NRK*afun/temp; delta_s = rgas*log((v-bb)/v0)+dadt/b0*log((v+b0)/v); return cp_integral+delta_s; /* (J/Kg/K) */ }


7-83

Physical Properties

/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_mw */ /* Returns molecular weight */ /*------------------------------------------------------------*/ double RKEOS_mw(double yi[]) { return MWT; /* (Kg/Kmol) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_speed_of_sound */ /* Returns s.o.s given T and rho */ /*------------------------------------------------------------*/ double RKEOS_speed_of_sound(double temp, double density, double yi[]) { double cp = RKEOS_specific_heat(temp, density, yi); double dvdp = RKEOS_dvdp(temp, density); double v = 1./density; return sqrt(cp/((rgas-cp)*dvdp))*v;

/* m/s */

} /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_rho_t */ /*------------------------------------------------------------*/ double RKEOS_rho_t(double temp, double density, double yi[]) { return -density*density*RKEOS_dvdt(temp, density); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_rho_p */ /*------------------------------------------------------------*/ double RKEOS_rho_p(double temp, double density, double yi[]) { return -density*density*RKEOS_dvdp(temp, density); }

7-84



/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy_t */ /*------------------------------------------------------------*/ double RKEOS_enthalpy_t(double temp, double density, double yi[]) { return RKEOS_specific_heat(temp, density, yi); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy_p */ /*------------------------------------------------------------*/ double RKEOS_enthalpy_p(double temp, double density, double yi[]) { double v = 1./density; double dvdt = RKEOS_dvdt(temp, density); return v-temp*dvdt; } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_viscosity */ /*------------------------------------------------------------*/ double RKEOS_viscosity(double temp, double density, double yi[]) { double tr, tc, pcatm, mu; tr = temp/TCRIT; tc = TCRIT; pcatm = PCRIT/101325.; mu = 6.3e-7*sqrt(MWT)*pow(pcatm,0.6666)/pow(tc,0.16666) *(pow(tr,1.5)/(tr+0.8)); return mu; }


7-85

Physical Properties

/*------------------------------------------------------------*/ /* FUNCTION: RKEOS_thermal_conductivity */ /*------------------------------------------------------------*/ double RKEOS_thermal_conductivity(double temp, double density, double yi[]) { double cp, mu; cp = RKEOS_Cp_ideal_gas(temp); mu = RKEOS_viscosity(temp, density, yi); return (cp+1.25*rgas)*mu; } /* Export Real Gas Functions to Solver */ UDF_EXPORT RGAS_Functions RealGasFunctionList = { RKEOS_Setup, /* initialize RKEOS_density, /* density RKEOS_enthalpy, /* enthalpy RKEOS_entropy, /* entropy RKEOS_specific_heat, /* specific_heat RKEOS_mw, /* molecular_weight RKEOS_speed_of_sound, /* speed_of_sound RKEOS_viscosity, /* viscosity RKEOS_thermal_conductivity, /* thermal_conductivity RKEOS_rho_t, /* drho/dT |const p RKEOS_rho_p, /* drho/dp |const T RKEOS_enthalpy_t, /* dh/dT |const p RKEOS_enthalpy_p /* dh/dp |const T };

7-86

*/ */ */ */ */ */ */ */ */ */ */ */ */


Chapter 8.

Modeling Basic Fluid Flow

This chapter describes the basic physical models that FLUENT provides for fluid flow and the commands for defining and using them. Models for flows in moving zones (including sliding and dynamic meshes) are explained in Chapter 9, models for turbulence are described in Chapter 10, and models for heat transfer (including radiation) are presented in Chapter 11. An overview of modeling species transport and reacting flows is provided in Chapter 12, details about models for species transport and reacting flows are described in Chapters 13–17, and models for pollutant formation are presented in Chapter 18. An overview of multiphase modeling is provided in Chapter 20, the discrete phase model is described in Chapter 21, general multiphase models are described in Chapter 22, and the melting and solidification model is described in Chapter 23. For information on modeling porous media, porous jumps, and lumped parameter fans and radiators, see Chapter 6. The information in this chapter is presented in the following sections: • Section 8.1: Overview of Physical Models in FLUENT • Section 8.2: Continuity and Momentum Equations • Section 8.3: Periodic Flows • Section 8.4: Swirling and Rotating Flows • Section 8.5: Compressible Flows • Section 8.6: Inviscid Flows


8-1


8.1

Overview of Physical Models in FLUENT

FLUENT provides comprehensive modeling capabilities for a wide range of incompressible and compressible, laminar and turbulent fluid flow problems. Steady-state or transient analyses can be performed. In FLUENT, a broad range of mathematical models for transport phenomena (like heat transfer and chemical reactions) is combined with the ability to model complex geometries. Examples of FLUENT applications include laminar non-Newtonian flows in process equipment; conjugate heat transfer in turbomachinery and automotive engine components; pulverized coal combustion in utility boilers; external aerodynamics; flow through compressors, pumps, and fans; and multiphase flows in bubble columns and fluidized beds. To permit modeling of fluid flow and related transport phenomena in industrial equipment and processes, various useful features are provided. These include porous media, lumped parameter (fan and heat exchanger), streamwise-periodic flow and heat transfer, swirl, and moving reference frame models. The moving reference frame family of models includes the ability to model single or multiple reference frames. A time-accurate sliding mesh method, useful for modeling multiple stages in turbomachinery applications, for example, is also provided, along with the mixing plane model for computing time-averaged flow fields. Another very useful group of models in FLUENT is the set of free surface and multiphase flow models. These can be used for analysis of gas-liquid, gas-solid, liquid-solid, and gas-liquid-solid flows. For these types of problems, FLUENT provides the volume-offluid (VOF), mixture, and Eulerian models, as well as the discrete phase model (DPM). The DPM performs Lagrangian trajectory calculations for dispersed phases (particles, droplets, or bubbles), including coupling with the continuous phase. Examples of multiphase flows include channel flows, sprays, sedimentation, separation, and cavitation. Robust and accurate turbulence models are a vital component of the FLUENT suite of models. The turbulence models provided have a broad range of applicability, and they include the effects of other physical phenomena, such as buoyancy and compressibility. Particular care has been devoted to addressing issues of near-wall accuracy via the use of extended wall functions and zonal models. Various modes of heat transfer can be modeled, including natural, forced, and mixed convection with or without conjugate heat transfer, porous media, etc. The set of radiation models and related submodels for modeling participating media are general and can take into account the complications of combustion. A particular strength of FLUENT is its ability to model combustion phenomena using a variety of models, including eddy dissipation and probability density function models. A host of other models that are very useful for reacting flow applications are also available, including coal and droplet combustion, surface reaction, and pollutant formation models.

8-2


8.2 Continuity and Momentum Equations

8.2

Continuity and Momentum Equations

For all flows, FLUENT solves conservation equations for mass and momentum. For flows involving heat transfer or compressibility, an additional equation for energy conservation is solved. For flows involving species mixing or reactions, a species conservation equation is solved or, if the non-premixed combustion model is used, conservation equations for the mixture fraction and its variance are solved. Additional transport equations are also solved when the flow is turbulent. In this section, the conservation equations for laminar flow (in an inertial (non-accelerating) reference frame) are presented. The equations that are applicable to rotating reference frames are presented in Chapter 9. The conservation equations relevant to heat transfer, turbulence modeling, and species transport will be discussed in the chapters where those models are described. The Euler equations solved for inviscid flow are presented in Section 8.6.

The Mass Conservation Equation The equation for conservation of mass, or continuity equation, can be written as follows: ∂ρ + ∇ · (ρ~v ) = Sm ∂t

(8.2-1)

Equation 8.2-1 is the general form of the mass conservation equation and is valid for incompressible as well as compressible flows. The source Sm is the mass added to the continuous phase from the dispersed second phase (e.g., due to vaporization of liquid droplets) and any user-defined sources. For 2D axisymmetric geometries, the continuity equation is given by ∂ρ ∂ ∂ ρvr + (ρvx ) + (ρvr ) + = Sm ∂t ∂x ∂r r

(8.2-2)

where x is the axial coordinate, r is the radial coordinate, vx is the axial velocity, and vr is the radial velocity.

Momentum Conservation Equations Conservation of momentum in an inertial (non-accelerating) reference frame is described by [11] ∂ (ρ~v ) + ∇ · (ρ~v~v ) = −∇p + ∇ · (τ ) + ρ~g + F~ ∂t


(8.2-3)

8-3

Modeling Basic Fluid Flow where p is the static pressure, τ is the stress tensor (described below), and ρ~g and F~ are the gravitational body force and external body forces (e.g., that arise from interaction with the dispersed phase), respectively. F~ also contains other model-dependent source terms such as porous-media and user-defined sources. The stress tensor τ is given by 2 τ = µ (∇~v + ∇~v ) − ∇ · ~v I 3

T

(8.2-4)

where µ is the molecular viscosity, I is the unit tensor, and the second term on the right hand side is the effect of volume dilation. For 2D axisymmetric geometries, the axial and radial momentum conservation equations are given by

"

!#

∂ 1 ∂ 1 ∂ ∂p 1 ∂ ∂vx 2 (ρvx ) + (rρvx vx ) + (rρvr vx ) = − + rµ 2 − (∇ · ~v ) ∂t r ∂x r ∂r ∂x r ∂x ∂x 3 " !# 1 ∂ ∂vx ∂vr + rµ + + Fx r ∂r ∂r ∂x (8.2-5) and "

∂ 1 ∂ 1 ∂ ∂p 1 ∂ ∂vr ∂vx (ρvr ) + (rρvx vr ) + (rρvr vr ) = − + rµ + ∂t r ∂x r ∂r ∂r r ∂x ∂x ∂r "

!#

1 ∂ ∂vr 2 + rµ 2 − (∇ · ~v ) r ∂r ∂r 3

− 2µ

vr 2 µ vz2 + (∇ · ~ v ) + ρ + Fr r2 3 r r

!#

(8.2-6)

where ∇ · ~v =

∂vx ∂vr vr + + ∂x ∂r r

(8.2-7)

and vz is the swirl velocity. (See Section 8.4 for information about modeling axisymmetric swirl.)

8-4


8.3 Periodic Flows

8.3

Periodic Flows

Periodic flow occurs when the physical geometry of interest and the expected pattern of the flow/thermal solution have a periodically repeating nature. Two types of periodic flow can be modeled in FLUENT. In the first type, no pressure drop occurs across the periodic planes. (Note to FLUENT 4 users: This type of periodic flow is modeled using a “cyclic” boundary in FLUENT 4.) In the second type, a pressure drop occurs across translationally periodic boundaries, resulting in “fully-developed” or “streamwise-periodic” flow. (In FLUENT 4, this type of periodic flow is modeled using a “periodic” boundary.) This section discusses streamwise-periodic flow. A description of no-pressure-drop periodic flow is provided in Section 6.15, and a description of streamwise-periodic heat transfer is provided in Section 11.4. Information about streamwise-periodic flow is presented in the following sections: • Section 8.3.1: Overview and Limitations • Section 8.3.2: Theory • Section 8.3.3: User Inputs for the Segregated Solver • Section 8.3.4: User Inputs for the Coupled Solvers • Section 8.3.5: Monitoring the Value of the Pressure Gradient • Section 8.3.6: Postprocessing for Streamwise-Periodic Flows

8.3.1


Overview FLUENT provides the ability to calculate streamwise-periodic—or “fully-developed”— fluid flow. These flows are encountered in a variety of applications, including flows in compact heat exchanger channels and flows across tube banks. In such flow configurations, the geometry varies in a repeating manner along the direction of the flow, leading to a periodic fully-developed flow regime in which the flow pattern repeats in successive cycles. Other examples of streamwise-periodic flows include fully-developed flow in pipes and ducts. These periodic conditions are achieved after a sufficient entrance length, which depends on the flow Reynolds number and geometric configuration. Streamwise-periodic flow conditions exist when the flow pattern repeats over some length L, with a constant pressure drop across each repeating module along the streamwise direction. Figure 8.3.1 depicts one example of a periodically repeating flow of this type which has been modeled by including a single representative module.


8-5


3.57e-03 3.33e-03 3.09e-03 2.86e-03 2.62e-03 2.38e-03 2.14e-03 1.90e-03 1.67e-03 1.43e-03 1.19e-03 9.53e-04 7.15e-04 4.77e-04 2.39e-04 1.01e-06


Figure 8.3.1: Example of Periodic Flow in a 2D Heat Exchanger Geometry

Constraints on the Use of Streamwise-Periodic Flow The following constraints apply to modeling streamwise-periodic flow: • The flow must be incompressible. • The geometry must be translationally periodic. • If one of the coupled solvers is used, you can specify only the pressure jump; for the segregated solver, you can specify either the pressure jump or the mass flow rate. • No net mass addition through inlets/exits or extra source terms is allowed. • Species can be modeled only if inlets/exits (without net mass addition) are included in the problem. Reacting flows are not permitted. • Discrete phase and multiphase modeling are not allowed.

8.3.2

Theory

Definition of the Periodic Velocity The assumption of periodicity implies that the velocity components repeat themselves in space as follows:

8-6


8.3 Periodic Flows

~ = u(~r + 2L) ~ = ··· u(~r) = u(~r + L) ~ = v(~r + 2L) ~ = ··· v(~r) = v(~r + L)

(8.3-1)

~ = w(~r + 2L) ~ = ··· w(~r) = w(~r + L) ~ is the periodic length vector of the domain considered where ~r is the position vector and L (see Figure 8.3.2). A

→ L

B

→ L

uA = uB = uC

∼ pC pA = ∼ pB = ∼

vA = vB = vC

pB - pA = pC - pB

C

Figure 8.3.2: Example of a Periodic Geometry

Definition of the Streamwise-Periodic Pressure For viscous flows, the pressure is not periodic in the sense of Equation 8.3-1. Instead, the pressure drop between modules is periodic: ~ = p(~r + L) ~ − p(~r + 2L) ~ = ··· ∆p = p(~r) − p(~r + L)

(8.3-2)

If one of the coupled solvers is used, ∆p is specified as a constant value. For the segregated solver, the local pressure gradient can be decomposed into two parts: the gradient of a ~ periodic component, ∇˜ p(~r), and the gradient of a linearly-varying component, β |LL| ~ : ∇p(~r) = β

~ L + ∇˜ p(~r) ~ |L|

(8.3-3)

where p˜(~r) is the periodic pressure and β|~r| is the linearly-varying component of the pressure. The periodic pressure is the pressure left over after subtracting out the linearlyvarying pressure. The linearly-varying component of the pressure results in a force acting on the fluid in the momentum equations. Because the value of β is not known a priori, it must be iterated on until the mass flow rate that you have defined is achieved in the computational model. This correction of β occurs in the pressure correction step of the SIMPLE, SIMPLEC, or PISO algorithm where the value of β is updated based on the difference between the desired mass flow rate and the actual one. You have some control over the number of sub-iterations used to update β, as described in Section 8.3.3.


8-7


8.3.3

User Inputs for the Segregated Solver

If you are using the segregated solver, in order to calculate a spatially periodic flow field with a specified mass flow rate or pressure derivative, you must first create a grid with translationally periodic boundaries that are parallel to each other and equal in size. You can specify translational periodicity in the Periodic panel, as described in Section 6.15. (If you need to create periodic boundaries, see Section 5.7.5.) Once the grid has been read into FLUENT, you will complete the following inputs in the Periodicity Conditions panel (Figure 8.3.3): Define −→Periodic Conditions...

Figure 8.3.3: The Periodicity Conditions Panel

1. Select either the specified mass flow rate (Specify Mass Flow) option or the specified pressure gradient (Specify Pressure Gradient) option. For most problems, the mass flow rate across the periodic boundary will be a known quantity; for others, the mass flow rate will be unknown, but the pressure gradient (β in Equation 8.3-3) will be a known quantity. 2. Specify the mass flow rate and/or the pressure gradient (β in Equation 8.3-3): • If you selected the Specify Mass Flow option, enter the desired value for the Mass Flow Rate. You can also specify an initial guess for the Pressure Gradient, but this is not required.

!

For axisymmetric problems, the mass flow rate is per 2π radians. • If you selected the Specify Pressure Gradient option, enter the desired value for Pressure Gradient.

8-8


8.3 Periodic Flows

3. Define the flow direction by setting the X,Y,Z (or X,Y in 2D) point under Flow Direction. The flow will move in the direction of the vector pointing from the origin to the specified point. The direction vector must be parallel to the periodic translation direction or its opposite. 4. If you chose in step 1 to specify the mass flow rate, set the parameters used for the calculation of β. These parameters are described in detail below. After completing these inputs, you can solve the periodic velocity field to convergence.

Setting Parameters for the Calculation of β If you choose to specify the mass flow rate, FLUENT will need to calculate the appropriate value of the pressure gradient β. You can control this calculation by specifying the Relaxation Factor and the Number of Iterations, and by supplying an initial guess for β. All of these inputs are entered in the Periodicity Conditions panel. The Number of Iterations sets the number of sub-iterations performed on the correction of β in the pressure correction equation. Because the value of β is not known a priori, it must be iterated on until the Mass Flow Rate that you have defined is achieved in the computational model. This correction of β occurs in the pressure correction step of the SIMPLE, SIMPLEC, or PISO algorithm. A correction to the current value of β is calculated based on the difference between the desired mass flow rate and the actual one. The sub-iterations referred to here are performed within the pressure correction step to improve the correction for β before the pressure correction equation is solved for the resulting pressure (and velocity) correction values. The default value of 2 sub-iterations should suffice in most problems, but can be increased to help speed convergence. The Relaxation Factor is an under-relaxation factor that controls convergence of this iteration process. You can also speed up convergence of the periodic calculation by supplying an initial guess for β in the Pressure Gradient field. Note that the current value of β will be displayed in this field if you have performed any calculations. To update the Pressure Gradient field with the current value at any time, click on the Update button.

8.3.4

User Inputs for the Coupled Solvers

If you are using one of the coupled solvers, in order to calculate a spatially periodic flow field with a specified pressure jump, you must first create a grid with translationally periodic boundaries that are parallel to each other and equal in size. (If you need to create periodic boundaries, see Section 5.7.5.)


8-9


Then, follow the steps below: 1. In the Periodic panel (Figure 8.3.4), which is opened from the Boundary Conditions panel, indicate that the periodicity is Translational (the default). Define −→Boundary Conditions...

Figure 8.3.4: The Periodic Panel

2. Also in the Periodic panel, set the Periodic Pressure Jump (∆p in Equation 8.3-2). After completing these inputs, you can solve the periodic velocity field to convergence.

8.3.5

Monitoring the Value of the Pressure Gradient

If you have specified the mass flow rate, you can monitor the value of the pressure gradient β during the calculation using the Statistic Monitors panel. Select per/pr-grad as the variable to be monitored. See Section 24.16.2 for details about using this feature.

8.3.6

Postprocessing for Streamwise-Periodic Flows

For streamwise-periodic flows, the velocity field should be completely periodic. If a coupled solver is used to compute the periodic flow, the pressure field reported will be the actual pressure p (which is not periodic). If the segregated solver is used, the pressure field reported will be the periodic pressure field p˜(~r) of Equation 8.3-3. Figure 8.3.5 displays the periodic pressure field in the geometry of Figure 8.3.1. If you specified a mass flow rate and had FLUENT calculate the pressure gradient, you can check the pressure gradient in the streamwise direction (β) by looking at the current value for Pressure Gradient in the Periodicity Conditions panel.

8-10


8.4 Swirling and Rotating Flows

1.68e-03 1.29e-03 8.98e-04 5.07e-04 1.16e-04 -2.74e-04 -6.65e-04 -1.06e-03 -1.45e-03 -1.84e-03 -2.23e-03 -2.62e-03 -3.01e-03 -3.40e-03 -3.79e-03 -4.18e-03

Contours of Static Pressure (pascal)

Figure 8.3.5: Periodic Pressure Field Predicted for Flow in a 2D Heat Exchanger Geometry

8.4

Swirling and Rotating Flows

Many important engineering flows involve swirl or rotation and FLUENT is well-equipped to model such flows. Swirling flows are common in combustion, with swirl introduced in burners and combustors in order to increase residence time and stabilize the flow pattern. Rotating flows are also encountered in turbomachinery, mixing tanks, and a variety of other applications. Information about rotating and swirling flows is provided in the following subsections: • Section 8.4.1: Overview of Swirling and Rotating Flows • Section 8.4.2: Physics of Swirling and Rotating Flows • Section 8.4.3: Turbulence Modeling in Swirling Flows • Section 8.4.4: Grid Setup for Swirling and Rotating Flows • Section 8.4.5: Modeling Axisymmetric Flows with Swirl or Rotation


8-11


When you begin the analysis of a rotating or swirling flow, it is essential that you classify your problem into one of the following five categories of flow: • axisymmetric flows with swirl or rotation • fully three-dimensional swirling or rotating flows • flows requiring a rotating reference frame • flows requiring multiple rotating reference frames or mixing planes • flows requiring sliding meshes Modeling and solution procedures for the first two categories are presented in this section. The remaining three, which all involve “moving zones”, are discussed in Chapter 9.

8.4.1

Overview of Swirling and Rotating Flows

Axisymmetric Flows with Swirl or Rotation Your problem may be axisymmetric with respect to geometry and flow conditions but still include swirl or rotation. In this case, you can model the flow in 2D (i.e., solve the axisymmetric problem) and include the prediction of the circumferential (or swirl) velocity. It is important to note that while the assumption of axisymmetry implies that there are no circumferential gradients in the flow, there may still be non-zero swirl velocities. Momentum Conservation Equation for Swirl Velocity The tangential momentum equation for 2D swirling flows may be written as

"

#

"

∂ 1 ∂ 1 ∂ 1 ∂ ∂w 1 ∂ ∂ (ρw)+ (rρuw)+ (rρvw) = rµ + 2 r3 µ ∂t r ∂x r ∂r r ∂x ∂x r ∂r ∂r

w r

#

−ρ

vw (8.4-1) r

where x is the axial coordinate, r is the radial coordinate, u is the axial velocity, v is the radial velocity, and w is the swirl velocity.

Three-Dimensional Swirling Flows When there are geometric changes and/or flow gradients in the circumferential direction, your swirling flow prediction requires a three-dimensional model. If you are planning a 3D FLUENT model that includes swirl or rotation, you should be aware of the setup constraints listed in Section 8.4.4. In addition, you may wish to consider simplifications

8-12



to the problem which might reduce it to an equivalent axisymmetric problem, especially for your initial modeling effort. Because of the complexity of swirling flows, an initial 2D study, in which you can quickly determine the effects of various modeling and design choices, can be very beneficial.

! For 3D problems involving swirl or rotation, there are no special inputs required during the problem setup and no special solution procedures. Note, however, that you may want to use the cylindrical coordinate system for defining velocity-inlet boundary condition inputs, as described in Section 6.4.1. Also, you may find the gradual increase of the rotational speed (set as a wall or inlet boundary condition) helpful during the solution process. This is described for axisymmetric swirling flows in Section 8.4.5.

Flows Requiring a Rotating Reference Frame If your flow involves a rotating boundary which moves through the fluid (e.g., an impeller blade or a grooved or notched surface), you will need to use a rotating reference frame to model the problem. Such applications are described in detail in Section 9.2. If you have more than one rotating boundary (e.g., several impellers in a row), you can use multiple reference frames (described in Section 9.3) or mixing planes (described in Section 9.4).

8.4.2

Physics of Swirling and Rotating Flows

In swirling flows, conservation of angular momentum (rw or r2 Ω = constant) tends to create a free vortex flow, in which the circumferential velocity, w, increases sharply as the radius, r, decreases (with w finally decaying to zero near r = 0 as viscous forces begin to dominate). A tornado is one example of a free vortex. Figure 8.4.1 depicts the radial distribution of w in a typical free vortex. r axis

Figure 8.4.1: Typical Radial Distribution of w in a Free Vortex It can be shown that for an ideal free vortex flow, the centrifugal forces created by the circumferential motion are in equilibrium with the radial pressure gradient: ∂p ρw2 = ∂r r

(8.4-2)

As the distribution of angular momentum in a non-ideal vortex evolves, the form of this radial pressure gradient also changes, driving radial and axial flows in response to the highly non-uniform pressures that result. Thus, as you compute the distribution of swirl in your FLUENT model, you will also notice changes in the static pressure distribution


8-13


and corresponding changes in the axial and radial flow velocities. It is this high degree of coupling between the swirl and the pressure field that makes the modeling of swirling flows complex. In flows that are driven by wall rotation, the motion of the wall tends to impart a forced vortex motion to the fluid, wherein w/r or Ω is constant. An important characteristic of such flows is the tendency of fluid with high angular momentum (e.g., the flow near the wall) to be flung radially outward (Figure 8.4.2). This is often referred to as “radial pumping”, since the rotating wall is pumping the fluid radially outward.

7.69e-03

6.92e-03

6.15e-03

5.38e-03

4.62e-03

3.85e-03

3.08e-03

2.31e-03

1.54e-03

7.69e-04

axis of rotation

0.00e+00

Contours of Stream Function (kg/s)

Figure 8.4.2: Stream Function Contours for Rotating Flow in a Cavity (Geometry of Figure 8.4.3)

8.4.3

Turbulence Modeling in Swirling Flows

If you are modeling turbulent flow with a significant amount of swirl (e.g., cyclone flows, swirling jets), you should consider using one of FLUENT’s advanced turbulence models: the RNG k- model, realizable k- model, or Reynolds stress model. The appropriate choice depends on the strength of the swirl, which can be gauged by the swirl number. The swirl number is defined as the ratio of the axial flux of angular momentum to the axial flux of axial momentum: Z

S=

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~ rw~v · dA Z

¯ u~v · dA ~ R

(8.4-3)


8.4 Swirling and Rotating Flows ¯ is the hydraulic radius. where R For flows with weak to moderate swirl (S < 0.5), both the RNG k- model and the realizable k- model yield appreciable improvements over the standard k- model. See Sections 10.4.2, 10.4.3, and 10.10.1 for details about these models. For highly swirling flows (S > 0.5), the Reynolds stress model (RSM) is strongly recommended. The effects of strong turbulence anisotropy can be modeled rigorously only by the second-moment closure adopted in the RSM. See Sections 10.6 and 10.10 for details about this model. For swirling flows encountered in devices such as cyclone separators and swirl combustors, near-wall turbulence modeling is quite often a secondary issue at most. The fidelity of the predictions in these cases is mainly determined by the accuracy of the turbulence model in the core region. However, in cases where walls actively participate in the generation of swirl (i.e., where the secondary flows and vortical flows are generated by pressure gradients), non-equilibrium wall functions can often improve the predictions since they use a law of the wall for mean velocity sensitized to pressure gradients. See Section 10.8 for additional details about near-wall treatments for turbulence.

8.4.4

Grid Setup for Swirling and Rotating Flows

Coordinate-System Restrictions Recall that for an axisymmetric problem, the axis of rotation must be the x axis and the grid must lie on or above the y = 0 line.

Grid Sensitivity in Swirling and Rotating Flows In addition to the setup constraint described above, you should be aware of the need for sufficient resolution in your grid when solving flows that include swirl or rotation. Typically, rotating boundary layers may be very thin, and your FLUENT model will require a very fine grid near a rotating wall. In addition, swirling flows will often involve steep gradients in the circumferential velocity (e.g., near the centerline of a free-vortex type flow), and thus require a fine grid for accurate resolution.

8.4.5

Modeling Axisymmetric Flows with Swirl or Rotation

As discussed in Section 8.4.1, you can solve a 2D axisymmetric problem that includes the prediction of the circumferential or swirl velocity. The assumption of axisymmetry implies that there are no circumferential gradients in the flow, but that there may be non-zero circumferential velocities. Examples of axisymmetric flows involving swirl or rotation are depicted in Figures 8.4.3 and 8.4.4.


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Rotating Cover

Ω

Region to be modeled

x

y

Figure 8.4.3: Rotating Flow in a Cavity

Region to be modeled

Ω

Figure 8.4.4: Swirling Flow in a Gas Burner

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Problem Setup for Axisymmetric Swirling Flows For axisymmetric problems, you will need to perform the following steps during the problem setup procedure. (Only those steps relevant specifically to the setup of axisymmetric swirl/rotation are listed here. You will need to set up the rest of the problem as usual.) 1. Activate solution of the momentum equation in the circumferential direction by turning on the Axisymmetric Swirl option for Space in the Solver panel. Define −→ Models −→Solver... 2. Define the rotational or swirling component of velocity, rΩ, at inlets or walls. Define −→Boundary Conditions...

!

Remember to use the axis boundary type for the axis of rotation. The procedures for input of rotational velocities at inlets and at walls are described in detail in Sections 6.4.1 and 6.13.1.

Solution Strategies for Axisymmetric Swirling Flows The difficulties associated with solving swirling and rotating flows are a result of the high degree of coupling between the momentum equations, which is introduced when the influence of the rotational terms is large. A high level of rotation introduces a large radial pressure gradient which drives the flow in the axial and radial directions. This, in turn, determines the distribution of the swirl or rotation in the field. This coupling may lead to instabilities in the solution process, and you may require special solution techniques in order to obtain a converged solution. Solution techniques that may be beneficial in swirling or rotating flow calculations include the following: • (Segregated solver only) Use the PRESTO! scheme (enabled in the Pressure list for Discretization in the Solution Controls panel), which is well-suited for the steep pressure gradients involved in swirling flows. • Ensure that the mesh is sufficiently refined to resolve large gradients in pressure and swirl velocity. • (Segregated solver only) Change the under-relaxation parameters on the velocities, perhaps to 0.3–0.5 for the radial and axial velocities and 0.8–1.0 for swirl. • (Segregated solver only) Use a sequential or step-by-step solution procedure, in which some equations are temporarily left inactive (see below). • If necessary, start the calculations using a low rotational speed or inlet swirl velocity, increasing the rotation or swirl gradually in order to reach the final desired operating condition (see below).


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See Chapter 24 for details on the procedures used to make these changes to the solution parameters. More details on the step-by-step procedure and on the gradual increase of the rotational speed are provided below. Step-By-Step Solution Procedures for Axisymmetric Swirling Flows Often, flows with a high degree of swirl or rotation will be easier to solve if you use the following step-by-step solution procedure, in which only selected equations are left active in each step. This approach allows you to establish the field of angular momentum, then leave it fixed while you update the velocity field, and then finally to couple the two fields by solving all equations simultaneously.

! Since the coupled solvers solve all the flow equations simultaneously, the following procedure applies only to the segregated solver. In this procedure, you will use the Equations list in the Solution Controls panel to turn individual transport equations on and off between calculations. 1. If your problem involves inflow/outflow, begin by solving the flow without rotation or swirl effects. That is, enable the Axisymmetric option instead of the Axisymmetric Swirl option in the Solver panel, and do not set any rotating boundary conditions. The resulting flow-field data can be used as a starting guess for the full problem. 2. Enable the Axisymmetric Swirl option and set all rotating/swirling boundary conditions. 3. Begin the prediction of the rotating/swirling flow by solving only the momentum equation describing the circumferential velocity. This is the Swirl Velocity listed in the Equations list in the Solution Controls panel. Let the rotation “diffuse” throughout the flow field, based on your boundary condition inputs. In a turbulent flow simulation, you may also want to leave the turbulence equations active during this step. This step will establish the field of rotation throughout the domain. 4. Turn off the momentum equations describing the circumferential motion (Swirl Velocity). Leaving the velocity in the circumferential direction fixed, solve the momentum and continuity (pressure) equations (Flow in the Equations list in the Solution Controls panel) in the other coordinate directions. This step will establish the axial and radial flows that are a result of the rotation in the field. Again, if your problem involves turbulent flow, you should leave the turbulence equations active during this calculation. 5. Turn on all of the equations simultaneously to obtain a fully coupled solution. Note the under-relaxation controls suggested above. In addition to the steps above, you may want to simplify your calculation by solving isothermal flow before adding heat transfer or by solving laminar flow before adding a

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turbulence model. These two methods can be used for any of the solvers (i.e., segregated or coupled). Gradual Increase of the Rotational or Swirl Speed to Improve Solution Stability Because the rotation or swirl defined by the boundary conditions can lead to large complex forces in the flow, your FLUENT calculations will be less stable as the speed of rotation or degree of swirl increases. Hence, one of the most effective controls you can apply to the solution is to solve your rotating flow problem starting with a low rotational speed or swirl velocity and then slowly increase the magnitude up to the desired level. The procedure for accomplishing this is as follows: 1. Set up the problem using a low rotational speed or swirl velocity in your inputs for boundary conditions. The rotation or swirl in this first attempt might be selected as 10% of the actual operating conditions. 2. Solve the problem at these conditions, perhaps using the step-by-step solution strategy outlined above. 3. Save this initial solution data. 4. Modify your inputs (boundary conditions). Increase the speed of rotation, perhaps doubling it. 5. Restart the calculation using the solution data saved in step 3 as the initial solution for the new calculation. Save the new data. 6. Continue to increment the speed of rotation, following steps 4 and 5, until you reach the desired operating condition.

Postprocessing for Axisymmetric Swirling Flows Reporting of results for axisymmetric swirling flows is the same as for other flows. The following additional variables are available for postprocessing when axisymmetric swirl is active: • Swirl Velocity (in the Velocity... category) • Swirl-Wall Shear Stress (in the Wall Fluxes... category)


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8.5

Compressible Flows

Compressibility effects are encountered in gas flows at high velocity and/or in which there are large pressure variations. When the flow velocity approaches or exceeds the speed of sound of the gas or when the pressure change in the system (∆p/p) is large, the variation of the gas density with pressure has a significant impact on the flow velocity, pressure, and temperature. Compressible flows create a unique set of flow physics for which you must be aware of the special input requirements and solution techniques described in this section. Figures 8.5.1 and 8.5.2 show examples of compressible flows computed using FLUENT.

1.57e+00 1.43e+00 1.29e+00 1.16e+00 1.02e+00 8.82e-01 7.45e-01 6.07e-01 4.70e-01 3.32e-01 1.95e-01

Contours of Mach Number

Figure 8.5.1: Transonic Flow in a Converging-Diverging Nozzle

Information about compressible flows is provided in the following subsections: • Section 8.5.1: When to Use the Compressible Flow Model • Section 8.5.2: Physics of Compressible Flows • Section 8.5.3: Modeling Inputs for Compressible Flows • Section 8.5.4: Floating Operating Pressure • Section 8.5.5: Solution Strategies for Compressible Flows • Section 8.5.6: Reporting of Results for Compressible Flows

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8.5 Compressible Flows

2.02e+04 1.24e+04 4.68e+03 -3.07e+03 -1.08e+04 -1.86e+04 -2.63e+04 -3.41e+04 -4.18e+04 -4.95e+04 -5.73e+04

Contours of Static Pressure (pascal)

Figure 8.5.2: Mach 0.675 Flow Over a Bump in a 2D Channel

8.5.1

When to Use the Compressible Flow Model

Compressible flows can be characterized by the value of the Mach number: M ≡ u/c

(8.5-1)

Here, c is the speed of sound in the gas: c=

q

γRT

(8.5-2)

and γ is the ratio of specific heats (cp /cv ). When the Mach number is less than 1.0, the flow is termed subsonic. At Mach numbers much less than 1.0 (M < 0.1 or so), compressibility effects are negligible and the variation of the gas density with pressure can safely be ignored in your flow modeling. As the Mach number approaches 1.0 (which is referred to as the transonic flow regime), compressibility effects become important. When the Mach number exceeds 1.0, the flow is termed supersonic, and may contain shocks and expansion fans which can impact the flow pattern significantly. FLUENT provides a wide range of compressible flow modeling capabilities for subsonic, transonic, and supersonic flows.


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8.5.2

Physics of Compressible Flows

Compressible flows are typically characterized by the total pressure p0 and total temperature T0 of the flow. For an ideal gas, these quantities can be related to the static pressure and temperature by the following:

p0 = p

γ−1 2 1+ M 2

γ/(γ−1)

(8.5-3)

T0 γ−1 2 = 1+ M T 2

(8.5-4)

These relationships describe the variation of the static pressure and temperature in the flow as the velocity (Mach number) changes under isentropic conditions. For example, given a pressure ratio from inlet to exit (total to static), Equation 8.5-3 can be used to estimate the exit Mach number which would exist in a one-dimensional isentropic flow. For air, Equation 8.5-3 predicts a choked flow (Mach number of 1.0) at an isentropic pressure ratio, p/p0 , of 0.5283. This choked flow condition will be established at the point of minimum flow area (e.g., in the throat of a nozzle). In the subsequent area expansion the flow may either accelerate to a supersonic flow in which the pressure will continue to drop, or return to subsonic flow conditions, decelerating with a pressure rise. If a supersonic flow is exposed to an imposed pressure increase, a shock will occur, with a sudden pressure rise and deceleration accomplished across the shock.

Basic Equations for Compressible Flows Compressible flows are described by the standard continuity and momentum equations solved by FLUENT, and you do not need to activate any special physical models (other than the compressible treatment of density as detailed below). The energy equation solved by FLUENT correctly incorporates the coupling between the flow velocity and the static temperature, and should be activated whenever you are solving a compressible flow. In addition, if you are using the segregated solver, you should activate the viscous dissipation terms in Equation 11.2-1, which become important in high-Mach-number flows.

The Compressible Form of the Gas Law For compressible flows, the ideal gas law is written in the following form: ρ=

pop + p R T Mw

(8.5-5)

where pop is the operating pressure defined in the Operating Conditions panel, p is the local static pressure relative to the operating pressure, R is the universal gas constant,

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and Mw is the molecular weight. The temperature, T , will be computed from the energy equation.

8.5.3

Modeling Inputs for Compressible Flows

To set up a compressible flow in FLUENT, you will need to follow the steps listed below. (Only those steps relevant specifically to the setup of compressible flows are listed here. You will need to set up the rest of the problem as usual.) 1. Set the Operating Pressure in the Operating Conditions panel. Define −→Operating Conditions... (You can think of pop as the absolute static pressure at a point in the flow where you will define the gauge pressure p to be zero. See Section 7.12 for guidelines on setting the operating pressure. For time-dependent compressible flows, you may want to specify a floating operating pressure instead of a constant operating pressure. See Section 8.5.4 for details.) 2. Activate solution of the energy equation in the Energy panel. Define −→ Models −→Energy... 3. (Segregated solver only) If you are modeling turbulent flow, activate the optional viscous dissipation terms in the energy equation by turning on Viscous Heating in the Viscous Model panel. Note that these terms can be important in high-speed flows. Define −→ Models −→Viscous... This step is not necessary if you are using one of the coupled solvers, because the coupled solvers always include the viscous dissipation terms in the energy equation. 4. Set the following items in the Materials panel: Define −→Materials... (a) Select ideal-gas in the drop-down list next to Density. (b) Define all relevant properties (specific heat, molecular weight, thermal conductivity, etc.). 5. Set boundary conditions (using the Boundary Conditions panel), being sure to choose a well-posed boundary condition combination that is appropriate for the flow regime. See below for details. Recall that all inputs for pressure (either total pressure or static pressure) must be relative to the operating pressure, and the temperature inputs at inlets should be total (stagnation) temperatures, not static temperatures. Define −→Boundary Conditions...


8-23


These inputs should ensure a well-posed compressible flow problem. You will also want to consider special solution parameter settings, as noted in Section 8.5.5, before beginning the flow calculation.

Boundary Conditions for Compressible Flows Well-posed inlet and exit boundary conditions for compressible flow are listed below: • For flow inlets: – Pressure inlet: Inlet total temperature and total pressure and, for supersonic inlets, static pressure – Mass flow inlet: Inlet mass flow and total temperature • For flow exits: – Pressure outlet: Exit static pressure (ignored if flow is supersonic at the exit) It is important to note that your boundary condition inputs for pressure (either total pressure or static pressure) must be in terms of gauge pressure—i.e., pressure relative to the operating pressure defined in the Operating Conditions panel, as described above. All temperature inputs at inlets should be total (stagnation) temperatures, not static temperatures.

8.5.4

Floating Operating Pressure

FLUENT provides a “floating operating pressure” option to handle time-dependent compressible flows with a gradual increase in the absolute pressure in the domain. This option is desirable for slow subsonic flows with static pressure build-up, since it efficiently accounts for the slow changing of absolute pressure without using acoustic waves as the transport mechanism for the pressure build-up. Examples of typical applications include the following: • combustion or heating of a gas in a closed domain • pumping of a gas into a closed domain

Limitations The floating operating pressure option should not be used for transonic or incompressible flows. In addition, it cannot be used if your model includes any pressure inlet, pressure outlet, exhaust fan, inlet vent, intake fan, outlet vent, or pressure far field boundaries.

8-24



Theory The floating operating pressure option allows FLUENT to calculate the pressure rise (or drop) from the integral mass balance, separately from the solution of the pressure correction equation. When this option is activated, the absolute pressure at each iteration can be expressed as pabs = pop,float + p

(8.5-6)

where p is the pressure relative to the reference location, which in this case is in the cell with the minimum pressure value. Thus the reference location itself is floating. pop,float is referred to as the floating operating pressure, and is defined as pop,float = p0op + ∆pop

(8.5-7)

where p0op is the initial operating pressure and ∆pop is the pressure rise. Including the pressure rise ∆pop in the floating operating pressure pop,float , rather than in the pressure p, helps to prevent roundoff error. If the pressure rise were included in p, the calculation of the pressure gradient for the momentum equation would give an inexact balance due to precision limits for 32-bit real numbers.

Enabling Floating Operating Pressure When time dependence is active, you can turn on the Floating Operating Pressure option in the Operating Conditions panel. Define −→Operating Conditions... (Note that the inputs for Reference Pressure Location will disappear when you enable Floating Operating Pressure, since these inputs are no longer relevant.)

! The floating operating pressure option should not be used for transonic flows or for incompressible flows. It is meaningful only for slow subsonic flows of ideal gases, when the characteristic time scale is much larger than the sonic time scale.

Setting the Initial Value for the Floating Operating Pressure When the floating operating pressure option is enabled, you will need to specify a value for the Initial Operating Pressure in the Solution Initialization panel. Solve −→ Initialize −→Initialize... This initial value is stored in the case file with all your other initial values.


8-25


Storage and Reporting of the Floating Operating Pressure The current value of the floating operating pressure is stored in the data file. If you visit the Operating Conditions panel after a number of time steps have been performed, the current value of the Operating Pressure will be displayed. Note that the floating operating pressure will automatically be reset to the initial operating pressure if you reset the data (i.e., start over at the first iteration of the first time step).

Monitoring Absolute Pressure You can monitor the absolute pressure during the calculation using the Surface Monitors panel (see Section 24.16.4 for details). You can also generate graphical plots or alphanumeric reports of absolute pressure when your solution is complete. The Absolute Pressure variable is contained in the Pressure... category of the variable selection drop-down list that appears in postprocessing panels. See Chapter 29 for its definition.

8.5.5

Solution Strategies for Compressible Flows

The difficulties associated with solving compressible flows are a result of the high degree of coupling between the flow velocity, density, pressure, and energy. This coupling may lead to instabilities in the solution process and, therefore, may require special solution techniques in order to obtain a converged solution. In addition, the presence of shocks (discontinuities) in the flow introduces an additional stability problem during the calculation. Solution techniques that may be beneficial in compressible flow calculations include the following: • (segregated solver only) Use conservative under-relaxation parameters on the velocities, perhaps values of 0.2 or 0.3. • (segregated solver only) Set the under-relaxation on pressure to a value of 0.1 or so and use the SIMPLE algorithm. • Set reasonable limits for the temperature and pressure (in the Solution Limits panel) to avoid solution divergence, especially at the start of the calculation. If FLUENT prints messages about temperature or pressure being limited as the solution nears convergence, the high or low computed values may be physical, and you will need to change the limits to allow these values. • If required, begin the calculations using a reduced pressure ratio at the boundaries, increasing the pressure ratio gradually in order to reach the final desired operating condition. You can also consider starting the compressible flow calculation from an incompressible flow solution (although the incompressible flow solution can in some cases be a rather poor initial guess for the compressible calculation).

8-26



• In some cases, computing an inviscid solution as a starting point may be helpful. See Chapter 24 for details on the procedures used to make these changes to the solution parameters.

8.5.6

Reporting of Results for Compressible Flows

You can display the results of your compressible flow calculations in the same manner that you would use for an incompressible flow. The variables listed below are of particular interest when you model compressible flow: • Total Temperature • Total Pressure • Mach Number These variables are contained in the variable selection drop-down list that appears in postprocessing panels. Total Temperature is in the Temperature... category, Total Pressure is in the Pressure... category, and Mach Number is in the Velocity... category. See Chapter 29 for their definitions.


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8.6

Inviscid Flows

Inviscid flow analyses neglect the effect of viscosity on the flow and are appropriate for high-Reynolds-number applications where inertial forces tend to dominate viscous forces. One example for which an inviscid flow calculation is appropriate is an aerodynamic analysis of some high-speed projectile. In a case like this, the pressure forces on the body will dominate the viscous forces. Hence, an inviscid analysis will give you a quick estimate of the primary forces acting on the body. After the body shape has been modified to maximize the lift forces and minimize the drag forces, you can perform a viscous analysis to include the effects of the fluid viscosity and turbulent viscosity on the lift and drag forces. Another area where inviscid flow analyses are routinely used is to provide a good initial solution for problems involving complicated flow physics and/or complicated flow geometry. In a case like this, the viscous forces are important, but in the early stages of the calculation the viscous terms in the momentum equations will be ignored. Once the calculation has been started and the residuals are decreasing, you can turn on the viscous terms (by enabling laminar or turbulent flow) and continue the solution to convergence. For some very complicated flows, this is the only way to get the calculation started. Information about inviscid flows is provided in the following subsections: • Section 8.6.1: Euler Equations • Section 8.6.2: Setting Up an Inviscid Flow Model • Section 8.6.3: Solution Strategies for Inviscid Flows • Section 8.6.4: Postprocessing for Inviscid Flows

8.6.1

Euler Equations

For inviscid flows, FLUENT solves the Euler equations. The mass conservation equation is the same as for a laminar flow, but the momentum and energy conservation equations are reduced due to the absence of molecular diffusion. In this section, the conservation equations for inviscid flow in an inertial (non-rotating) reference frame are presented. The equations that are applicable to non-inertial reference frames are described in Chapter 9. The conservation equations relevant for species transport and other models will be discussed in the chapters where those models are described.

8-28


8.6 Inviscid Flows

The Mass Conservation Equation The equation for conservation of mass, or continuity equation, can be written as follows: ∂ρ + ∇ · (ρ~v ) = Sm ∂t

(8.6-1)

Equation 8.6-1 is the general form of the mass conservation equation and is valid for incompressible as well as compressible flows. The source Sm is the mass added to the continuous phase from the dispersed second phase (e.g., due to vaporization of liquid droplets) and any user-defined sources. For 2D axisymmetric geometries, the continuity equation is given by ∂ρ ∂ ∂ ρvr + (ρvx ) + (ρvr ) + = Sm ∂t ∂x ∂r r

(8.6-2)

where x is the axial coordinate, r is the radial coordinate, vx is the axial velocity, and vr is the radial velocity.

Momentum Conservation Equations Conservation of momentum is described by ∂ (ρ~v ) + ∇ · (ρ~v~v ) = −∇p + ρ~g + F~ ∂t

(8.6-3)

where p is the static pressure and ρ~g and F~ are the gravitational body force and external body forces (e.g., forces that arise from interaction with the dispersed phase), respectively. F~ also contains other model-dependent source terms such as porous-media and userdefined sources. For 2D axisymmetric geometries, the axial and radial momentum conservation equations are given by ∂ 1 ∂ 1 ∂ ∂p (ρvx ) + (rρvx vx ) + (rρvr vx ) = − + Fx ∂t r ∂x r ∂r ∂x

(8.6-4)

∂ 1 ∂ 1 ∂ ∂p (ρvr ) + (rρvx vr ) + (rρvr vr ) = − + Fr ∂t r ∂x r ∂r ∂r

(8.6-5)

and

where


8-29


∇ · ~v =

∂vx ∂vr vr + + ∂x ∂r r

(8.6-6)

Energy Conservation Equation Conservation of energy is described by 



X ∂ (ρE) + ∇ · (~v (ρE + p)) = −∇ ·  hj Jj  + Sh ∂t j

8.6.2

(8.6-7)

Setting Up an Inviscid Flow Model

For inviscid flow problems, you will need to perform the following steps during the problem setup procedure. (Only those steps relevant specifically to the setup of inviscid flow are listed here. You will need to set up the rest of the problem as usual.) 1. Activate the calculation of inviscid flow by selecting Inviscid in the Viscous Model panel. Define −→ Models −→Viscous... 2. Set boundary conditions and flow properties. Define −→Boundary Conditions... Define −→Materials... 3. Solve the problem and examine the results.

8.6.3

Solution Strategies for Inviscid Flows

Since inviscid flow problems will usually involve high-speed flow, you may have to reduce the under-relaxation factors for momentum (if you are using the segregated solver) or reduce the Courant number (if you are using the coupled solver), in order to get the solution started. Once the flow is started and the residuals are monotonically decreasing, you can start increasing the under-relaxation factors or Courant number back up to the default values. Modifications to the under-relaxation factors and the Courant number can be made in the Solution Controls panel. Solve −→ Controls −→Solution... The solution strategies for compressible flows apply also to inviscid flows. See Section 8.5.5 for details.

8-30


8.6 Inviscid Flows

8.6.4

Postprocessing for Inviscid Flows

If you are interested in the lift and drag forces acting on your model, you can use the Force Reports panel to compute them. Report −→Forces... See Section 28.3 for details.


8-31


8-32


Chapter 9. Modeling Flows in Moving and Deforming Zones FLUENT can model flow involving moving reference frames and moving cell zones, using several different approaches, and flow in moving and deforming domains (dynamic meshes). Solving flows in moving reference frames requires the use of moving cell zones. This cell zone motion is interpreted as the motion of a reference frame to which the cell zone is attached. With this capability, a wide variety of problems that involve moving parts can be set up and solved using FLUENT. Depending on the level of complexity of the motion, and on the flow physics involved, one of FLUENT’s moving cell zone models may be the most suited to your application. The most general model for flow in moving and deforming cell zones in FLUENT is the dynamic mesh model, covered in Section 9.6. The information in this chapter is divided into the following sections: • Section 9.1: Overview of Moving Zone Approaches • Section 9.2: Flow in a Rotating Reference Frame • Section 9.3: The Multiple Reference Frame Model • Section 9.4: The Mixing Plane Model • Section 9.5: Sliding Meshes • Section 9.6: Dynamic Meshes


9-1

Modeling Flows in Moving and Deforming Zones

9.1

Overview of Moving Zone Approaches

The moving cell zone capability in FLUENT provides a powerful set of features for solving problems in which the domain or parts of the domain are in motion. Problems that can be addressed include the following: • flow in a (single) rotating frame • flow in multiple rotating and/or translating reference frames The single rotating frame option can be used to model flows in turbomachinery, mixing tanks, and related devices. In each of these cases, the flow is unsteady in an inertial frame (i.e., a domain fixed in the laboratory frame) because the rotor/impeller blades sweep the domain periodically. However, in the absence of stators or baffles, it is possible to perform calculations in a domain that moves with the rotating part. In this case, the flow is steady relative to the rotating (non-inertial) frame, which simplifies the analysis. If stators or baffles are present in addition to a rotor or impeller, then it is not possible to render the computational problem steady by choosing a calculation domain that rotates with the rotor or impeller. This situation occurs, for example, in turbomachinery applications where rotor and stator blades are in close proximity (and hence rotor-stator interaction is important). FLUENT provides three approaches to address this class of problems: • the multiple reference frame (MRF) model • the mixing plane model • the sliding mesh model Both the MRF and mixing plane models assume that the flow field is steady, with the rotor-stator or impeller-baffle effects being accounted for by approximate means. These can be acceptable models in cases where the rotor-stator interaction is weak or an approximate solution for the system is desired. The sliding mesh model, on the other hand, assumes that the flow field is unsteady, and hence models the interaction with complete fidelity. This is the model of choice if rotor-stator interaction is strong and a more accurate simulation of the system is desired. Note, however, that because the sliding mesh model requires an unsteady numerical solution, it is computationally more demanding than the MRF and mixing plane models.

9-2


9.2 Flow in a Rotating Reference Frame

9.2 9.2.1

Flow in a Rotating Reference Frame Overview

When you create a model using FLUENT, you are typically modeling the flow in an inertial reference frame (i.e., in a non-accelerating coordinate system). However, FLUENT also has the ability to model flows in an accelerating reference frame. In this situation, the acceleration of the coordinate system is included in the equations of motion describing the flow. A common example of an accelerating reference frame in engineering applications is flow in rotating equipment. Many such flows can be modeled in a coordinate system that is moving with the rotating equipment and thus experiences a constant acceleration in the radial direction. This class of rotating flows can be treated using the rotating reference frame capability in FLUENT. Figure 9.2.1 depicts an example of a flow in a rotating reference frame, and illustrates the coordinate transformation from the stationary frame to the rotating frame.

Applications Involving a Rotating Reference Frame Several examples of problems that can be modeled using a rotating reference frame are depicted in Figure 9.2.2. The applications illustrated here include: • Impellers in mixing tanks • Rotating turbomachinery blades (centrifugal impellers, axial fans, etc.) • Flows in rotating passages (e.g., cooling ducts, secondary air flow circuits, and disk cavities in rotating equipment) When such problems are defined in a rotating reference frame, the rotating boundaries become stationary relative to the rotating frame, since they are moving at the same speed as the reference frame.

Modeling Rotor-Stator Interaction As mentioned in Section 9.1, rotor-stator interaction problems (as illustrated in Figure 9.2.3) cannot be modeled by a simple coordinate transformation to a rotating reference frame. In FLUENT, rotor-stator interaction must be treated by applying the MRF, mixing plane, or sliding mesh approach. These approaches are described in detail in Sections 9.3, 9.4, and 9.5.

9.2.2

Equations for a Rotating Reference Frame

When the equations of motion (see Section 8.2) are solved in a rotating frame of reference, the acceleration of the fluid is augmented by additional terms that appear in the


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Stationary

Rotating at speed Ω y Ω x

(a) Original Reference Frame

Rotating at speed -Ω

-Ω Stationary

y1

x1

(b) Rotating Reference Frame

Figure 9.2.1: Transforming Coordinates to a Rotating Reference Frame

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Ω

z

y x

(a) Rotating Impeller in a Mixing Tank Ω

y x

(b) Centrifugal Impeller Blades

Figure 9.2.2: Applications That Can Be Modeled by FLUENT in a Rotating Reference Frame


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Ω

y

z x

(c) Cooling Passages in a Spinning Rotor

Ω

x z y

(d) Axial Impeller Blades

Figure 9.2.2: Applications That Can Be Modeled by FLUENT in a Rotating Reference Frame

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Stationary

Rotating

Ω

(a) 2D Rotor-Stator Interaction

Stationary baffles Ω

Rotating impeller

(b) Rotating Impeller in a Baffled Tank

Figure 9.2.3: Problems That Require MRF, Mixing Plane, or Sliding Meshes


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momentum equations [11]. FLUENT allows you to solve rotating frame problems using either the absolute velocity, ~v , or the relative velocity, ~vr , as the dependent variable. The two velocities are related by the following equation: ~ × ~r) ~vr = ~v − (Ω

(9.2-1)

~ is the angular velocity vector (that is, the angular velocity of the rotating frame) Here, Ω and ~r is the position vector in the rotating frame. The left-hand side of the momentum equations appears as follows for an inertial reference frame: ∂ (ρ~v ) + ∇ · (ρ~v~v ) ∂t

(9.2-2)

For a rotating reference frame, the left-hand side written in terms of absolute velocities becomes ∂ ~ × ~v ) (ρ~v ) + ∇ · (ρ~vr~v ) + ρ(Ω ∂t

(9.2-3)

In terms of relative velocities the left-hand side is given by ~ ∂ ~ × ~vr + Ω ~ ×Ω ~ × ~r) + ρ ∂ Ω × ~r (ρ~vr ) + ∇ · (ρ~vr~vr ) + ρ(2Ω ∂t ∂t

(9.2-4) ~

~ × ~vr ) is the Coriolis force. Note that FLUENT neglects the ρ ∂ Ω × ~r term, where ρ(2Ω ∂t so it cannot accurately model a time-varying angular velocity using the relative velocity formulation. For flows in rotating domains, the equation for conservation of mass, or continuity equation, can be written as follows for both the absolute and the relative velocity formulations: ∂ρ + ∇ · (ρ~vr ) = Sm ∂t

9.2.3

(9.2-5)

Grid Setup for a Single Rotating Reference Frame

It is important to remember the following coordinate-system constraints when you are setting up a problem involving a rotating reference frame: • For 2D problems, the axis of rotation must be parallel to the z axis. • For 2D axisymmetric problems, the axis of rotation must be the x axis.

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• For 3D geometries, you should generate the mesh with a specific rotational axis in mind for the rotating cell zone. Usually it is convenient to use the x, y, or z axis, but FLUENT can accommodate arbitrary rotational axes.

9.2.4

Problem Setup for a Single Rotating Reference Frame

When you want to model a problem involving a single rotating reference frame, you will need to complete the following modeling inputs. (Only those steps relevant specifically to the setup of a rotating reference frame problem are listed here. You will need to set up the rest of the problem as usual.) 1. Select the Velocity Formulation to be used in the Solver panel: either Relative or Absolute. (See Section 9.2.5 for details.) Define −→ Models −→Solver... (Note that this step is irrelevant if you are using one of the coupled solvers; these solvers always use an absolute velocity formulation.) 2. For each cell zone in the domain, specify the angular velocity (Ω) of the reference frame and the axis about which it rotates. Define −→Boundary Conditions... (a) In the Fluid panel or Solid panel, specify the Rotation-Axis Origin and RotationAxis Direction to define the axis of rotation. (b) Also in the Fluid or Solid panel, select Moving Reference Frame in the Motion Type drop-down list and then set the Speed under Rotational Velocity in the expanded portion of the panel. Details about these inputs are presented in Section 6.17.1 for fluid zones, and in Section 6.18.1 for solid zones. 3. Define the velocity boundary conditions at walls. You can choose to define either an absolute velocity or a velocity relative to the moving reference frame (i.e., relative to the velocity of the adjacent cell zone specified in step 2). If the wall is moving at the speed of the rotating frame (and hence stationary in the rotating frame), it is convenient to specify a relative angular velocity of zero. Likewise, a wall that is stationary in the non-rotating frame of reference should be given a velocity of zero in the absolute reference frame. Specifying the wall velocities in this manner obviates the need to modify these inputs later if a change is made in the rotational velocity of the fluid zone. Details about these inputs are presented in Section 6.13.1.


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4. Define the velocity at any velocity inlets and the flow direction and total pressure at any pressure inlets. For velocity inlets, you can choose to define either absolute velocities or velocities relative to the motion of the adjacent cell zone (specified in step 2). For pressure inlets, the specification of the flow direction and total pressure will be relative or absolute, depending on the velocity formulation you selected in step 1. See Section 9.2.5 for details. (If you use one of the coupled solution algorithms, the specification is always in the absolute frame.) Details about these inputs are presented in Sections 6.3.1 and 6.4.1.

9.2.5

Choosing the Relative or Absolute Velocity Formulation

The absolute velocity formulation is preferred in applications where the flow in most of the domain is not rotating (e.g., a fan in a large room). The relative velocity formulation is appropriate when most of the fluid in the domain is rotating, as in the case of a large impeller in a mixing tank. For most applications, either formulation may be used.

! When one of the coupled solution algorithms is used, the absolute formulation is always used; the relative velocity formulation is not available in the coupled solvers. For velocity inlets and walls, you may specify velocity in either the absolute or the relative frame, regardless of whether the absolute or relative velocity is used in the computation. For pressure boundary conditions, however, FLUENT imposes several restrictions on how total pressure and flow direction are specified in rotating reference frames. The total pressure and flow direction at a pressure inlet must be specified in the absolute frame if the absolute velocity formulation is used. For calculations using relative velocities, the total pressure and flow direction must be specified with respect to the rotating frame. For pressure outlets, the specified static pressure is independent of frame. When there is backflow at a pressure outlet, however, the specified static pressure is used as the total pressure. For calculations using absolute velocities, the specified static pressure is used as the total pressure in the absolute frame; for the relative velocity formulation, the specified static pressure is assumed to be the total pressure in the relative frame. As for flow direction in reverse flows, FLUENT assumes the absolute velocity to be normal to the pressure outlet for the absolute velocity formulation; for the relative velocity formulation, it is the relative velocity that is assumed to be normal to the pressure outlet.

9.2.6

Solution Strategies for a Rotating Reference Frame

The difficulties associated with solving flows in rotating reference frames are similar to those discussed in Section 8.4.5 for axisymmetric swirling or rotating flows. The primary issue you must confront is the high degree of coupling between the momentum equations when the influence of the rotational terms is large. A high degree of rotation introduces a large radial pressure gradient which drives the flow in the axial and radial directions,

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thereby setting up a distribution of the swirl or rotation in the field. This coupling may lead to instabilities in the solution process, and hence require special solution techniques to obtain a converged solution. Some techniques that may be beneficial include the following: • (Segregated solver only) Consider switching the frame in which velocities are solved by changing the velocity formulation setting in the Solver panel. (See Section 9.2.5 for details.) • (Segregated solver only) Use the PRESTO! scheme (enabled in the Solution Controls panel), which is well-suited for the steep pressure gradients involved in rotating flows. • Ensure that the mesh is sufficiently refined to resolve large gradients in pressure and swirl velocity. • (Segregated solver only) Reduce the under-relaxation factors for the velocities, perhaps to 0.3–0.5 or lower, if necessary. • Begin the calculations using a low rotational speed, increasing the rotational speed gradually in order to reach the final desired operating condition (see below). See Chapter 24 for details on the procedures used to make these changes to the solution parameters.

Gradual Increase of the Rotational Speed to Improve Solution Stability Because the rotation of the reference frame and the rotation defined via boundary conditions can lead to large complex forces in the flow, your FLUENT calculations may be less stable as the speed of rotation (and hence the magnitude of these forces) increases. One of the most effective controls you can exert on the solution is to start with a low rotational speed and then slowly increase the rotation up to the desired level. The procedure you use to accomplish this is as follows: 1. Set up the problem using a low rotational speed in your inputs for boundary conditions and for the angular velocity of the reference frame. The rotational speed in this first attempt might be selected as 10% of the actual operating condition. 2. Solve the problem at these conditions. 3. Save this initial solution data. 4. Modify your inputs (i.e., boundary conditions and angular velocity of the reference frame). Increase the speed of rotation, perhaps doubling it.


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5. Restart or continue the calculation using the solution data saved in Step 3 as the initial guess for the new calculation. Save the new data. 6. Continue to increment the rotational speed, following Steps 4 and 5, until you reach the desired operating condition.

9.2.7

Postprocessing for a Single Rotating Reference Frame

When you solve a problem in a rotating reference frame, you can plot or report both absolute and relative velocities. For all velocity parameters (e.g., Velocity Magnitude and Mach Number), corresponding relative values will be available for postprocessing (e.g., Relative Velocity Magnitude and Relative Mach Number). These variables are contained in the Velocity... category of the variable selection drop-down list that appears in postprocessing panels. Relative values are also available for postprocessing of total pressure, total temperature, and any other parameters that include a dynamic contribution dependent on the reference frame (e.g., Relative Total Pressure, Relative Total Temperature). When plotting velocity vectors, you can choose to plot vectors in the absolute frame (the default), or you can select Relative Velocity in the Vectors Of drop-down list in the Vectors panel to plot vectors in the rotating frame. If you plot relative velocity vectors, you might want to color the vectors by relative velocity magnitude (by choosing Relative Velocity Magnitude in the Color By list); by default they will be colored by absolute velocity magnitude. Figures 9.2.4 and 9.2.5 show absolute and relative velocity vectors in a rotating domain with a stationary outer wall.

1.29e+00 1.18e+00 1.06e+00 9.46e-01 8.31e-01 7.16e-01 6.01e-01 4.87e-01 3.72e-01 2.57e-01 1.42e-01


Figure 9.2.4: Absolute Velocity Vectors

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9.3 The Multiple Reference Frame (MRF) Model

1.81e+00 1.63e+00 1.45e+00 1.27e+00 1.09e+00 9.07e-01 7.27e-01 5.47e-01 3.67e-01 1.87e-01 7.09e-03

Velocity Vectors Colored By Relative Velocity Magnitude (m/s)

Figure 9.2.5: Relative Velocity Vectors

9.3 9.3.1

The Multiple Reference Frame (MRF) Model Overview

As mentioned in Section 9.1, FLUENT provides three approaches for modeling problems that involve both stationary and moving zones: • the multiple reference frame (MRF) model • the mixing plane model • the sliding mesh model The MRF model [159] is the simplest of the three. It is a steady-state approximation in which individual cell zones move at different rotational/translational speeds. This approach is appropriate when the flow at the boundary between these zones is nearly uniform (“mixed out”). While the multiple reference frame approach is clearly an approximation, it can provide a reasonable model of the time-averaged flow for many applications. For example, the MRF model can be used for a turbomachinery application in which rotor-stator interaction is relatively weak. In mixing tanks, since the impeller-baffle interactions are relatively weak, large-scale transient effects are not present and the MRF model can be used. In general, any problems where transients due to rotor-stator interaction are small are candidates for the MRF model.


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Another potential use of the MRF model is to compute a flow field that can be used as an initial condition for a transient sliding mesh calculation. This eliminates the need for a startup calculation. The multiple reference frame model should not be used, however, if it is necessary to actually simulate the transients that may occur in strong impeller-baffle interactions. For such cases, the sliding mesh model (see Section 9.5) should be used.

Examples For a mixing tank with a single impeller, you can define a rotating reference frame that encompasses the impeller and the flow surrounding it, and use a stationary frame for the flow outside the impeller region. An example of this configuration is illustrated in Figure 9.3.1. (The dashes denote the interface between the two reference frames.) Steadystate flow conditions are assumed at the interface between the two reference frames. That is, the velocity at the interface must be the same (in absolute terms) for each reference frame. The grid does not move.

Figure 9.3.1: Geometry with One Rotating Impeller

You can also model a problem that includes more than one rotating reference frame. Figure 9.3.2 shows a geometry that contains two rotating impellers side by side. This problem would be modeled using three reference frames: the stationary frame outside both impeller regions and two separate rotating reference frames for the two impellers. (As noted above, the dashes denote the interfaces between reference frames.)

Restrictions The following restrictions apply to the use of multiple reference frames: • Use of the realizable k- model with multiple reference frames is not recommended. • The boundaries separating a moving region from adjacent regions must be oriented such that the component of the frame velocity normal to the boundary is zero. For

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Figure 9.3.2: Geometry with Two Rotating Impellers

the example shown in Figure 9.3.1, this requires the dashed boundary to be circular (not square or any other shape). For a translationally moving frame, the moving zone’s boundaries must be parallel to the translational velocity vector. • Strictly speaking, the use of multiple reference frames is meaningful only for steady flow. However, FLUENT will allow you to solve an unsteady flow when multiple reference frames are being used. In this case, unsteady terms (as described in Section 24.2.8) are added to all the governing transport equations. You should carefully consider whether this will yield meaningful results for your application, because, for unsteady flows, a sliding mesh calculation will generally yield more meaningful results than an MRF calculation. • Particle trajectories and pathlines drawn by FLUENT use the velocity relative to the cell zone motion. For massless particles, the resulting pathlines follow the streamlines based on relative velocity and are meaningful. For particles with mass, however, the particle tracks displayed are meaningless. Similarly, coupled discretephase calculations are meaningless. An alternative approach for particle tracking and coupled discrete-phase calculations with multiple reference frames is to track particles based on absolute velocity instead of relative velocity. To make this change, use the define/models/dpm/ tracking/track-in-absolute-frame text command. Note, that the results may strongly depend on the location of walls inside the multiple reference frame. The particle injection velocities (specified in the Set Injection Properties panel) are defined relative to the frame of reference in which the particles are tracked. By default, the injection velocities are specified relative to the local reference frame. If you enable the track-in-absolute-frame option, the injection velocities are specified relative to the absolute frame.


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• You cannot accurately model axisymmetric swirl in the presence of multiple reference frames using the relative velocity formulation. This is because the current implementation does not apply the transformation used in Equation 9.3-3 to the swirl velocity derivatives. • Translational and rotational velocities are assumed to be constant (time varying ω, vt are not allowed).

9.3.2

The MRF Formulation

The MRF formulation will depend on the velocity formulation being used.

Relative Velocity Formulation In FLUENT’s implementation of the multiple reference frame feature, the calculation domain is divided into subdomains, each of which may be rotating/translating with respect to the laboratory (inertial) frame. The governing equations in each subdomain are written with respect to that subdomain’s reference frame. Thus, the flow in stationary and translating subdomains is governed by the equations in Section 8.2, while the flow in rotating subdomains is governed by the equations presented in Section 9.2.2. At the boundary between two subdomains, the diffusion and other terms in the governing equations in one subdomain require values for the velocities in the adjacent subdomain. FLUENT enforces the continuity of the absolute velocity, ~v , to provide the correct neighbor values of velocity for the subdomain under consideration. (This approach differs from the mixing plane approach described in Section 9.4, where a circumferential averaging technique is used.) When the relative velocity formulation is used, velocities in each subdomain are computed relative to the motion of the subdomain. Velocities and velocity gradients are converted from a moving reference frame to the absolute inertial frame as described below. The position vector relative to the origin of the zone rotation axis is defined as ~r = ~x − ~xo

(9.3-1)

where ~x is the position in absolute Cartesian coordinates and ~xo is the origin of the zone rotation axis, as shown in Figure 9.3.3. The relative velocity in the moving reference frame can be converted to the absolute (stationary) frame of reference using the following equation: ~v = ~vr + (~ω × ~r) + ~vt

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(9.3-2)



y r Y

x xo

Z

x

moving reference frame

z

X

absolute reference frame

Figure 9.3.3: Coordinate System for Relative Velocity

where ~v is the velocity in the absolute inertial reference frame, ~vr is the velocity in the relative non-inertial reference frame, and ~vt is the translational velocity of the noninertial reference frame. Using this definition of absolute velocity, the gradient of the absolute velocity vector is given by ∇~v = ∇~vr + ∇ (~ω × ~r)

(9.3-3)

Absolute Velocity Formulation When the absolute velocity formulation is used, the governing equations in each subdomain are written with respect to that subdomain’s reference frame, but the velocities are stored in the absolute frame. Therefore no special transformation is required at the interface between two subdomains.

9.3.3

Grid Setup for Multiple Reference Frames

Two grid setup methods are available. Choose the method that is appropriate for your model, noting the restrictions in Section 9.3.1. • If the boundary between two zones that are in different reference frames is conformal (i.e., the grid node locations are identical at the boundary where the two zones meet), you can simply create the grid as usual, with all cell zones contained in the same grid file. A different cell zone should exist for each portion of the domain that is modeled in a different reference frame. Use an interior zone for the boundary between reference frames.


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• If the boundary between two zones that are in different reference frames is nonconformal (i.e., the grid node locations are not identical at the boundary where the two zones meet), follow the non-conformal grid setup procedure described in Section 5.4.3.

9.3.4

Problem Setup for Multiple Reference Frames

When you want to model a problem involving multiple reference frames, you will need to complete the following modeling inputs. (Only those steps relevant specifically to the setup of a multiple reference frame problem are listed here. You will need to set up the rest of the problem as usual.)

! The grid-setup constraints for a rotating reference frame listed in Section 9.2.3 apply to multiple reference frames as well. 1. Select the Velocity Formulation to be used in the Solver panel: either Absolute or Relative. (See Section 9.2.5 for details.) Define −→ Models −→Solver... (Note that this step is irrelevant if you are using one of the coupled solution algorithms; these algorithms always use an absolute velocity formulation.) 2. For each cell zone in the domain, specify its translational velocity and/or its angular velocity (Ω) and the axis about which it rotates. Define −→Boundary Conditions... (a) If the zone is rotating, or if you plan to specify cylindrical velocity or flowdirection components at inlets to the zone, you will need to define the axis of rotation. In the Fluid panel or Solid panel, specify the Rotation-Axis Origin and Rotation-Axis Direction. (b) Also in the Fluid or Solid panel, select Moving Reference Frame in the Motion Type drop-down list and then set the Speed under Rotational Velocity and/or the X, Y, and Z components of the Translational Velocity in the expanded portion of the panel. Details about these inputs are presented in Section 6.17.1 for fluid zones, and in Section 6.18.1 for solid zones. 3. Define the velocity boundary conditions at walls. You can choose to define either an absolute velocity or a velocity relative to the velocity of the adjacent cell zone specified in step 2. If the wall is moving at the speed of the moving frame (and hence stationary relative to the moving frame), it is convenient to specify a relative angular velocity of zero. Likewise, a wall that is stationary in the non-moving frame of reference should

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be given a velocity of zero in the absolute reference frame. Specifying the wall velocities in this manner obviates the need to modify these inputs later if a change is made in the rotational velocity of the fluid zone. An example for which you would specify a relative velocity is as follows: If an impeller is defined as wall-3 and the fluid region within the impeller’s radius is defined as fluid-5, you would need to specify the angular velocity and axis of rotation for fluid-5 and then assign wall-3 a relative velocity of 0. If you later wanted to model a different angular velocity for the impeller, you would need to change only the angular velocity of the fluid region; you would not need to modify the wall velocity conditions. Details about these inputs are presented in Section 6.13.1. 4. Define the velocity at any velocity inlets and the flow direction and total pressure at any pressure inlets. For velocity inlets, you can choose to define either absolute velocities or velocities relative to the motion of the adjacent cell zone (specified in step 2). For pressure inlets, the specification of the flow direction and total pressure will be relative or absolute, depending on the velocity formulation you selected in step 1. See Section 9.2.5 for details. (If you use one of the coupled solution algorithms, the specification is always in the absolute frame.) Details about these inputs are presented in Sections 6.3.1 and 6.4.1.

9.3.5

Solution Strategies for Multiple Reference Frames

No special solution strategies are necessary for translating reference frames. For multiple rotating reference frames, follow the guidelines presented in Section 9.2.6 for a single rotating reference frame.

9.3.6

Postprocessing for Multiple Reference Frames

When you solve a problem in multiple reference frames, you can plot or report both absolute and relative velocities. For all velocity parameters (e.g., Velocity Magnitude and Mach Number), corresponding relative values will be available for postprocessing (e.g., Relative Velocity Magnitude and Relative Mach Number). These variables are contained in the Velocity... category of the variable selection drop-down list that appears in postprocessing panels. Relative values are also available for postprocessing of total pressure, total temperature, and any other parameters that include a dynamic contribution dependent on the reference frame (e.g., Relative Total Pressure, Relative Total Temperature).

! Relative velocities are relative to the translational/rotational velocity of the “reference zone” (specified in the Reference Values panel). The velocity of the reference zone is the velocity defined in the Fluid panel for that zone. When plotting velocity vectors, you can choose to plot vectors in the absolute frame (the default), or you can select Relative Velocity in the Vectors Of drop-down list in the Vectors


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panel to plot vectors relative to the translational/rotational velocity of the “reference zone” (specified in the Reference Values panel). If you plot relative velocity vectors, you might want to color the vectors by relative velocity magnitude (by choosing Relative Velocity Magnitude in the Color By list); by default they will be colored by absolute velocity magnitude. You can also generate a plot of circumferential averages in FLUENT. This allows you to find the average value of a quantity at several different radial or axial positions in your model. FLUENT computes the average of the quantity over a specified circumferential area, and then plots the average against the radial or axial coordinate. For more information on generating XY plots of circumferential averages, see Section 27.8.4.

9.4 9.4.1

The Mixing Plane Model Overview and Limitations

The mixing plane model in FLUENT provides an alternative to the multiple reference frame and sliding mesh models for simulating flow through domains with one or more regions in relative motion. This section provides a brief overview of the model and a list of its limitations.

Overview As discussed in Section 9.3.1, the MRF model is applicable when the flow at the boundary between adjacent zones that move at different speeds is nearly uniform (“mixed out”). If the flow at this boundary is not uniform, the MRF model may not provide a physically meaningful solution. The sliding mesh model (see Section 9.5) may be appropriate for such cases, but in many situations it is not practical to employ a sliding mesh. For example, in a multistage turbomachine, if the number of blades is different for each blade row, a large number of blade passages is required in order to maintain circumferential periodicity. Moreover, sliding mesh calculations are necessarily unsteady, and thus require significantly more computation to achieve a final, time-periodic solution. For situations where using the sliding mesh model is not feasible, the mixing plane model can be a cost-effective alternative. In the mixing plane approach, each fluid zone is treated as a steady-state problem. Flow-field data from adjacent zones are passed as boundary conditions that are spatially averaged or “mixed” at the mixing plane interface. This mixing removes any unsteadiness that would arise due to circumferential variations in the passage-to-passage flow field (e.g., wakes, shock waves, separated flow), thus yielding a steady-state result. Despite the simplifications inherent in the mixing plane model, the resulting solutions can provide reasonable approximations of the time-averaged flow field.

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9.4 The Mixing Plane Model

Limitations Note the following limitations of the mixing plane model: • The mixing plane model requires the use of the absolute velocity formulation; you cannot use the relative velocity formulation with the mixing plane model. • The LES turbulence model cannot be used with the mixing plane model. • The models for species transport and combustion cannot be used with the mixing plane model. • The general multiphase models (VOF, mixture, and Eulerian) cannot be used with the mixing plane model. • The discrete phase model cannot be used with the mixing plane model for coupled flows. Non-coupled computations can be done, but you should note that the particles leave the domain of the mixing plane.

9.4.2

Mixing Plane Theory

Rotor and Stator Domains Consider the turbomachine stages shown schematically in Figures 9.4.1 and 9.4.2. Figure 9.4.1 shows a constant radial plane within a single stage of an axial machine, while Figure 9.4.2 shows a constant θ plane within a mixed-flow device. In each case, the stage consists of two flow domains: the rotor domain, which is rotating at a prescribed angular velocity, followed by the stator domain, which is stationary. The order of the rotor and stator is arbitrary (that is, a situation where the rotor is downstream of the stator is equally valid). In a numerical simulation, each domain will be represented by a separate mesh. The flow information between these domains will be coupled at the mixing plane interface (as shown in Figures 9.4.1 and 9.4.2) using the mixing plane model. Note that you may couple any number of fluid zones in this manner; for example, four blade passages can be coupled using three mixing planes.

! Note that the stator and rotor meshes do not have to be conformal; that is, the nodes on the stator exit boundary do not have to match the nodes on the rotor inlet boundary. In addition, the meshes can be of different types (e.g., the stator can have a hexahedral mesh while the rotor has a tetrahedral mesh).


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rotor

stator

rotor outlet: ps α r α t α z

stator inlet: p0 α r αt α z k ε

Rθ x

mixing plane interface

Figure 9.4.1: Axial Rotor-Stator Interaction (Schematic Illustrating the Mixing Plane Concept)

stator

stator inlet: p α α α k ε 0 r t z

mixing plane r

interface x

rotor outlet: p α α α s r t z rotor

Ω

Figure 9.4.2: Radial Rotor-Stator Interaction (Schematic Illustrating the Mixing Plane Concept)

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The Mixing Plane Concept The essential idea behind the mixing plane concept is that each fluid zone is solved as a steady-state problem. At some prescribed iteration interval, the flow data at the mixing plane interface are averaged in the circumferential direction on both the stator outlet and the rotor inlet boundaries. The FLUENT implementation uses area-weighted averages. By performing circumferential averages at specified radial or axial stations, “profiles” of flow properties can be defined. These profiles—which will be functions of either the axial or the radial coordinate, depending on the orientation of the mixing plane—are then used to update boundary conditions along the two zones of the mixing plane interface. In the examples shown in Figures 9.4.1 and 9.4.2, profiles of averaged total pressure (p0 ), direction cosines of the local flow angles in the radial, tangential, and axial directions (αr , αt , αz ), total temperature (T0 ), turbulence kinetic energy (k), and turbulence dissipation rate () are computed at the rotor exit and used to update boundary conditions at the stator inlet. Likewise, a profile of static pressure (ps ), direction cosines of the local flow angles in the radial, tangential, and axial directions (αr , αt , αz ), are computed at the stator inlet and used as a boundary condition on the rotor exit. Passing profiles in the manner described above assumes specific boundary condition types have been defined at the mixing plane interface. The coupling of an upstream outlet boundary zone with a downstream inlet boundary zone is called a “mixing plane pair”. In order to create mixing plane pairs in FLUENT, the boundary zones must be of the following types: upstream downstream pressure outlet pressure inlet pressure outlet velocity inlet pressure outlet mass flow inlet Specific instructions for setting up mixing planes are provided in Section 9.4.3.

FLUENT’s Mixing Plane Algorithm FLUENT’s basic mixing plane algorithm can now be described: 1. Update the flow field solutions in the stator and rotor domains. 2. Average the flow properties at the stator exit and rotor inlet boundaries, obtaining profiles for use in updating boundary conditions. 3. Pass the profiles to the boundary condition inputs required for the stator exit and rotor inlet. 4. Repeat steps 1–3 until convergence.


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! Note that it may be desirable to under-relax the changes in boundary condition values in order to prevent divergence of the solution (especially early in the computation). FLUENT allows you to control the under-relaxation of the mixing plane variables.

Mass Conservation Note that the algorithm described above will not rigorously conserve mass flow across the mixing plane if it is represented by a pressure inlet and pressure outlet mixing plane pair. If you use a mass flow inlet and pressure outlet pair instead, FLUENT will force mass conservation across the mixing plane. The basic technique consists of computing the mass flow rate across the upstream zone (pressure outlet) and adjusting the mass flux profile applied at the mass flow inlet such that the downstream mass flow matches the upstream mass flow. This adjustment occurs at every iteration, thus ensuring rigorous conservation of mass flow throughout the course of the calculation.

! Note that, since mass flow is being fixed in this case, there will be a jump in total pressure across the mixing plane. The magnitude of this jump is usually small compared with total pressure variations elsewhere in the flow field.

Swirl Conservation By default, FLUENT does not conserve swirl across the mixing plane. For applications such as torque converters, where the sum of the torques acting on the components should be zero, enforcing swirl conservation across the mixing plane is essential, and is available in FLUENT as a modeling option. Ensuring conservation of swirl is important because, otherwise, sources or sinks of tangential momentum will be present at the mixing plane interface. Consider a control volume containing a stationary or rotating component (e.g., a pump impeller or turbine vane). Using the moment of momentum equation from fluid mechanics, it can be shown that for steady flow, T =

ZZ

S

rvθ ρ~v · n ˆ dS

(9.4-1)

where T is the torque of the fluid acting on the component, r is the radial distance from the axis of rotation, vθ is the absolute tangential velocity, ~v is the total absolute velocity, and S is the boundary surface. (The product rvθ is referred to as swirl.) For a circumferentially periodic domain, with well-defined inlet and outlet boundaries, Equation 9.4-1 becomes T =

ZZ

outlet

rvθ ρ~v · n ˆ dS +

ZZ

inlet


(9.4-2)

where inlet and outlet denote the inlet and outlet boundary surfaces.

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Now consider the mixing plane interface to have a finite streamwise thickness. Applying Equation 9.4-2 to this zone and noting that, in the limit as the thickness shrinks to zero, the torque should vanish, the equation becomes ZZ

downstream

rvθ ρ~v · n ˆ dS =

ZZ

upstream


(9.4-3)

where upstream and downstream denote the upstream and downstream sides of the mixing plane interface. Note that Equation 9.4-3 applies to the full area (360 degrees) at the mixing plane interface. Equation 9.4-3 provides a rational means of determining the tangential velocity component. That is, FLUENT computes a profile of tangential velocity and then uniformly adjusts the profile such that the swirl integral is satisfied. Note that interpolating the tangential (and radial) velocity component profiles at the mixing plane does not affect mass conservation because these velocity components are orthogonal to the face-normal velocity used in computing the mass flux.

Total Enthalpy Conservation By default, FLUENT does not conserve total enthalpy across the mixing plane. For some applications, total enthalpy conservation across the mixing plane is very desirable, because global parameters such as efficiency are directly related to the change in total enthalpy across a blade row or stage. This is available in FLUENT as a modeling option. The procedure for ensuring conservation of total enthalpy simply involves adjusting the downstream total temperature profile such that the integrated total enthalpy matches the upstream integrated total enthalpy.

9.4.3

Problem Setup for a Mixing Plane Model

The model inputs for mixing planes are presented in this section. Only those steps relevant specifically to the setup of a mixing plane problem are listed here. You will need to set up the rest of the problem as usual. Note that the use of wall and periodic boundaries in a mixing plane model is consistent with their use when the model is not active. 1. Select the (default) absolute velocity formulation in the Solver panel. Define −→ Models −→Solver... 2. For each cell zone in the domain, specify its angular velocity (Ω) and the axis about which it rotates. Define −→Boundary Conditions...


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(a) If the zone is rotating, or if you plan to specify cylindrical-velocity or flowdirection components at inlets to the zone, you will need to define the axis of rotation. In the Fluid panel or Solid panel, specify the Rotation-Axis Origin and Rotation-Axis Direction. (b) Also in the Fluid or Solid panel, select Moving Reference Frame in the Motion Type drop-down list and then set the Speed under Rotational Velocity and/or the X, Y, and Z components of the Translational Velocity in the expanded portion of the panel. Details about these inputs are presented in Section 6.17.1 for fluid zones, and in Section 6.18.1 for solid zones.

!

It is important to define the axis of rotation for the cell zones on both sides of the mixing plane interface, including the stationary zone. 3. Define the velocity boundary conditions at walls. You can choose to define either an absolute velocity or a velocity relative to the velocity of the adjacent cell zone specified in step 2. If the wall is moving at the speed of the moving frame (and hence stationary relative to the moving frame), it is convenient to specify a relative angular velocity of zero. Likewise, a wall that is stationary in the non-moving frame of reference should be given a velocity of zero in the absolute reference frame. Specifying the wall velocities in this manner obviates the need to modify these inputs later if a change is made in the rotational velocity of the fluid zone. An example for which you would specify a relative velocity is as follows: If an impeller is defined as wall-3 and the fluid region within the impeller’s radius is defined as fluid-5, you would need to specify the angular velocity and axis of rotation for fluid-5 and then assign wall-3 a relative velocity of 0. If you later wanted to model a different angular velocity for the impeller, you would need to change only the angular velocity of the fluid region; you would not need to modify the wall velocity conditions. Details about these inputs are presented in Section 6.13.1. 4. Define the velocity at any velocity inlets and the flow direction and total pressure at any pressure inlets or mass flow inlets. For velocity inlets, you can choose to define either absolute velocities or velocities relative to the motion of the adjacent cell zone (specified in step 2). For pressure inlets and mass flow inlets, the specification of the flow direction and total pressure will always be absolute, because the absolute velocity formulation is always used for mixing plane calculations. For a mass flow inlet, you do not need to specify the mass flow rate or mass flux. FLUENT will automatically select the Mass Flux with Average Mass Flux specification method and set the correct values when you create the mixing plane, as described in Section 6.5.1. Details about these inputs are presented in Sections 6.3.1, 6.4.1, and 6.5.1.

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!

Note that the outlet boundary zone at the mixing plane interface must be defined as a pressure outlet, and the inlet boundary zone at the mixing plane interface must be defined as a velocity inlet (incompressible flow only), a pressure inlet, or a mass flow inlet. The overall inlet and exit boundary conditions can be any suitable combination permitted by the solver (e.g., velocity inlet, pressure inlet, or mass flow inlet; pressure outlet). Keep in mind, however, that if mass conservation across the mixing plane is important, you need to use a mass flow inlet as the downstream boundary; mass conservation is not maintained across the mixing plane when you use a velocity inlet or pressure inlet. 5. Define the mixing planes in the Mixing Planes panel (Figure 9.4.3). Define −→Mixing Planes...

Figure 9.4.3: The Mixing Planes Panel

(a) Specify the two zones that comprise the mixing plane by selecting an upstream zone in the Upstream Zone list and a downstream zone in the Downstream Zone list. It is essential that the correct pairs be chosen from these lists (i.e., that the boundary zones selected lie on the mixing plane interface). You can check this by displaying the grid. Display −→Grid... (b) (3D only) Indicate the geometry of the mixing plane interface by choosing one of the options under Mixing Plane Geometry. A Radial geometry signifies that information at the mixing plane interface is to be circumferentially averaged into profiles that vary in the radial direction, e.g., p(r), T (r). This is the case for axial-flow machines, for example.


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An Axial geometry signifies that circumferentially averaged profiles are to be constructed that vary in the axial direction, e.g., p(x), T (x). This is the situation for a radial-flow device.

!

Note that the radial direction is normal to the rotation axis for the fluid zone and the axial direction is parallel to the rotation axis. (c) (3D only) Set the number of Interpolation Points. This is the number of radial or axial locations used in constructing the boundary profiles for circumferential averaging. You should choose a number that approximately corresponds to the resolution of the surface mesh in the radial or axial direction. Note that while you can use more points if you wish, the resolution of the boundary profile will only be as fine as the resolution of the surface mesh itself. In 2D the flow data are averaged over the entire interface to create a profile consisting of a single data point. For this reason you do not need to set the number of Interpolation Points or select a Mixing Plane Geometry in 2D. (d) Set the Global Parameters for the mixing plane. i. Set the Under-Relaxation parameter. It is sometimes desirable to underrelax the changes in boundary values at mixing planes as these may change very rapidly during the early iterations of the solution and cause the calculation to diverge. The changes can be relaxed by specifying an underrelaxation less than 1. The new boundary profile values are then computed using φnew = φold + α(φcalculated − φold )

(9.4-4)

where α is the under-relaxation factor. Once the flow field is established, the value of α can be increased. ii. Click Apply to set the Global Parameters. If the Default button is visible to the right of the Apply button, clicking the Default button will return Global Parameters back to their default values. The Default button will then change to be a Reset button. Clicking the Reset button will change the Global Parameters back to the values that were last applied. (e) Click Create to create a new mixing plane. FLUENT will name the mixing plane by combining the names of the zones selected as the Upstream Zone and Downstream Zone and enter the new mixing plane in the Mixing Plane list. If you create an incorrect mixing plane, you can select it in the Mixing Plane list and click the Delete button to delete it.

Modeling Options There are two options available for use with the mixing plane model: a fixed pressure level for incompressible flows, and the swirl conservation described in Section 9.4.2.

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Fixing the Pressure Level for an Incompressible Flow For certain turbomachinery configurations, such as a torque converter, there is no fixedpressure boundary when the mixing plane model is used. The mixing plane model is usually used to model the three interfaces that connect the components of the torque converter. In this configuration, the pressure is no longer fixed. As a result, the pressure may float unbounded, making it difficult to obtain a converged solution. To resolve this problem, FLUENT offers an option for fixing the pressure level. When this option is enabled, FLUENT will adjust the gauge pressure field after each iteration by subtracting from it the pressure value in the cell closest to the Reference Pressure Location in the Operating Conditions panel.

! This option is available only for incompressible flows calculated using the segregated solver. To enable the fixed pressure option, use the fix-pressure-level text command: define −→ mixing-planes −→ set −→fix-pressure-level Conserving Swirl Across the Mixing Plane As discussed in Section 9.4.2, conservation of swirl is important for applications such as torque converters. If you want to enable swirl conservation across the mixing plane, you can use the commands in the conserve-swirl text menu: define −→ mixing-planes −→ set −→conserve-swirl To turn on swirl conservation, use the enable? text command. Once the option is turned on, you can ask the solver to report information about the swirl conservation during the calculation. If you turn on verbosity?, FLUENT will report for every iteration the zone ID for the zone on which the swirl conservation is active, the upstream and downstream swirl integration per zone area, and the ratio of upstream to downstream swirl integration before and after the correction. To obtain a report of the swirl integration at every pressure inlet, pressure outlet, velocity inlet, and mass flow inlet in the domain, use the report-swirl-integration command. You can use this information to determine the torque acting on each component of the turbomachinery according to Equation 9.4-2. Conserving Total Enthalpy Across the Mixing Plane One of the options available in the mixing plane model is to conserve total enthalpy across the mixing plane. This is a desirable feature because global parameters such as efficiency are directly related to the change in total enthalpy across a blade row or stage. The procedure for ensuring conservation of total enthalpy simply involves adjusting the downstream total temperature profile such that the integrated total enthalpy matches


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the upstream integrated total enthalpy. If you want to enable total enthalpy conservation, you can use the commands in the conserve-total-enthalpy text menu: define −→ mixing-planes −→ set −→conserve-total-enthalpy To turn on total enthalpy conservation, use the enable? text command. Once the option is turned on, you can ask the solver to report information about the total enthalpy conservation during the calculation. If you turn on verbosity?, FLUENT will report at every iteration the zone ID for the zone on which the total enthalpy conservation is active, the upstream and downstream heat flux, and the ratio of upstream to downstream heat flux.

9.4.4

Solution Strategies for Problems with Mixing Planes

It should be emphasized that the mixing plane model is a reasonable approximation so long as there is not significant reverse flow in the vicinity of the mixing plane. If significant reverse flow occurs, the mixing plane will not be a satisfactory model of the actual flow. In a numerical simulation, reverse flow often occurs during the early stages of the computation even though the flow at convergence is not reversed. Therefore, it is helpful in these situations to first obtain a provisional solution using fixed conditions at the rotor-stator interface. The mixing plane model can then be enabled and the solution run to convergence. Under-relaxing the changes in the mixing plane boundary values can also help in troublesome situations. In many cases, setting the under-relaxation factor to a value less than one can be helpful. Once the flow field is established, you can gradually increase the under-relaxation factor.

9.4.5

Postprocessing for the Mixing Plane Model

When you solve a problem using the mixing plane model, you can plot or report both absolute and relative velocities. For all velocity parameters (e.g., Velocity Magnitude and Mach Number), corresponding relative values will be available for postprocessing (e.g., Relative Velocity Magnitude and Relative Mach Number). These variables are contained in the Velocity... category of the variable selection drop-down list that appears in postprocessing panels. Relative values are also available for postprocessing of total pressure, total temperature, and any other parameters that include a dynamic contribution dependent on the reference frame (e.g., Relative Total Pressure, Relative Total Temperature).

! Relative velocities are relative to the translational/rotational velocity of the “reference zone” (specified in the Reference Values panel). The velocity of the reference zone is the velocity defined in the Fluid panel for that zone. When plotting velocity vectors, you can choose to plot vectors in the absolute frame (the default), or you can select Relative Velocity in the Vectors Of drop-down list in the Vectors

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9.5 Sliding Meshes

panel to plot vectors relative to the translational/rotational velocity of the “reference zone” (specified in the Reference Values panel). If you plot relative velocity vectors, you might want to color the vectors by relative velocity magnitude (by choosing Relative Velocity Magnitude in the Color By list); by default they will be colored by absolute velocity magnitude. See also Section 27.9 for details about turbomachinery-specific postprocessing features.

9.5 9.5.1

Sliding Meshes Overview

When a time-accurate solution for rotor-stator interaction (rather than a time-averaged solution) is desired, you must use the sliding mesh model to compute the unsteady flow field. As mentioned in Section 9.1, the sliding mesh model is the most accurate method for simulating flows in multiple moving reference frames, but also the most computationally demanding. Most often, the unsteady solution that is sought in a sliding mesh simulation is timeperiodic. That is, the unsteady solution repeats with a period related to the speeds of the moving domains. However, you can model other types of transients, including translating sliding mesh zones (e.g., two cars or trains passing in a tunnel, as shown in Figure 9.5.1).

Figure 9.5.1: Two Passing Trains in a Tunnel

Note that for flow situations where there is no interaction between stationary and moving parts (i.e., when there is only a rotor), the computational domain can be made stationary by using a rotating reference frame. (See Section 9.2 for details.) When transient rotorstator interaction is desired (as in the examples in Figures 9.5.2 and 9.5.3), you must use sliding meshes. If you are interested in a steady approximation of the interaction, you may use the multiple reference frame model or the mixing plane model, as described in Sections 9.3 and 9.4.

The Sliding Mesh Technique In the sliding mesh technique two or more cell zones are used. (If you generate the mesh in each zone independently, you will need to merge the mesh files prior to starting the calculation, as described in Section 5.3.10.) Each cell zone is bounded by at least one


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stationary vanes rotating blades

flow

direction of motion

Figure 9.5.2: Rotor-Stator Interaction (Stationary Guide Vanes with Rotating Blades)

Figure 9.5.3: Blower

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9.5 Sliding Meshes

“interface zone” where it meets the opposing cell zone. The interface zones of adjacent cell zones are associated with one another to form a “grid interface.” The two cell zones will move relative to each other along the grid interface.

! Note that the grid interface must be positioned so that it has fluid cells on both sides. For example, the grid interface for the geometry shown in Figure 9.5.2 must lie in the fluid region between the rotor and stator; it cannot be on the edge of any part of the rotor or stator. During the calculation, the cell zones slide (i.e., rotate or translate) relative to one another along the grid interface in discrete steps. Figures 9.5.4 and 9.5.5 show the initial position of two grids and their positions after some translation has occurred.

Figure 9.5.4: Initial Position of the Grids As the rotation or translation takes place, node alignment along the grid interface is not required. Since the flow is inherently unsteady, a time-dependent solution procedure is required.

Grid Interface Shapes The grid interface and the associated interface zones can be any shape, provided that the two interface boundaries are based on the same geometry. Figure 9.5.6 shows an example with a linear grid interface and Figure 9.5.7 shows a circular-arc grid interface. (In both figures, the grid interface is designated by a dashed line.) If Figure 9.5.6 were extruded to 3D, the resulting sliding interface would be a planar rectangle; if Figure 9.5.7 were extruded to 3D, the resulting interface would be a cylinder.


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Figure 9.5.5: Rotor Mesh Slides with Respect to the Stator

Figure 9.5.6: 2D Linear Grid Interface

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9.5 Sliding Meshes

Figure 9.5.7: 2D Circular-Arc Grid Interface

Figure 9.5.8 shows an example that would use a conical grid interface. (The slanted, dashed lines represent the intersection of the conical interface with a 2D plane.) For an axial rotor/stator configuration, in which the rotating and stationary parts are aligned axially instead of being concentric (see Figure 9.5.9), the interface will be a planar sector. This planar sector is a cross-section of the domain perpendicular to the axis of rotation at a position along the axis between the rotor and the stator.

9.5.2

Sliding Mesh Theory

As discussed in Section 9.5.1, the sliding mesh model allows adjacent grids to slide relative to one another. In doing so, the grid faces do not need to be aligned on the grid interface. This situation requires a means of computing the flux across the two non-conformal interface zones of each grid interface. To compute the interface flux, the intersection between the interface zones is determined at each new time step. The resulting intersection produces one interior zone (a zone with fluid cells on both sides) and one or more periodic zones. If the problem is not periodic, the intersection produces one interior zone and a pair of wall zones (which will be empty if the two interface zones intersect entirely), as shown in Figure 9.5.10. (You will need to change these wall zones to some other appropriate boundary type.) The resultant interior zone corresponds to where the two interface zones overlap; the resultant periodic zone corresponds to where they do not. The number of faces in these intersection zones will vary as the interface zones move relative to one another. Principally, fluxes across the grid interface are computed using the faces resulting from the intersection of the two


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Figure 9.5.8: 3D Conical Grid Interface

portion of domain being modeled

planar sector grid interface

Figure 9.5.9: 3D Planar-Sector Grid Interface

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9.5 Sliding Meshes

interface zones, rather than from the interface zone faces themselves. "wall" zone

interior zone

"wall" zone

Figure 9.5.10: Zones Created by Non-Periodic Interface Intersection

In the example shown in Figure 9.5.11, the interface zones are composed of faces A-B and B-C, and faces D-E and E-F. The intersection of these zones produces the faces a-d, d-b, b-e, etc. Faces produced in the region where the two cell zones overlap (d-b, b-e, and e-c) are grouped to form an interior zone, while the remaining faces (a-d and c-f) are paired up to form a periodic zone. To compute the flux across the interface into cell IV, for example, face D-E is ignored and faces d-b and b-e are used instead, bringing information into cell IV from cells I and III, respectively. cell zone 1

II

I

III A a

B b

d

interface zone 2

interface zone 1

C e

D

c

f F

E VI

IV V

cell zone 2

Figure 9.5.11: Two-Dimensional Grid Interface


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9.5.3

Setup and Solution of a Sliding Mesh Problem

Grid Requirements Before beginning the problem setup in FLUENT, be sure that the grid you have created meets the following requirements: • A different cell zone exists for each portion of the domain that is sliding at a different speed. • The grid interface must be situated such that there is no motion normal to it. • The grid interface can be any shape (including a non-planar surface, in 3D), provided that the two interface boundaries are based on the same geometry. If there are sharp features in the mesh (e.g., 90-degree angles), it is especially important that both sides of the interface closely follow that feature. • If you create a single grid with multiple cell zones, you must be sure that each cell zone has a distinct face zone on the sliding boundary. The face zones for two adjacent cell zones will have the same position and shape, but one will correspond to one cell zone and one to the other. (Note that it is also possible to create a separate grid file for each of the cell zones, and then merge them as described in Section 5.3.10.) • If you are modeling a rotor/stator geometry using periodicity, the periodic angle of the mesh around the rotor blade(s) must be the same as that of the mesh around the stationary vane(s). • All periodic zones must be correctly oriented (either rotational or translational) before you create the grid interface. • For 3D cases, if the interface is periodic, only one pair of periodic boundaries can neighbor the interface. See Section 9.5.1 for details about these restrictions and general information about how the sliding mesh model works in FLUENT.

Setting Up the Problem The steps for setting up a sliding mesh problem are listed below. (Note that this procedure includes only those steps necessary for the sliding mesh model itself; you will need to set up other models, boundary conditions, etc. as usual.) 1. Enable the appropriate option for modeling unsteady flow in the Solver panel. (See Section 24.15 for details about the unsteady modeling capabilities in FLUENT.) Define −→ Models −→Solver...

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9.5 Sliding Meshes

2. Set boundary conditions for the sliding action: Define −→Boundary Conditions... (a) Change the zone type of the interface zones of adjacent cell zones to interface in the Boundary Conditions panel. (b) In the Fluid panel or Solid panel for each moving fluid or solid zone, select Moving Mesh in the Motion Type drop-down list and set the translational and/or rotational velocity. (Note that a solid zone cannot move at a different speed than an adjacent fluid zone.)

!

Note that simultaneous translation and rotation can be modeled only if the rotation axis and the translation direction are the same (i.e., the origin is fixed). By default, the velocity of a wall is set to zero relative to the adjacent mesh’s motion. For walls bounding a moving mesh this results in a “no-slip” condition in the reference frame of the mesh. Therefore, you need not modify the wall velocity boundary conditions unless the wall is stationary in the absolute frame, and therefore moving in the relative frame. See Section 6.13.1 for details about wall motion. See Chapter 6 for details about input of boundary conditions. 3. Define the grid interfaces in the Grid Interfaces panel (Figure 9.5.12). Define −→Grid Interfaces...

Figure 9.5.12: The Grid Interfaces Panel


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(a) Enter a name for the interface in the Grid Interface field. (b) Specify the two interface zones that comprise the grid interface by selecting one in the Interface Zone 1 list and one in the Interface Zone 2 list. (The order does not matter.) (c) Set the Interface Type, if appropriate. There are two options: • Enable Periodic for periodic problems. • Enable Coupled if the interface lies between a solid zone and a fluid zone. (d) Click on Create to create a new grid interface. For all types of interfaces, FLUENT will create boundary zones for the interface (e.g., wall-9, wall-10), which will appear under Boundary Zone 1 and Boundary Zone 2. You can use the Boundary Conditions panel to change them to another zone type (e.g., pressure far-field, symmetry, pressure outlet). If you have enabled the Coupled option, FLUENT will also create wall interface zones (e.g., wall-4, wall-4-shadow), which will appear under Interface Wall Zone 1 and Interface Wall Zone 2. If you create an incorrect grid interface, you can select it in the Grid Interface list and click on the Delete button to delete it. (Any boundary zones that were created when the interface was created will also be deleted.)

! When you have completed the problem setup, you should save an initial case file so that you can easily return to the original grid position (i.e., the positions before any sliding occurs). The grid position is stored in the case file, so case files that you save at different times during the unsteady calculation will contain grids at different positions.

Solving the Problem You will begin the sliding mesh calculation by initializing the solution (as described in Section 24.13.1) and then specifying the time step size and number of time steps in the Iterate panel, as for any other unsteady calculation. (See Section 24.15 for details about time-dependent solutions. Note that if you wish to save the time step size in the initial case file, you can click Apply instead of Iterate and then save a case file before starting to iterate.) FLUENT will iterate on the current time step solution until satisfactory residual reduction is achieved, or the maximum number of iterations per time step is reached. When it advances to the next time step, the cell and wall zones will automatically be moved according to the specified translational or rotational velocities (set in step 2b above). The new interface-zone intersections will be computed automatically, and resultant interior/periodic/external boundary zones will be updated (as described in Section 9.5.2).

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9.5 Sliding Meshes

Saving Case and Data Files FLUENT’s automatic saving of case and data files (see Section 3.3.4) can be used with the sliding mesh model. This provides a convenient way for you to save results at successive time steps for later postprocessing.

! You must save a case file each time you save a data file because the grid position is stored in the case file. Since the grid position changes with each time step, reading data for a given time step will require the case file at that time step so that the grid will be in the proper position. You should also save your initial case file so that you can easily return to the grid’s original position to restart the solution if desired.

! If you are planning to solve your sliding mesh model in several stages, whereby you run the calculation for some period of time, save case and data files, exit FLUENT, start a new FLUENT session, read the case and data files, continue the calculation for some time, save case and data files, exit FLUENT, and so on, there may be some distortion in the mesh with each subsequent continuation of the calculation. To avoid this problem, you can delete the grid interface before saving the case file, and then create it again (as described in step 3 above) after you read the case file into a new FLUENT session. Time-Periodic Solutions For some problems (e.g., rotor-stator interactions), you may be interested in a timeperiodic solution. That is, the startup transient behavior may not be of interest to you. Once this startup phase has passed, the flow will start to exhibit time-periodic behavior. If T is the period of unsteadiness, then for some flow property φ at a given point in the flow field: φ(t) = φ(t + N T )

(N = 1, 2, 3, ...)

(9.5-1)

For rotating problems, the period (in seconds) can be calculated by dividing the sector angle of the domain (in radians) by the rotor speed (in radians/sec): T = θ/Ω. For 2D rotor-stator problems, T = P/vb , where P is the pitch and vb is the blade speed. The number of time steps in a period can be determined by dividing the time period by the time step size. When the solution field does not change from one period to the next (for example, if the change is less than 5%), a time-periodic solution has been reached. To determine how the solution changes from one period to the next, you will need to compare the solution at some point in the flow field over two periods. For example, if the time period is 10 seconds, you can compare the solution at a given point after 22 seconds with the solution after 32 seconds to see if a time-periodic solution has been reached. If not, you can continue the calculation for another period and compare the solutions after 32 and 42 seconds, and so on until you see little or no change from one period to the next. You can also track global quantities, such as lift and drag coefficients and mass


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flow, in the same manner. Figure 9.5.13 shows a lift coefficient plot for a time-periodic solution.

-5.00e+00 -5.10e+00 -5.20e+00 -5.30e+00 -5.40e+00

Cl

-5.50e+00 -5.60e+00 -5.70e+00 -5.80e+00 -5.90e+00 -6.00e+00 0

Y X

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Time

Z

Cl

Figure 9.5.13: Lift Coefficient Plot for a Time-Periodic Solution

The final time-periodic solution is independent of the time steps taken during the initial stages of the solution procedure. You can therefore define “large” time steps in the initial stages of the calculation, since you are not interested in a time-accurate solution for the startup phase of the flow. Starting out with large time steps will allow the solution to become time-periodic more quickly. As the solution becomes time-periodic, however, you should reduce the time step in order to achieve a time-accurate result.

! If you are solving with second-order time accuracy, the temporal accuracy of the solution will be affected if you change the time step during the calculation. You may start out with larger time steps, but you should not change the time step by more than 20% during the solution process. You should not change the time step at all during the last several periods to ensure that the solution has approached a time-periodic state.

9.5.4

Postprocessing for Sliding Meshes

Postprocessing for sliding mesh problems is the same as for other unsteady problems. You will read in the case and data file for the time of interest and display and report results as usual. For spatially-periodic problems, you may want to use periodic repeats (set in the Views panel, as described in Section 27.4) to display the geometry. Figure 9.5.14 shows the flow field for the rotor-stator example of Figure 9.5.4 at one instant in time, using 1 periodic repeat.

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9.5 Sliding Meshes

1.01e+05 1.01e+05 9.98e+04 9.91e+04 9.83e+04 9.75e+04 9.68e+04 9.60e+04 9.52e+04 9.45e+04 9.37e+04 Contours of Static Pressure (pascal) (Time=1.0400e-01)

Figure 9.5.14: Contours of Static Pressure for the Rotor-Stator Example

When displaying velocity vectors, note that absolute velocities (i.e., velocities in the inertial, or laboratory, reference frame) are displayed by default. You may also choose to display relative velocities by selecting Relative Velocity in the Vectors Of drop-down list in the Vectors panel. In this case, velocities relative to the translational/rotational velocity of the “reference zone” (specified in the Reference Values panel) will be displayed. (The velocity of the reference zone is the velocity defined in the Fluid panel for that zone.) Note that you cannot create zone surfaces for the intersection boundaries (i.e., the interior/periodic/external zones created from the intersection of the interface zones). You may instead create zone surfaces for the interface zones. Data displayed on these surfaces will be “one-sided”. That is, nodes on the interface zones will “see” only the cells on one side of the grid interface, and slight discontinuities may appear when you plot contour lines across the interface. Note also that, for non-planar interface shapes in 3D, you may see small gaps in your plots of filled contours. These discontinuities and gaps are only graphical in nature. The solution does not have these discontinuities or gaps. You can also generate a plot of circumferential averages in FLUENT. This allows you to find the average value of a quantity at several different radial or axial positions in your model. FLUENT computes the average of the quantity over a specified circumferential area, and then plots the average against the radial or axial coordinate. For more information on generating XY plots of circumferential averages, see Section 27.8.4.


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9.6

Dynamic Meshes

This section describes the theoretical background, and setup and use of the dynamic mesh model in FLUENT and its options and parameters. • Section 9.6.1: Introduction • Section 9.6.2: Dynamic Mesh Conservation Equations • Section 9.6.3: Dynamic Mesh Update Methods • Section 9.6.4: Solid-Body Kinematics • Section 9.6.5: Problem Setup for Dynamic Meshes • Section 9.6.6: Setting Dynamic Mesh Modeling Parameters • Section 9.6.7: Specifying the Motion of Dynamic Zones • Section 9.6.8: Previewing the Dynamic Mesh • Section 9.6.9: Defining In-Cylinder Events • Section 9.6.10: Guidelines for Setting Up an In-Cylinder Case • Section 9.6.11: Crevice Model

9.6.1

Introduction

The dynamic mesh model in FLUENT can be used to model flows where the shape of the domain is changing with time due to motion on the domain boundaries. The motion can be a prescribed motion (e.g., you can specify the linear and angular velocities about the center of gravity of a solid body with time) or an unprescribed motion where the subsequent motion is determined based on the solution at the current time (e.g., the linear and angular velocities are calculated from the force balance on a solid body). The update of the volume mesh is handled automatically by FLUENT at each time step based on the new positions of the boundaries. To use the dynamic mesh model, you need to provide a starting volume mesh and the description of the motion of any moving zones in the model. FLUENT allows you to describe the motion using either boundary profiles or user-defined functions (UDFs). FLUENT expects the description of the motion to be specified on either face or cell zones. If the model contains moving and non-moving regions, you need to identify these regions by grouping them into their respective face or cell zones in the starting volume mesh that you generate. Furthermore, regions that are deforming due to motion on their adjacent regions must also be grouped into separate zones in the starting volume mesh. The boundary between the various regions need not be conformal. You can use the nonconformal or sliding interface capability in FLUENT to connect the various zones in the final model.

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9.6 Dynamic Meshes

9.6.2

Dynamic Mesh Conservation Equations

The integral form of the conservation equation for a general scalar, φ, on an arbitrary control volume, V , whose boundary is moving can be written as Z Z Z d Z ~ ~ ρφdV + ρφ (~u − ~ug ) · dA = Γ∇φ · dA + Sφ dV dt V ∂V ∂V V

where

(9.6-1)

ρ is the fluid density ~u is the flow velocity vector ~ug is the grid velocity of the moving mesh Γ is the diffusion coefficient Sφ is the source term of φ

Here ∂V is used to represent the boundary of the control volume V . The time derivative term in Equation 9.6-1 can be written, using a first-order backward difference formula, as d Z (ρφV )n+1 − (ρφV )n ρφdV = dt V ∆t

(9.6-2)

where n and n + 1 denote the respective quantity at the current and next time level. The (n + 1)th time level volume V n+1 is computed from V n+1 = V n +

dV ∆t dt

(9.6-3)

where dV /dt is the volume time derivative of the control volume. In order to satisfy the grid conservation law, the volume time derivative of the control volume is computed from n

Z f X dV ~ ~j = ~ug · dA = ~ug,j · A dt ∂V j

(9.6-4)

~ j is the j face area vector. where nf is the number of faces on the control volume and A ~ j on each control volume face is calculated from The dot product ~ug,j · A ~ j = δVj ~ug,j · A ∆t

(9.6-5)

where δVj is the volume swept out by the control volume face j over the time step ∆t.


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9.6.3

Dynamic Mesh Update Methods

Three mesh motion methods are available in FLUENT to update the volume mesh in the deforming regions subject to the motion defined at the boundaries: • spring-based smoothing • dynamic layering • local remeshing

Spring-Based Smoothing Method In the spring-based smoothing method, the edges between any two mesh nodes are idealized as a network of interconnected springs. The initial spacings of the edges before any boundary motion constitute the equilibrium state of the mesh. A displacement at a given boundary node will generate a force proportional to the displacement along all the springs connected to the node. Using Hook’s Law, the force on a mesh node can be written as F~i =

ni X

kij (∆~xj − ∆~xi )

(9.6-6)

j

where ∆~xi and ∆~xj are the displacements of node i and its neighbor j, ni is the number of neighboring nodes connected to node i, and kij is the spring constant (or stiffness) between node i and its neighbor j. The spring constant for the edge connecting nodes i and j is defined as 1

kij = q

| ~xi − ~xj |

(9.6-7)

At equilibrium, the net force on a node due to all the springs connected to the node must be zero. This condition results in an iterative equation such that ∆~xm+1 i

=

Pni j

kij ∆~xm j k ij j

Pni

(9.6-8)

Since displacements are known at the boundaries (after boundary node positions have been updated), Equation 9.6-8 is solved using a Jacobi sweep on all interior nodes. At convergence, the positions are updated such that ~xn+1 = ~xni + ∆~xm,converged i i

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(9.6-9)


9.6 Dynamic Meshes

where n + 1 and n are used to denote the positions at the next time step and the current time step, respectively. The spring-based smoothing is shown in Figures 9.6.1 and 9.6.2 for a cylindrical cell zone where one end of the cylinder is moving.

Figure 9.6.1: Spring-Based Smoothing on Interior Nodes: Start

Figure 9.6.2: Spring-Based Smoothing on Interior Nodes: End

Applicability of the Spring-Based Smoothing Methods You can use the spring-based smoothing method to update any cell or face zone whose boundary is moving or deforming. For non-tetrahedral cell zones (non-triangular in 2D), the spring-based method is recommended when the following conditions are met: • The boundary of the cell zone moves predominantly in one direction (i.e., no excessive anisotropic stretching or compression of the cell zone).


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• The motion is predominantly normal to the boundary zone. If these conditions are not met, the resulting cells may have high skewness values, since not all possible combinations of node pairs in non-tetrahedral cells (or non-triangular in 2D) are idealized as springs. By default, spring-based smoothing on non-triangular or non-tetrahedral cell zones are turned off. If you want to use spring-based smoothing on all cell shapes, you can turn on the model for these zones using the text-interface command spring-on-all-shapes? in the dynamic-mesh-menu.

Dynamic Layering Method In prismatic (hexahedral and/or wedge) mesh zones, you can use dynamic layering to add or remove layers of cells adjacent to a moving boundary, based on the height of the layer adjacent to the moving surface. The dynamic mesh model in FLUENT allows you to specify an ideal layer height on each moving boundary. The layer of cells adjacent to the moving boundary (layer j in Figure 9.6.3) is split or merged with the layer of cells next to it (layer i in Figure 9.6.3) based on the height (h) of the cells in layer j.

Layer i Layer j

h

Moving boundary

Figure 9.6.3: Dynamic Layering

If the cells in layer j are expanding, they cell heights are allowed to increase until hmin > (1 + αs )hideal

(9.6-10)

where hmin is the minimum cell height of cell layer j, hideal is the ideal cell height, and αs is the layer split factor. When this condition is met, the cells are split based on the specified layering option: constant height or constant ratio. With the constant height option, the cells are split to create a layer of cells with constant height hideal and a layer of cells of height h − hideal . With the constant ratio option, the cells are split such that locally, the ratio of the new cell heights is exactly αs everywhere. Figures 9.6.4 and 9.6.5 shows the result of splitting a layer of cells above a valve geometry using the constant height and constant ratio option.

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9.6 Dynamic Meshes

Figure 9.6.4: Results of Splitting Layer By Constant Height

Figure 9.6.5: Results of Splitting Layer By Constant Ratio


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If the cells in layer j are being compressed, they can be compressed until hmin < αc hideal

(9.6-11)

where αc is the layer collapse factor. When this condition is met, the compressed layer of cells is merged into the layer of cells above the compressed layer; i.e., the cells in layer j are merged with those in layer i. Applicability of the Dynamic Layering Method You can use the dynamic layering method to split or merge cells adjacent to any moving boundary provided the following conditions are met: • All cells adjacent to the moving face zone are either wedges or hexahedra (quadrilaterals in 2D) even though the cell zone may contain mixed cell shapes. • The cell layers must be completely bounded by one-sided face zones, except when sliding interfaces are used (see Section 9.6.3). • If the bounding face zones are two-sided walls, you must split the wall and wallshadow pair and use the coupled sliding interface option to couple the two adjacent cell zones. • If your model contains periodic face zones in the cell zone where dynamic layering is used, you can only use the serial version of the solver. However, if you model the periodic zones as periodic non-conformal interfaces, then you can use the parallel solver for dynamic layering. If the moving boundary is an internal zone, cells on both sides (possibly with different ideal cell layer heights) of the internal zone are considered for dynamic layering. If you want to use dynamic layering on cells adjacent to a moving wall that do not span from boundary to boundary, you must separate those cells which are involved in the dynamic layering and use the sliding interfaces capability in FLUENT to transition from the deforming cells to the adjacent non-deforming cells (see Figure 9.6.6).

Local Remeshing Method On zones with a triangular or tetrahedral mesh, the spring-based smoothing method (described in Section 9.6.3) is normally used. When the boundary displacement is large compared to the local cell sizes, the cell quality can deteriorate or the cells can become degenerate. This will invalidate the mesh (e.g., result in negative cell volumes) and consequently, will lead to convergence problems when the solution is updated to the next time step.

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9.6 Dynamic Meshes

Sliding Interfaces

Moving Face Zone Dynamic Layering Zone

Figure 9.6.6: Use of Sliding Interfaces to Transition Between Adjacent Cell Zones and the Dynamic Layering Cell Zone

To circumvent this problem, FLUENT agglomerates cells that violate the skewness or size criteria and locally remeshes the agglomerated cells. If the new cells satisfy the skewness and the size criteria, the mesh is locally updated with the new cells (with the solution interpolated from the old cells). Otherwise, the new cells are discarded. FLUENT evaluates each cell and marks it for remeshing if it meets one or more of the following criteria: • It is smaller than a specified minimum size. • It is larger than a specified maximum size. • It has a skewness that is greater than a specified maximum skewness. In addition to remeshing the volume mesh, FLUENT also allows triangular and linear faces on a deforming boundary to be remeshed. FLUENT marks deforming boundary faces for remeshing based on moving and deforming loops of faces. FLUENT requires that these loops are closed. FLUENT automatically extracts loops on the boundary of the face zone whose nodes are moving or deforming. Consider a simple tetrahedral mesh of a cylinder whose bottom wall is moving (see Figure 9.6.7). On the deforming boundary, a single loop is generated at the bottom end of the cylinder (where the nodes are moving). In a similar approach as in the dynamic layering technique described in Section 9.6.3, FLUENT analyzes the height of the faces connected to the nodes on the loop and subsequently, splits or merges the faces depending on the specified ideal face height and split/merge factor. If the faces in layer j are expanding, they are allowed to expand until


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Deforming boundary

Layer i Layer j

h

Moving boundary

Figure 9.6.7: Remeshing at a Deforming Boundary

h > (1 + αh )hideal

(9.6-12)

where hideal is the ideal face height, and αh is a height factor. When this condition is met, the faces are split according to the predefined face height such that the new faces on layer i have exactly the face height hideal . Conversely, if the layer is contracting, they are allowed to contract until h < αh hideal

(9.6-13)

When this condition is met, the compressed layer of faces is merged into the layer of faces above it. The face remeshing is illustrated in Figure 9.6.9. Applicability of the Local Remeshing Method You can use the local remeshing method only in cell zones that contain tetrahedral or triangular cells. If you define deforming face zones in your model and you use local remeshing in the adjacent cell zone, the faces on the deforming face zone can be remeshed only if the following conditions are met: • The faces are triangular (or linear in 2D). • The faces to be remeshed are all adjacent to moving loops (i.e., moving nodes). • The faces are on the same face zone, and form an annular (i.e., closed loop). • The faces are not part of a symmetry or conformal periodic boundary.

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9.6 Dynamic Meshes

Figure 9.6.8: Expanding Cylinder Before Local Face Remeshing

Figure 9.6.9: Expanding Cylinder After Local Face Remeshing


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Volume Mesh Update Procedure The volume mesh is updated automatically based on the methods described in Sections 9.6.3–9.6.3. FLUENT decides which method to use for a particular zone based on the shape of the cells in the zone. For example, if the boundaries of a tetrahedral cell zone are moving, the spring-based smoothing and local remeshing methods will be used to update the volume mesh in this zone. If the zone consists of prismatic (hexahedral and/or wedge) cells, then the dynamic layer method will be used to determine where and when to insert and remove cell layers. FLUENT automatically determines which method to use by visiting the adjacent cell zones and setting appropriate flags for the volume mesh update methods to be used. If you specify the motion for a cell zone, FLUENT will visit all of the neighboring cell zones and set the flags appropriately. If you specify the motion of a boundary zone, FLUENT will analyze only the adjacent cell zones. If a cell zone does not have any moving boundaries, then no volume mesh update method will be applied to the zone.

! Note that as a result of the local remeshing procedures, updated meshes may be slightly different when dynamic meshes are used in parallel FLUENT, and local remeshing is selected, and therefore very small differences may arise in the solutions.

9.6.4

Solid-Body Kinematics

FLUENT uses solid-body kinematics if the motion is prescribed based on the position and orientation of the center of gravity of a moving object. This is applicable to both cell and face zones. The motion of the solid-body can be specified by the linear and angular velocity of the center of gravity. FLUENT allows the velocities to be specified either as profiles or userdefined functions (UDF). FLUENT assumes that the motion is specified in the inertial coordinate system. If the motion is specified using a profile, the components of the velocities must be described using the following profile fields: • linear velocity (vx , vy , vz ) as a function of time • angular velocity (ωx , ωy , ωz ) as a function of time In addition to the motion description, you must also specify the starting location of the center of gravity and orientation of the solid body. FLUENT automatically updates the center of gravity position and orientation at every time step such that

~xn+1 = ~xnc.g. + ~vc.g. ∆t c.g. n+1 n ~ c.g. ∆t θ~c.g. = θ~c.g. + GΩ

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(9.6-14) (9.6-15)


9.6 Dynamic Meshes ~ c.g. where ~xc.g. and θ~c.g. are the position and orientation of the center of gravity, ~vc.g. and Ω are the linear and angular velocities of the center of gravity, and G is the transformation ~ By default, G is taken to be the identity matrix. matrix that defines the choice of θ. Typically, θ~ is chosen to be an appropriate set of Euler angles. In this case, the solid-body motion must be specified using a user-defined function (DEFINE CG MOTION) where the appropriate form of G can be specified.

Ω c.g.

∆θ

∆x eθ er x rn+1

n

xr

x c.g. Figure 9.6.10: Solid Body Rotation Coordinates

The position vectors on the solid body are updated based on rotation about the instan~ c.g. . For a finite rotation angle ∆θ = |Ω ~ c.g. |∆t, the final taneous angular velocity vector Ω position of a vector ~xr on the solid body with respect to ~xc.g. can be expressed as (See Figure 9.6.4) ~xn+1 = ~xnr + ∆~x r


(9.6-16)

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where ∆~x can be shown to be ∆~x = |~xnr | [sin (∆θ)ˆ eθ + (cos (∆θ) − 1) eˆr ]

(9.6-17)

The unit vectors eˆθ and ~er are defined as

eˆθ =

~ c.g. × ~xr Ω ~ c.g. × ~xr | |Ω

(9.6-18)

eˆr =

~ c.g. eˆθ × Ω ~ c.g. | |ˆ eθ × Ω

(9.6-19)

If the solid body is also translating with ~vc.g , the n + 1 position vector on the solid body can be expressed as ~xn+1 = ~xnc.g. + ~vc.g. ∆t + ~xn+1 r

(9.6-20)

where ~xn+1 is given by Equation 9.6-16. r

9.6.5

Problem Setup for Dynamic Meshes

The steps for setting up a dynamic mesh problem are listed below. (Note that this procedure includes only those steps necessary for the dynamic mesh model itself; you will need to set up other models, boundary conditions, etc. as usual.) 1. Enable the appropriate option for modeling unsteady flow in the Solver panel. (See Section 24.15 for details about the unsteady modeling capabilities in FLUENT.) Define −→ Models −→Solver... 2. Set boundary conditions as required. Define −→Boundary Conditions... See Chapter 6 for details about input of boundary conditions. The wall velocity is set up automatically when the motion attribute is set for wall zones, so you will not specify wall motion in the Wall panel. 3. Enable the dynamic mesh model, and specify related parameters. Define −→ Dynamic Mesh −→Parameters... See Section 9.6.6 for details.

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9.6 Dynamic Meshes

4. Specify the motion of the dynamic zones in your model. Define −→ Dynamic Mesh −→Zones... See Section 9.6.7 for details. 5. Save case and data. File −→ Write −→Case & Data... 6. Preview your dynamic mesh setup (when the motion is a prescribed motion). Solve −→Mesh Motion... See Section 9.6.8 for details. 7. If you are solving an in-cylinder problem, define the events that will occur during the in-cylinder calculation. Define −→ Dynamic Mesh −→Events... See Section 9.6.9 for details. You can also display the motion of the valves and piston walls to verify the incylinder setup. Display −→IC Zone Motion... 8. Use the automatic saving feature to specify the file name and frequency with which case and data files should be saved during the solution process. File −→ Write −→Autosave... See Section 3.3.4 for details about the use of this feature. This provides a convenient way for you to save results at successive time steps for later postprocessing.

!

You must save a case file each time you save a data file because the mesh position is stored in the case file. Since the mesh position changes with each time step, reading data for a given time step will require the case file at that time step so that the mesh will be in the proper position. You should also save your initial case file so that you can easily return to the mesh’s original position to restart the solution if desired. 9. (optional) If you want to create a graphical animation of the mesh over time during the solution procedure, you can use the Solution Animation panel to set up the graphical displays that you want to use in the animation. See Section 24.17 for details.

9.6.6

Setting Dynamic Mesh Modeling Parameters

To enable the dynamic mesh model, turn on Dynamic Mesh in the Dynamic Mesh panel (Figure 9.6.11).


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Define −→ Dynamic Mesh −→Parameters... If you are modeling in-cylinder motion, turn on the In-Cylinder option. Next, you will need to select the appropriate mesh update methods, and set the associated parameters, as well as the in-cylinder parameters, if relevant.

Figure 9.6.11: The Dynamic Mesh Panel

Selecting the Mesh Update Methods Under Mesh Methods, select Smoothing, Layering, and/or Remeshing. Details about these methods and their applicability to different cases are provided in Sections 9.6.3, 9.6.3, and 9.6.3, respectively. See Section 9.6.6 for information about setting parameters for the mesh update methods.

Setting Mesh Update Parameters Smoothing To turn on spring-based smoothing, enable the Smoothing option under Mesh Methods in the Dynamic Mesh panel (Figure 9.6.11). The relevant parameters are specified in the Smoothing tab. You can control the spring stiffness by adjusting the value of the Spring Constant Factor between 0 and 1. A value of 0 indicates that there is no damping on the springs, and boundary node displacements have more influence on the motion of the interior nodes.

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9.6 Dynamic Meshes

A value of 1 imposes the default level of damping on the interior node displacements as determined by solving Equation 9.6-8. The effect of the Spring Constant Factor is illustrated in Figures 9.6.12 and 9.6.13, which show the trailing edge of a NACA-0012 airfoil after a counter-clockwise rotation of 2.3◦ and the mesh is smoothed using the spring-based smoother but limited to 20 iterations. Degenerate cells (Figure 9.6.12) are created with the default value of 1 for the Spring Constant Factor. However, the original mesh distribution (Figure 9.6.13) is recovered if the Spring Constant Factor is set to 0 (i.e., no damping on the displacement of nodes on the airfoil surface).

Figure 9.6.12: Effect of a Spring Constant Factor of 1 on Interior Node Motion

Figure 9.6.13: Effect of a Spring Constant Factor of 0 on Interior Node Motion

If your model contains deforming boundary zones, you can use the Boundary Node Relaxation to control how the node positions on the deforming boundaries are updated. On deforming boundaries, the node positions are updated such that


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~xn+1 = ~xn + β∆~xm,converged

(9.6-21)

where β is the Boundary Node Relaxation. A value of 0 prevents deforming boundary nodes from moving (equivalent to turning off smoothing on deforming boundary zones) and a value of 1 indicates no under-relaxation. You can control the solution of Equation 9.6-8 using the values of Convergence Tolerance and Number of Iterations. FLUENT solves Equation 9.6-8 iteratively during each time step until one of the following criteria is met: • the specified number of iterations has been performed • the solution is converged for that time step: ∆~xm rms ∆~x1rms

!

< convergence tolerance

(9.6-22)

where ∆~x1rms is the interior and deforming nodes RMS displacement at the first iteration. Dynamic Layering To turn on dynamic layering, enable the Layering option under Mesh Methods in the Dynamic Mesh panel (Figure 9.6.11). The layering control is specified in the Layering tab. You can control how a cell layer is split by specifying either Constant Height or Constant Ratio under Options. The Split Factor and Collapse Factor (αs in Equation 9.6-10 and αc in Equation 9.6-11, respectively) are the factors that determine when a layer of cells (hexahedra or wedges in 3D, or quadrilaterals in 2D) that is next to a moving boundary is split or merged with the adjacent cell layer, respectively. Local Remeshing To turn on local remeshing, enable the Remeshing option under Mesh Methods in the Dynamic Mesh panel (Figure 9.6.11). The local remeshing controls are specified in the Remeshing tab. In local remeshing, FLUENT agglomerates cells based on skewness, size, and height (adjacent moving face zones). The value of Maximum Cell Skewness specifies the desired skewness of the mesh. Cells with skewness above the maximum skewness are marked for remeshing. The size criteria are specified with Minimum Cell Volume and Maximum Cell Volume. Cells with volume below minimum volume and above maximum volume are marked for remeshing.

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9.6 Dynamic Meshes

The marking of cells based on skewness is done at every time step when the local remeshing method is enabled. However, marking based on size is performed between the specified Size Remesh Interval since the change in cell size distribution is typically small over one time step. By default, FLUENT replaces the agglomerated cells only if the quality of the remeshed cells has improved. However, you can override this behavior by disabling Must Improve Skewness under Options. In addition to marking cells based on minimum and maximum volumes, FLUENT also marks cells based on the size distribution generated by the sizing function if the Sizing Function option under Options is enabled. You can control the size distribution by specifying the Size Function Variation and the Size Function Rate. If you have enabled the Sizing Function option, FLUENT will agglomerate a cell if 4 5 size 6∈ γsizeb , γsizeb 5 4

(9.6-23)

where γ is some factor and sizeb is the ideal cell size of its closest boundary cell. The the factor γ is computed from

γ = 1 + αd1+2β b 1 1−β

γ = 1 + αdb

if α > 0 if α < 0

(9.6-24) (9.6-25)

where db is the distance from the closest boundary cell and α and β are the Size Function Variation and Size Function Rate, respectively. You can use Size Function Variation (or α) to control how large or small an interior cell can be with respect to its closest boundary cell. An α value of 0.5 indicates that the interior cell size can be, at most, 1.5 the size of the closest boundary cell. Conversely, an α value of −0.5 indicates that the cell size interior of the boundary can be half of that at the closest boundary cell. A value of 0 indicates a constant size distribution away from the boundary. You can use Size Function Rate (or β) to control how rapidly the cell size varies from the boundary. The value of β should be specified between −1 and 1. A positive value indicates a slower transition from the boundary to the specified Size Function Variation value. Conversely, a negative value indicates a faster transition from the boundary to the Size Function Variation value. A value of 0 indicates a linear variation of cell size away from the boundary. You can also control the resolution of the sizing function with Size Function Resolution. The resolution determines the size of the background bins used to evaluate the size distribution with respect to the minimum characteristic length of the current mesh.


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A set of default values (based on the current mesh) is automatically generated if you click Use Defaults.

Setting In-Cylinder Parameters If you turn on the In-Cylinder model in the Dynamic Mesh panel (Figure 9.6.11), you need to specify the Crank Shaft Speed, the Starting Crank Angle, and the Crank Period which are used to convert between flow time and crank angle. You must also specify the time step to use for advancing the solution in terms of crank angle in Crank Angle Step Size. By default, FLUENT assumes a Crank Angle Step Size of 0.5 degree. FLUENT provides a built-in function to calculate the piston location as a function of crank angle. If the piston motion is specified using this function, you need to specify the Piston Stroke and Connecting Rod Length. The piston location is calculated using A ps = L + (1 − cos (θc )) − 2

s

L2 −

A2 sin2 (θc ) 4

(9.6-26)

where ps is the piston location (0 at top-dead-center (TDC) and A at bottom-dead-center (BDC)), L is the connecting rod length, A is the piston stroke, and θc is the current crank angle. The current crank angle is calculated from θc = θs + tΩshaft

(9.6-27)

where θs is the Starting Crank Angle and Ωshaft is the Crank Shaft Speed. The Piston Stroke Cutoff and Minimum Valve Lift values are used to control the actual values of the valve lift and piston stroke such that

c min vlift = max(vlift , vlift ) c min ps = max(ps , ps )

(9.6-28) (9.6-29)

c min where vlift is the valve lift computed from the appropriate valve profiles, vlift is the c Minimum Valve Lift, ps is the stroke calculated from Equation 9.6-26, and pmin is the s Piston Stroke Cutoff. (See Section 9.6.10 on how the Piston Stroke Cutoff is used to control the onset of layering in the cylinder chamber.)

9.6.7

Specifying the Motion of Dynamic Zones

You need to define the motion of the dynamic zones in your model. If the zone is a rigid body, you can use a profile or user-defined function (UDF) to define the motion of the rigid body. If the zone is a deforming zone, you can define the geometry and the

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9.6 Dynamic Meshes

parameters that control face remeshing, if applicable. For a zone that is deforming and moving at the same time, you can use a user-defined function to define the geometry and motion of the zone as they change with time.

General Procedure You will specify the motion of the dynamic zones in your model using the Dynamic Zones panel (e.g., Figure 9.6.14). Define −→ Dynamic Mesh −→Zones...

Figure 9.6.14: The Dynamic Zones Panel for a Rigid Body Motion Details about specifying different types of motion are provided in Sections 9.6.7, 9.6.7, and 9.6.7. When you have completed the specification of a dynamic zone, click Create in the Dynamic Zones panel to complete the specification and add the zone to the Dynamic Zones list. Modifying the Motion of a Dynamic Zone If you want to make a change to the specification of a dynamic zone, select the zone in the Dynamic Zones list, change the specification, and then click Create to update the specification.


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Checking the Center of Gravity If a dynamic zone has solid body motion, you can view its current position and orientation of the center of gravity by selecting the zone in the Dynamic Zones list and then clicking on Update. Deleting a Dynamic Zone To delete a dynamic zone that you have specified, select the zone in the Dynamic Zones list, and click the Delete button. The zone will be removed from the Dynamic Zones list.

Stationary Motion By default, if no motion (moving or deforming) attributes are assigned to a face or cell zone, then the zone is not considered when updating the mesh to the next time step. However, there are cases where an explicit declaration of a stationary zone is required. For example, if a cell zone is assigned some solid body motion, the positions of all nodes belonging to the cell zone will be updated even though some of the nodes may also be part of a non-moving boundary zone. An explicit declaration of a stationary zone excludes the nodes on these zones when updating the node positions. To define a stationary zone in your model, follow the steps below. 1. Select the stationary zone in the Zone Names drop-down list. 2. Select Stationary under Type. 3. If the stationary zone is a face zone, then specify Cell Height on any Adjacent Zone which is involved in local remeshing or dynamic layering in the Remeshing Options tab. The Cell Height specifies the ideal height of the adjacent cells as described earlier in the dynamic layering section. 4. Click Create.

Rigid Body Motion To define a rigid-body zone in your model, follow the steps below. 1. Select the rigid body zone in the Zone Names drop-down list. 2. Select the Rigid Body option under Type. 3. Specify the motion of the rigid body zone by selecting a profile or user-defined function from the Motion UDF/Profile drop-down listin the Motion Attributes tab. See Section 6.26 for information on profiles, and see the separate UDF Manual for information on user-defined functions.

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4. Specify the initial location of the center of gravity for the rigid body by entering the coordinates of the center of gravity in C.G. Location. 5. Specify the orientation of the center of gravity with respect to the inertia coordinate system by entering the orientations of the center of gravity in C.G. Orientation. 6. If you are solving an in-cylinder problem, specify the direction of the reference axis of the valves or piston in Valve/Piston Axis. The current valve lift or piston stroke is automatically updated in Lift/Stroke when you click Create based on the parameters you have specified earlier when you first invoke the in-cylinder model. If you are specifying motion on a cell zone, you can exclude certain cells (based on cell shape) from the motion attributes by selecting the appropriate cell shapes under Motion Mask. 7. If the rigid body zone is a face zone, specify the ideal height for cells in the adjacent cell zones by entering a value in the Cell Height field for each Adjacent Zone in the Remeshing Options tab. The ideal cell height (hideal in Equations 9.6-10 and 9.6-11) is used by FLUENT to determine when the prismatic layer next to the rigid body should be split or merged with the layer next to it. If the adjacent zone is tetrahedral or triangular, the ideal height is used by FLUENT to determine if adjacent cells need to be agglomerated for local remeshing. 8. Click Create.

Deforming Motion To define a deforming zone in your model, follow the steps below. 1. Select the deforming zone in the Zone Names drop-down list. 2. Select the Deforming option under Type. 3. Specify the geometry of the deforming zone in the Geometry Definition tab. There are four options: • If no geometry is available, select none in the Definition drop-down list. • If the geometry is a plane, select plane in the Definition drop-down list. To define the plane, enter the position of a point on the plane in Point on Plane and the plane normal in Plane Normal. • If the geometry is a cylinder, select cylinder in the Definition drop-down list. To define the cylinder, enter the Cylinder Radius, the Cylinder Origin and the Cylinder Axis.


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• If the geometry is described by a user-defined function, select user-defined in the Definition drop-down list and the appropriate user-defined functions in the Geometry UDF drop-down list. See the separate UDF Manual for information on user-defined functions. When available, the geometry information is used to project nodes on the deforming zone after remeshing the face zone, or if nodes are moved from the spring-based smoothing method. 4. Specify the appropriate remeshing parameters in the Remeshing Options tab. You can locally disable or enable any remeshing methods (the methods must be globally enabled in the Dynamic Mesh panel) by selecting or deselecting Smoothing, Layering (only for prismatic cell zones), or Remeshing under Mesh Methods. If you selected a face zone, you need to enter the face remeshing controls Height, Height Factor and Maximum Skewness. Recall that Height (hideal in Equations 9.6-12 and 9.6-13) and Height Factor (αh in Equations 9.6-12 and 9.6-13) are used by FLUENT to determine when the faces adjacent to moving nodes should be split or merged during local remeshing of the face zone. If you selected a cell zone, you need to enter Minimum Volume, Maximum Volume and Maximum Skewness if you want impose a different set of remeshing criteria, other than those you specified globally in the Dynamic Mesh panel. 5. Click Create.

User-Defined Motion For a zone that is deforming and moving, you can define the position of each node on the general deforming/moving zone using a user-defined function (UDF). To define a moving and deforming zone, follow the steps below. 1. Select the moving and deforming zone in the Zone Names drop-down list. 2. Select the User-Defined option under Type. 3. In the Motion Attributes tab, select the user-defined function that defines the geometry and motion of the zone from the Mesh Motion UDF drop-down list. See the separate UDF Manual for information on user-defined functions used to specify user-defined motion. 4. Click Create.

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9.6.8

Previewing the Dynamic Mesh

When you have specified the mesh update methods and their associated parameters, and you have defined the motion of dynamic zones, as described in Sections 9.6.6 and 9.6.7, you can preview the dynamic mesh as it changes with time before you start your simulation. The same dynamic mesh motion will be executed when you start your simulation. To preview the dynamic mesh, you can use the Mesh Motion panel (Figure 9.6.15). Solve −→Mesh Motion...

Figure 9.6.15: The Mesh Motion Panel The procedure is as follows: 1. Save the case file. File −→ Write −→Case...

!

Note that the mesh motion will actually update the node locations as well as the connectivity of the mesh, so you must be sure to save your case file before doing the dynamic mesh motion. Once you have advanced the mesh by a certain number of time steps, you will not be able to recover the previous status of the mesh, other than by reloading the appropriate FLUENT case file. 2. Specify the Number of Time Steps and the size of each time step (Time Step Size). The current time will be displayed in the Current Mesh Time field after the dynamic mesh has been advanced the specified number of steps. Note that if you turned on the in-cylinder model, the Time Step Size is automatically calculated from the Crank Angle Step Size and the Crank Shaft Speed that you have specified in the Dynamic Mesh panel. 3. To view the dynamic mesh on the graphics window, turn on the Display Grid option. In addition, you can control the frequency at which FLUENT should display an updated mesh in the Display Frequency field. To save a hardcopy file of the mesh each time FLUENT updates it during the preview, turn on the Save Hardcopy option.


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4. Click Preview to start the preview. FLUENT will update the dynamic mesh by moving and deforming the face and cell zones that you have specified as dynamic zones. If you are setting up an in-cylinder model, you can preview the motion of the piston and valves using the IC Zone Motion panel (Figure 9.6.16). Display −→IC Zone Motion...

Figure 9.6.16: The IC Zone Motion Panel The IC zone motion preview is different from the mesh motion described above in that the mesh connectivity is not changed. The IC zone motion preview only updates the graphical representation (in the graphics window) of the zones that you have selected using the Grid Display panel. The IC zone motion preview will only update those zones that have solid body motion specified. To use the IC Zone Motion preview: 1. Select the appropriate zones to display in the Display Grid panel 2. In the IC Zone Motion panel, enter the crank angle Increment and the Number of Steps 3. Click Preview You can also use the slider bar on the IC Zone Motion panel to fast-forward or rewind the motion of the selected zones.

9.6.9

Defining In-Cylinder Events

If you are simulating an in-cylinder flow, you can use the in-cylinder events in FLUENT to control the timing of specific events during the course of the simulation. For example, you may want to open the exhaust valve (represented by a pair of deforming sliding

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interfaces) by creating an event to create the sliding interfaces at some crank angle. You can also use events to control when to suspend the motion of a face or cell zone by creating the appropriate events based on the crank angle.

Procedure for Defining Events You can define the in-cylinder events using the Dynamic Mesh Events panel (Figure 9.6.17). Note that this panel is available only if you turned on the In-Cylinder model in the Dynamic Mesh panel. Define −→ Dynamic Mesh −→Events...

Figure 9.6.17: The Dynamic Mesh Events Panel The procedure for defining in-cylinder events is as follows: 1. Increase the Number of Events value to the number of in-cylinder events you wish to specify. As this value is increased, additional event entries in the panel will become editable. 2. Turn on the check box next to the first event and enter a name for the event under the Name heading.


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3. Specify the crank angle at which you want the event to occur under At Crank Angle. It is not necessary to specify the events in order of increasing crank angle, but it may be easier to keep track of events if you specify them in the order of increasing angle. 4. Click the Define... button to open the Define Event panel (Figure 9.6.18).

Figure 9.6.18: The Define Event Panel

5. In the Define Event panel, choose the type of in-cylinder event by selecting Change Zone Type, Change Zone BC, Create Sliding Interface, Delete Sliding Interface, Change Motion Attribute, Change Time Step Size, Insert Boundary Layer, Remove Boundary Layer, Insert Interior Layer or Remove Interior Layer in the Type drop-down list. These event types and their definitions are described in Section 9.6.9. 6. Repeat steps 2–5 for the other events, if relevant. 7. Click Apply in the Dynamic Mesh Events panel after you finish defining all in-cylinder events. 8. To play the events to check that they are defined correctly, click the Preview... button in the Dynamic Mesh Events panel. In the Events Preview panel (Figure 9.6.19), enter the crank angles at which you want to start and end the playback in the Start

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Crank Angle and End Crank Angle fields, respectively. Specify the size of the step to take during the playback in the Increment field. Click Preview to play back the events. FLUENT will play the events at the crank angle specified for each event and report when each event occurs in the text (console) window.

Figure 9.6.19: The Events Preview Panel You need to specify the in-cylinder events for one complete engine cycle. In the subsequent cycles, the events are executed whenever θevent = θc ± nθperiod

(9.6-30)

where θevent is the event crank angle, θc is the current crank angle calculated from Equation 9.6-27, θperiod is the crank angle period for one cycle, and n is some integer. You are not required to specify the event crank angle to correspond exactly to the current crank angle calculated from Equation 9.6-27. FLUENT will execute an event if the current crank angle is between ±0.5∆θ where ∆θ is the equivalent change in crank angle for the time step. For example, if the event preview is executed between crank angle of 340◦ and 1060◦ (crank period is 720◦ ) using an increment of 1◦ , FLUENT will report the following in the text window. Execute Execute Execute Execute Execute Execute Execute Execute

Event: Event: Event: Event: Event: Event: Event: Event:

open-in-valve-left (defined at: 353.10, current angle: 353.00) open-in-valve-right (defined at: 353.00, current angle: 353.00) close-ex-valve-right (defined at: 355.60, current angle: 356.00) close-ex-valve-left (defined at: 357.80, current angle: 358.00) close-in-valve-left (defined at: 571.60, current angle: 572.00) close-in-valve-right (defined at: 571.80, current angle: 572.00) open-ex-valve-right (defined at: 137.10, current angle: 857.00) open-ex-valve-left (defined at: 139.00, current angle: 859.00)

Notice that events defined at 137.10◦ and 139◦ are executed at 857◦ and 859◦ , respectively, because they satisfy the condition of Equation 9.6-30.

Events Each of the available in-cylinder events is described below.


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Changing the Zone Type You can change the type of a zone to be a wall, or an interface, fluid, or solid zone during your in-cylinder simulation. To change the type of a zone, select Change Zone Type in the Type drop-down list in the Define Event panel (Figure 9.6.18). Select the zone(s) that you want to change in the Zone(s) list, and then select the new zone type in the New Zone Type drop-down list. Copying Zone Boundary Conditions You can copy boundary conditions from one zone to other zones during your in-cylinder simulation. If, for example, you have changed an inlet zone to type wall with the Change Zone Type event, you can set the boundary conditions of the new zone type by simply copying the boundary conditions from a known zone with the corresponding zone type. To copy boundary conditions from one zone to another, select Copy Zone BC in the Type drop-down list in the Define Event panel (Figure 9.6.18). In the From Zone drop-down list, select the zone that has the conditions you want to copy. In the To Zone(s) list, select the zone or zones to which you want to copy the conditions. FLUENT will set all of the boundary conditions for the zones selected in the To Zone(s) list to be the same as the conditions for the zone selected in the From Zone list. (You cannot copy a subset of the conditions, such as only the thermal conditions.) Note that you cannot copy conditions from external walls to internal (i.e., two-sided) walls, or vice versa, if the energy equation is being solved, since the thermal conditions for external and internal walls are different. Creating a Sliding Interface To create a sliding interface during your in-cylinder simulation, select Create Sliding Interface in the Type drop-down list in the Define Event panel (Figure 9.6.18). Enter a name for the sliding interface in the Interface Name field. Select the two zones on either side of the interface in the Interface Zone 1 and Interface Zone 2 drop-down lists. If the interface zones that you selected above do not overlap each other completely, the non-overlapped regions on each interface zones are put into separate wall zones by FLUENT. If these wall zones (i.e., non-overlapped regions) have motion attributes associated with them, their motion can only be specified by copying the motion from another dynamic zone by selecting the appropriate dynamic zones in the Wall 1 Motion and Wall 2 Motion drop-down lists, respectively. Note that you don’t have to change the boundary type from wall to interface. When the Create Sliding Interface event is executed, FLUENT will automatically change the boundary type of the face zones selected in Interface Zone 1 and Interface Zone 2 to type interface before the sliding interface is created.

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9.6 Dynamic Meshes

Deleting a Sliding Interface To delete a sliding interface that has been created earlier in your in-cylinder simulation, select Delete Sliding Interface in the Type drop-down list in the Define Event panel (Figure 9.6.18). Enter the name of the sliding interface to be deleted in the Interface Name field. As with the Create Sliding Interface event, FLUENT will automatically change the corresponding interface zones to wall. However, you may want to use the Copy Zone BC event to set any boundary conditions that are not the default conditions that FLUENT assumes. Changing the Motion Attribute of a Dynamic Zone To change the motion attribute of a dynamic zone during your in-cylinder calculation, select Change Motion Attribute in the Type drop-down list in the Define Event panel (Figure 9.6.18). Select the Attribute (slide, moving, or remesh) and set the appropriate Status (enable or disable). Select the corresponding dynamic zones for which you want to change the motion attributes in the Dynamic Zones list. The slide attribute is used to enable or disable smoothing of nodes on selected deforming face zones, the moving attribute is used to suspend the motion of selected moving zones, and the remesh attribute is used to enable and disable face remeshing on selected deforming face zones. Changing the Time Step To change the time step at some point during the simulation, select Change Time Step Size in the Type drop-down list in the Define Event panel. Specify the new physical time step by entering the new Crank Angle Step Size value in degrees. The physical time step is calculated from ∆t =

∆θc 6Ωshaft

(9.6-31)

where the unit of Ωshaft is assumed to be in RPM. Inserting Boundary Cell Layer To insert a new cell layer as a separate cell zone adjacent to a boundary, select Insert Boundary Layer in the Type drop-down list in the Define Event panel. Specify the Base Dynamic Zone, from which the layer of cells is to be created, and the Side Dynamic Zone, which represents the deforming face zone adjacent to the Base Dynamic Zone before the layer is inserted. The new cell zone will inherit the boundary conditions of the cell zone adjacent to the Base Dynamic Zone before the layer is inserted.


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Note that a new cell layer can be inserted only from a one-sided Base Dynamic Zone. You cannot insert a new cell layer from an interior face zone. Deleting Boundary Cell Layer To remove the cell layer inserted using the Insert Boundary Layer event, select Remove Boundary Layer in the Type drop-down list in the Define Event panel. Specify the same Base Dynamic Zone that you use when you defined the insert boundary layer event. Note that a cell layer can be removed only from a one-sided Base Dynamic Zone. Insert Interior Cell Layer To insert a new cell layer as a separate cell zone adjacent to the internal side of a boundary, select Insert Interior Layer in the Type drop-down list in the Define Event panel. Specify the Base Dynamic Zone and the Side Dynamic Zone as described in the Insert Boundary Layer event. You also need to specify the names of the new interior face zones (Internal Zone 1 Name and Internal Zone 2 Name) that will be created after the cell layer is created by FLUENT. FLUENT inserts the interior cell layer by splitting the cell zone adjacent to the Base Dynamic Zone with a plane. The position of the plane and the normal direction of the plane are implicitly defined by the cylinder origin and cylinder axis of the Side Dynamic Zone. Remove Interior Cell Layer To remove the cell layer inserted using the Insert Interior Layer event, select Remove Interior Layer in the Type drop-down list in the Define Event panel. Specify the same Internal Zone 1 Name and Internal Zone 2 Name that you used to define the Insert Interior Layer event.

Exporting and Importing Events If you want to save the events you have defined to a file, click Write... in the Dynamic Mesh Events panel and specify the Event File in the Select File dialog box. To read the events back into FLUENT, click Read... in the Dynamic Mesh Events panel and specify the Event File in the Select File dialog box.

Defining Starting Position Mesh for In-Cylinder Model If you are solving an in-cylinder flow problem, it is recommended that you generate your initial mesh to coincide with the TDC (top-dead-center) position. You can then use FLUENT to position the valves and piston to correspond to the starting crank angle of your simulation using the text-interface command position-starting-mesh in the dynamesh-mesh-control text menu.

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9.6 Dynamic Meshes

/define/models/dynamic-mesh-controls> position-starting-mesh Start Crank Angle (deg) [0] 340 Updating mesh position ... Done Subdividing mesh layers ... Done Remeshing cell zone fluid-chamber (id = 18) remeshing face zone cyl-wall-deform (id = 30) with length scale = 1.65000e-03 remeshing face zone intf-exv-lt-ob-t (id = 72) with length scale = 8.66000e-04 remeshing face zone intf-exv-rt-ob-t (id = 77) with length scale = 8.66000e-04 remeshing face zone intf-inv-lt-ob-t (id = 92) with length scale = 8.66000e-04 remeshing face zone intf-inv-rt-ob-t (id = 97) with length scale = 8.66000e-04 Remeshing cell zone fluid-export (id = 41) remeshing face zone exvalve-deform-lt (id = 7) with length scale = 1.60000e-03 remeshing face zone intf-exv-rt-ib-t (id = 67) with length scale = 8.66000e-04 remeshing face zone intf-exv-lt-ib-t (id = 46) with length scale = 8.66000e-04 remeshing face zone exvalve-deform-rt (id = 39) with length scale = 1.60000e-03 Remeshing cell zone fluid-inport (id = 43) remeshing face zone invalve-deform-rt (id = 8) with length scale = 1.60000e-03 remeshing face zone intf-inv-lt-ib-t (id = 82) with length scale = 8.66000e-04 remeshing face zone intf-inv-rt-ib-t (id = 87) with length scale = 8.66000e-04 remeshing face zone invalve-deform-lt (id = 40) with length scale = 1.60000e-03

FLUENT will automatically remesh any deforming face zones and the adjacent cell zones (both remeshing and layering) based on the remeshing and dynamic layering parameters that you have set up for your model. In the above example, the starting crank angle for the in-cylinder simulation is 340 degrees (20 degrees before TDC). Figure 9.6.9 shows the initial and the starting mesh generated by FLUENT.

9.6.10

Guidelines for Setting Up an In-Cylinder Case

This section describes the problem setup procedure for an in-cylinder dynamic mesh simulation.

Overview Consider the 2D in-cylinder example shown in Figure 9.6.22 for a typical pent-roof engine. In setting up the dynamic mesh model for an in-cylinder problem, you need to consider the following issues: • how to provide the proper mesh topology for the volume mesh update methods (spring-based smoothing, dynamic layering, and local remeshing) • how to define the motion attributes and geometry for the valve and piston surfaces • how to address the opening and closing of the intake and exhaust valves • how to specify the sequence of events that controls the in-cylinder simulation


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Figure 9.6.20: In-Cylinder Initial Mesh

Figure 9.6.21: In-Cylinder Starting Mesh Generated by FLUENT at Crank Angle of 340 degrees

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9.6 Dynamic Meshes

Intake Valve

Exhaust Valve

Piston Head

Figure 9.6.22: A 2D In-Cylinder Geometry

Defining the Mesh Topology FLUENT requires that you provide an initial volume mesh with the appropriate mesh topology such that the various mesh update methods described in Section 9.6.3 can be used to automatically update the dynamic mesh. However, FLUENT does not require you to set up all in-cylinder problems using the same mesh topology. When you generate the mesh for your in-cylinder model (using GAMBIT or other mesh generation tools), you need to consider the various mesh regions that you can identify as moving, deforming, or stationary, and generate these mesh regions with the appropriate cell shape. The mesh topology for the example problem in Figure 9.6.22 is shown in Figure 9.6.23, and the corresponding volume mesh is shown in Figure 9.6.24. Stationary Exhaust Zone Stationary Intake Zone

Layering Zone Above Exhaust Valve Layering Zone Above Intake Valve

Remeshing Zone

Layering Zone Above Piston

Figure 9.6.23: Mesh Topology Showing the Various Mesh Regions

Because of the rectilinear motion of the moving surfaces, you can use dynamic layering zones to represent the mesh regions swept out by the moving surfaces. These regions are the regions above the top surfaces of the intake and exhaust valves and above the piston head surface, and must be meshed with quadrilateral or hexahedral cells (as required by the dynamic layering method).


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Figure 9.6.24: Mesh Associated With the Chosen Topology

For the chamber region, you need to define a remeshing zone (triangular cells) to accommodate the various positions of the valves in the course of the simulation. In this region, the motion of the boundaries (valves and piston surfaces) is propagated to the interior nodes using the spring-based smoothing method. If the cell quality violates any of the remeshing criteria that you have specified, FLUENT will automatically agglomerate these cells and remesh them. Furthermore, FLUENT will also remesh the deforming faces (based on the face heights and factors that you have specified) on the cylinder walls as well as those on the sliding interfaces used to connect the chamber cell zone to the layering zones above the valve surfaces. For the intake and exhaust port regions, you can use either triangular or quadrilateral cell zones because these zones are not moving or deforming. FLUENT will automatically mark these regions as stationary zones and will not apply any mesh motion method on these cell zones. The dynamic layering regions above the piston and valves are conformal with the adjacent cell zone in the chamber and ports, respectively, so you do not have to use sliding interfaces to connect these cell zones together. However, you need to use sliding interfaces to connect the dynamic layering regions above the valves and the remeshing region in the chamber. This is shown in Figure 9.6.25 with the exhaust valve almost at full extension. Notice that cells on the chamber side of the interface zone are remeshed (i.e., split or merged) as the interface zone opens and closes because of the motion of the exhaust valve.

Defining Motion/Geometry Attributes of Mesh Zones As the piston moves down from the TDC to the BDC position, you need to expand the remeshing region such that it can accommodate the valves when they are fully extended. To accomplish this, you need to specify the dynamic layering zone adjacent to the piston surface to move with the piston until some specified distance from the TDC position.

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9.6 Dynamic Meshes

Sliding Interfaces

Figure 9.6.25: The Use of Sliding Interfaces to Connect the Exhaust Valve Layering Zone to the Remeshing Zone

Beyond this cutoff distance, the motion of the layering zone is stopped and the piston wall is allowed to continue to the BDC position. Because there is relative motion between the piston head surface and the now non-moving dynamic layering zone, cell layers will be added when the ideal layer height criteria is violated. Figures 9.6.26 to 9.6.30 show the sequence of meshes before and after the onset of cell layering when the motion in the layering zone above the piston surface is stopped (shown with ∆θ = 5◦ ).

Figure 9.6.26: Mesh Sequence 1 FLUENT provides built-in functions to handle the full piston motion and the limited piston motion for the dynamic layering zone above the piston surface. When you define the motion attribute of the dynamic layering zone above the piston surface, you need to use the limited piston motion function (**piston-limit** in the C.G. Motion UDF/Profile field in the Dynamic Zone panel). Note that you must define the parameters used by these functions before you can use them. In the current example, the piston stroke is 80 mm and the connecting rod length is 140 mm. The piston stroke cutoff is assumed to happen at 25 mm from TDC position. The lift as a function of crank angle between 344◦ and 1064◦ is shown in Figure 9.6.32 for both limited and full piston motion.


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Figure 9.6.27: Mesh Sequence 2



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9.6 Dynamic Meshes



**piston-full** **piston-limit** 8.00e-02 7.00e-02 6.00e-02 5.00e-02 4.00e-02 3.00e-02 2.00e-02 1.00e-02 0.00e+00 300

400

500

600

700

800

900

1000

1100

Crank Angle (deg)

Figure 9.6.32: Piston Position (m) as a Function of Crank Angle (deg)


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To define the motion of the valves, you need to use profiles that describe the variation of valve lift with crank angle. FLUENT expects certain profile fields to be used to define the lift and the crank angle. For example, consider the following simplified profile definition: ((ex-valve 5 point) (angle 0 180 270 (lift 0.05 0.05 1.8

360 720) 0.05 0.05))

((in-valve 5 point) (angle 0 355 440 540 720) (lift 0.05 0.05 2.0 0.05 0.05))

FLUENT expects the angle and lift fields to define the crank angle and lift variations, respectively. The angle must be specified in degrees and the lift values must be in meters. The actual valve lift profiles that you will use for the current example are shown in Figure 9.6.33. Notice that there is an overlapped period where both the intake and exhaust valves are open. in-valve ex-valve 1.40e-02

1.20e-02

1.00e-02

8.00e-03

6.00e-03

4.00e-03

2.00e-03

0.00e+00 300

400

500

600

700

800

900

1000

1100

Crank Angle (deg)

Figure 9.6.33: Intake and Exhaust Valve Lift (m) as a Function of Crank Angle (deg)

The valve lift profiles and the built-in functions will describe how each surface moves as a function of crank angle with respect to some reference point. For example, the valve lift is zero when the valve is fully closed and the valve lift is maximum when it is fully open. In order to move the surfaces, FLUENT requires that you specify the direction of motion for each surface. FLUENT will then update the “center of gravity” of each surface such that ~x = ~xref − l~eaxis

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(9.6-32)


9.6 Dynamic Meshes

where ~xref is some reference position, ~eaxis is the unit vector in the direction of motion, and l is either the valve or the piston distance with respect to the reference position ~xref . Note that the unit vector of the direction of motion is specified to point in the negative direction. For example, the correct intake valve axis for this example is (−0.3421, 0.9397), as shown in Figure 9.6.34. Reference axis

Reference origin

lift (l=0.05mm t=0) at Center of gravity

Figure 9.6.34: Definition of Valve Zone Attributes (Intake Valve)

Defining Valve Opening and Closure FLUENT assumes that once you have set up the mesh topology, the mesh topology is unchanged throughout the entire simulation. Therefore, FLUENT does not allow you to completely close the valves such that the cells between the valve and the valve seat become degenerate (flat cells) when these surfaces come in contact (removing these flat cells would require the creation of new boundary face zones). To prevent the collapse, you need to define a minimum valve lift and FLUENT will automatically stop the motion of the valve when the valve lift is smaller than the minimum valve lift value. The minimum valve lift value can be specified in the Dynamic Mesh panel. For the current example, a minimum valve lift value of 0.1 mm is assumed. When the valve position is smaller than the minimum valve lift value, it is normal practice to assume that the valve is closed. The actual closing of the valves is accomplished by deleting the sliding interfaces that connect the chamber cell zone to the dynamic layering zones on the valves. The interface zones are then converted to walls to close off the “gaps” between the valves and the valve seats. The valve opening is achieved by the reverse process. When the valve lift has reached beyond the minimum valve lift value, the valve is assumed to be open and you can redefine the sliding interfaces such that the chamber zone is now connected to the dynamic layering zones above the valves.


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Defining In-Cylinder Events FLUENT will automatically limit the valve lift values depending on the specified minimum valve lift value. However, the conversion of the sliding interface zones to walls (and vice versa) is accomplished via the in-cylinder events (see Section 9.6.9). For example, if the exhaust valve closes at −5◦ before TDC position, you must define a Delete Sliding Interface event at the crank angle of 355◦. You need to define similar events for the intake valve opening (using the Create Sliding Interface event), the intake valve closing (Delete Sliding Interface event), and the exhaust valve opening (Create Sliding Interface event) at the respective crank angles. For the current example, the exhaust valve is assumed to be open between 131◦ and 371◦ and the intake valve is open between at 345◦ and 584◦.

9.6.11

Crevice Model

Overview The crevice model implemented in FLUENT is a zero-dimensional ring-flow model based on the model outlined in Namazian and Heywood [181] and Roberts and Matthews [215]. The model is geared toward in-cylinder specific flows, and more specifically, directinjection (DI) diesel engines, and thus is available only for time-dependent simulations. that is The model takes mass, momentum, and energy from cells adjoining two boundaries and accounts for the storage of mass in the volumes of the crevices in the piston. Detailed geometric information regarding the ring and piston—typically a ring pack around the bore of an engine—is necessary to use the crevice model. An example representation is shown in Figures 9.6.35–9.6.37. Model Parameters • Piston to bore clearance—the distance between the piston and the bore. Typical values are 2 to 5 mil (80 to 120 µm) in a spark engine (SI) and 4 to 7 mil (100 to 240 µm) in some diesel engines (CI). • Ring thickness—the variable Tr in Figure 9.6.36. Typical values range from 1 to 3 mm for SI engines and 2 to 4 mm for CI engines. • Ring width—the variable Wr in Figure 9.6.36. Typical values range from 3 to 3.5 mm for SI engines and 4 to 6 mm for DI diesel engines. • Ring spacing—the distance between the bottom of one ring land and the top of the next ring land. Typical values of the ring spacing are 3 to 5 mm for SI engines and 4 to 8 mm for DI diesel engines.

9-84


9.6 Dynamic Meshes

Cylinder wall

Land length

1

p

0

Ring spacing

2 3 1: Top gap 2: Middle gap 3: Bottom gap

Piston to bore clearance

p

6

Figure 9.6.35: Crevice Model Geometry (Piston)

Wr Tr

Figure 9.6.36: Crevice Model Geometry (Ring)

Ring 1 Ring 2 Ring 3

p 1• p• 3 p• 5

p = cylinder pressure • 0 • p2 • p4 • p = crankcase pressure 6

Figure 9.6.37: Crevice Model “Network” Representation


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• Land length—the depth of the ring land (i.e., the cutout into the piston); always deeper than the width of the ring by about 1 mm. Typical values are 4 to 4.5 mm for SI engines and 5 to 7 mm for DI diesel engines. • Top gap—the clearance between the ring land and the top of the ring (40 to 80 µm). • Middle gap—the distance between the ring and the bore (10 to 40 µm). • Bottom gap—the clearance between the ring land and the bottom of the ring (40 to 80 µm). • Shared boundary and Leaking wall—the piston (e.g., wall-8) and the cylinder wall (e.g., wall.1) in most in-cylinder simulations. Cells that share a boundary with the top of the piston and the cylinder wall are defined as the crevice cells. The ring pack is the set of rings that seal the piston in the cylinder bore. As the piston moves upward in the cylinder when the valves are closed (e.g., during the compression stroke in a four-stroke cycle engine), the pressure in the cylinder rises and flow begins to move past the rings. The pressure distribution in the ring pack is modeled by assuming either fully-developed compressible flow through the spaces between the rings and the piston, or choked compressible flow between the rings and the cylinder wall. Since the temperature in the ring pack is fixed and the geometry is known, once a pressure distribution is calculated, the mass in each volume can be found using the ideal gas equation of state. The overall mass flow out of the ring pack is also calculated at each discrete step in the FLUENT solution; i.e., it is the flow past the last ring specified.

Limitations The limitations of the crevice model are that it is zero-dimensional, transient, and currently limited to two threads that share a boundary. A zero-dimensional approach is used because it is difficult to accurately predict lateral diffusion of species in the crevice. If the lateral diffusion of species is important in the simulation, as in when a spray plume in a DI engine is in close proximity to the boundary and the net mass flow is into the crevice, it is recommended that the full multidimensional crevice geometry be simulated in FLUENT using a non-conformal mesh. Additionally, this approach does not specifically track individual species, as any individual species would be instantly distributed over the entire ring pack. The mass flux into the domain from the crevice is assumed to have the same composition as the cell into which mass is flowing. The formulation of the crevice flow equations is inherently transient and is solved using FLUENT’s stiff-equation solver. A steady problem with leakage flow can be solved by running the transient problem to steady state. Additional limitations of the crevice

9-86


9.6 Dynamic Meshes

model in its current form are that only a single crevice is allowed and only one thread can have leakage. Ring dynamics are not explicitly accounted for, although ring positions can be set during the simulation. In this context, the crevice model solution is a stiff initial boundary-value problem. The stiffness increases as the pressure difference between the ring crevices increases and also as the overall pressure difference across the ring pack increases. Thus, if the initial conditions are very far from the solution during a time step, the ODE solver may not be able to integrate the equations successfully. One solution to this problem is to decrease the flow time step for several iterations. Another solution is to start with initial conditions that are closer to the solution at the end of the time step.

Crevice Model Theory FLUENT solves the equations for mass conservation in the crevice geometry by assuming laminar compressible flow in the region between the piston and the top and bottom faces of the ring, and by assuming an orifice flow between the ring and the cylinder wall. The equation for the mass flow through the ring end gaps is of the form m ˙ ij = Cd Aij ρcηij

(9.6-33)

where Cd is the discharge coefficient, Aij is the gap area, ρ is the gas density, c is the local speed of sound, and ηij is a compressibility factor given by

ηij =

            

2 γ−1

"

pi pj

2 γ

−

2 γ−1

pi pj

γ−1 γ

#0.5

pi pj

> 0.52 (9.6-34)

γ+1 2(γ−1)

pi pj

≤ 0.52

where γ is the ratio of specific heats, pi the upstream pressure and pj the downstream pressure. The equation for the mass flow through the top and bottom faces of the ring (i.e., into and out of the volume behind the piston ring) is given by

m ˙ ij =

h2ij p2i − p2j Aij 24Wr µgas RT

(9.6-35)

where hij is the cross-sectional area of the gap, Wr is the width of the ring along which the gas is flowing, µgas is the local gas viscosity, T is the temperature of the gas and R is the universal gas constant. The system of equations for a set of three rings is of the following form:


9-87


dp1 dt dp2 dt dp3 dt dp4 dt dp5 dt

= = = = =

p1 m1 p2 m2 p3 m3 p4 m4 p5 m5

(m ˙ 01 − m ˙ 12 )

(9.6-36)

(m ˙ 02 + m ˙ 12 − m ˙ 23 − m ˙ 24 )

(9.6-37)

(m ˙ 23 − m ˙ 34 )

(9.6-38)

(m ˙ 24 + m ˙ 34 − m ˙ 45 − m ˙ 46 )

(9.6-39)

(m ˙ 45 − m ˙ 56 )

(9.6-40)

where p0 is the average pressure in the crevice cells and p6 is the crankcase pressure input from the text interface. The expressions for the mass flows for numerically adjacent zones (e.g., 0-1, 1-2, 2-3, etc.) are given by Equation 9.6-35 and expressions for the mass flows for zones separated by two integers (e.g., 0-2, 2-4, 4-6) are given by Equations 9.6-33 and 9.6-34. Thus, there are 2nr − 1 equations needed for the solution to the ring-pack equations, where nr is the number of rings in the simulation.

Using the Crevice Model An optical experimental engine from Dec [53] is used below to show a working example of how to use the crevice model as it is implemented in FLUENT. The grid at ten crank angle degrees before top center is shown in Figure 9.6.38. The following example shows the necessary steps to enable the crevice model for a typical in-cylinder flow. 1. From the > prompt, enter the define/models menu: define −→models 2. Enable the crevice model: /define/models> crevice-model Enable crevice model? [yes] yes /define/models> dpm/ solidification-melting? dynamic-mesh? dynamic-mesh-controls/ crevice-model?

9-88

energy? multiphase/ nox? radiation/ crevice-model-controls/

steady? unsteady-1st-order? viscous/ unsteady-2nd-order? solver/

species/


9.6 Dynamic Meshes

Z Y

X

Grid (Time=2.2222e-02) Crank Angle=-5.00(deg)

Dec 04, 2002 FLUENT 6.1 (3d, segregated, dynamesh, spe5, rke, unsteady)

Figure 9.6.38: Experimental Engine Grid


9-89


3. Enter the ring pack geometry:

/define/models> crevice-model-controls Cylinder bore (m) [0.1] 0.1397 Piston to bore clearance (m) [3.0e-5] 5.08e-05 Piston crevice temperature (K) [400] 433 Piston sector angle (deg) [360] 45 Ring discharge coefficient [0.8] 0.7 Pressure in crankcase (exit pressure) (Pa) [101325] Write out crevice data to a file? [no] yes output file name ["crev.out"] Available wall threads are: (wall.1 wall wall-8) Leaking wall [] wall.1 Shared boundary [] wall-8 Selected boundary threads : (wall.1 wall-8) Use these zones? [yes] yes Solve crevice model ? [no] Number of rings [3] Width of ring number Thickness of ring number Spacing of ring number Land Length for ring number Top Gap of ring number Middle Gap of ring number Bottom Gap of ring number

yes 0 0 0 0 0 0 0

is: is: is: is: is: is: is:

[0.00375] [0.0015] [0.008] [0.00391] [6e-05] [4e-05] [6e-05]

Width of Thickness of Spacing of Land Length for Top Gap of Middle Gap of Bottom Gap of

ring ring ring ring ring ring ring

number number number number number number number

1 1 1 1 1 1 1


[0.00375] [0.0015] [0.008] [0.00391] [6e-05] [4e-05] [6e-05]

Width of Thickness of Spacing of Land Length for Top Gap of Middle Gap of Bottom Gap of

ring ring ring ring ring ring ring

number number number number number number number

2 2 2 2 2 2 2


[0.00375] [0.0015] [0.00391] [0.00391] [6e-05] [4e-05] [6e-05]

Initial conditions in Pressure 1 is: Pressure 2 is: Pressure 3 is: Pressure 4 is: Pressure 5 is:

ring pack [4600623.5] [4173522.5] [3689110.5] [3130620] [2214841.8]

A fast way to set up multiple rings in the ring pack is to specify only one ring and enter the geometry. Once the ring geometry is entered, invoke the crevice-modelcontrols menu a second time and specify the number of rings desired. When the number of rings changes, the geometry from the first ring is copied to all subsequent rings. Default values can be taken for the rest of the way through the menu structure.

9-90


9.6 Dynamic Meshes

A summary of the crevice model is printed out by entering the (crevice-summary) command at the command prompt: >(crevice-summary) crevice/n-rings crevice/ring-width crevice/ring-thickness crevice/ring-spacing crevice/land-length crevice/top-ring-gap crevice/mid-ring-gap crevice/bot-ring-gap crevice/piston-temperature crevice/sector-angle crevice/mid-gap-cd crevice/exit-pressure crevice/threads names of crevice/threads crevice/unit-roundoff crevice/piston-bore-clearance crevice/write? crevice/output-file crevice/solve? crevice/enabled? crevice/pressures

: : : : : : : : : : : : : : : : : : : : :

3 (0.00375 0.00375 0.00375) (0.0015 0.0015 0.0015) (0.008 0.008 0.00391) (0.00391 0.00391 0.00391) (6e-05 6e-05 6e-05) (4e-05 4e-05 4e-05) (6e-05 6e-05 6e-05) 433 45 0.7 101325 (5 6) (wall.1 wall-8) 5.9604645e-08 5.08e-05 #t crev.out #t #t (4600623.5 4173522.5 3689110.5 3130620 2214841)

Crevice Model Solution Details The under-relaxation factor for the crevice model source terms can be found in the Solution Controls panel. The default value for Crevice Model Sources is 0.8, which has been found to work well for motored engine simulations. Once the crevice model is enabled, the solution proceeds normally. Solve −→ Controls −→Solution... Solve −→ Initialize −→Initialize... Solve −→Iterate...

Postprocessing for the Crevice Model A plot of cylinder mass with and without the crevice model during the motored engine simulation is shown in Figure 9.6.39. The rate of mass loss from the crevice is proportional to the pressure difference between the cylinder and the crankcase pressure defined in the text interface. A plot of cylinder pressure with and without the crevice model for the same engine simulation is shown in Figure 9.6.40. The effect of the mass loss from the crevice is to lower the peak pressure in proportion to the total mass loss from the cylinder.


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Cylinder Mass (kg) With Crevice Without Crevice

4.60e-03

4.40e-03

4.20e-03

4.00e-03

3.80e-03

3.60e-03

3.40e-03

3.20e-03 0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055

Cylinder Mass vs. Time (Time=0.0000e+00) Dec 06, 2002 FLUENT 6.1 (axi, segregated, dynamesh, spe5, ske, unsteady)

Figure 9.6.39: Cylinder Mass vs. Crank Angle

Cylinder Pressure With Crevice Without Crevice

5.50e+06 5.00e+06 4.50e+06 4.00e+06 3.50e+06 3.00e+06 2.50e+06 2.00e+06 1.50e+06 1.00e+06 5.00e+05 0.00e+00 0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055

Cylinder Pressure vs Time (Time=0.0000e+00) Dec 06, 2002 FLUENT 6.1 (axi, segregated, dynamesh, spe5, ske, unsteady)

Figure 9.6.40: Cylinder Pressure vs. Crank Angle

9-92


9.6 Dynamic Meshes

Using the Crevice Output File The pressure in the top ring land is defined as the cylinder pressure; i.e., the pressure in the cells defining the ring landing. Intermediate pressures are available at any point during the FLUENT session through the (crevice-summary) command as previously shown. If the optional data file output is chosen in the crevice-model-controls, the intermediate pressures in the defined crevices are printed to the file crev.out at the start of each new time step. The format of the file is: # crank (deg) 1.955000e+02 1.960000e+02 1.965000e+02 1.970000e+02 1.975000e+02 1.980000e+02

data->press[0...1...2...3...4...5...6] total_mdot 2.166500e+05 1.013250e+05 1.013250e+05 1.013250e+05 2.099454e+05 1.067941e+05 1.815534e+05 1.041111e+05 2.177870e+05 1.130700e+05 1.882422e+05 1.079601e+05 2.174335e+05 1.190647e+05 1.880596e+05 1.117052e+05 2.176519e+05 1.247770e+05 1.882994e+05 1.152856e+05 2.179366e+05 1.302149e+05 1.885935e+05 1.187111e+05

1.013250e+05 1.485818e+05 1.535441e+05 1.534752e+05 1.536681e+05 1.539003e+05

1.013250e+05 1.022020e+05 1.035259e+05 1.048300e+05 1.060806e+05 1.072825e+05

1.013250e+05 1.013250e+05 1.013250e+05 1.013250e+05 1.013250e+05 1.013250e+05

0.0 -1.6 -1.6 -1.6 -1.6 -1.6

where the first column is the current flow time (or crank angle), and the next ncv + 2 columns are the ring pressures (where ncv is the number of crevice volumes, or 2nr − 1), including the face pressure on the crevice cell, and the defined pressure at the crevice exit. The final column is the mass flow past the top ring. This file is currently formatted so that it can be read into the free Gnuplot plotting package, which is available at www.gnuplot.info. To read the crevice output file into FLUENT as a data file, you will need to put each column of the crevice output file in its own individual file. The first three lines of each column of the data file should be of the form "Title" "X-Label" "Y-Label" 0 0 0 0 where the title, x-label, and y-label strings are enclosed by double quotes and the third line of the file contains four zeros. The lines following the first three lines of the file are the columns you wish to plot. For example, to plot column 1 versus column 3 of the crevice model output file in FLUENT, you would enter the following commands in a Unix terminal: cat > crev_col_1_3.dat "Column 1 vs Column 3" "Crank Angle (deg)" "Pressure behind ring 1 (Pa)" 0 0 0 0 ctrl-d where ctrl-d is the end-of-file character made holding down the key and pressing d. To append columns 1 and 3 to this file, enter


9-93


tail +2 crev.out | awk ’{print $1, $3}’ >> crev_col_1_3.dat The file crev col 1 3.dat can now be read into FLUENT using the File XY Plot panel. See Section 27.8.3 for details about creating x-y plots. For Windows users, the file crev.out can be imported into Excel for plotting purposes without any modification. A Gnuplot plot of the pressure in the ring pack crevices for the above engine simulation is shown in Figure 9.6.41. After an initial transient period where the flows in the network settle down, Figure 9.6.41 shows that the pressure in the ring crevices follows the cylinder pressure in form, though with pressure magnitudes that are controlled by the ring pack geometry. Pressures in Ring Pack vs Crank Angle 5.5e+06 Cylinder Ring 1 1-2 Gap Ring 2 2-3 Gap Ring 3 Exit Pressure

5e+06 4.5e+06 4e+06

Pressure (Pa)

3.5e+06 3e+06 2.5e+06 2e+06 1.5e+06 1e+06 500000 0 150

200

250

300

350

400

450

500

550

600

Crank Angle (deg ATDC)

Figure 9.6.41: Crevice Pressures

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Chapter 10.

Modeling Turbulence

This chapter provides details about the turbulence models available in FLUENT. Information is presented in the following sections: • Section 10.1: Introduction • Section 10.2: Choosing a Turbulence Model • Section 10.3: The Spalart-Allmaras Model • Section 10.4: The Standard, RNG, and Realizable k- Models • Section 10.5: The Standard and Shear-Stress Transport (SST) k-ω Models • Section 10.6: The Reynolds Stress Model (RSM) • Section 10.7: The Large Eddy Simulation (LES) Model • Section 10.8: Near-Wall Treatments for Wall-Bounded Turbulent Flows • Section 10.9: Grid Considerations for Turbulent Flow Simulations • Section 10.10: Problem Setup for Turbulent Flows • Section 10.11: Solution Strategies for Turbulent Flow Simulations • Section 10.12: Postprocessing for Turbulent Flows

10.1

Introduction

Turbulent flows are characterized by fluctuating velocity fields. These fluctuations mix transported quantities such as momentum, energy, and species concentration, and cause the transported quantities to fluctuate as well. Since these fluctuations can be of small scale and high frequency, they are too computationally expensive to simulate directly in practical engineering calculations. Instead, the instantaneous (exact) governing equations can be time-averaged, ensemble-averaged, or otherwise manipulated to remove the small scales, resulting in a modified set of equations that are computationally less expensive to solve. However, the modified equations contain additional unknown variables, and turbulence models are needed to determine these variables in terms of known quantities.


10-1

Modeling Turbulence

FLUENT provides the following choices of turbulence models: • Spalart-Allmaras model • k- models – Standard k- model – Renormalization-group (RNG) k- model – Realizable k- model • k-ω models – Standard k-ω model – Shear-stress transport (SST) k-ω model • v 2 -f model • Reynolds stress model (RSM) • Large eddy simulation (LES) model

10.2

Choosing a Turbulence Model

It is an unfortunate fact that no single turbulence model is universally accepted as being superior for all classes of problems. The choice of turbulence model will depend on considerations such as the physics encompassed in the flow, the established practice for a specific class of problem, the level of accuracy required, the available computational resources, and the amount of time available for the simulation. To make the most appropriate choice of model for your application, you need to understand the capabilities and limitations of the various options. The purpose of this section is to give an overview of issues related to the turbulence models provided in FLUENT. The computational effort and cost in terms of CPU time and memory of the individual models is discussed. While it is impossible to state categorically which model is best for a specific application, general guidelines are presented to help you choose the appropriate turbulence model for the flow you want to model.

10.2.1

Reynolds-Averaged Approach vs. LES

A complete time-dependent solution of the exact Navier-Stokes equations for high-Reynoldsnumber turbulent flows in complex geometries is unlikely to be attainable for some time to come. Two alternative methods can be employed to transform the Navier-Stokes equations in such a way that the small-scale turbulent fluctuations do not have to be directly simulated: Reynolds averaging and filtering. Both methods introduce additional terms in the governing equations that need to be modeled in order to achieve “closure”. (Closure implies that there are a sufficient number of equations for all the unknowns.)

10-2


10.2 Choosing a Turbulence Model

The Reynolds-averaged Navier-Stokes (RANS) equations represent transport equations for the mean flow quantities only, with all the scales of the turbulence being modeled. The approach of permitting a solution for the mean flow variables greatly reduces the computational effort. If the mean flow is steady, the governing equations will not contain time derivatives and a steady-state solution can be obtained economically. A computational advantage is seen even in transient situations, since the time step will be determined by the global unsteadiness in the mean flow rather than by the turbulence. The Reynoldsaveraged approach is generally adopted for practical engineering calculations, and uses models such as Spalart-Allmaras, k- and its variants, k-ω and its variants, and the RSM. LES provides an alternative approach in which the large eddies are computed in a timedependent simulation that uses a set of “filtered” equations. Filtering is essentially a manipulation of the exact Navier-Stokes equations to remove only the eddies that are smaller than the size of the filter, which is usually taken as the mesh size. Like Reynolds averaging, the filtering process creates additional unknown terms that must be modeled in order to achieve closure. Statistics of the mean flow quantities, which are generally of most engineering interest, are gathered during the time-dependent simulation. The attraction of LES is that, by modeling less of the turbulence (and solving more), the error induced by the turbulence model will be reduced. One might also argue that it ought to be easier to find a “universal” model for the small scales, which tend to be more isotropic and less affected by the macroscopic flow features than the large eddies. It should, however, be stressed that the application of LES to industrial fluid simulations is in its infancy. As highlighted in a recent review publication [81], typical applications to date have been for simple geometries. This is mainly because of the large computer resources required to resolve the energy-containing turbulent eddies. Most successful LES has been done using high-order spatial discretization, with great care being taken to resolve all scales larger than the inertial subrange. The degradation of accuracy in the mean flow quantities with poorly resolved LES is not well documented. In addition, the use of wall functions with LES is an approximation that requires further validation. As a general guideline, therefore, it is recommended that the conventional turbulence models employing the Reynolds-averaged approach be used for practical calculations. The LES approach, described further in Section 10.7, has been made available for you to try if you have the computational resources and are willing to invest the effort. The rest of this section will deal with the choice of models using the Reynolds-averaged approach.

10.2.2

Reynolds (Ensemble) Averaging

In Reynolds averaging, the solution variables in the instantaneous (exact) Navier-Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged) and fluctuating components. For the velocity components: ui = u¯i + u0i


(10.2-1)

10-3

Modeling Turbulence

where u¯i and u0i are the mean and fluctuating velocity components (i = 1, 2, 3). Likewise, for pressure and other scalar quantities: φ = φ¯ + φ0

(10.2-2)

where φ denotes a scalar such as pressure, energy, or species concentration. Substituting expressions of this form for the flow variables into the instantaneous continuity and momentum equations and taking a time (or ensemble) average (and dropping the overbar on the mean velocity, u¯) yields the ensemble-averaged momentum equations. They can be written in Cartesian tensor form as: ∂ρ ∂ + (ρui ) = 0 ∂t ∂xi

(10.2-3)

"

∂ ∂ ∂p ∂ ∂ui ∂uj 2 ∂ul (ρui ) + (ρui uj ) = − + µ + − δij ∂t ∂xj ∂xi ∂xj ∂xj ∂xi 3 ∂xl

!#

+

∂ (−ρu0i u0j ) ∂xj (10.2-4)

Equations 10.2-3 and 10.2-4 are called Reynolds-averaged Navier-Stokes (RANS) equations. They have the same general form as the instantaneous Navier-Stokes equations, with the velocities and other solution variables now representing ensemble-averaged (or time-averaged) values. Additional terms now appear that represent the effects of turbulence. These Reynolds stresses, −ρu0i u0j , must be modeled in order to close Equation 10.2-4. For variable-density flows, Equations 10.2-3 and 10.2-4 can be interpreted as Favreaveraged Navier-Stokes equations [102], with the velocities representing mass-averaged values. As such, Equations 10.2-3 and 10.2-4 can be applied to density-varying flows.

10.2.3

Boussinesq Approach vs. Reynolds Stress Transport Models

The Reynolds-averaged approach to turbulence modeling requires that the Reynolds stresses in Equation 10.2-4 be appropriately modeled. A common method employs the Boussinesq hypothesis [102] to relate the Reynolds stresses to the mean velocity gradients: − ρu0i u0j = µt

∂ui ∂uj + ∂xj ∂xi

!

!

2 ∂ui − ρk + µt δij 3 ∂xi

(10.2-5)

The Boussinesq hypothesis is used in the Spalart-Allmaras model, the k- models, and the k-ω models. The advantage of this approach is the relatively low computational

10-4



cost associated with the computation of the turbulent viscosity, µt . In the case of the Spalart-Allmaras model, only one additional transport equation (representing turbulent viscosity) is solved. In the case of the k- and k-ω models, two additional transport equations (for the turbulence kinetic energy, k, and either the turbulence dissipation rate, , or the specific dissipation rate, ω) are solved, and µt is computed as a function of k and . The disadvantage of the Boussinesq hypothesis as presented is that it assumes µt is an isotropic scalar quantity, which is not strictly true. The alternative approach, embodied in the RSM, is to solve transport equations for each of the terms in the Reynolds stress tensor. An additional scale-determining equation (normally for ) is also required. This means that five additional transport equations are required in 2D flows and seven additional transport equations must be solved in 3D. In many cases, models based on the Boussinesq hypothesis perform very well, and the additional computational expense of the Reynolds stress model is not justified. However, the RSM is clearly superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flow. Such cases include highly swirling flows and stressdriven secondary flows.

10.2.4

The Spalart-Allmaras Model

The Spalart-Allmaras model is a relatively simple one-equation model that solves a modeled transport equation for the kinematic eddy (turbulent) viscosity. This embodies a relatively new class of one-equation models in which it is not necessary to calculate a length scale related to the local shear layer thickness. The Spalart-Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity for turbomachinery applications. In its original form, the Spalart-Allmaras model is effectively a low-Reynolds-number model, requiring the viscous-affected region of the boundary layer to be properly resolved. In FLUENT, however, the Spalart-Allmaras model has been implemented to use wall functions when the mesh resolution is not sufficiently fine. This might make it the best choice for relatively crude simulations on coarse meshes where accurate turbulent flow computations are not critical. Furthermore, the near-wall gradients of the transported variable in the model are much smaller than the gradients of the transported variables in the k- or k-ω models. This might make the model less sensitive to numerical error when non-layered meshes are used near walls. See Section 5.1.2 for further discussion of numerical error. On a cautionary note, however, the Spalart-Allmaras model is still relatively new, and no claim is made regarding its suitability to all types of complex engineering flows. For instance, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence. Furthermore, one-equation models are often criticized for their inability to rapidly accommodate changes in length scale, such as might be necessary when the flow changes


10-5

Modeling Turbulence

abruptly from a wall-bounded to a free shear flow.

The Detached Eddy Simulation (DES) Model The detached eddy simulation (DES) model is a modified version of the Spalart-Allmaras model and can be considered a more practical alternative to LES for predicting the flow around high-Reynolds-number, high-lift airfoils. The DES approach combines an unsteady RANS version of the Spalart-Allmaras model with a filtered version of the same model to create two separate regions inside the flow domain: one that is LES-based and another that is close to the wall where the modeling is dominated by the RANSbased approach. The LES region is normally associated with the high-Re core turbulent region where large turbulence scales play a dominant role. In this region, the DES model recovers the pure LES model based on a one-equation sub-grid model. Close to the wall, where viscous effects prevail, the standard RANS model is recovered.

10.2.5


The simplest “complete models” of turbulence are two-equation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined. The standard k- model in FLUENT falls within this class of turbulence model and has become the workhorse of practical engineering flow calculations in the time since it was proposed by Launder and Spalding [140]. Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations. It is a semi-empirical model, and the derivation of the model equations relies on phenomenological considerations and empiricism. As the strengths and weaknesses of the standard k- model have become known, improvements have been made to the model to improve its performance. Two of these variants are available in FLUENT: the RNG k- model [299] and the realizable k- model [232].

10.2.6

The RNG k- Model

The RNG k- model was derived using a rigorous statistical technique (called renormalization group theory). It is similar in form to the standard k- model, but includes the following refinements: • The RNG model has an additional term in its equation that significantly improves the accuracy for rapidly strained flows. • The effect of swirl on turbulence is included in the RNG model, enhancing accuracy for swirling flows. • The RNG theory provides an analytical formula for turbulent Prandtl numbers, while the standard k- model uses user-specified, constant values.

10-6



• While the standard k- model is a high-Reynolds-number model, the RNG theory provides an analytically-derived differential formula for effective viscosity that accounts for low-Reynolds-number effects. Effective use of this feature does, however, depend on an appropriate treatment of the near-wall region. These features make the RNG k- model more accurate and reliable for a wider class of flows than the standard k- model.

10.2.7

The Realizable k- Model

The realizable k- model is a relatively recent development and differs from the standard k- model in two important ways: • The realizable k- model contains a new formulation for the turbulent viscosity. • A new transport equation for the dissipation rate, , has been derived from an exact equation for the transport of the mean-square vorticity fluctuation. The term “realizable” means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows. Neither the standard k- model nor the RNG k- model is realizable. An immediate benefit of the realizable k- model is that it more accurately predicts the spreading rate of both planar and round jets. It is also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation. Both the realizable and RNG k- models have shown substantial improvements over the standard k- model where the flow features include strong streamline curvature, vortices, and rotation. Since the model is still relatively new, it is not clear in exactly which instances the realizable k- model consistently outperforms the RNG model. However, initial studies have shown that the realizable model provides the best performance of all the k- model versions for several validations of separated flows and flows with complex secondary flow features. One limitation of the realizable k- model is that it produces non-physical turbulent viscosities in situations when the computational domain contains both rotating and stationary fluid zones (e.g., multiple reference frames, rotating sliding meshes). This is due to the fact that the realizable k- model includes the effects of mean rotation in the definition of the turbulent viscosity (see Equations 10.4-17–10.4-19). This extra rotation effect has been tested on single rotating reference frame systems and showed superior behavior over the standard k- model. However, due to the nature of this modification, its application to multiple reference frame systems should be taken with some caution. See Section 10.4.3 for information about how to include or exclude this term from the model.


10-7

Modeling Turbulence

10.2.8

The Standard k-ω Model

The standard k-ω model in FLUENT is based on the Wilcox k-ω model [294], which incorporates modifications for low-Reynolds-number effects, compressibility, and shear flow spreading. The Wilcox model predicts free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wall-bounded flows and free shear flows. A variation of the standard k-ω model called the SST k-ω model is also available in FLUENT, and is described in Section 10.2.9.

10.2.9

The Shear-Stress Transport (SST) k-ω Model

The shear-stress transport (SST) k-ω model was developed by Menter [166] to effectively blend the robust and accurate formulation of the k-ω model in the near-wall region with the free-stream independence of the k- model in the far field. To achieve this, the k- model is converted into a k-ω formulation. The SST k-ω model is similar to the standard k-ω model, but includes the following refinements: • The standard k-ω model and the transformed k- model are both multiplied by a blending function and both models are added together. The blending function is designed to be one in the near-wall region, which activates the standard k-ω model, and zero away from the surface, which activates the transformed k- model. • The SST model incorporates a damped cross-diffusion derivative term in the ω equation. • The definition of the turbulent viscosity is modified to account for the transport of the turbulent shear stress. • The modeling constants are different. These features make the SST k-ω model more accurate and reliable for a wider class of flows (e.g., adverse pressure gradient flows, airfoils, transonic shock waves) than the standard k-ω model.

10.2.10

The v 2 -f Model

The v 2 -f model is similar to the standard k- model, but incorporates near-wall turbulence anisotropy and non-local pressure-strain effects. It is a general low-Reynoldsnumber turbulence model that is valid all the way up to solid walls, and therefore does not need to make use of wall functions. Although the model was originally developed for attached or mildly separated boundary layers [65], it also accurately simulates flows dominated by separation [17].

10-8



The distinguishing feature of the v 2 -f model is its use of the velocity scale, v 2 , instead of the turbulent kinetic energy, k, for evaluating the eddy viscosity. v 2 , which can be thought of as the velocity fluctuation normal to the streamlines, has shown to provide the right scaling in representing the damping of turbulent transport close to the wall, a feature that k does not provide. For more information about the theoretical background and usage of the v 2 -f model, please visit the Fluent User Services Center (www.fluentusers.com).

10.2.11

The Reynolds Stress Model (RSM)

The Reynolds stress model (RSM) is the most elaborate turbulence model that FLUENT provides. Abandoning the isotropic eddy-viscosity hypothesis, the RSM closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. This means that five additional transport equations are required in 2D flows and seven additional transport equations must be solved in 3D. Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than one-equation and two-equation models, it has greater potential to give accurate predictions for complex flows. However, the fidelity of RSM predictions is still limited by the closure assumptions employed to model various terms in the exact transport equations for the Reynolds stresses. The modeling of the pressure-strain and dissipation-rate terms is particularly challenging, and often considered to be responsible for compromising the accuracy of RSM predictions. The RSM might not always yield results that are clearly superior to the simpler models in all classes of flows to warrant the additional computational expense. However, use of the RSM is a must when the flow features of interest are the result of anisotropy in the Reynolds stresses. Among the examples are cyclone flows, highly swirling flows in combustors, rotating flow passages, and the stress-induced secondary flows in ducts.

10.2.12

Computational Effort: CPU Time and Solution Behavior

In terms of computation, the Spalart-Allmaras model is the least expensive turbulence model of the options provided in FLUENT, since only one turbulence transport equation is solved. The standard k- model clearly requires more computational effort than the SpalartAllmaras model since an additional transport equation is solved. The realizable k- model requires only slightly more computational effort than the standard k- model. However, due to the extra terms and functions in the governing equations and a greater degree of non-linearity, computations with the RNG k- model tend to take 10–15% more CPU time than with the standard k- model. Like the k- models, the k-ω models are also two-equation models, and thus require about the same computational effort.


10-9

Modeling Turbulence

Compared with the k- and k-ω models, the RSM requires additional memory and CPU time due to the increased number of the transport equations for Reynolds stresses. However, efficient programming in FLUENT has reduced the CPU time per iteration significantly. On average, the RSM in FLUENT requires 50–60% more CPU time per iteration compared to the k- and k-ω models. Furthermore, 15–20% more memory is needed. Aside from the time per iteration, the choice of turbulence model can affect the ability of FLUENT to obtain a converged solution. For example, the standard k- model is known to be slightly over-diffusive in certain situations, while the RNG k- model is designed such that the turbulent viscosity is reduced in response to high rates of strain. Since diffusion has a stabilizing effect on the numerics, the RNG model is more likely to be susceptible to instability in steady-state solutions. However, this should not necessarily be seen as a disadvantage of the RNG model, since these characteristics make it more responsive to important physical instabilities such as time-dependent turbulent vortex shedding. Similarly, the RSM may take more iterations to converge than the k- and k-ω models due to the strong coupling between the Reynolds stresses and the mean flow.

10.3

The Spalart-Allmaras Model

In turbulence models that employ the Boussinesq approach, the central issue is how the eddy viscosity is computed. The model proposed by Spalart and Allmaras [251] solves a transport equation for a quantity that is a modified form of the turbulent kinematic viscosity.

10.3.1

Transport Equation for the Spalart-Allmaras Model

The transported variable in the Spalart-Allmaras model, ν˜, is identical to the turbulent kinematic viscosity except in the near-wall (viscous-affected) region. The transport equation for ν˜ is



∂ ∂ 1 ∂ (ρ˜ ν )+ (ρ˜ ν ui ) = G ν +  ∂t ∂xi σν˜ ∂xj

(

∂ ν˜ (µ + ρ˜ ν) ∂xj

)

∂ ν˜ + Cb2 ρ ∂xj

!2   −Yν +Sν˜ (10.3-1)

where Gν is the production of turbulent viscosity and Yν is the destruction of turbulent viscosity that occurs in the near-wall region due to wall blocking and viscous damping. σν˜ and Cb2 are constants and ν is the molecular kinematic viscosity. Sν˜ is a user-defined source term. Note that since the turbulence kinetic energy k is not calculated in the Spalart-Allmaras model, the last term in Equation 10.2-5 is ignored when estimating the Reynolds stresses.

10-10


10.3 The Spalart-Allmaras Model

10.3.2

Modeling the Turbulent Viscosity

The turbulent viscosity, µt , is computed from µt = ρ˜ ν fv1

(10.3-2)

where the viscous damping function, fv1 , is given by fv1 =

χ3 3 χ3 + Cv1

(10.3-3)

ν˜ ν

(10.3-4)

and χ≡

10.3.3

Modeling the Turbulent Production

The production term, Gν , is modeled as Gν = Cb1 ρS˜ν˜

(10.3-5)

ν˜ S˜ ≡ S + 2 2 fv2 κd

(10.3-6)

where

and fv2 = 1 −

χ 1 + χfv1

(10.3-7)

Cb1 and κ are constants, d is the distance from the wall, and S is a scalar measure of the deformation tensor. By default in FLUENT, as in the original model proposed by Spalart and Allmaras, S is based on the magnitude of the vorticity: S≡

q

2Ωij Ωij

(10.3-8)

where Ωij is the mean rate-of-rotation tensor and is defined by 1 Ωij = 2


∂ui ∂uj − ∂xj ∂xi

!

(10.3-9)

10-11

Modeling Turbulence

The justification for the default expression for S is that, for the wall-bounded flows that were of most interest when the model was formulated, turbulence is found only where vorticity is generated near walls. However, it has since been acknowledged that one should also take into account the effect of mean strain on the turbulence production, and a modification to the model has been proposed [49] and incorporated into FLUENT. This modification combines measures of both rotation and strain tensors in the definition of S: S ≡ |Ωij | + Cprod min (0, |Sij | − |Ωij |)

(10.3-10)

where Cprod = 2.0, |Ωij | ≡

q

2Ωij Ωij , |Sij | ≡

q

2Sij Sij

with the mean strain rate, Sij , defined as 1 Sij = 2

∂uj ∂ui + ∂xi ∂xj

!

(10.3-11)

Including both the rotation and strain tensors reduces the production of eddy viscosity and consequently reduces the eddy viscosity itself in regions where the measure of vorticity exceeds that of strain rate. One such example can be found in vortical flows, i.e., flow near the core of a vortex subjected to a pure rotation where turbulence is known to be suppressed. Including both the rotation and strain tensors more correctly accounts for the effects of rotation on turbulence. The default option (including the rotation tensor only) tends to overpredict the production of eddy viscosity and hence overpredicts the eddy viscosity itself in certain circumstances. You can select the modified form for calculating production in the Viscous Model panel.

10.3.4

Modeling the Turbulent Destruction

The destruction term is modeled as

Yν = Cw1 ρfw

2

ν˜ d

(10.3-12)

where 6 1 + Cw3 fw = g 6 6 g + Cw3

"

10-12

#1/6

(10.3-13)


10.3 The Spalart-Allmaras Model

g = r + Cw2 r6 − r

r≡

ν˜ ˜ 2 d2 Sκ

(10.3-14)

(10.3-15)

Cw1 , Cw2 , and Cw3 are constants, and S˜ is given by Equation 10.3-6. Note that the modification described above to include the effects of mean strain on S will also affect the value of S˜ used to compute r.

10.3.5

The DES Model

The standard Spalart-Allmaras model uses the distance to the closest wall as the definition for the length scale d, which plays a major role in determining the level of production and destruction of turbulent viscosity (Equations 10.3-6, 10.3-12, and 10.3-15). The DES ˜ model, as proposed by Shur et al. [233] replaces d everywhere with a new length scale d, defined as d˜ = min(d, Cdes ∆)

(10.3-16)

where the grid spacing, ∆, is based on the largest grid space in the x, y, or z directions forming the computational cell. The empirical constant Cdes has a value of 0.65.

10.3.6

Model Constants

The model constants Cb1 , Cb2 , σν˜ , Cv1 , Cw1 , Cw2 , Cw3 , and κ have the following default values [251]: 2 Cb1 = 0.1355, Cb2 = 0.622, σν˜ = , Cv1 = 7.1 3 Cw1 =

10.3.7

Cb1 (1 + Cb2 ) + , Cw2 = 0.3, Cw3 = 2.0, κ = 0.4187 κ2 σν˜

Wall Boundary Conditions

At walls, the modified turbulent kinematic viscosity, ν˜, is set to zero. When the mesh is fine enough to resolve the laminar sublayer, the wall shear stress is obtained from the laminar stress-strain relationship: u ρuτ y = uτ µ


(10.3-17)

10-13

Modeling Turbulence

If the mesh is too coarse to resolve the laminar sublayer, it is assumed that the centroid of the wall-adjacent cell falls within the logarithmic region of the boundary layer, and the law-of-the-wall is employed: 1 ρuτ y u = ln E uτ κ µ

!

(10.3-18)

where u is the velocity parallel to the wall, uτ is the shear velocity, y is the distance from the wall, κ is the von Kármán constant (0.4187), and E = 9.793.

10.3.8

Convective Heat and Mass Transfer Modeling

In FLUENT, turbulent heat transport is modeled using the concept of Reynolds’ analogy to turbulent momentum transfer. The “modeled” energy equation is thus given by the following: ∂ ∂ ∂ (ρE) + [ui (ρE + p)] = ∂t ∂xi ∂xj

"

c p µt k+ Prt

#

∂T + ui (τij )eff + Sh ∂xj

(10.3-19)

where k, in this case, is the thermal conductivity, E is the total energy, and (τij )eff is the deviatoric stress tensor, defined as

(τij )eff = µeff


!

2 ∂ui − µeff δij 3 ∂xi

The term involving (τij )eff represents the viscous heating, and is always computed in the coupled solvers. It is not computed by default in the segregated solver, but it can be enabled in the Viscous Model panel. The default value of the turbulent Prandtl number is 0.85. You can change the value of Prt in the Viscous Model panel. Turbulent mass transfer is treated similarly, with a default turbulent Schmidt number of 0.7. This default value can be changed in the Viscous Model panel. Wall boundary conditions for scalar transport are handled analogously to momentum, using the appropriate “law-of-the-wall”.

10-14


10.4 The Standard, RNG, and Realizable k- Models

10.4

The Standard, RNG, and Realizable k- Models

This section presents the standard, RNG, and realizable k- models. All three models have similar forms, with transport equations for k and . The major differences in the models are as follows: • the method of calculating turbulent viscosity • the turbulent Prandtl numbers governing the turbulent diffusion of k and • the generation and destruction terms in the equation The transport equations, methods of calculating turbulent viscosity, and model constants are presented separately for each model. The features that are essentially common to all models follow, including turbulent production, generation due to buoyancy, accounting for the effects of compressibility, and modeling heat and mass transfer.

10.4.1


The standard k- model [140] is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (). The model transport equation for k is derived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart. In the derivation of the k- model, it was assumed that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard k- model is therefore valid only for fully turbulent flows.

Transport Equations for the Standard k- Model The turbulence kinetic energy, k, and its rate of dissipation, , are obtained from the following transport equations: ∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj

"

µt µ+ σk

#

∂k + Gk + Gb − ρ − YM + Sk ∂xj

(10.4-1)

and

∂ ∂ ∂ (ρ) + (ρui ) = ∂t ∂xi ∂xj

"

µt µ+ σ

∂ 2 + C1 (Gk + C3 Gb ) − C2 ρ + S (10.4-2) ∂xj k k #

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated as described in Section 10.4.4. Gb is the generation


10-15

Modeling Turbulence

of turbulence kinetic energy due to buoyancy, calculated as described in Section 10.4.5. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, calculated as described in Section 10.4.6. C1 , C2 , and C3 are constants. σk and σ are the turbulent Prandtl numbers for k and , respectively. Sk and S are user-defined source terms.

Modeling the Turbulent Viscosity The turbulent (or eddy) viscosity, µt , is computed by combining k and as follows: µt = ρCµ

k2

(10.4-3)

where Cµ is a constant.

Model Constants The model constants C1 , C2 , Cµ , σk , and σ have the following default values [140]: C1 = 1.44, C2 = 1.92, Cµ = 0.09, σk = 1.0, σ = 1.3 These default values have been determined from experiments with air and water for fundamental turbulent shear flows including homogeneous shear flows and decaying isotropic grid turbulence. They have been found to work fairly well for a wide range of wallbounded and free shear flows. Although the default values of the model constants are the standard ones most widely accepted, you can change them (if needed) in the Viscous Model panel.

10.4.2

The RNG k- Model

The RNG-based k- turbulence model is derived from the instantaneous Navier-Stokes equations, using a mathematical technique called “renormalization group” (RNG) methods. The analytical derivation results in a model with constants different from those in the standard k- model, and additional terms and functions in the transport equations for k and . A more comprehensive description of RNG theory and its application to turbulence can be found in [40].

Transport Equations for the RNG k- Model The RNG k- model has a similar form to the standard k- model: ∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj

10-16

∂k αk µeff ∂xj

!

+ Gk + Gb − ρ − YM + Sk

(10.4-4)



and ∂ ∂ ∂ (ρ) + (ρui ) = ∂t ∂xi ∂xj

∂ 2 α µeff + C1 (Gk + C3 Gb ) − C2 ρ − R + S (10.4-5) ∂xj k k !

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated as described in Section 10.4.4. Gb is the generation of turbulence kinetic energy due to buoyancy, calculated as described in Section 10.4.5. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, calculated as described in Section 10.4.6. The quantities αk and α are the inverse effective Prandtl numbers for k and , respectively. Sk and S are user-defined source terms.

Modeling the Effective Viscosity The scale elimination procedure in RNG theory results in a differential equation for turbulent viscosity: ρ2 k d √ µ

!

= 1.72 √

νˆ3

νˆ dˆ ν − 1 + Cν

(10.4-6)

where

νˆ = µeff /µ Cν ≈ 100 Equation 10.4-6 is integrated to obtain an accurate description of how the effective turbulent transport varies with the effective Reynolds number (or eddy scale), allowing the model to better handle low-Reynolds-number and near-wall flows. In the high-Reynolds-number limit, Equation 10.4-6 gives µt = ρCµ

k2

(10.4-7)

with Cµ = 0.0845, derived using RNG theory. It is interesting to note that this value of Cµ is very close to the empirically-determined value of 0.09 used in the standard k- model. In FLUENT, by default, the effective viscosity is computed using the high-Reynoldsnumber form in Equation 10.4-7. However, there is an option available that allows you to use the differential relation given in Equation 10.4-6 when you need to include lowReynolds-number effects.


10-17

Modeling Turbulence

RNG Swirl Modification Turbulence, in general, is affected by rotation or swirl in the mean flow. The RNG model in FLUENT provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately. The modification takes the following functional form:

µt = µt0

k f αs , Ω,

!

(10.4-8)

where µt0 is the value of turbulent viscosity calculated without the swirl modification using either Equation 10.4-6 or Equation 10.4-7. Ω is a characteristic swirl number evaluated within FLUENT, and αs is a swirl constant that assumes different values depending on whether the flow is swirl-dominated or only mildly swirling. This swirl modification always takes effect for axisymmetric, swirling flows and three-dimensional flows when the RNG model is selected. For mildly swirling flows (the default in FLUENT), αs is set to 0.05 and cannot be modified. For strongly swirling flows, however, a higher value of αs can be used.

Calculating the Inverse Effective Prandtl Numbers The inverse effective Prandtl numbers, αk and α , are computed using the following formula derived analytically by the RNG theory: α − 1.3929

α0 − 1.3929

0.6321 α + 2.3929

α0 + 2.3929

0.3679 µmol =

µeff

(10.4-9)

where α0 = 1.0. In the high-Reynolds-number limit (µmol /µeff 1), αk = α ≈ 1.393.

The R Term in the Equation The main difference between the RNG and standard k- models lies in the additional term in the equation given by R =

Cµ ρη 3 (1 − η/η0 ) 2 1 + βη 3 k

(10.4-10)

where η ≡ Sk/, η0 = 4.38, β = 0.012. The effects of this term in the RNG equation can be seen more clearly by rearranging Equation 10.4-5. Using Equation 10.4-10, the third and fourth terms on the right-hand side of Equation 10.4-5 can be merged, and the resulting equation can be rewritten as

10-18



∂ ∂ ∂ (ρui ) = (ρ) + ∂t ∂xi ∂xj

∂ α µeff ∂xj

!

2 ∗ + C1 (Gk + C3 Gb ) − C2 ρ k k

(10.4-11)

∗ where C2 is given by

∗ C2 ≡ C2 +

Cµ ρη 3 (1 − η/η0 ) 1 + βη 3

(10.4-12)

∗ In regions where η < η0 , the R term makes a positive contribution, and C2 becomes larger than C2 . In the logarithmic layer, for instance, it can be shown that η ≈ 3.0, ∗ giving C2 ≈ 2.0, which is close in magnitude to the value of C2 in the standard k- model (1.92). As a result, for weakly to moderately strained flows, the RNG model tends to give results largely comparable to the standard k- model.

In regions of large strain rate (η > η0 ), however, the R term makes a negative contribu∗ tion, making the value of C2 less than C2 . In comparison with the standard k- model, the smaller destruction of augments , reducing k and, eventually, the effective viscosity. As a result, in rapidly strained flows, the RNG model yields a lower turbulent viscosity than the standard k- model. Thus, the RNG model is more responsive to the effects of rapid strain and streamline curvature than the standard k- model, which explains the superior performance of the RNG model for certain classes of flows.

Model Constants The model constants C1 and C2 in Equation 10.4-5 have values derived analytically by the RNG theory. These values, used by default in FLUENT, are C1 = 1.42, C2 = 1.68

10.4.3

The Realizable k- Model

In addition to the standard and RNG-based k- models described in Sections 10.4.1 and 10.4.2, FLUENT also provides the so-called realizable k- model [232]. The term “realizable” means that the model satisfies certain mathematical constraints on the normal stresses, consistent with the physics of turbulent flows. To understand this, consider combining the Boussinesq relationship (Equation 10.2-5) and the eddy viscosity definition (Equation 10.4-3) to obtain the following expression for the normal Reynolds stress in an incompressible strained mean flow: 2 ∂U u2 = k − 2 νt 3 ∂x


(10.4-13)

10-19

Modeling Turbulence

Using Equation 10.4-3 for νt ≡ µt /ρ, one obtains the result that the normal stress, u2 , which by definition is a positive quantity, becomes negative, i.e., “non-realizable”, when the strain is large enough to satisfy k ∂U 1 > ≈ 3.7 ∂x 3Cµ

(10.4-14)

Similarly, it can also be shown that the Schwarz inequality for shear stresses (uα uβ 2 ≤ u2α u2β ; no summation over α and β) can be violated when the mean strain rate is large. The most straightforward way to ensure the realizability (positivity of normal stresses and Schwarz inequality for shear stresses) is to make Cµ variable by sensitizing it to the mean flow (mean deformation) and the turbulence (k, ). The notion of variable Cµ is suggested by many modelers including Reynolds [212], and is well substantiated by experimental evidence. For example, Cµ is found to be around 0.09 in the inertial sublayer of equilibrium boundary layers, and 0.05 in a strong homogeneous shear flow. Another weakness of the standard k- model or other traditional k- models lies with the modeled equation for the dissipation rate (). The well-known round-jet anomaly (named based on the finding that the spreading rate in planar jets is predicted reasonably well, but prediction of the spreading rate for axisymmetric jets is unexpectedly poor) is considered to be mainly due to the modeled dissipation equation. The realizable k- model proposed by Shih et al. [232] was intended to address these deficiencies of traditional k- models by adopting the following: • a new eddy-viscosity formula involving a variable Cµ originally proposed by Reynolds [212] • a new model equation for dissipation () based on the dynamic equation of the mean-square vorticity fluctuation

Transport Equations for the Realizable k- Model The modeled transport equations for k and in the realizable k- model are

∂ ∂ ∂ (ρk) + (ρkuj ) = ∂t ∂xi ∂xi

"

µt µ+ σk

#

∂k + Gk + Gb − ρ − YM + Sk ∂xj

(10.4-15)

and

∂ ∂ ∂ (ρ) + (ρuj ) = ∂t ∂xj ∂xj

10-20

"

µt µ+ σ

∂ 2 √ + C1 C3 Gb + S + ρ C1 S − ρ C2 ∂xj k + ν k (10.4-16) #



where "

#

η C1 = max 0.43, , η+5

η=S

k

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated as described in Section 10.4.4. Gb is the generation of turbulence kinetic energy due to buoyancy, calculated as described in Section 10.4.5. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, calculated as described in Section 10.4.6. C2 and C1 are constants. σk and σ are the turbulent Prandtl numbers for k and , respectively. Sk and S are user-defined source terms. Note that the k equation (Equation 10.4-15) is the same as that in the standard k model (Equation 10.4-1) and the RNG k- model (Equation 10.4-4), except for the model constants. However, the form of the equation is quite different from those in the standard and RNG-based k- models (Equations 10.4-2 and 10.4-5). One of the noteworthy features is that the production term in the equation (the second term on the right-hand side of Equation 10.4-16) does not involve the production of k; i.e., it does not contain the same Gk term as the other k- models. It is believed that the present form better represents the spectral energy transfer. Another desirable feature is that the destruction term (the next to last term on the right-hand side of Equation 10.4-16) does not have any singularity; i.e., its denominator never vanishes, even if k vanishes or becomes smaller than zero. This feature is contrasted with traditional k- models, which have a singularity due to k in the denominator. This model has been extensively validated for a wide range of flows [129, 232], including rotating homogeneous shear flows, free flows including jets and mixing layers, channel and boundary layer flows, and separated flows. For all these cases, the performance of the model has been found to be substantially better than that of the standard k- model. Especially noteworthy is the fact that the realizable k- model resolves the round-jet anomaly; i.e., it predicts the spreading rate for axisymmetric jets as well as that for planar jets.

Modeling the Turbulent Viscosity As in other k- models, the eddy viscosity is computed from µt = ρCµ

k2

(10.4-17)

The difference between the realizable k- model and the standard and RNG k- models is that Cµ is no longer constant. It is computed from


10-21

Modeling Turbulence

1 ∗ A0 + As kU

(10.4-18)

˜ ij Ω ˜ ij Sij Sij + Ω

(10.4-19)

Cµ = where ∗

U ≡

q

and

˜ ij = Ωij − 2ijk ωk Ω Ωij = Ωij − ijk ωk where Ωij is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity ωk . The model constants A0 and As are given by A0 = 4.04, As =

√

6 cos φ

where √ 1 Sij Sjk Ski ˜ q 1 , S = Sij Sij , Sij = φ = cos−1 ( 6W ), W = 3 2 S˜


!

It can be seen that Cµ is a function of the mean strain and rotation rates, the angular velocity of the system rotation, and the turbulence fields (k and ). Cµ in Equation 10.4-17 can be shown to recover the standard value of 0.09 for an inertial sublayer in an equilibrium boundary layer.

! In FLUENT, the term −2ijk ωk is, by default, not included in the calculation of Ω˜ ij . This is an extra rotation term that is not compatible with cases involving sliding meshes or multiple reference frames. If you want to include this term in the model, you can enable it by using the define/models/viscous/turbulence-expert/rke-cmu-rotation-term? text command and entering yes at the prompt.

Model Constants The model constants C2 , σk , and σ have been established to ensure that the model performs well for certain canonical flows. The model constants are C1 = 1.44, C2 = 1.9, σk = 1.0, σ = 1.2

10-22



10.4.4

Modeling Turbulent Production in the k- Models

The term Gk , representing the production of turbulence kinetic energy, is modeled identically for the standard, RNG, and realizable k- models. From the exact equation for the transport of k, this term may be defined as Gk = −ρu0i u0j

∂uj ∂xi

(10.4-20)

To evaluate Gk in a manner consistent with the Boussinesq hypothesis, G k = µt S 2

(10.4-21)

where S is the modulus of the mean rate-of-strain tensor, defined as S≡

10.4.5

q

2Sij Sij

(10.4-22)

Effects of Buoyancy on Turbulence in the k- Models

When a non-zero gravity field and temperature gradient are present simultaneously, the k- models in FLUENT account for the generation of k due to buoyancy (Gb in Equations 10.4-1, 10.4-4, and 10.4-15), and the corresponding contribution to the production of in Equations 10.4-2, 10.4-5, and 10.4-16. The generation of turbulence due to buoyancy is given by Gb = βgi

µt ∂T Prt ∂xi

(10.4-23)

where Prt is the turbulent Prandtl number for energy and gi is the component of the gravitational vector in the ith direction. For the standard and realizable k- models, the default value of Prt is 0.85. In the case of the RNG k- model, Prt = 1/α, where α is given by Equation 10.4-9, but with α0 = 1/Pr = k/µcp . The coefficient of thermal expansion, β, is defined as 1 β=− ρ

∂ρ ∂T

!

(10.4-24)

p

For ideal gases, Equation 10.4-23 reduces to Gb = −gi


µt ∂ρ ρPrt ∂xi

(10.4-25)

10-23

Modeling Turbulence

It can be seen from the transport equations for k (Equations 10.4-1, 10.4-4, and 10.4-15) that turbulence kinetic energy tends to be augmented (Gb > 0) in unstable stratification. For stable stratification, buoyancy tends to suppress the turbulence (Gb < 0). In FLUENT, the effects of buoyancy on the generation of k are always included when you have both a non-zero gravity field and a non-zero temperature (or density) gradient. While the buoyancy effects on the generation of k are relatively well understood, the effect on is less clear. In FLUENT, by default, the buoyancy effects on are neglected simply by setting Gb to zero in the transport equation for (Equation 10.4-2, 10.4-5, or 10.4-16). However, you can include the buoyancy effects on in the Viscous Model panel. In this case, the value of Gb given by Equation 10.4-25 is used in the transport equation for (Equation 10.4-2, 10.4-5, or 10.4-16). The degree to which is affected by the buoyancy is determined by the constant C3 . In FLUENT, C3 is not specified, but is instead calculated according to the following relation [101]: C3

v = tanh

u

(10.4-26)

where v is the component of the flow velocity parallel to the gravitational vector and u is the component of the flow velocity perpendicular to the gravitational vector. In this way, C3 will become 1 for buoyant shear layers for which the main flow direction is aligned with the direction of gravity. For buoyant shear layers that are perpendicular to the gravitational vector, C3 will become zero.

10.4.6

Effects of Compressibility on Turbulence in the k- Models

For high-Mach-number flows, compressibility affects turbulence through so-called “dilatation dissipation”, which is normally neglected in the modeling of incompressible flows [294]. Neglecting the dilatation dissipation fails to predict the observed decrease in spreading rate with increasing Mach number for compressible mixing and other free shear layers. To account for these effects in the k- models in FLUENT, the dilatation dissipation term, YM , is included in the k equation. This term is modeled according to a proposal by Sarkar [220]: YM = 2ρM2t

(10.4-27)

where Mt is the turbulent Mach number, defined as

Mt =

10-24

s

k a2

(10.4-28)



where a (≡

√

γRT ) is the speed of sound.

This compressibility modification always takes effect when the compressible form of the ideal gas law is used.

10.4.7

Convective Heat and Mass Transfer Modeling in the k- Models

In FLUENT, turbulent heat transport is modeled using the concept of Reynolds’ analogy to turbulent momentum transfer. The “modeled” energy equation is thus given by the following: ∂ ∂ ∂ (ρE) + [ui (ρE + p)] = ∂t ∂xi ∂xj

!

∂T keff + ui (τij )eff + Sh ∂xj

(10.4-29)

where E is the total energy, keff is the effective thermal conductivity, and (τij )eff is the deviatoric stress tensor, defined as (τij )eff = µeff


!


The term involving (τij )eff represents the viscous heating, and is always computed in the coupled solvers. It is not computed by default in the segregated solver, but it can be enabled in the Viscous Model panel. Additional terms may appear in the energy equation, depending on the physical models you are using. See Section 11.2.1 for more details. For the standard and realizable k- models, the effective thermal conductivity is given by keff = k +

c p µt Prt

where k, in this case, is the thermal conductivity. The default value of the turbulent Prandtl number is 0.85. You can change the value of the turbulent Prandtl number in the Viscous Model panel. For the RNG k- model, the effective thermal conductivity is keff = αcp µeff where α is calculated from Equation 10.4-9, but with α0 = 1/Pr = k/µcp .


10-25

Modeling Turbulence

The fact that α varies with µmol /µeff , as in Equation 10.4-9, is an advantage of the RNG k model. It is consistent with experimental evidence indicating that the turbulent Prandtl number varies with the molecular Prandtl number and turbulence [124]. Equation 10.4-9 works well across a very broad range of molecular Prandtl numbers, from liquid metals (Pr ≈ 10−2 ) to paraffin oils (Pr ≈ 103 ), which allows heat transfer to be calculated in lowReynolds-number regions. Equation 10.4-9 smoothly predicts the variation of effective Prandtl number from the molecular value (α = 1/Pr) in the viscosity-dominated region to the fully turbulent value (α = 1.393) in the fully turbulent regions of the flow. Turbulent mass transfer is treated similarly. For the standard and realizable k- models, the default turbulent Schmidt number is 0.7. This default value can be changed in the Viscous Model panel. For the RNG model, the effective turbulent diffusivity for mass transfer is calculated in a manner that is analogous to the method used for the heat transport. The value of α0 in Equation 10.4-9 is α0 = 1/Sc, where Sc is the molecular Schmidt number.

10.5

The Standard and SST k-ω Models

This section presents the standard and shear-stress transport (SST) k-ω models. Both models have similar forms, with transport equations for k and ω. The major ways in which the SST model differs from the standard model are as follows: • gradual change from the standard k-ω model in the inner region of the boundary layer to a high-Reynolds-number version of the k- model in the outer part of the boundary layer • modified turbulent viscosity formulation to account for the transport effects of the principal turbulent shear stress The transport equations, methods of calculating turbulent viscosity, and methods of calculating model constants and other terms are presented separately for each model.

10.5.1

The Standard k-ω Model

The standard k-ω model is an empirical model based on model transport equations for the turbulence kinetic energy (k) and the specific dissipation rate (ω), which can also be thought of as the ratio of to k [294]. As the k-ω model has been modified over the years, production terms have been added to both the k and ω equations, which have improved the accuracy of the model for predicting free shear flows.

10-26


10.5 The Standard and SST k-ω Models

Transport Equations for the Standard k-ω Model The turbulence kinetic energy, k, and the specific dissipation rate, ω, are obtained from the following transport equations: ∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj

∂k Γk ∂xj

!

+ G k − Yk + S k

(10.5-1)

∂ ∂ ∂ (ρω) + (ρωui ) = ∂t ∂xi ∂xj

∂ω Γω ∂xj

!

+ G ω − Yω + S ω

(10.5-2)

and

In these equations, Gk represents the generation of turbulence kinetic energy due to mean velocity gradients. Gω represents the generation of ω. Γk and Γω represent the effective diffusivity of k and ω, respectively. Yk and Yω represent the dissipation of k and ω due to turbulence. All of the above terms are calculated as described below. Sk and Sω are user-defined source terms.

Modeling the Effective Diffusivity The effective diffusivities for the k-ω model are given by µt σk µt = µ+ σω

Γk = µ +

(10.5-3)

Γω

(10.5-4)

where σk and σω are the turbulent Prandtl numbers for k and ω, respectively. The turbulent viscosity, µt , is computed by combining k and ω as follows: µt = α ∗

ρk ω

(10.5-5)

Low-Reynolds-Number Correction The coefficient α∗ damps the turbulent viscosity causing a low-Reynolds-number correction. It is given by ∗

α =

∗ α∞

α0∗ + Ret /Rk 1 + Ret /Rk

!

(10.5-6)

where


10-27

Modeling Turbulence

ρk µω = 6 βi = 3 = 0.072

Ret =

(10.5-7)

Rk

(10.5-8)

α0∗ βi

(10.5-9) (10.5-10)

∗ Note that, in the high-Reynolds-number form of the k-ω model, α∗ = α∞ = 1.

Modeling the Turbulence Production Production of k The term Gk represents the production of turbulence kinetic energy. From the exact equation for the transport of k, this term may be defined as Gk = −ρu0i u0j

∂uj ∂xi

(10.5-11)

To evaluate Gk in a manner consistent with the Boussinesq hypothesis, G k = µt S 2

(10.5-12)

where S is the modulus of the mean rate-of-strain tensor, defined in the same way as for the k- model (see Equation 10.4-22). Production of ω The production of ω is given by ω Gω = α Gk k

(10.5-13)

where Gk is given by Equation 10.5-11. The coefficient α is given by α∞ α= ∗ α

α0 + Ret /Rω 1 + Ret /Rω

!

(10.5-14)

where Rω = 2.95. α∗ and Ret are given by Equations 10.5-6 and 10.5-7, respectively. Note that, in the high-Reynolds-number form of the k-ω model, α = α∞ = 1.

10-28



Modeling the Turbulence Dissipation Dissipation of k The dissipation of k is given by Yk = ρ β ∗ fβ ∗ k ω

(10.5-15)

where   1

fβ ∗ = 

1+680χ2k 1+400χ2k

χk ≤ 0 χk > 0

(10.5-16)

where χk ≡

1 ∂k ∂ω ω 3 ∂xj ∂xj

(10.5-17)

and

β ∗ = βi∗ [1 + ζ ∗ F (Mt )] ! 4 4/15 + (Re /R ) t β ∗ βi∗ = β∞ 1 + (Ret /Rβ )4 ζ ∗ = 1.5 Rβ = 8 ∗ β∞ = 0.09

(10.5-18) (10.5-19) (10.5-20) (10.5-21) (10.5-22)

where Ret is given by Equation 10.5-7. Dissipation of ω The dissipation of ω is given by Yω = ρ β fβ ω 2

(10.5-23)

where

fβ =


1 + 70χω 1 + 80χω

(10.5-24)

10-29

Modeling Turbulence

χω

Ω Ω S ij jk ki = (β ∗ ω)3

(10.5-25)

∞

Ωij

1 = 2


!

(10.5-26)

The strain rate tensor, Sij is defined in Equation 10.3-11. Also, β∗ β = βi 1 − i ζ ∗ F (Mt ) βi "

#

(10.5-27)

βi∗ and F (Mt ) are defined by Equations 10.5-19 and 10.5-28, respectively. Compressibility Correction The compressibility function, F (Mt ), is given by F (Mt ) =

(

0 Mt ≤ Mt0 M2t − M2t0 Mt > Mt0

(10.5-28)

where

2k a2 = 0.25

M2t ≡ Mt0

a =

(10.5-29) (10.5-30)

q

γRT

(10.5-31)

∗ Note that, in the high-Reynolds-number form of the k-ω model, βi∗ = β∞ . In the incom∗ ∗ pressible form, β = βi .

Model Constants 1 ∗ ∗ α∞ = 1, α∞ = 0.52, α0 = , β∞ = 0.09, βi = 0.072, Rβ = 8 9 Rk = 6, Rω = 2.95, ζ ∗ = 1.5, Mt0 = 0.25, σk = 2.0, σω = 2.0

Wall Boundary Conditions The wall boundary conditions for the k equation in the k-ω models are treated in the same way as the k equation is treated when enhanced wall treatments are used with the k- models. This means that all boundary conditions for wall-function meshes will correspond to the wall function approach, while for the fine meshes, the appropriate low-Reynolds-number boundary conditions will be applied.

10-30



In FLUENT the value of ω at the wall is specified as ωw =

ρ (u∗ )2 + ω µ

(10.5-32)

The asymptotic value of ω + in the laminar sublayer is given by +

ω = min

ωw+ ,

6 ∗ (y + )2 β∞

!

(10.5-33)

where  2 50    ks+

ωw+ =   

100 ks+

ks+ < 25 (10.5-34) ks+

≥ 25

where ks+

ρks u∗ = max 1.0, µ

!

(10.5-35)

and ks is the roughness height. In the logarithmic (or turbulent) region, the value of ω + is 1 du+ turb ω+ = q + ∗ dy β∞

(10.5-36)

which leads to the value of ω in the wall cell as u∗ ω=q ∗ κy β∞

(10.5-37)

Note that in the case of a wall cell being placed in the buffer region, FLUENT will blend ω + between the logarithmic and laminar sublayer values.

10.5.2

The Shear-Stress Transport (SST) k-ω Model

In addition to the standard k-ω model described in Section 10.5.1, FLUENT also provides a variation called the shear-stress transport (SST) k-ω model, so named because the definition of the turbulent viscosity is modified to account for the transport of the principal turbulent shear stress. It is this feature that gives the SST k-ω model an advantage in


10-31

Modeling Turbulence

terms of performance over both the standard k-ω model and the standard k- model. Other modifications include the addition of a cross-diffusion term in the ω equation and a blending function to ensure that the model equations behave appropriately in both the near-wall and far-field zones.

Transport Equations for the SST k-ω Model The SST k-ω model has a similar form to the standard k-ω model: ∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj

∂k Γk ∂xj

!

+ G k − Yk + S k

(10.5-38)

+ G ω − Y ω + Dω + S ω

(10.5-39)

and ∂ ∂ ∂ (ρω) + (ρωui ) = ∂t ∂xi ∂xj

∂ω Γω ∂xj

!

In these equations, Gk represents the generation of turbulence kinetic energy due to mean velocity gradients, calculated as described in Section 10.5.1. Gω represents the generation of ω, calculated as described in Section 10.5.1. Γk and Γω represent the effective diffusivity of k and ω, respectively, which are calculated as described below. Yk and Yω represent the dissipation of k and ω due to turbulence, calculated as described in Section 10.5.1. Dω represents the cross-diffusion term, calculated as described below. Sk and Sω are user-defined source terms.

Modeling the Effective Diffusivity The effective diffusivities for the SST k-ω model are given by µt σk µt = µ+ σω

Γk = µ +

(10.5-40)

Γω

(10.5-41)

where σk and σω are the turbulent Prandtl numbers for k and ω, respectively. The turbulent viscosity, µt , is computed as follows: µt =

ρk 1 h i ω max 1∗ , ΩF2 α

(10.5-42)

a1 ω

where

10-32



Ω ≡

q

2Ωij Ωij

(10.5-43)

1 F1 /σk,1 + (1 − F1 )/σk,2 1 = F1 /σω,1 + (1 − F1 )/σω,2

σk =

(10.5-44)

σω

(10.5-45)

Ωij is the mean rate-of-rotation tensor and α∗ is defined in Equation 10.5-6. The blending functions, F1 and F2 , are given by

F1 = tanh Φ41 "

(10.5-46)

√

!

k 500µ 4ρk , 2 , 0.09ωy ρy ω σω,2 Dω+ y 2 " # 1 1 ∂k ∂ω −20 = max 2ρ , 10 σω,2 ω ∂xj ∂xj

Φ1 = min max Dω+

F2 = tanh Φ22 "

Φ2 = max 2

√

k 500µ , 0.09ωy ρy 2 ω

#

(10.5-47) (10.5-48)

(10.5-49) #

(10.5-50)

where y is the distance to the next surface and Dω+ is the positive portion of the crossdiffusion term (see Equation 10.5-60).

Modeling the Turbulence Production Production of k The term Gk represents the production of turbulence kinetic energy, and is defined in the same manner as in the standard k-ω model. See Section 10.5.1 for details. Production of ω The term Gω represents the production of ω and is given by Gω =

α Gk νt

(10.5-51)

Note that this formulation differs from the standard k-ω model. The difference between the two models also exists in the way the term α∞ is evaluated. In the standard k-ω model, α∞ is defined as a constant (0.52). For the SST k-ω model, α∞ is given by


10-33

Modeling Turbulence

α∞ = F1 α∞,1 + (1 − F1 )α∞,2

(10.5-52)

where

α∞,1 =

βi,1 κ2 q − ∗ ∗ β∞ σw,1 β∞

(10.5-53)

α∞,2 =

κ2 βi,2 q − ∗ ∗ β∞ σw,2 β∞

(10.5-54)

where κ is 0.41. βi,1 and βi,2 are given by Equations 10.5-58 and 10.5-59, respectively.

Modeling the Turbulence Dissipation Dissipation of k The term Yk represents the dissipation of turbulence kinetic energy, and is defined in a similar manner as in the standard k-ω model (see Section 10.5.1). The difference is in the way the term fβ ∗ is evaluated. In the standard k-ω model, fβ ∗ is defined as a piecewise function. For the SST k-ω model, fβ ∗ is a constant equal to 1. Thus, Yk = ρβ ∗ kω

(10.5-55)

Dissipation of ω The term Yω represents the dissipation of ω, and is defined in a similar manner as in the standard k-ω model (see Section 10.5.1). The difference is in the way the terms βi and fβ are evaluated. In the standard k-ω model, βi is defined as a constant (0.072) and fβ is defined in Equation 10.5-24. For the SST k-ω model, fβ is a constant equal to 1. Thus, Yk = ρβω 2

(10.5-56)

Instead of a having a constant value, βi is given by βi = F1 βi,1 + (1 − F1 )βi,2

(10.5-57)

βi,1 = 0.075 βi,2 = 0.0828

(10.5-58) (10.5-59)

where

10-34


10.6 The Reynolds Stress Model (RSM)

and F1 is obtained from Equation 10.5-46.

Cross-Diffusion Modification The SST k-ω model is based on both the standard k-ω model and the standard k- model. To blend these two models together, the standard k- model has been transformed into equations based on k and ω, which leads to the introduction of a cross-diffusion term (Dω in Equation 10.5-39). Dω is defined as Dω = 2 (1 − F1 ) ρσω,2

1 ∂k ∂ω ω ∂xj ∂xj

(10.5-60)

For details about the various k- models, see Section 10.4.

Model Constants σk,1 = 1.176, σω,1 = 2.0, σk,2 = 1.0, σω,2 = 1.168

a1 = 0.31, βi,1 = 0.075 βi,2 = 0.0828 ∗ ∗ All additional model constants (α∞ , α∞ , α0 , β∞ , Rβ , Rk , Rω , ζ ∗ , and Mt0 ) have the same values as for the standard k-ω model (see Section 10.5.1).

10.6

The Reynolds Stress Model (RSM)

The Reynolds stress model [85, 137, 138] involves calculation of the individual Reynolds stresses, u0i u0j , using differential transport equations. The individual Reynolds stresses are then used to obtain closure of the Reynolds-averaged momentum equation (Equation 10.2-4). The exact form of the Reynolds stress transport equations may be derived by taking moments of the exact momentum equation. This is a process wherein the exact momentum equations are multiplied by a fluctuating property, the product then being Reynoldsaveraged. Unfortunately, several of the terms in the exact equation are unknown and modeling assumptions are required in order to close the equations. In this section, the Reynolds stress transport equations are presented together with the modeling assumptions required to attain closure.

10.6.1

The Reynolds Stress Transport Equations

The exact transport equations for the transport of the Reynolds stresses, ρu0i u0j , may be written as follows:


10-35

Modeling Turbulence

∂ ∂ ∂ (ρ u0i u0j ) + (ρuk u0i u0j ) = − ρ u0i u0j u0k + p δkj u0i + δik u0j ∂x ∂xk |∂t {z } | k {z } | {z } Local Time Derivative Cij ≡ Convection DT,ij ≡ Turbulent Diffusion

"

#

∂uj ∂ui − ρ u0i u0k + u0j u0k ∂xk ∂xk

}

|

∂ ∂ µ (u0 u0 ) ∂xk ∂xk i j

+

|

{z

DL,ij ≡ Molecular Diffusion

{z

|

}

Pij ≡ Stress Production

∂u0i ∂u0j p + ∂xj ∂xi

+

!

{z

!

−

}

φij ≡ Pressure Strain

−2ρΩk u0j u0m ikm + u0i u0m jkm

|

}

{z

Fij ≡ Production by System Rotation

− ρβ(gi u0j θ + gj u0i θ) |

{z

}

Gij ≡ Buoyancy Production

∂u0i ∂u0j 2µ ∂xk ∂xk |

{z

}

ij ≡ Dissipation

+

(10.6-1)

Suser | {z }

User-Defined Source Term

Of the various terms in these exact equations, Cij , DL,ij , Pij , and Fij do not require any modeling. However, DT,ij , Gij , φij , and ij need to be modeled to close the equations. The following sections describe the modeling assumptions required to close the equation set.

10.6.2

Modeling Turbulent Diffusive Transport

DT,ij can be modeled by the generalized gradient-diffusion model of Daly and Harlow [51]:

DT,ij

∂ ku0 u0 ∂u0 u0 = Cs ρ k ` i j ∂xk ∂x`

!

(10.6-2)

However, this equation can result in numerical instabilities, so it has been simplified in FLUENT to use a scalar turbulent diffusivity as follows [150]:

DT,ij

∂ = ∂xk

µt ∂u0i u0j σk ∂xk

!

(10.6-3)

The turbulent viscosity, µt , is computed using Equation 10.6-27. Lien and Leschziner [150] derived a value of σk = 0.82 by applying the generalized gradient-diffusion model, Equation 10.6-2, to the case of a planar homogeneous shear flow. Note that this value of σk is different from that in the standard and realizable k- models, in which σk = 1.0.

10-36



10.6.3

Modeling the Pressure-Strain Term

Linear Pressure-Strain Model By default in FLUENT, the pressure-strain term, φij , in Equation 10.6-1 is modeled according to the proposals by Gibson and Launder [85], Fu et al. [80], and Launder [136, 137]. The classical approach to modeling φij uses the following decomposition: φij = φij,1 + φij,2 + φij,w

(10.6-4)

where φij,1 is the slow pressure-strain term, also known as the return-to-isotropy term, φij,2 is called the rapid pressure-strain term, and φij,w is the wall-reflection term. The slow pressure-strain term, φij,1 , is modeled as φij,1

0 0 2 ≡ −C1 ρ u u − δij k k i j 3

(10.6-5)

with C1 = 1.8. The rapid pressure-strain term, φij,2 , is modeled as φij,2 ≡ −C2

2 (Pij + Fij + Gij − Cij ) − δij (P + G − C) 3

(10.6-6)

where C2 = 0.60, Pij , Fij , Gij , and Cij are defined as in Equation 10.6-1, P = 12 Pkk , G = 12 Gkk , and C = 12 Ckk . The wall-reflection term, φij,w , is responsible for the redistribution of normal stresses near the wall. It tends to damp the normal stress perpendicular to the wall, while enhancing the stresses parallel to the wall. This term is modeled as

φij,w

3 3 k 3/2 ≡ u0k u0m nk nm δij − u0i u0k nj nk − u0j u0k ni nk k 2 2 C` d 3/2 3 3 k + C20 φkm,2 nk nm δij − φik,2 nj nk − φjk,2 ni nk 2 2 C` d C10

(10.6-7) where C10 = 0.5, C20 = 0.3, nk is the xk component of the unit normal to the wall, d is the normal distance to the wall, and C` = Cµ3/4 /κ, where Cµ = 0.09 and κ is the von Kármán constant (= 0.4187). φij,w is included by default in the Reynolds stress model.


10-37

Modeling Turbulence

Low-Re Modifications to the Linear Pressure-Strain Model When the RSM is applied to near-wall flows using the enhanced wall treatment described in Section 10.8.3, the pressure-strain model needs to be modified. The modification used in FLUENT specifies the values of C1 , C2 , C10 , and C20 as functions of the Reynolds stress invariants and the turbulent Reynolds number, according to the suggestion of Launder and Shima [139]:

q

n

h

C1 = 1 + 2.58A A2 1 − exp −(0.0067Ret )2 √ C2 = 0.75 A 2 C10 = − C1 + 1.67 3 " # 2 C − 16 0 3 2 C2 = max ,0 C2

io

(10.6-8) (10.6-9) (10.6-10) (10.6-11)

with the turbulent Reynolds number defined as Ret = (ρk 2 /µ). The parameter A and tensor invariants, A2 and A3 , are defined as 9 A ≡ 1 − (A2 − A3 ) 8 A2 ≡ aik aki A3 ≡ aik akj aji

(10.6-12) (10.6-13) (10.6-14)

aij is the Reynolds-stress anisotropy tensor, defined as −ρu0i u0j + 23 ρkδij aij = − ρk

!

(10.6-15)

The modifications detailed above are employed only when the enhanced wall treatment is selected in the Viscous Model panel.

Quadratic Pressure-Strain Model An optional pressure-strain model proposed by Speziale, Sarkar, and Gatski [254] is provided in FLUENT. This model has been demonstrated to give superior performance in a range of basic shear flows, including plane strain, rotating plane shear, and axisymmetric expansion/contraction. This improved accuracy should be beneficial for a wider class of complex engineering flows, particularly those with streamline curvature. The quadratic pressure-strain model can be selected as an option in the Viscous Model panel. This model is written as follows:

10-38



φij = − (C1 ρ +

C1∗ P ) bij

q 1 + C2 ρ bik bkj − bmn bmn δij + C3 − C3∗ bij bij ρkSij 3

2 + C4 ρk bik Sjk + bjk Sik − bmn Smn δij + C5 ρk (bik Ωjk + bjk Ωik ) 3

(10.6-16)

where bij is the Reynolds-stress anisotropy tensor defined as −ρu0i u0j + 23 ρkδij bij = − 2ρk

!

(10.6-17)

The mean strain rate, Sij , is defined as 1 Sij = 2


!

(10.6-18)

!

(10.6-19)

The mean rate-of-rotation tensor, Ωij , is defined by 1 Ωij = 2


The constants are C1 = 3.4, C1∗ = 1.8, C2 = 4.2, C3 = 0.8, C3∗ = 1.3, C4 = 1.25, C5 = 0.4 The quadratic pressure-strain model does not require a correction to account for the wall-reflection effect in order to obtain a satisfactory solution in the logarithmic region of a turbulent boundary layer. It should be noted, however, that the quadratic pressurestrain model is not available when the enhanced wall treatment is selected in the Viscous Model panel.

10.6.4

Effects of Buoyancy on Turbulence

The production terms due to buoyancy are modeled as µt ∂T ∂T Gij = β gi + gj Prt ∂xj ∂xi

!

(10.6-20)

where Prt is the turbulent Prandtl number for energy, with a default value of 0.85.


10-39

Modeling Turbulence

Using the definition of the coefficient of thermal expansion, β, given by Equation 10.4-24, the following expression is obtained for Gij for ideal gases: ∂ρ ∂ρ µt gi + gj Gij = − ρPrt ∂xj ∂xi

10.6.5

!

(10.6-21)

Modeling the Turbulence Kinetic Energy

In general, when the turbulence kinetic energy is needed for modeling a specific term, it is obtained by taking the trace of the Reynolds stress tensor: 1 k = u0i u0i 2

(10.6-22)

As described in Section 10.6.8, an option is available in FLUENT to solve a transport equation for the turbulence kinetic energy in order to obtain boundary conditions for the Reynolds stresses. In this case, the following model equation is used:

∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj

"

µt µ+ σk

#

∂k 1 + (Pii + Gii ) − ρ(1 + 2M2t ) + Sk (10.6-23) ∂xj 2

where σk = 0.82 and Sk is a user-defined source term. Equation 10.6-23 is obtainable by contracting the modeled equation for the Reynolds stresses (Equation 10.6-1). As one might expect, it is essentially identical to Equation 10.4-1 used in the standard k- model. Although Equation 10.6-23 is solved globally throughout the flow domain, the values of k obtained are used only for boundary conditions. In every other case, k is obtained from Equation 10.6-22. This is a minor point, however, since the values of k obtained with either method should be very similar.

10.6.6

Modeling the Dissipation Rate

The dissipation tensor, ij , is modeled as 2 ij = δij (ρ + YM ) 3

(10.6-24)

where YM = 2ρM2t is an additional “dilatation dissipation” term according to the model by Sarkar [220]. The turbulent Mach number in this term is defined as

Mt =

10-40

s

k a2

(10.6-25)


10.6 The Reynolds Stress Model (RSM) √ where a (≡ γRT ) is the speed of sound. This compressibility modification always takes effect when the compressible form of the ideal gas law is used. The scalar dissipation rate, , is computed with a model transport equation similar to that used in the standard k- model:

∂ ∂ ∂ (ρ) + (ρui ) = ∂t ∂xi ∂xj

"

µt µ+ σ

∂ 1 2 C1 [Pii + C3 Gii ] − C2 ρ + S (10.6-26) ∂xj 2 k k #

where σ = 1.0, C1 = 1.44, C2 = 1.92, C3 is evaluated as a function of the local flow direction relative to the gravitational vector, as described in Section 10.4.5, and S is a user-defined source term.

10.6.7

Modeling the Turbulent Viscosity

The turbulent viscosity, µt , is computed similarly to the k- models: µt = ρCµ

k2

(10.6-27)

where Cµ = 0.09.

10.6.8

Boundary Conditions for the Reynolds Stresses

Whenever flow enters the domain, FLUENT requires values for individual Reynolds stresses, u0i u0j , and for the turbulence dissipation rate, . These quantities can be input directly or derived from the turbulence intensity and characteristic length, as described in Section 10.10.2. At walls, FLUENT computes the near-wall values of the Reynolds stresses and from wall functions (see Section 10.8.2). FLUENT applies explicit wall boundary conditions for the Reynolds stresses by using the log-law and the assumption of equilibrium, disregarding convection and diffusion in the transport equations for the stresses (Equation 10.6-1). Using a local coordinate system, where τ is the tangential coordinate, η is the normal coordinate, and λ is the binormal coordinate, the Reynolds stresses at the wall-adjacent cells are computed from 0 u0η2 u0 u0 u0τ2 uλ2 = 1.098, = 0.247, = 0.655, − τ η = 0.255 k k k k

(10.6-28)

To obtain k, FLUENT solves the transport equation of Equation 10.6-23. For reasons of computational convenience, the equation is solved globally, even though the values of k thus computed are needed only near the wall; in the far field k is obtained directly from the


10-41

Modeling Turbulence

normal Reynolds stresses using Equation 10.6-22. By default, the values of the Reynolds stresses near the wall are fixed using the values computed from Equation 10.6-28, and the transport equations in Equation 10.6-1 are solved only in the bulk flow region. Alternatively, the Reynolds stresses can be explicitly specified in terms of wall-shear stress, instead of k: 0 u0η2 u0τ u0η u0τ2 uλ2 = 5.1, = 1.0, = 2.3, − = 1.0 u2τ u2τ u2τ u2τ

(10.6-29)

q

where uτ is the friction velocity defined by uτ ≡ τw /ρ, where τw is the wall-shear stress. When this option is chosen, the k transport equation is not solved.

10.6.9

Convective Heat and Mass Transfer Modeling

With the Reynolds stress model in FLUENT, turbulent heat transport is modeled using the concept of Reynolds’ analogy to turbulent momentum transfer. The “modeled” energy equation is thus given by the following: ∂ ∂ ∂ (ρE) + [ui (ρE + p)] = ∂t ∂xi ∂xj

"

c p µt k+ Prt

#

∂T + ui (τij )eff + Sh ∂xj

(10.6-30)

where E is the total energy and (τij )eff is the deviatoric stress tensor, defined as (τij )eff = µeff


!


The term involving (τij )eff represents the viscous heating, and is always computed in the coupled solvers. It is not computed by default in the segregated solver, but it can be enabled in the Viscous Model panel. The default value of the turbulent Prandtl number is 0.85. You can change the value of Prt in the Viscous Model panel. Turbulent mass transfer is treated similarly, with a default turbulent Schmidt number of 0.7. This default value can be changed in the Viscous Model panel.

10-42


10.7 The Large Eddy Simulation (LES) Model

10.7

The Large Eddy Simulation (LES) Model

Turbulent flows are characterized by eddies with a wide range of length and time scales. The largest eddies are typically comparable in size to the characteristic length of the mean flow. The smallest scales are responsible for the dissipation of turbulence kinetic energy. It is theoretically possible to directly resolve the whole spectrum of turbulent scales using an approach known as direct numerical simulation (DNS). DNS is not, however, feasible for practical engineering problems. To understand the large computational cost of DNS, consider that the ratio of the large (energy-containing) scales to the small (energy3/4 dissipating) scales is proportional to Ret , where Ret is the turbulent Reynolds number. Therefore, to resolve all the scales, the mesh size in three dimensions will be proportional 9/4 to Ret . Simple arithmetic shows that, for high Reynolds numbers, the mesh sizes required for DNS are prohibitive. Adding to the computational cost is the fact that the simulation will be a transient one with very small time steps, since the temporal resolution requirements are governed by the dissipating scales, rather than the mean flow or the energy-containing eddies. As explained in Section 10.2.1, the conventional approach to flow simulations employs the solution of the Reynolds-averaged Navier-Stokes (RANS) equations. In the RANS approach, all the turbulent motions are modeled, resulting in a significant savings in computational effort. Conceptually, large eddy simulation (LES) is situated somewhere between DNS and the RANS approach. Basically large eddies are resolved directly in LES, while small eddies are modeled. The rationale behind LES can be summarized as follows: • Momentum, mass, energy, and other passive scalars are transported mostly by large eddies. • Large eddies are more problem-dependent. They are dictated by the geometries and boundary conditions of the flow involved. • Small eddies are less dependent on the geometry, tend to be more isotropic, and are consequently more universal. • The chance of finding a universal model is much higher when only small eddies are modeled. Solving only for the large eddies and modeling the smaller scales results in mesh resolution requirements that are much less restrictive than with DNS. Typically, mesh sizes can be at least one order of magnitude smaller than with DNS. Furthermore, the time step sizes will be proportional to the eddy-turnover time, which is much less restrictive than with DNS. In practical terms, however, extremely fine meshes are still required. It is only due to the explosive increases in computer hardware performance coupled with the


10-43

Modeling Turbulence

availability of parallel processing that LES can even be considered as a possibility for engineering calculations. The following sections give details of the governing equations for LES, present the two options for modeling the subgrid-scale stresses (necessary to achieve closure of the governing equations), and discuss the relevant boundary conditions.

10.7.1

Filtered Navier-Stokes Equations

The governing equations employed for LES are obtained by filtering the time-dependent Navier-Stokes equations in either Fourier (wave-number) space or configuration (physical) space. The filtering process effectively filters out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. The resulting equations thus govern the dynamics of large eddies. A filtered variable (denoted by an overbar) is defined by φ(x) =

Z

φ(x0 )G(x, x0 )dx0

(10.7-1)

D

where D is the fluid domain, and G is the filter function that determines the scale of the resolved eddies. In FLUENT, the finite-volume discretization itself implicitly provides the filtering operation: φ(x) =

1 Z φ(x0 ) dx0 , x0 ∈ V V V

(10.7-2)

where V is the volume of a computational cell. The filter function, G(x, x0 ), implied here is then 0

G(x, x )

(

1/V, x0 ∈ V 0, x0 otherwise

(10.7-3)

Since the application of LES to compressible flows is still in its infancy, the theory is presented here for incompressible flows. It is assumed that the LES model in FLUENT will be applied to essentially incompressible (but not necessarily constant-density) flows. Filtering the incompressible Navier-Stokes equations, one obtains ∂ρ ∂ + (ρui ) = 0 ∂t ∂xi

(10.7-4)

and

10-44


10.7 The Large Eddy Simulation (LES) Model

∂ ∂ ∂ (ρui ) + (ρui uj ) = ∂t ∂xj ∂xj

∂ui µ ∂xj

!

−

∂p ∂τij − ∂xi ∂xj

(10.7-5)

where τij is the subgrid-scale stress defined by τij ≡ ρui uj − ρui uj

(10.7-6)

The similarity between the filtered equations, 10.7-4 through 10.7-6, and the incompressible form of the RANS equations, Equations 10.2-3 and 10.2-4, is obvious. The major difference is that the dependent variables are now filtered quantities rather than mean quantities, and the expressions for the turbulent stresses differ.

10.7.2

Subgrid-Scale Models

The subgrid-scale stresses resulting from the filtering operation are unknown, and require modeling. The majority of subgrid-scale models in use today are eddy viscosity models of the following form: 1 τij − τkk δij = −2µt S ij 3

(10.7-7)

where µt is the subgrid-scale turbulent viscosity, and S ij is the rate-of-strain tensor for the resolved scale defined by 1 S ij ≡ 2

∂ui ∂uj + ∂xj ∂xi

!

(10.7-8)

FLUENT contains two models for µt : the Smagorinsky-Lilly model and the RNG-based subgrid-scale model.

Smagorinsky-Lilly Model The most basic of subgrid-scale models was proposed by Smagorinsky [239] and further developed by Lilly [152]. In the Smagorinsky-Lilly model, the eddy viscosity is modeled by

µt = ρL2s S

(10.7-9)

where Ls is the mixing length for subgrid scales and S ≡ sky constant. In FLUENT, Ls is computed using


q

2S ij S ij . Cs is the Smagorin-

10-45

Modeling Turbulence

Ls = min κd, Cs V 1/3

(10.7-10)

where κ is the von Kármán constant, d is the distance to the closest wall, and V is the volume of the computational cell. Lilly derived a value of 0.23 for Cs from homogeneous isotropic turbulence in the inertial subrange. However, this value was found to cause excessive damping of large-scale fluctuations in the presence of mean shear or in transitional flows. Cs =0.1 has been found to yield the best results for a wide range of flows, and is the default value in FLUENT.

RNG-Based Subgrid-Scale Model Renormalization group (RNG) theory can be used to derive a model for the subgridscale eddy viscosity [298]. The RNG procedure results in an effective subgrid viscosity, µeff = µ + µt , given by µeff = µ [1 + H(x)]1/3

(10.7-11)

H(x) is the Heaviside function:

H(x) =

(

x, x > 0 0, x ≤ 0

(10.7-12)

where µ2s µeff x= −C µ3

(10.7-13)

and q

µs = ρ(Crng V 1/3 )2 2S ij S ij

(10.7-14)

where V is the volume of the computational cell. The theory gives Crng = 0.157 and C = 100. In highly turbulent regions of the flow (µt µ), µeff ≈ µs , and the RNG-based subgridscale model reduces to the Smagorinsky-Lilly model with a different model constant. In low-Reynolds-number regions of the flow, the argument of the ramp function becomes negative and the effective viscosity recovers molecular viscosity. This enables the RNGbased subgrid-scale eddy viscosity to model the low-Reynolds-number effects encountered in transitional flows and near-wall regions.

10-46


10.8 Near-Wall Treatments for Wall-Bounded Turbulent Flows

10.7.3

Boundary Conditions for the LES Model

The stochastic components of the flow at the velocity-specified inlet boundaries are accounted for by superposing random perturbations on individual velocity components as ui =< ui > +I ψ |u|

(10.7-15)

where I is the q intensity of the fluctuation, ψ is a Gaussian random number satisfying ψ = 0, and ψ 0 = 1. When the mesh is fine enough to resolve the laminar sublayer, the wall shear stress is obtained from the laminar stress-strain relationship: u ρuτ y = uτ µ

(10.7-16)

If the mesh is too coarse to resolve the laminar sublayer, it is assumed that the centroid of the wall-adjacent cell falls within the logarithmic region of the boundary layer, and the law-of-the-wall is employed: u 1 ρuτ y = ln E uτ κ µ

!

(10.7-17)

where κ is the von Kármán constant and E = 9.793.

10.8 10.8.1

Near-Wall Treatments for Wall-Bounded Turbulent Flows Overview

Turbulent flows are significantly affected by the presence of walls. Obviously, the mean velocity field is affected through the no-slip condition that has to be satisfied at the wall. However, the turbulence is also changed by the presence of the wall in non-trivial ways. Very close to the wall, viscous damping reduces the tangential velocity fluctuations, while kinematic blocking reduces the normal fluctuations. Toward the outer part of the nearwall region, however, the turbulence is rapidly augmented by the production of turbulence kinetic energy due to the large gradients in mean velocity. The near-wall modeling significantly impacts the fidelity of numerical solutions, inasmuch as walls are the main source of mean vorticity and turbulence. After all, it is in the nearwall region that the solution variables have large gradients, and the momentum and other scalar transports occur most vigorously. Therefore, accurate representation of the flow in the near-wall region determines successful predictions of wall-bounded turbulent flows. The k- models, the RSM, and the LES model are primarily valid for turbulent core flows (i.e., the flow in the regions somewhat far from walls). Consideration therefore


10-47

Modeling Turbulence

needs to be given as to how to make these models suitable for wall-bounded flows. The Spalart-Allmaras and k-ω models were designed to be applied throughout the boundary layer, provided that the near-wall mesh resolution is sufficient. Numerous experiments have shown that the near-wall region can be largely subdivided into three layers. In the innermost layer, called the “viscous sublayer”, the flow is almost laminar, and the (molecular) viscosity plays a dominant role in momentum and heat or mass transfer. In the outer layer, called the fully-turbulent layer, turbulence plays a major role. Finally, there is an interim region between the viscous sublayer and the fully turbulent layer where the effects of molecular viscosity and turbulence are equally important. Figure 10.8.1 illustrates these subdivisions of the near-wall region, plotted in semi-log coordinates. U/Uτ = 2.5 ln(U τ y/ ν) + 5.45 inner layer

U/Uτ

U/Uτ = Uτ y/ν outer layer

viscous sublayer

buffer layer or blending region

y+ ∼ −5

fully turbulent region or log-law region

∼ 60 y+ −

Upper limit depends on Reynolds no.

ln Uτ y/ ν

Figure 10.8.1: Subdivisions of the Near-Wall Region

Wall Functions vs. Near-Wall Model Traditionally, there are two approaches to modeling the near-wall region. In one approach, the viscosity-affected inner region (viscous sublayer and buffer layer) is not resolved. Instead, semi-empirical formulas called “wall functions” are used to bridge the viscosity-affected region between the wall and the fully-turbulent region. The use of wall functions obviates the need to modify the turbulence models to account for the presence of the wall. In another approach, the turbulence models are modified to enable the viscosity-affected region to be resolved with a mesh all the way to the wall, including the viscous sublayer. For purposes of discussion, this will be termed the “near-wall modeling” approach. These two approaches are depicted schematically in Figure 10.8.2.

10-48


turbulent core


?

buffer & sublayer

Wall Function Approach

Near-Wall Model Approach

The viscosity-affected region is not resolved, instead is bridged by the wall functions.

The near-wall region is resolved all the way down to the wall.

High-Re turbulence models can be used.

The turbulence models ought to be valid throughout the near-wall region.

Figure 10.8.2: Near-Wall Treatments in FLUENT

In most high-Reynolds-number flows, the wall function approach substantially saves computational resources, because the viscosity-affected near-wall region, in which the solution variables change most rapidly, does not need to be resolved. The wall function approach is popular because it is economical, robust, and reasonably accurate. It is a practical option for the near-wall treatments for industrial flow simulations. The wall function approach, however, is inadequate in situations where the low-Reynoldsnumber effects are pervasive in the flow domain in question, and the hypotheses underlying the wall functions cease to be valid. Such situations require near-wall models that are valid in the viscosity-affected region and accordingly integrable all the way to the wall. FLUENT provides both the wall function approach and the near-wall modeling approach.

Near-Wall Treatments for the Spalart-Allmaras, k-ω, and LES Models See Sections 10.3.7, 10.5.1, and 10.7.3, respectively, for a description of the near-wall treatments applied by the Spalart-Allmaras, k-ω, and LES models.

10.8.2

Wall Functions

Wall functions are a collection of semi-empirical formulas and functions that in effect “bridge” or “link” the solution variables at the near-wall cells and the corresponding quantities on the wall. The wall functions comprise


10-49

Modeling Turbulence

• laws-of-the-wall for mean velocity and temperature (or other scalars) • formulas for near-wall turbulent quantities FLUENT offers two choices of wall function approaches: • standard wall functions • non-equilibrium wall functions

Standard Wall Functions The standard wall functions in FLUENT are based on the proposal of Launder and Spalding [141], and have been most widely used for industrial flows. They are provided as a default option in FLUENT. Momentum The law-of-the-wall for mean velocity yields U∗ =

1 ln(Ey ∗ ) κ

(10.8-1)

where 1/2

UP Cµ1/4 kP U ≡ τw /ρ ∗

(10.8-2)

1/2

ρCµ1/4 kP yP y ≡ µ ∗

and κ E UP kP yP µ

= = = = = =

(10.8-3)

von Kármán constant (= 0.42) empirical constant (= 9.793) mean velocity of the fluid at point P turbulence kinetic energy at point P distance from point P to the wall dynamic viscosity of the fluid

The logarithmic law for mean velocity is known to be valid for y ∗ > about 30 to 60. In FLUENT, the log-law is employed when y ∗ > 11.225. When the mesh is such that y ∗ < 11.225 at the wall-adjacent cells, FLUENT applies the laminar stress-strain relationship that can be written as

10-50



U ∗ = y∗

(10.8-4)

It should be noted that, in FLUENT, the laws-of-the-wall for mean velocity and temperature are based on the wall unit, y ∗ , rather than y + (≡ ρuτ y/µ). These quantities are approximately equal in equilibrium turbulent boundary layers. Energy Reynolds’ analogy between momentum and energy transport gives a similar logarithmic law for mean temperature. As in the law-of-the-wall for mean velocity, the law-of-the-wall for temperature employed in FLUENT comprises the following two different laws: • linear law for the thermal conduction sublayer where conduction is important • logarithmic law for the turbulent region where effects of turbulence dominate conduction The thickness of the thermal conduction layer is, in general, different from the thickness of the (momentum) viscous sublayer, and changes from fluid to fluid. For example, the thickness of the thermal sublayer for a high-Prandtl-number fluid (e.g., oil) is much less than its momentum sublayer thickness. For fluids of low Prandtl numbers (e.g., liquid metal), on the contrary, it is much larger than the momentum sublayer thickness. In highly compressible flows, the temperature distribution in the near-wall region can be significantly different from that of low subsonic flows, due to the heating by viscous dissipation. In FLUENT, the temperature wall functions include the contribution from the viscous heating [273]. The law-of-the-wall implemented in FLUENT has the following composite form:

1/2

(Tw − TP ) ρcp Cµ1/4 kP T ≡ q˙ ∗

 1/4 1/2 C k   Pr y ∗ + 12 ρPr µ q˙ P UP2   h i    Pr 1 ln(Ey ∗ ) + P + t κ = 1/4 1/2   1 C µ kP  ρ {Prt UP2 + (Pr − Prt )Uc2 }   2 q˙  

(y ∗ < yT∗ ) (y ∗ > yT∗ ) (10.8-5)

where P is computed by using the formula given by Jayatilleke [117]:

P = 9.24

"

Pr Prt

3/4

#

−1

h

1 + 0.28e−0.007Pr/Prt

i

(10.8-6)

and


10-51

Modeling Turbulence

kf ρ cp q˙ TP Tw Pr Prt A κ E Uc

= = = = = = = = = = = =

thermal conductivity of fluid density of fluid specific heat of fluid wall heat flux temperature at the cell adjacent to wall temperature at the wall molecular Prandtl number (µcp /kf ) turbulent Prandtl number (0.85 at the wall) 26 (Van Driest constant) 0.4187 (von Kármán constant) 9.793 (wall function constant) mean velocity magnitude at y ∗ = yT∗

Note that, for the segregated solver, the terms 1/2

C 1/4 k 1 ρPr µ P UP2 2 q˙ and

1/2 o 1 Cµ1/4 kP n ρ Prt UP2 + (Pr − Prt )Uc2 2 q˙

will be included in Equation 10.8-5 only for compressible flow calculations. The non-dimensional thermal sublayer thickness, yT∗ , in Equation 10.8-5 is computed as the y ∗ value at which the linear law and the logarithmic law intersect, given the molecular Prandtl number of the fluid being modeled. The procedure of applying the law-of-the-wall for temperature is as follows. Once the physical properties of the fluid being modeled are specified, its molecular Prandtl number is computed. Then, given the molecular Prandtl number, the thermal sublayer thickness, yT∗ , is computed from the intersection of the linear and logarithmic profiles, and stored. During the iteration, depending on the y ∗ value at the near-wall cell, either the linear or the logarithmic profile in Equation 10.8-5 is applied to compute the wall temperature Tw or heat flux q˙ (depending on the type of the thermal boundary conditions). Species When using wall functions for species transport, FLUENT assumes that species transport behaves analogously to heat transfer. Similarly to Equation 10.8-5, the law-of-the-wall for species can be expressed for constant property flow with no viscous dissipation as 1/2

(Yi,w − Yi ) ρCµ1/4 kP Y ≡ Ji,w ∗

10-52

=

(

Sc yh∗ i Sct κ1 ln(Ey ∗ ) + Pc

(y ∗ < yc∗ ) (y ∗ > yc∗ )

(10.8-7)



where Yi is the local species mass fraction, Sc and Sct are molecular and turbulent Schmidt numbers, and Ji,w is the diffusion flux of species i at the wall. Note that Pc and yc∗ are calculated in a similar way as P and yT∗ , with the difference being that the Prandtl numbers are always replaced by the corresponding Schmidt numbers. Turbulence In the k- models and in the RSM (if the option to obtain wall boundary conditions from the k equation is enabled), the k equation is solved in the whole domain including the wall-adjacent cells. The boundary condition for k imposed at the wall is ∂k =0 ∂n

(10.8-8)

where n is the local coordinate normal to the wall. The production of kinetic energy, Gk , and its dissipation rate, , at the wall-adjacent cells, which are the source terms in the k equation, are computed on the basis of the local equilibrium hypothesis. Under this assumption, the production of k and its dissipation rate are assumed to be equal in the wall-adjacent control volume. Thus, the production of k is computed from G k ≈ τw

∂U τw = τw 1/4 1/2 ∂y κρCµ kP yP

(10.8-9)

and is computed from 3/2

C 3/4 k P = µ P κyP

(10.8-10)

The equation is not solved at the wall-adjacent cells, but instead is computed using Equation 10.8-10. Note that, as shown here, the wall boundary conditions for the solution variables, including mean velocity, temperature, species concentration, k, and , are all taken care of by the wall functions. Therefore, you do not need to be concerned about the boundary conditions at the walls. The standard wall functions described so far are provided as a default option in FLUENT. The standard wall functions work reasonably well for a broad range of wall-bounded flows. However, they tend to become less reliable when the flow situations depart too much from the ideal conditions that are assumed in their derivation. Among others, the constantshear and local equilibrium hypotheses are the ones that most restrict the universality of the standard wall functions. Accordingly, when the near-wall flows are subjected to


10-53

Modeling Turbulence

severe pressure gradients, and when the flows are in strong non-equilibrium, the quality of the predictions is likely to be compromised. The non-equilibrium wall functions offered as an additional option can improve the results in such situations.

Non-Equilibrium Wall Functions In addition to the standard wall function described above (which is the default near-wall treatment) a two-layer-based, non-equilibrium wall function [128] is also available. The key elements in the non-equilibrium wall functions are as follows: • Launder and Spalding’s log-law for mean velocity is sensitized to pressure-gradient effects. • The two-layer-based concept is adopted to compute the budget of turbulence kinetic energy (Gk ,) in the wall-neighboring cells. The law-of-the-wall for mean temperature or species mass fraction remains the same as in the standard wall function described above. The log-law for mean velocity sensitized to pressure gradients is ! U˜ Cµ1/4 k 1/2 ρCµ1/4 k 1/2 y 1 = ln E τw /ρ κ µ

(10.8-11)

where "

1 dp yv y √ ln U˜ = U − 2 dx ρκ k yv

!

y − yv y 2 + √ + v µ ρκ k

#

(10.8-12)

and yv is the physical viscous sublayer thickness, and is computed from yv ≡

µyv∗ 1/4 1/2

ρCµ kP

(10.8-13)

where yv∗ = 11.225. The non-equilibrium wall function employs the two-layer concept in computing the budget of turbulence kinetic energy at the wall-adjacent cells, which is needed to solve the k equation at the wall-neighboring cells. The wall-neighboring cells are assumed to consist of a viscous sublayer and a fully turbulent layer. The following profile assumptions for turbulence quantities are made:

10-54



τt =

(



 y 0, y < yv k =  yv τw , y > yv kP ,

2



 k P , y < yv = y > yv

2νk , y2 k3/2 , C` y

y < yv y > yv

(10.8-14)

where C` = κCµ−3/4 , and yv is the dimensional thickness of the viscous sublayer, defined in Equation 10.8-13. Using these profiles, the cell-averaged production of k, Gk , and the cell-averaged dissipation rate, , can be computed from the volume average of Gk and of the wall-adjacent cells. For quadrilateral and hexahedral cells for which the volume average can be approximated with a depth-average, ! 1 Z yn ∂U 1 τw2 yn Gk ≡ τt dy = ln yn 0 ∂y κyn ρCµ1/4 kP1/2 yv

(10.8-15)

and 



! 1/2 1 Z yn 1  2ν kP yn  ≡ dy = + ln kP yn 0 yn yv C` yv

(10.8-16)

where yn is the height of the cell (yn = 2yP ). For cells with other shapes (e.g., triangular and tetrahedral grids), the appropriate volume averages are used. In Equations 10.8-15 and 10.8-16, the turbulence kinetic energy budget for the wallneighboring cells is effectively sensitized to the proportions of the viscous sublayer and the fully turbulent layer, which varies widely from cell to cell in highly non-equilibrium flows. It effectively relaxes the local equilibrium assumption (production = dissipation) that is adopted by the standard wall function in computing the budget of the turbulence kinetic energy at wall-neighboring cells. Thus, the non-equilibrium wall functions, in effect, partly account for non-equilibrium effects neglected in the standard wall function.

Standard Wall Functions vs. Non-Equilibrium Wall Functions Because of the capability to partly account for the effects of pressure gradients and departure from equilibrium, the non-equilibrium wall functions are recommended for use in complex flows involving separation, reattachment, and impingement where the mean flow and turbulence are subjected to severe pressure gradients and change rapidly. In such flows, improvements can be obtained, particularly in the prediction of wall shear (skin-friction coefficient) and heat transfer (Nusselt or Stanton number).

Limitations of the Wall Function Approach The standard wall functions give reasonably accurate predictions for the majority of high-Reynolds-number, wall-bounded flows. The non-equilibrium wall functions further


10-55

Modeling Turbulence

extend the applicability of the wall function approach by including the effects of pressure gradient and strong non-equilibrium. However, the wall function approach becomes less reliable when the flow conditions depart too much from the ideal conditions underlying the wall functions. Examples are as follows: • Pervasive low-Reynolds-number or near-wall effects (e.g., flow through a small gap or highly viscous, low-velocity fluid flow) • Massive transpiration through the wall (blowing/suction) • Severe pressure gradients leading to boundary layer separations • Strong body forces (e.g., flow near rotating disks, buoyancy-driven flows) • High three-dimensionality in the near-wall region (e.g., Ekman spiral flow, strongly skewed 3D boundary layers) If any of the items listed above is a prevailing feature of the flow you are modeling, and if it is considered critically important to capture that feature for the success of your simulation, you must employ the near-wall modeling approach combined with adequate mesh resolution in the near-wall region. FLUENT provides the enhanced wall treatment for such situations. This approach can be used with the three k- models and the RSM.

10.8.3

Enhanced Wall Treatment

Enhanced wall treatment is a near-wall modeling method that combines a two-layer model with enhanced wall functions. If the near-wall mesh is fine enough to be able to resolve the laminar sublayer (typically y + ≈ 1), then the enhanced wall treatment will be identical to the traditional two-layer zonal model (see below for details). However, the restriction that the near-wall mesh must be sufficiently fine everywhere might impose too large a computational requirement. Ideally, then, one would like to have a near-wall formulation that can be used with coarse meshes (usually referred to as wall-function meshes) as well as fine meshes (low-Reynolds-number meshes). In addition, excessive error should not be incurred for intermediate meshes that are too fine for the near-wall cell centroid to lie in the fully turbulent region, but also too coarse to properly resolve the sublayer. To achieve the goal of having a near-wall modeling approach that will possess the accuracy of the standard two-layer approach for fine near-wall meshes and that, at the same time, will not significantly reduce accuracy for wall-function meshes, FLUENT can combine the two-layer model with enhanced wall functions, as described in the following sections.

10-56



Two-Layer Model for Enhanced Wall Treatment In FLUENT’s near-wall model, the viscosity-affected near-wall region is completely resolved all the way to the viscous sublayer. The two-layer approach is an integral part of the enhanced wall treatment and is used to specify both and the turbulent viscosity in the near-wall cells. In this approach, the whole domain is subdivided into a viscosity-affected region and a fully-turbulent region. The demarcation of the two regions is determined by a wall-distance-based, turbulent Reynolds number, Rey , defined as √ ρy k Rey ≡ µ

(10.8-17)

where y is the normal distance from the wall at the cell centers. In FLUENT, y is interpreted as the distance to the nearest wall: y ≡ min k~r − ~rw k

(10.8-18)

~ rw ∈Γw

where ~r is the position vector at the field point, and ~rw is the position vector on the wall boundary. Γw is the union of all the wall boundaries involved. This interpretation allows y to be uniquely defined in flow domains of complex shape involving multiple walls. Furthermore, y defined in this way is independent of the mesh topology used, and is definable even on unstructured meshes. In the fully turbulent region (Rey > Re∗y ; Re∗y = 200), the k- models or the RSM (described in Sections 10.4 and 10.6) are employed. In the viscosity-affected near-wall region (Rey < Re∗y ), the one-equation model of Wolfstein [296] is employed. In the one-equation model, the momentum equations and the k equation are retained as described in Sections 10.4 and 10.6. However, the turbulent viscosity, µt , is computed from √ µt,2layer = ρ Cµ `µ k

(10.8-19)

where the length scale that appears in Equation 10.8-19 is computed from [37]

`µ = yc` 1 − e−Rey /Aµ

(10.8-20)

The two-layer formulation for turbulent viscosity described above is used as a part of the enhanced wall treatment, in which the two-layer definition is smoothly blended with the high-Reynolds-number µt definition from the outer region, as proposed by Jongen [119]: µt,enh = λ µt + (1 − λ )µt,2layer


(10.8-21)

10-57

Modeling Turbulence

where µt is the high-Reynolds-number definition as described in Section 10.4 or 10.6 for the k- models or the RSM. A blending function, λ , is defined in such a way that it is equal to unity far from walls and is zero very near to walls. The blending function chosen is Rey − Re∗y 1 λ = 1 + tanh 2 A "

!#

(10.8-22)

The constant A determines the width of the blending function. By defining a width such that the value of λ will be within 1% of its far-field value given a variation of ∆Rey , the result is A=

|∆Rey | tanh(0.98)

(10.8-23)

Typically, ∆Rey would be assigned a value that is between 5% and 20% of Re∗y . The main purpose of the blending function λ is to prevent solution convergence from being impeded when the k- solution in the outer layer does not match with the two-layer formulation. The field is computed from

=

k 3/2 `

(10.8-24)

The length scales that appear in Equation 10.8-24 are again computed from Chen and Patel [37]:

` = yc` 1 − e−Rey /A

(10.8-25)

If the whole flow domain is inside the viscosity-affected region (Rey < 200), is not obtained by solving the transport equation; it is instead obtained algebraically from Equation 10.8-24. FLUENT uses a procedure for the specification that is similar to the µt blending in order to ensure a smooth transition between the algebraically-specified in the inner region and the obtained from solution of the transport equation in the outer region. The constants in the length scale formulas, Equations 10.8-20 and 10.8-25, are taken from [37]: c` = κCµ−3/4 ,

10-58

Aµ = 70,

A = 2c`

(10.8-26)



Enhanced Wall Functions To have a method that can extend its applicability throughout the near-wall region (i.e., laminar sublayer, buffer region, and fully-turbulent outer region) it is necessary to formulate the law-of-the wall as a single wall law for the entire wall region. FLUENT achieves this by blending linear (laminar) and logarithmic (turbulent) laws-of-the-wall using a function suggested by Kader [121]: 1

+ Γ u+ = eΓ u+ lam + e uturb

(10.8-27)

where the blending function is given by:

a(y + )4 1 + by + E c = exp − 1.0 E 00 a = 0.01c 5 b = c

Γ = −

(10.8-28) (10.8-29) (10.8-30) (10.8-31)

where E = 9.793 and E 00 is equal to E/fr , where fr is a roughness function. See Section 6.13.1 for more information about wall roughness effects. Similarly, the general equation for the derivative

du+ dy +

is

+ + 1 du du+ turb Γ dulam Γ =e +e + + dy dy dy +

(10.8-32)

This approach allows the fully turbulent law to be easily modified and extended to take into account other effects such as pressure gradients or variable properties. This formula also guarantees the correct asymptotic behavior for large and small values of y + and reasonable representation of velocity profiles in the cases where y + falls inside the wall buffer region (3 < y + < 10). The enhanced wall functions were developed by smoothly blending an enhanced turbulent wall law with the laminar wall law. The enhanced turbulent law-of-the-wall for compressible flow with heat transfer and pressure gradients has been derived by combining the approaches of White and Cristoph [293] and Huang et al. [107]: i du+ 1 h 0 turb + + 2 1/2 = S (1 − βu − γ(u ) ) dy + κy +

(10.8-33)

where


10-59

Modeling Turbulence

0

S =

(

1 + αy + for y + < ys+ 1 + αys+ for y + ≥ ys+

(10.8-34)

and µ dp νw dp = 2 ∗ 3 ∗ τw u dx ρ (u ) dx ∗ σt qw σt qw u β ≡ = cp τw Tw ρcp u∗ Tw σt (u∗ )2 γ ≡ 2cp Tw

α ≡

(10.8-35) (10.8-36) (10.8-37)

where ys+ is the location at which the log-law slope will remain fixed. By default, ys+ = 60. The coefficient α in Equation 10.8-33 represents the influences of pressure gradients while the coefficients β and γ represent thermal effects. Equation 10.8-33 is an ordinary differential equation and FLUENT will provide an appropriate analytical solution. If α, β, and γ all equal 0, an analytical solution would lead to the classical turbulent logarithmic law-of-the-wall. The laminar law-of-the-wall is determined from the following expression: du+ lam = 1 + αy + dy +

(10.8-38)

Note that the above expression only includes effects of pressure gradients through α, while the effects of variable properties due to heat transfer and compressibility on the laminar wall law are neglected. These effects are neglected because they are thought to be of minor importance when they occur close to the wall. Integration of Equation 10.8-38 results in u+ lam

=y

+

α 1 + y+ 2

(10.8-39)

Enhanced thermal wall functions follow the same approach developed for the profile of u+ . The unified wall thermal formulation blends the laminar and logarithmic profiles according to the method of Kader [121]: 1

+ + T + = eΓ Tlam + e Γ Tturb

(10.8-40)

where Γ = −

10-60

a(Pr y + )4 1 + bPr3 y +

(10.8-41)


10.9 Grid Considerations for Turbulent Flow Simulations

where Pr is the molecular Prandtl number, and the coefficients a and b are defined as in Equations 10.8-30 and 10.8-31. Apart from the above formulation for T + , enhanced thermal wall functions follow the same logic as previously described for standard thermal wall functions (see Section 10.8.2). A similar procedure is also used for species wall functions when the enhanced wall treatment is used. See Section 10.8.2 for details about species wall functions. The boundary condition for turbulence kinetic energy is the same as for standard wall functions (Equation 10.8-8). However, the production of turbulence kinetic energy Gk is computed using the velocity gradients that are consistent with the enhanced law-of-thewall (Equations 10.8-27 and 10.8-32), ensuring a formulation that is valid throughout the near-wall region.

10.9

Grid Considerations for Turbulent Flow Simulations

Successful computations of turbulent flows require some consideration during the mesh generation. Since turbulence (through the spatially-varying effective viscosity) plays a dominant role in the transport of mean momentum and other scalars for the majority of complex turbulent flows, you must ascertain that turbulence quantities are properly resolved, if high accuracy is required. Due to the strong interaction of the mean flow and turbulence, the numerical results for turbulent flows tend to be more susceptible to grid dependency than those for laminar flows. It is therefore recommended that you resolve, with sufficiently fine meshes, the regions where the mean flow changes rapidly and there are shear layers with a large mean rate of strain. You can check the near-wall mesh by displaying or plotting the values of y + , y ∗ , and Rey , which are all available in the postprocessing panels. It should be remembered that y + , y ∗ , and Rey are not fixed, geometrical quantities. They are all solution-dependent. For example, when you double the mesh (thereby halving the wall distance), the new y + does not necessarily become half of the y + for the original mesh. For the mesh in the near-wall region, different strategies must be used depending on which near-wall option you are using. In Sections 10.9.1 and 10.9.2 are general guidelines for the near-wall mesh.

10.9.1

Near-Wall Mesh Guidelines for Wall Functions

The distance from the wall at the wall-adjacent cells must be determined by considering the range over which the log-law is valid. The distance is usually measured in the wall unit, y + (≡ ρuτ y/µ), or y ∗ . Note that y + and y ∗ have comparable values when the first cell is placed in the log-layer.


10-61

Modeling Turbulence

• It is known that the log-law is valid for y + > 30 to 60. • Although FLUENT employs the linear (laminar) law when y + < 11.225, using an excessively fine mesh near the walls should be avoided, because the wall functions cease to be valid in the viscous sublayer. • The upper bound of the log-layer depends on, among others, pressure gradients and Reynolds number. As the Reynolds number increases, the upper bound tends to also increase. y + values that are too large are not desirable, because the wake component becomes substantially large above the log-layer. • A y + value close to the lower bound (y + ≈ 30) is most desirable. • Using excessive stretching in the direction normal to the wall should be avoided. • It is important to have at least a few cells inside the boundary layer.

10.9.2

Near-Wall Mesh Guidelines for the Enhanced Wall Treatment

Although the enhanced wall treatment is designed to extend the validity of near-wall modeling beyond the viscous sublayer, it is still recommended that you construct a mesh that will fully resolve the viscosity-affected near-wall region. In such a case, the two-layer component of the enhanced wall treatment will be dominant and the following mesh requirements are recommended (note that, here, the mesh requirements are in terms of y + , not y ∗ ): • When the enhanced wall treatment is employed with the intention of resolving the laminar sublayer, y + at the wall-adjacent cell should be on the order of y + = 1. However, a higher y + is acceptable as long as it is well inside the viscous sublayer (y + < 4 to 5). • You should have at least 10 cells within the viscosity-affected near-wall region (Rey < 200) to be able to resolve the mean velocity and turbulent quantities in that region.

10.9.3

Near-Wall Mesh Guidelines for the Spalart-Allmaras Model

The Spalart-Allmaras model in its complete implementation is a low-Reynolds-number model. This means that it is designed to be used with meshes that properly resolve the viscous-affected region, and damping functions have been built into the model in order to properly attenuate the turbulent viscosity in the viscous sublayer. Therefore, to obtain

10-62


10.9 Grid Considerations for Turbulent Flow Simulations

the full benefit of the Spalart-Allmaras model, the near-wall mesh spacing should be as described in Section 10.9.2 for the enhanced wall treatment. However, as discussed in Section 10.3.7, the boundary conditions for the Spalart-Allmaras model have been implemented so that the model will work on coarser meshes, such as would be appropriate for the wall function approach. If you are using a coarse mesh, you should follow the guidelines described in Section 10.9.1. In summary, for best results with the Spalart-Allmaras model, you should use either a very fine near-wall mesh spacing (on the order of y + = 1) or a mesh spacing such that y + ≥ 30.

10.9.4

Near-Wall Mesh Guidelines for the k-ω Models

Both k-ω models available in FLUENT are available as low-Reynolds-number models as well as high-Reynolds-number models. If the Transitional Flows option is enabled in the Viscous Model panel, low-Reynolds-number variants will be used, and, in that case, mesh guidelines should be the same as for the enhanced wall treatment. However, if this option is not active, then the mesh guidelines should be the same as for the wall functions.

10.9.5

Near-Wall Mesh Guidelines for Large Eddy Simulation

For the LES implementation in FLUENT, the wall boundary conditions have been implemented using a law-of-the-wall approach as described in Section 10.7.3. This means that there are no computational restrictions on the near-wall mesh spacing. However, for best results, it might be necessary to use a very fine near-wall mesh spacing (on the order of y + = 1).


10-63

Modeling Turbulence

10.10

Problem Setup for Turbulent Flows

When your FLUENT model includes turbulence you need to activate the relevant model and options, and supply turbulent boundary conditions. These inputs are described in this section. The procedure for setting up a turbulent flow problem is described below. (Note that this procedure includes only those steps necessary for the turbulence model itself; you will need to set up other models, boundary conditions, etc. as usual.) 1. To activate the turbulence model, select Spalart-Allmaras, k-epsilon, k-omega, Reynolds Stress, or (in 3D) Large Eddy Simulation under Model in the Viscous Model panel (Figure 10.10.1). Define −→ Models −→Viscous...

Figure 10.10.1: The Viscous Model Panel

10-64


10.10 Problem Setup for Turbulent Flows

If you choose the k-epsilon model, select Standard, RNG, or Realizable under k-epsilon Model. If you choose the k-omega model, select Standard or SST under k-omega Model.

!

The Large Eddy Simulation model is available only for 3D cases. 2. If the flow involves walls, and you are using one of the k- models or the RSM, choose one of the following options for the Near-Wall Treatment in the Viscous Model panel: • Standard Wall Functions • Non-Equilibrium Wall Functions • Enhanced Wall Treatment These near-wall options are described in detail in Section 10.8. By default, the standard wall function is enabled. The near-wall treatment for the Spalart-Allmaras, k-ω, and LES models is defined automatically, as described in Sections 10.3.7, 10.5.1, and 10.7.3, respectively. 3. Enable the appropriate turbulence modeling options in the Viscous Model panel. See Section 10.10.1 for details. 4. Specify the boundary conditions for the solution variables. Define −→Boundary Conditions... See Section 10.10.2 for details. 5. Specify the initial guess for the solution variables. Solve −→ Initialize −→Initialize... See Section 10.10.3 for details. Note that Reynolds stresses are automatically initialized using k, and therefore need not be initialized.

10.10.1

Turbulence Options

The various options available for the turbulence models are described in detail in Sections 10.3 through 10.7. Instructions for activating these options are provided here. If you choose the Spalart-Allmaras model, the following options are available: • Vorticity-based production • Strain/vorticity-based production • Viscous heating (always activated for the coupled solvers)


10-65

Modeling Turbulence

Once you have enabled the Spalart-Allmaras model, you can enable the DES model using the define/models/viscous/turbulence-expert/detached-eddy-simulation? text command. If you choose the standard k- model or the realizable k- model, the following options are available: • Viscous heating (always activated for the coupled solvers) • Inclusion of buoyancy effects on If you choose the RNG k- model, the following options are available: • Differential viscosity model • Swirl modification • Viscous heating (always activated for the coupled solvers) • Inclusion of buoyancy effects on If you choose the standard k-ω model, the following options are available: • Transitional flows • Shear flow corrections • Viscous heating (always activated for the coupled solvers) If you choose the shear-stress transport k-ω model, the following options are available: • Transitional flows • Viscous heating (always activated for the coupled solvers) If you choose the RSM, the following options are available: • Wall reflection effects on Reynolds stresses • Wall boundary conditions for the Reynolds stresses from the k equation • Quadratic pressure-strain model • Viscous heating (always activated for the coupled solvers)

10-66



• Inclusion of buoyancy effects on If you choose the enhanced wall treatment (available for the k- models and the RSM), the following options are available: • Pressure gradient effects • Thermal effects If you choose the LES model, the following options are available: • Smagorinsky-Lilly model for the subgrid-scale viscosity • RNG model for the subgrid-scale viscosity • Viscous heating (always activated for the coupled solvers) It is also possible to modify the Model Constants, but this is not necessary for most applications. See Sections 10.3 through 10.7 for details about these constants. Note that C1-PS and C2-PS are the constants C1 and C2 in the linear pressure-strain approximation of Equations 10.6-5 and 10.6-6, and C1’-PS and C2’-PS are the constants C10 and C20 in Equation 10.6-7. C1-SSG-PS, C1’-SSG-PS, C2-SSG-PS, C3-SSG-PS, C3’-SSG-PS, C4-SSGPS, and C5-SSG-PS are the constants C1 , C1∗ , C2 , C3 , C3∗ , C4 , and C5 in the quadratic pressure-strain approximation of Equation 10.6-16.

Including the Viscous Heating Effects See Sections 11.2.1 and 11.2.2 for information on including viscous heating effects in your model.

Including Turbulence Generation Due to Buoyancy If you specify a non-zero gravity force (in the Operating Conditions panel), and you are modeling a non-isothermal flow, the generation of turbulent kinetic energy due to buoyancy (Gb in Equation 10.4-1) is, by default, always included in the k equation. However, FLUENT does not, by default, include the buoyancy effects on . To include the buoyancy effects on , you must turn on the Full Buoyancy Effects option under Options in the Viscous Model panel. This option is available for the three k- models and for the RSM.


10-67

Modeling Turbulence

Vorticity- and Strain/Vorticity-Based Production For the Spalart-Allmaras model, you can choose either Vorticity-Based Production or Strain/Vorticity-Based Production under Spalart-Allmaras Options in the Viscous Model panel. If you choose Vorticity-Based Production, FLUENT will use Equation 10.3-8 to compute the value of the deformation tensor S; if you choose Strain/Vorticity-Based Production, it will use Equation 10.3-10. (These options will not appear unless you have activated the Spalart-Allmaras model.)

Detached Eddy Simulation (DES) Modeling If you enabled DES for the Sparlart-Allmaras model as described at the beginning of this ˜ section, FLUENT will use Equation 10.3-16 to compute the value of the length scale d. By default, the empirical constant Cdes is set to 0.65. You can change its value in the Cdes field under Model Constants.

Differential Viscosity Modification In the RNG turbulence model in FLUENT, you have an option to use a differential formula for effective viscosity µeff (Equation 10.4-6) to account for low-Reynolds-number effects. To enable this option, turn on Differential Viscosity Model under RNG Options in the Viscous Model panel. (This option will not appear unless you have activated the RNG k- model.)

Swirl Modification Once you choose the RNG model, the swirl modification takes effect, by default, for all three-dimensional flows and axisymmetric flows with swirl. The default swirl constant (αs in Equation 10.4-8) is set to 0.05, which works well for weakly to moderately swirling flows. However, for strongly swirling flows, you may need to use a larger swirl constant. To change the value of the swirl constant, you must first turn on the Swirl Dominated Flow option under RNG Options in the Viscous Model panel. (This option will not appear unless you have activated the RNG k- model.) Once you turn on the Swirl Dominated Flow option, the swirl constant αs is increased to 0.07. You can change its value in the Swirl Factor field under Model Constants.

Transitional Flows If either of the k-ω models are used, you may enable a low-Reynolds-number correction to the turbulent viscosity by enabling the Transitional Flows option under k-omega Options in the Viscous Model panel. By default, this option is not enabled, and the damping coefficient (α∗ in Equation 10.5-6) is equal to 1.

10-68



Shear Flow Corrections In the standard k-ω model, you also have the option of including corrections to improve the accuracy in predicting free shear flows. The Shear Flow Corrections option under k-omega Options is enabled by default in the Viscous Model panel, as these corrections are included in the standard k-ω model [294]. When this option is enabled, FLUENT will calculate fβ∗ and fβ using Equations 10.5-16 and 10.5-24, respectively. If this option is disabled, fβ∗ and fβ will be set equal to 1.

Including Pressure Gradient Effects If the enhanced wall treatment is used, you may include the effects of pressure gradients by enabling the Pressure Gradient Effects option under Enhanced Wall Treatment Options. When this option is enabled, FLUENT will include the coefficient α in Equation 10.8-33.

Including Thermal Effects If the enhanced wall treatment is used, you may include thermal effects by enabling the Thermal Effects option under Enhanced Wall Treatment Options. When this option is enabled, FLUENT will include the coefficient β in Equation 10.8-33. γ will also be included in Equation 10.8-33 when the Thermal Effects option is enabled if the ideal gas law is selected for the fluid density in the Materials panel.

Including the Wall Reflection Term If the RSM is used with the default model for pressure strain, FLUENT will, by default, include the wall-reflection effects in the pressure-strain term. That is, FLUENT will calculate φij,w using Equation 10.6-7 and include it in Equation 10.6-4. Note that wallreflection effects are not included if you have selected the quadratic pressure-strain model.

! The empirical constants and the function f used in the calculation of φij,w are calibrated for simple canonical flows such as channel flows and flat-plate boundary layers involving a single wall. If the flow involves multiple walls and the wall has significant curvature (e.g., an axisymmetric pipe or curvilinear duct), the inclusion of the wall-reflection term in Equation 10.6-7 may not improve the accuracy of the RSM predictions. In such cases, you can disable the wall-reflection effects by turning off the Wall Reflection Effects under Reynolds-Stress Options in the Viscous Model panel.

Solving the k Equation to Obtain Wall Boundary Conditions In the RSM, FLUENT, by default, uses the explicit setting of boundary conditions for the Reynolds stresses near the walls, with the values computed with Equation 10.6-28. k is calculated by solving the k equation obtained by summing Equation 10.6-1 for normal stresses. To disable this option and use the wall boundary conditions given in


10-69

Modeling Turbulence

Equation 10.6-29, turn off Wall B.C. from k Equation under Reynolds-Stress Options in the Viscous Model panel. (This option will not appear unless you have activated the RSM.)

Quadratic Pressure-Strain Model To use the quadratic pressure-strain model described in Section 10.6.3, turn on the Quadratic Pressure-Strain Model option under Reynolds-Stress Options in the Viscous Model panel. (This option will not appear unless you have activated the RSM.) The following options are not available when the Quadratic Pressure-Strain Model is enabled: • Wall Reflection Effects under Reynolds-Stress Options • Enhanced Wall Treatment under Near-Wall Treatment

Subgrid-Scale Model If you have selected the Large Eddy Simulation model, you will be able to choose which of the two subgrid-scale models described in Section 10.7.2 is to be used. You can choose either the Smagorinsky-Lilly or the RNG subgrid-scale model. (These options will not appear unless you have activated the LES model.)

Customizing the Turbulent Viscosity If you are using the Spalart-Allmaras, k-, k-ω, or LES model, a user-defined function can be used to customize the turbulent viscosity. This option will enable you to modify µt in the case of the Spalart-Allmaras, k-, and k-ω models, and incorporate completely new subgrid models in the case of the LES model. See the separate UDF Manual for information about user-defined functions. In the Viscous Model panel, under User-Defined Functions, select the appropriate userdefined function in the Turbulent Viscosity drop-down list. For the LES model, select the appropriate UDF in the Subgrid-Scale Turbulent Viscosity drop-down list.

Customizing the Turbulent Prandtl Numbers If you are using the standard or realizable k- model or the standard k-ω model, a userdefined function can be used to customize the turbulent Prandtl numbers. This option will allow you to calculate σk and either σ or σω (depending on if you have enabled the appropriate k- or k-ω model) by using a UDF. You will also be able to calculate the value of the energy Prandtl number (Prt in Equation 10.4-23) and the Prandtl number at the wall (Prt in Equation 10.8-5) in this way. See the separate UDF Manual for information about user-defined functions.

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In the Viscous Model panel, under User-Defined Functions, select the appropriate userdefined function from the drop-down lists under Prandtl Numbers. Options include: TKE Prandtl Number, TDR Prandtl Number (k- models only), SDR Prandtl Number (k-ω model only), Energy Prandtl Number, and Wall Prandtl Number.

Modeling Turbulence with Non-Newtonian Fluids If the turbulent flow involves non-Newtonian fluids, you can use the define/models/ viscous/turbulence-expert/turb-non-newtonian? text command to enable the selection of non-Newtonian options for the material viscosity. See Section 7.3.5 for details about these options.

10.10.2

Defining Turbulence Boundary Conditions

k- Models and k-ω Models When you are modeling turbulent flows in FLUENT using one of the k- models or one of the k-ω models, you must provide the boundary conditions for k and (or k and ω) in addition to other mean solution variables. The boundary conditions for k and (or k and ω) at the walls are internally taken care of by FLUENT, which obviates the need for your inputs. The boundary condition inputs for k and (or k and ω) you must supply to FLUENT are the ones at inlet boundaries (velocity inlet, pressure inlet, etc.). In many situations, it is important to specify correct or realistic boundary conditions at the inlets, because the inlet turbulence can significantly affect the downstream flow. See Section 6.2.2 for details about specifying the boundary conditions for k and (or k and ω) at the inlets. You may want to include the effects of the wall roughness on selected wall boundaries. In such cases, you can specify the roughness parameters (roughness height and roughness constant) in the panels for the corresponding wall boundaries (see Section 6.13.1). Additionally, you can control whether or not to set the turbulent viscosity to zero within a laminar zone. If the fluid zone in question is laminar, the text command define/ boundary-conditions/fluid will contain an option called Set Turbulent Viscosity to zero within laminar zone?. By setting this option to no, FLUENT will set only the production term in the turbulence transport equation to zero, allowing µt inside the laminar zone to be calculated. In contrast, when the Laminar Zone option is turned on in a Fluid boundary condition panel, both µt and the production term are set to zero. See Section 6.17.1 for details about laminar zones.

! Note that this laminar zone feature is also available for the Spalart-Allmaras model.


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Modeling Turbulence

The Spalart-Allmaras Model When you are modeling turbulent flows in FLUENT using the Spalart-Allmaras model, you must provide the boundary conditions for ν˜ in addition to other mean solution variables. The boundary conditions for ν˜ at the walls are internally taken care of by FLUENT, which obviates the need for your inputs. The boundary condition input for ν˜ you must supply to FLUENT is the one at inlet boundaries (velocity inlet, pressure inlet, etc.). In many situations, it is important to specify correct or realistic boundary conditions at the inlets, because the inlet turbulence can significantly affect the downstream flow. See Section 6.2.2 for details about specifying the boundary condition for ν˜ at the inlets. You may want to include the effects of the wall roughness on selected wall boundaries. In such cases, you can specify the roughness parameters (roughness height and roughness constant) in the panels for the corresponding wall boundaries (see Section 6.13.1).

! Note that if the DES model is enabled, the wall boundary conditions will be treated the same as for the Spalart-Allmaras model. All other boundaries will be treated the same as for the LES model (see below for details about LES boundary conditions).

Reynolds Stress Model The specification of turbulent boundary conditions for the RSM is the same as for the other turbulence models for all boundaries except at boundaries where flow enters the domain. Additional input methods are available for these boundaries and are described here. When you choose to use the RSM, the default inlet boundary condition inputs required are identical to those required when the k- model is active. You can input the turbulence quantities using any of the turbulence specification methods described in Section 6.2.2. FLUENT then uses the specified turbulence quantities to derive the Reynolds stresses at the inlet from the assumption of isotropy of turbulence:

0

2 k 3 = 0.0

ui2 = u0i u0j

(i = 1, 2, 3)

(10.10-1) (10.10-2)

0

where ui2 is the normal Reynolds stress component in each direction. The boundary condition for is determined in the same manner as for the k- turbulence models (see Section 6.2.2). To use this method, you will select K or Turbulence Intensity as the Reynolds-Stress Specification Method in the appropriate boundary condition panel. Alternately, you can directly specify the Reynolds stresses by selecting Reynolds-Stress Components as the Reynolds-Stress Specification Method in the boundary condition panel. When this option is enabled, you should input the Reynolds stresses directly.

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You can set the Reynolds stresses by using constant values, profile functions of coordinates (see Section 6.26), or user-defined functions (see the separate UDF Manual).

Large Eddy Simulation Model It is possible to specify the magnitude of random fluctuations of the velocity components at an inlet only if the velocity inlet boundary condition is selected. In this case, you must specify a Turbulence Intensity that determines the magnitude of the random perturbations on individual mean velocity components as described in Section 10.7.3. For all boundary types other than velocity inlets, the boundary conditions for LES remain the same as for laminar flows.

10.10.3

Providing an Initial Guess for k and (or k and ω)

For flows using one of the k- models, one of the k-ω models, or the RSM, the converged solutions or (for unsteady calculations) the solutions after a sufficiently long time has elapsed should be independent of the initial values for k and (or k and ω). For better convergence, however, it is beneficial to use a reasonable initial guess for k and (or k and ω). In general, it is recommended that you start from a fully-developed state of turbulence. When you use the enhanced wall treatment for the k- models or the RSM, it is critically important to specify fully-developed turbulence fields. Guidelines are provided below. • If you were able to specify reasonable boundary conditions at the inlet, it may be a good idea to compute the initial values for k and (or k and ω) in the whole domain from these boundary values. (See Section 24.13 for details.) • For more complex flows (e.g., flows with multiple inlets with different conditions) it may be better to specify the initial values in terms of turbulence intensity. 5–10% is enough to represent fully-developed turbulence. k can then be computed from the turbulence intensity and the characteristic mean velocity magnitude of your problem (k = 1.5(Iuavg )2 ). 2

You should specify an initial guess for so that the resulting eddy viscosity (Cµ k ) is sufficiently large in comparison to the molecular viscosity. In fully-developed turbulence, the turbulent viscosity is roughly two orders of magnitude larger than the molecular viscosity. From this, you can compute . Note that, for the RSM, Reynolds stresses are initialized automatically using Equations 10.10-1 and 10.10-2.


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Modeling Turbulence

Figure 10.10.2: Specifying Inlet Boundary Conditions for the Reynolds Stresses

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10.11 Solution Strategies for Turbulent Flow Simulations

10.11

Solution Strategies for Turbulent Flow Simulations

Compared to laminar flows, simulations of turbulent flows are more challenging in many ways. For the Reynolds-averaged approach, additional equations are solved for the turbulence quantities. Since the equations for mean quantities and the turbulent quantities (µt , k, , ω, or the Reynolds stresses) are strongly coupled in a highly non-linear fashion, it takes more computational effort to obtain a converged turbulent solution than to obtain a converged laminar solution. The LES model, while embodying a simpler, algebraic model for the subgrid-scale viscosity, requires a transient solution on a very fine mesh. The fidelity of the results for turbulent flows is largely determined by the turbulence model being used. Here are some guidelines that can enhance the quality of your turbulent flow simulations.

10.11.1

Mesh Generation

The following are suggestions to follow when generating the mesh for use in your turbulent flow simulation: • Picture in your mind the flow under consideration using your physical intuition or any data for a similar flow situation, and identify the main flow features expected in the flow you want to model. Generate a mesh that can resolve the major features that you expect. • If the flow is wall-bounded, and the wall is expected to significantly affect the flow, take additional care when generating the mesh. You should avoid using a mesh that is too fine (for the wall function approach) or too coarse (for the enhanced wall treatment approach). See Section 10.9 for details.

10.11.2

Accuracy

The suggestions below are provided to help you obtain better accuracy in your results: • Use the turbulence model that is better suited for the salient features you expect to see in the flow (see Section 10.2). • Because the mean quantities have larger gradients in turbulent flows than in laminar flows, it is recommended that you use high-order schemes for the convection terms. This is especially true if you employ a triangular or tetrahedral mesh. Note that excessive numerical diffusion adversely affects the solution accuracy, even with the most elaborate turbulence model. • In some flow situations involving inlet boundaries, the flow downstream of the inlet is dictated by the boundary conditions at the inlet. In such cases, you should exercise care to make sure that reasonably realistic boundary values are specified.


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Modeling Turbulence

10.11.3

Convergence

The suggestions below are provided to help you enhance convergence for turbulent flow calculations: • Starting with excessively crude initial guesses for mean and turbulence quantities may cause the solution to diverge. A safe approach is to start your calculation using conservative (small) under-relaxation parameters and (for the coupled solvers) a conservative Courant number, and increase them gradually as the iterations proceed and the solution begins to settle down. • It is also helpful for faster convergence to start with reasonable initial guesses for the k and (or k and ω) fields. Particularly when the enhanced wall treatment is used, it is important to start with a sufficiently developed turbulence field, as recommended in Section 10.10.3, to avoid the need for an excessive number of iterations to develop the turbulence field. • When you are using the RNG k- model, an approach that might help you achieve better convergence is to obtain a solution with the standard k- model before switching to the RNG model. Due to the additional non-linearities in the RNG model, lower under-relaxation factors and (for the coupled solvers) a lower Courant number might also be necessary. Note that when you use the enhanced wall treatment, you may sometimes find during the calculation that the residual for is reported to be zero. This happens when your flow is such that Rey is less than 200 in the entire flow domain, and is obtained from the algebraic formula (Equation 10.8-24) instead of from its transport equation.

10.11.4

RSM-Specific Solution Strategies

Using the RSM creates a high degree of coupling between the momentum equations and the turbulent stresses in the flow, and thus the calculation can be more prone to stability and convergence difficulties than with the k- models. When you use the RSM, therefore, you may need to adopt special solution strategies in order to obtain a converged solution. The following strategies are generally recommended: • Begin the calculations using the standard k- model. Turn on the RSM and use the k- solution data as a starting point for the RSM calculation. • Use low under-relaxation factors (0.2 to 0.3) and (for the coupled solvers) a low Courant number for highly swirling flows or highly complex flows. In these cases, you may need to reduce the under-relaxation factors both for the velocities and for all of the stresses.

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10.11 Solution Strategies for Turbulent Flow Simulations

Instructions for setting these solution parameters are provided below. If you are applying the RSM to prediction of a highly swirling flow, you will want to consider the solution strategies discussed in Section 8.4 as well.

Under-Relaxation of the Reynolds Stresses FLUENT applies under-relaxation to the Reynolds stresses. You can set under-relaxation factors using the Solution Controls panel. Solve −→ Controls −→Solution... The default settings of 0.5 are recommended for most cases. You may be able to increase these settings and speed up the convergence when the RSM solution begins to converge.

Disabling Calculation Updates of the Reynolds Stresses In some instances, you may wish to let the current Reynolds stress field remain fixed, skipping the solution of the Reynolds transport equations while solving the other transport equations. You can activate/deactivate all Reynolds stress equations in the Solution Controls panel. Solve −→ Controls −→Solution...

Residual Reporting for the RSM When you use the RSM for turbulence, FLUENT reports the equation residuals for the individual Reynolds stress transport equations. You can apply the usual convergence criteria to the Reynolds stress residuals: normalized residuals in the range of 10−3 usually indicate a practically-converged solution. However, you may need to apply tighter convergence criteria (below 10−4 ) to ensure full convergence.

10.11.5

LES-Specific Solution Strategies

Large eddy simulation involves running a transient solution from some initial condition, on an appropriately fine grid, using an appropriate time step size. The solution must be run long enough to become independent of the initial condition and to enable the statistics of the flow field to be determined. The following are suggestions to follow when running a large eddy simulation: 1. Start by running a flow simulation assuming laminar flow or using a simple Reynoldsaveraged turbulence model such as standard k- or Spalart-Allmaras. Since this is only an initial condition, you need run only until the flow field is somewhat converged. This step is optional.


10-77

Modeling Turbulence

2. When you enable LES, FLUENT will automatically turn on the unsteady solver option and choose the second-order implicit formulation. You will need to set the appropriate time step size and all the needed solution parameters. (See Section 24.15.1 for guidelines on setting solution parameters for transient calculations in general.) Use the central-differencing spatial discretization scheme for all equations. 3. Run LES until the flow becomes statistically steady. The best way to see if the flow is fully developed and statistically steady is to monitor forces and solution variables (e.g., velocity components or pressure) at selected locations in the flow. 4. Zero out the initial statistics using the solve/initialize/init-flow-statistics text command. Before you restart the solution, enable Data Sampling for Time Statistics in the Iterate panel, as described in Section 24.15.1. 5. Continue until you get statistically stable data. The duration of the simulation can be determined beforehand by estimating the mean flow residence time in the solution domain (L/U , where L is the characteristic length of the solution domain and U is a characteristic mean flow velocity). The simulation should be run for at least a few mean flow residence times. Instructions for setting the solution parameters for LES are provided below.

Temporal Discretization FLUENT provides both first-order and second-order temporal discretizations. For LES, the second-order discretization is recommended. Define −→ Models −→Solver...

Spatial Discretization Overly diffusive schemes such as the first-order upwind or power law scheme should be avoided, because they may unduly damp out the energy of the resolved eddies. The central-differencing scheme is recommended for all equations when you use the LES model. Solve −→ Controls −→Solution...

10-78


10.12 Postprocessing for Turbulent Flows

10.12

Postprocessing for Turbulent Flows

FLUENT provides postprocessing options for displaying, plotting, and reporting various turbulence quantities, which include the main solution variables and other auxiliary quantities. Turbulence quantities that can be reported for the k- models are as follows: • Turbulent Kinetic Energy (k) • Turbulence Intensity • Turbulent Dissipation Rate (Epsilon) • Production of k • Turbulent Viscosity • Effective Viscosity • Turbulent Viscosity Ratio • Effective Thermal Conductivity • Effective Prandtl Number • Wall Yplus • Wall Ystar • Turbulent Reynolds Number (Re y) (only when the enhanced wall treatment is used for the near-wall treatment) Turbulence quantities that can be reported for the k-ω models are as follows: • Turbulent Kinetic Energy (k) • Turbulence Intensity • Specific Dissipation Rate (Omega) • Production of k • Turbulent Viscosity • Effective Viscosity • Turbulent Viscosity Ratio


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Modeling Turbulence

• Effective Thermal Conductivity • Effective Prandtl Number • Wall Ystar • Wall Yplus Turbulence quantities that can be reported for the Spalart-Allmaras model are as follows: • Modified Turbulent Viscosity • Turbulent Viscosity • Effective Viscosity • Turbulent Viscosity Ratio • Effective Thermal Conductivity • Effective Prandtl Number • Wall Yplus Turbulence quantities that can be reported for the RSM are as follows: • Turbulent Kinetic Energy (k) • Turbulence Intensity • UU Reynolds Stress • VV Reynolds Stress • WW Reynolds Stress • UV Reynolds Stress • VW Reynolds Stress • UW Reynolds Stress • Turbulent Dissipation Rate (Epsilon) • Production of k • Turbulent Viscosity • Effective Viscosity

10-80


10.12 Postprocessing for Turbulent Flows

• Turbulent Viscosity Ratio • Effective Thermal Conductivity • Effective Prandtl Number • Wall Yplus • Wall Ystar • Turbulent Reynolds Number (Re y) Turbulence quantities that can be reported for the LES model are as follows: • Subgrid Turbulent Kinetic Energy • Subgrid Turbulent Viscosity • Subgrid Effective Viscosity • Subgrid Turbulent Viscosity Ratio • Effective Thermal Conductivity • Effective Prandtl Number • Wall Yplus All of these variables can be found in the Turbulence... category of the variable selection drop-down list that appears in postprocessing panels. See Chapter 29 for their definitions.

10.12.1

Custom Field Functions for Turbulence

In addition to the quantities listed above, you can define your own turbulence quantities using the Custom Field Function Calculator panel. Define −→Custom Field Functions... The following functions may be useful: • Ratio of production of k to its dissipation (Gk /ρ) • Ratio of the mean flow to turbulent time scale, η (≡ Sk/) • Reynolds stresses derived from the Boussinesq formula (e.g., −uv = νt ∂u ) ∂y


10-81

Modeling Turbulence

10.12.2

Postprocessing LES Statistics

As described in Section 10.7, LES involves the solution of a transient flow field, but it is the mean flow quantities that are of most engineering interest. If you turn on the Data Sampling for Time Statistics option in the Iterate panel, FLUENT will gather data for time statistics while performing a large eddy simulation. You can then view both the mean and the root-mean-square (RMS) values in FLUENT. See Section 24.15.3 for details.

10.12.3

Troubleshooting

You can use the postprocessing options not only for the purpose of interpreting your results but also for investigating any anomalies that may appear in the solution. For instance, you may want to plot contours of the k field to check if there are any regions where k is erroneously large or small. You should see a high k region in the region where the production of k is large. You may want to display the turbulent viscosity ratio field in order to see whether or not turbulence takes full effect. Usually turbulent viscosity is at least two orders of magnitude larger than molecular viscosity for fullydeveloped turbulent flows modeled using the RANS approach (i.e., not using LES). You may also want to see whether you are using a proper near-wall mesh for the enhanced wall treatment. In this case, you can display filled contours of Rey (turbulent Reynolds number) overlaid on the mesh.

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Chapter 11.

Modeling Heat Transfer

This chapter provides details about the heat transfer models available in FLUENT. Information is presented in the following sections: • Section 11.1: Overview of Heat Transfer Models in FLUENT • Section 11.2: Convective and Conductive Heat Transfer • Section 11.3: Radiative Heat Transfer • Section 11.4: Periodic Heat Transfer • Section 11.5: Buoyancy-Driven Flows

11.1

Overview of Heat Transfer Models in FLUENT

The flow of thermal energy from matter occupying one region in space to matter occupying a different region in space is known as heat transfer. Heat transfer can occur by three main methods: conduction, convection, and radiation. Physical models involving only conduction and/or convection are the simplest, while buoyancy-driven flow, or natural convection, and radiation models are more complex. Depending on your problem, FLUENT will solve a variation of the energy equation that takes into account the heat transfer methods you have specified. FLUENT is also able to predict heat transfer in periodically repeating geometries, thus greatly reducing the required computational effort in certain cases.

11.2

Convective and Conductive Heat Transfer

FLUENT allows you to include heat transfer within the fluid and/or solid regions in your model. Problems ranging from thermal mixing within a fluid to conduction in composite solids can thus be handled by FLUENT using the physical models and inputs described in this section. Radiation modeling is described in Section 11.3 and natural convection is described in Section 11.5.


11-1


Information about heat transfer is presented in the following subsections: • Section 11.2.1: Theory • Section 11.2.2: User Inputs for Heat Transfer • Section 11.2.3: Solution Process for Heat Transfer • Section 11.2.4: Reporting and Displaying Heat Transfer Quantities • Section 11.2.5: Exporting Heat Flux Data

11.2.1

Theory

The Energy Equation FLUENT solves the energy equation in the following form: 



X ∂ (ρE) + ∇ · (~v (ρE + p)) = ∇ · keff ∇T − hj J~j + (τ eff · ~v ) + Sh ∂t j

(11.2-1)

where keff is the effective conductivity (k + kt , where kt is the turbulent thermal conductivity, defined according to the turbulence model being used), and J~j is the diffusion flux of species j. The first three terms on the right-hand side of Equation 11.2-1 represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. Sh includes the heat of chemical reaction, and any other volumetric heat sources you have defined. In Equation 11.2-1, E =h−

p v2 + ρ 2

(11.2-2)

where sensible enthalpy h is defined for ideal gases as h=

X

Yj hj

(11.2-3)

j

and for incompressible flows as h=

X j

Yj hj +

p ρ

(11.2-4)

In Equations 11.2-3 and 11.2-4, Yj is the mass fraction of species j and

11-2


11.2 Convective and Conductive Heat Transfer

hj =

Z

T

Tref

cp,j dT

(11.2-5)

where Tref is 298.15 K.

The Energy Equation for the Non-Premixed Combustion Model When the non-adiabatic non-premixed combustion model is enabled, FLUENT solves the total enthalpy form of the energy equation: !

∂ kt (ρH) + ∇ · (ρ~v H) = ∇ · ∇H + Sh ∂t cp

(11.2-6)

Under the assumption that the Lewis number (Le) = 1, the conduction and species diffusion terms combine to give the first term on the right-hand side of the above equation while the contribution from viscous dissipation appears in the non-conservative form as the second term. The total enthalpy H is defined as H=

X

Yj H j

(11.2-7)

j

where Yj is the mass fraction of species j and Hj =

Z

T

Tref,j

cp,j dT + h0j (Tref,j )

(11.2-8)

h0j (Tref,j ) is the formation enthalpy of species j at the reference temperature Tref,j .

Inclusion of Pressure Work and Kinetic Energy Terms Equation 11.2-1 includes pressure work and kinetic energy terms which are often negligible in incompressible flows. For this reason, the segregated solver by default does not include the pressure work or kinetic energy when you are solving incompressible flow. If you wish to include these terms, use the define/models/energy? text command to turn them on. Pressure work and kinetic energy are always accounted for when you are modeling compressible flow or using one of the coupled solvers.


11-3


Inclusion of the Viscous Dissipation Terms Equations 11.2-1 and 11.2-6 include viscous dissipation terms, which describe the thermal energy created by viscous shear in the flow. When the segregated solver is used, FLUENT’s default form of the energy equation does not include them (because viscous heating is often negligible). Viscous heating will be important when the Brinkman number, Br, approaches or exceeds unity, where Br =

µUe2 k∆T

(11.2-9)

and ∆T represents the temperature difference in the system. When your problem requires inclusion of the viscous dissipation terms and you are using the segregated solver, you should activate the terms using the Viscous Heating option in the Viscous Model panel. Compressible flows typically have Br ≥ 1. Note, however, that when the segregated solver is used, FLUENT does not automatically activate the viscous dissipation if you have defined a compressible flow model. When one of the coupled solvers is used, the viscous dissipation terms are always included when the energy equation is solved.

Inclusion of the Species Diffusion Term Equations 11.2-1 and 11.2-6 both include the effect of enthalpy transport due to species diffusion. When the segregated solver is used, the term   X ∇ ·  hj J~j  j

is included in Equation 11.2-1 by default. If you do not want to include it, you can turn off the Diffusion Energy Source option in the Species Model panel. When the non-adiabatic non-premixed combustion model is being used, this term does not explicitly appear in the energy equation, because it is included in the first term on the right-hand side of Equation 11.2-6. When one of the coupled solvers is used, this term is always included in the energy equation.

Energy Sources Due to Reaction Sources of energy, Sh , in Equation 11.2-1 include the source of energy due to chemical reaction:

11-4



Sh,rxn = −

X j

Z T h0j cp,j dT Rj + Mj Tref,j !

(11.2-10)

where h0j is the enthalpy of formation of species j and Rj is the volumetric rate of creation of species j. In the energy equation used for non-adiabatic non-premixed combustion (Equation 11.2-6), the heat of formation is included in the definition of enthalpy (see Equation 11.2-7), so reaction sources of energy are not included in Sh .

Energy Sources Due To Radiation When one of the radiation models is being used, Sh in Equation 11.2-1 or 11.2-6 also includes radiation source terms. See Section 11.3 for details.

Interphase Energy Sources It should be noted that the energy sources, Sh , also include heat transfer between the continuous and the discrete phase. This is discussed further in Section 21.5.

Boundary Conditions for Heat Transfer at Walls Heat transfer boundary conditions at walls are discussed in Section 10.8.2.

Energy Equation in Solid Regions In solid regions, the energy transport equation used by FLUENT has the following form: ∂ (ρh) + ∇ · (~v ρh) = ∇ · (k∇T ) + Sh ∂t where

ρ h k T Sh

(11.2-11)

= density R = sensible enthalpy, TTref cp dT = conductivity = temperature = volumetric heat source

The second term on the left-hand side of Equation 11.2-11 represents convective energy transfer due to rotational or translational motion of the solids. The velocity field ~v is computed from the motion specified for the solid zone (see Section 6.18). The terms on the right-hand side of Equation 11.2-11 are the heat flux due to conduction and volumetric heat sources within the solid, respectively.


11-5


Anisotropic Conductivity in Solids When you use the segregated solver, FLUENT allows you to specify anisotropic conductivity for solid materials. The conduction term for an anisotropic solid has the form ∇ · (kij ∇T )

(11.2-12)

where kij is the conductivity matrix. See Section 7.4.5 for details on specifying anisotropic conductivity for solid materials.

Diffusion at Inlets The net transport of energy at inlets consists of both the convection and diffusion components. The convection component is fixed by the inlet temperature specified by you. The diffusion component, however, depends on the gradient of the computed temperature field. Thus the diffusion component (and therefore the net inlet transport) is not specified a priori. In some cases, you may wish to specify the net inlet transport of energy rather than the inlet temperature. If you are using the segregated solver, you can do this by disabling inlet energy diffusion. By default, FLUENT includes the diffusion flux of energy at inlets. To turn off inlet diffusion, use the define/models/energy? text command. Inlet diffusion cannot be turned off if you are using one of the coupled solvers.

11.2.2

User Inputs for Heat Transfer

When your FLUENT model includes heat transfer you need to activate the relevant models, supply thermal boundary conditions, and input material properties that govern heat transfer and/or may vary with temperature. These inputs are described in this section. The procedure for setting up a heat transfer problem is described below. (Note that this procedure includes only those steps necessary for the heat transfer model itself; you will need to set up other models, boundary conditions, etc. as usual.) 1. To activate the calculation of heat transfer, turn on the Energy Equation option in the Energy panel (Figure 11.2.1). Define −→ Models −→Energy... 2. (optional, segregated solver only) If you are modeling viscous flow and you want to include the viscous heating terms in the energy equation, turn on the Viscous Heating option in the Viscous Model panel. As noted in Section 11.2.1, the viscous heating terms in the energy equation are (by default) ignored by FLUENT when the segregated solver is used. (They are always included when one of the coupled solvers is used.) Viscous dissipation should be enabled when the shear stress in the

11-6



Figure 11.2.1: The Energy Panel

fluid is large (e.g., in lubrication problems) and/or in high-velocity, compressible flows (see Equation 11.2-9). Define −→ Models −→Viscous... 3. Define thermal boundary conditions at flow inlets, flow outlets, and walls. Define −→Boundary Conditions... At flow inlets and exits you will set the temperature; at walls you may use any of the following thermal conditions: • Specified heat flux • Specified temperature • Convective heat transfer • External radiation • Combined external radiation and external convective heat transfer Section 6.13.1 provides details on the model inputs that govern these thermal boundary conditions. The default thermal boundary condition at inlets is a specified temperature of 300 K; at walls the default condition is zero heat flux (adiabatic). See Chapter 6 for details about boundary condition inputs.

!

If your heat transfer application involves two separated fluid regions, see the information provided below. 4. Define material properties for heat transfer. Define −→Materials... Heat capacity and thermal conductivity must be defined, and you can specify many properties as functions of temperature, as described in Chapter 7.

!

If your heat transfer application involves two separated fluid regions, see the information provided below.


11-7


The Temperature Floor and Ceiling For stability reasons, FLUENT includes a limit on the predicted temperature range. The purpose of the temperature ceiling and floor is to improve the stability of calculations in which the temperature should physically lie within known limits. Sometimes intermediate solutions of the equations give rise to temperatures beyond these limits for which property definitions, etc. are not well defined. The temperature limits keep the temperatures within the expected range for your problem. If the FLUENT calculation predicts a temperature above the maximum limit, the stored temperature values are “pegged” at this maximum value. The default for the temperature ceiling is 5000 K. If the FLUENT calculation predicts a temperature below the minimum limit, the stored temperature values are “pegged” at this minimum value. The default for the temperature minimum is 1 K. If you expect the temperature in your domain to exceed 5000 K, you should use the Solution Limits panel to increase the Maximum Temperature. Solve −→ Controls −→Limits...

Modeling Heat Transfer in Two Separated Fluid Regions If your heat transfer application involves two fluid regions separated by a solid zone or a wall, as illustrated in Figure 11.2.2, you will need to define the problem with some care. Specifically: • You should not use outflow boundary conditions in either fluid. • You can establish separate fluid properties by selecting a different fluid material for each zone. (For species calculations, however, you can only select a single mixture material for the entire domain.)

➞

fluid 2

➞

fluid 1

Figure 11.2.2: Typical Counterflow Heat Exchanger Involving Heat Transfer Between Two Separated Fluid Streams

11-8



11.2.3

Solution Process for Heat Transfer

Although many simple heat transfer problems can be successfully solved using the default solution parameters assumed by FLUENT, you may accelerate the convergence of your problem and/or improve the stability of the solution process using some of the guidelines provided in this section.

Under-Relaxation of the Energy Equation When you use the segregated solver, FLUENT under-relaxes the energy equation using the under-relaxation parameter defined by you in the Solution Controls panel, as described in Section 24.9. Solve −→ Controls −→Solution... If you are using the non-adiabatic non-premixed combustion model, you will set the energy under-relaxation factor as usual, but you will also set an under-relaxation factor for temperature, which will be used as described below. FLUENT uses a default under-relaxation factor of 1.0 for the energy equation, regardless of the form in which it is solved (temperature or enthalpy). In problems where the energy field impacts the fluid flow (via temperature-dependent properties or buoyancy) you should use a lower value for the under-relaxation factor, in the range of 0.8–1.0. In problems where the flow field is decoupled from the temperature field (no temperaturedependent properties or buoyancy forces), you can usually retain the default value of 1.0.

Under-Relaxation of Temperature When the Enthalpy Equation is Solved When the enthalpy form of the energy equation is solved (i.e., when you are using the nonadiabatic non-premixed combustion model), FLUENT also under-relaxes the temperature, updating the temperature by only a fraction of the change that would result from the change in the (under-relaxed) enthalpy values. This second level of under-relaxation can be used to good advantage when you would like to let the enthalpy field change rapidly, but the temperature response (and its effect on fluid properties) to lag. FLUENT uses a default setting of 1.0 for the under-relaxation on temperature and you can modify this setting using the Solution Controls panel.

Disabling the Species Diffusion Term If you are solving for species transport using the segregated solver and you encounter convergence difficulties, you may want to consider turning off the Diffusion Energy Source option in the Species Model panel. Define −→ Models −→Species...


11-9


When this option is disabled, FLUENT will neglect the effects of species diffusion on the energy equation. Note that species diffusion effects are always included when one of the coupled solvers is used.

Step-by-Step Solutions Often the most efficient strategy for predicting heat transfer is to compute an isothermal flow first and then to add the calculation of the energy equation. The procedure differs slightly, depending on whether or not the flow and heat transfer are coupled. Decoupled Flow and Heat Transfer Calculations If your flow and heat transfer are decoupled (no temperature-dependent properties or buoyancy forces), you can first solve the isothermal flow (energy equation turned off) to yield a converged flow-field solution and then solve the energy transport equation alone.

! Since the coupled solvers always solve the flow and energy equations together, the procedure for solving for energy alone applies only to the segregated solver. You can temporarily turn off the flow equations or the energy equation by deselecting Energy in the Equations list in the Solution Controls panel. (See also Section 24.19.2.) Solve −→ Controls −→Solution... Coupled Flow and Heat Transfer Calculations If your flow and heat transfer are coupled (i.e., your model includes temperature-dependent properties or buoyancy forces), you can first solve the flow equations before turning on energy. Once you have a converged flow-field solution, you can turn on energy and solve the flow and energy equations simultaneously to complete the heat transfer simulation.

11.2.4

Reporting and Displaying Heat Transfer Quantities

FLUENT provides several additional reporting options for simulations involving heat transfer. You can generate graphical plots or reports of the following variables/functions: • Static Temperature • Total Temperature • Enthalpy • Relative Total Temperature • Rothalpy

11-10



• Wall Temperature (Outer Surface) • Wall Temperature (Inner Surface) • Total Enthalpy • Total Enthalpy Deviation • Entropy • Total Energy • Internal Energy • Total Surface Heat Flux • Surface Heat Transfer Coef. • Surface Nusselt Number • Surface Stanton Number The first 12 variables listed above are contained in the Temperature... category of the variable selection drop-down list that appears in postprocessing panels, and the remaining variables are in the Wall Fluxes... category. See Chapter 29 for their definitions.

Definition of Enthalpy and Energy in Reports and Displays The definitions of the reported values of enthalpy and energy will be different depending on whether the flow is compressible or incompressible. See Section 29.4 for a complete list of definitions.

Reporting Heat Transfer Through Boundaries You can use the Flux Reports panel to compute the heat transfer through each boundary of the domain, or to sum the heat transfer through all boundaries to check the heat balance. Report −→Fluxes... It is recommended that you perform a heat balance check to ensure that your solution is truly converged. See Section 28.2 for details about generating flux reports.


11-11


Reporting Heat Transfer Through a Surface You can use the Surface Integrals panel (described in Section 28.5) to compute the heat transfer through any boundary or any surface created using the methods described in Chapter 26. Report −→Surface Integrals... To report the flow rate of enthalpy Q=

Z

~ Hρ~v · dA

(11.2-13)

choose the Mass Flow Rate option in the Surface Integrals panel, select Enthalpy (in the Temperature... category) as the Field Variable, and pick the surface(s) on which to integrate.

Reporting Averaged Heat Transfer Coefficients The Surface Integrals panel can also be used to generate a report of averaged heat transfer R coefficient h on a surface ( A1 h dA). Report −→Surface Integrals... In the Surface Integrals panel, choose the Area-Weighted Average option, select Surface Heat Transfer Coef. (in the Wall Fluxes... category) as the Field Variable, and pick the surface.

11.2.5

Exporting Heat Flux Data

It is possible to export heat flux data on wall zones (including radiation) to a generic file that you can examine or use in an external program. To save a heat flux file, you will use the custom-heat-flux text command. file −→ export −→custom-heat-flux Heat transfer data will be exported in the following free format for each face zone that you select for export: zone-name nfaces x_f y_f z_f A . . .

Q

T_w

T_c

Each block of data starts with the name of the face zone (zone-name) and the number of faces in the zone (nfaces). Next there is a line for each face (i.e., nfaces lines), each

11-12


11.3 Radiative Heat Transfer

containing the components of the face centroid (x f, y f, and, in 3D, z f), the face area (A), the total heat transfer including radiation heat transfer (Q), the face temperature (T w), and the adjacent cell temperature (T c).

11.3

Radiative Heat Transfer

Information about radiation modeling is presented in the following sections: • Section 11.3.1: Introduction to Radiative Heat Transfer • Section 11.3.2: Choosing a Radiation Model • Section 11.3.3: The Discrete Transfer Radiation Model (DTRM) • Section 11.3.4: The P-1 Radiation Model • Section 11.3.5: The Rosseland Radiation Model • Section 11.3.6: The Discrete Ordinates (DO) Radiation Model • Section 11.3.7: The Surface-to-Surface (S2S) Radiation Model • Section 11.3.8: Radiation in Combusting Flows • Section 11.3.9: Overview of Using the Radiation Models • Section 11.3.10: Selecting the Radiation Model • Section 11.3.11: Defining the Ray Tracing for the DTRM • Section 11.3.12: Computing or Reading the View Factors for the S2S Model • Section 11.3.13: Defining the Angular Discretization for the DO Model • Section 11.3.14: Defining Non-Gray Radiation for the DO Model • Section 11.3.15: Defining Material Properties for Radiation • Section 11.3.16: Setting Radiation Boundary Conditions • Section 11.3.17: Setting Solution Parameters for Radiation • Section 11.3.18: Solving the Problem • Section 11.3.19: Reporting and Displaying Radiation Quantities • Section 11.3.20: Displaying Rays and Clusters for the DTRM


11-13


11.3.1

Introduction to Radiative Heat Transfer

FLUENT provides five radiation models which allow you to include radiation, with or without a participating medium, in your heat transfer simulations: • Discrete transfer radiation model (DTRM) [33, 231] • P-1 radiation model [38, 234] • Rosseland radiation model [234] • Surface-to-surface (S2S) radiation model [234] • Discrete ordinates (DO) radiation model [41, 203] Heating or cooling of surfaces due to radiation and/or heat sources or sinks due to radiation within the fluid phase can be included in your model using one of these radiation models.

Radiative Transfer Equation The radiative transfer equation (RTE) for an absorbing, emitting, and scattering medium at position ~r in the direction ~s is 4 dI(~r, ~s) σs Z 4π 2 σT + (a + σs )I(~r, ~s) = an + I(~r, ~s 0 ) Φ(~s · ~s 0 ) dΩ0 ds π 4π 0

where ~r ~s ~s 0 s a n σs σ I T Φ Ω0

= = = = = = = = = = = =

(11.3-1)

position vector direction vector scattering direction vector path length absorption coefficient refractive index scattering coefficient Stefan-Boltzmann constant (5.672 × 10−8 W/m2 -K4 ) radiation intensity, which depends on position (~r) and direction (~s) local temperature phase function solid angle

(a + σs )s is the optical thickness or opacity of the medium. The refractive index n is important when considering radiation in semi-transparent media. Figure 11.3.1 illustrates the process of radiative heat transfer. The DTRM and the P-1, Rosseland, and DO radiation models require the absorption coefficient a as input. a and the scattering coefficient σs can be constants, and a can also

11-14


11.3 Radiative Heat Transfer Absorption and scattering loss: I (a+ σs) ds

Outgoing radiation I + (dI/ds)ds

Incoming radiation (I)

Gas emission: (aσT 4/ π) ds

Scattering addition

ds

Figure 11.3.1: Radiative Heat Transfer

be a function of local concentrations of H2 O and CO2 , path length, and total pressure. FLUENT provides the weighted-sum-of-gray-gases model (WSGGM) for computation of a variable absorption coefficient. See Section 11.3.8 for details. The discrete ordinates implementation can model radiation in semi-transparent media. The refractive index n of the medium must be provided as a part of the calculation for this type of problem.

Applications of Radiative Heat Transfer Typical applications well suited for simulation using radiative heat transfer include the following: • Radiative heat transfer from flames • Surface-to-surface radiant heating or cooling • Coupled radiation, convection, and/or conduction heat transfer • Radiation through windows in HVAC applications, and cabin heat transfer analysis in automotive applications • Radiation in glass processing, glass fiber drawing, and ceramic processing You should include radiative heat transfer in your simulation when the radiant heat flux, 4 4 Qrad = σ(Tmax − Tmin ), is large compared to the heat transfer rate due to convection or conduction. Typically this will occur at high temperatures where the fourth-order dependence of the radiative heat flux on temperature implies that radiation will dominate.


11-15


11.3.2

Choosing a Radiation Model

For certain problems, one radiation model may be more appropriate than the others. When deciding which radiation model to use, consider the following: • Optical thickness: The optical thickness aL is a good indicator of which model to use in your problem. Here, L is an appropriate length scale for your domain. For flow in a combustor, for example, L is the diameter of the combustion chamber. If aL 1, your best alternatives are the P-1 and Rosseland models. The P-1 model should typically be used for optical thicknesses > 1. For optical thickness > 3, the Rosseland model is cheaper and more efficient. The DTRM and the DO model work across the range of optical thicknesses, but are substantially more expensive to use. So you should use the “thick-limit” models, P-1 and Rosseland, if the problem allows it. For optically thin problems (aL < 1), only the DTRM and the DO model are appropriate. • Scattering and emissivity: The P-1, Rosseland, and DO models account for scattering, while the DTRM neglects it. Since the Rosseland model uses a temperature slip condition at walls, it is insensitive to wall emissivity. • Particulate effects: Only the P-1 and DO models account for exchange of radiation between gas and particulates (see Equation 11.3-15). • Semi-transparent media and specular boundaries: Only the DO model allows specular reflection (e.g., for mirrors) and calculation of radiation in semi-transparent media such as glass. • Non-gray radiation: Only the DO model allows you to compute non-gray radiation using a gray band model. • Localized heat sources: In problems with localized sources of heat, the P-1 model may overpredict the radiative fluxes. The DO model is probably the best suited for computing radiation for this case, although the DTRM, with a sufficiently large number of rays, is also acceptable. • Enclosure radiative transfer with non-participating media: The surface-to-surface (S2S) model is suitable for this type of problem. The radiation models used with participating media may, in principle, be used to compute the surface-to-surface radiation, but they are not always efficient.

External Radiation If you need to include radiative heat transfer from the exterior of your physical model, you can include an external radiation boundary condition in your model (see Section 6.13.1). If you are not concerned with radiation within the domain, this boundary condition can be used without activating one of the radiation models.

11-16



Advantages and Limitations of the DTRM The primary advantages of the DTRM are threefold: it is a relatively simple model, you can increase the accuracy by increasing the number of rays, and it applies to a wide range of optical thicknesses. You should be aware of the following limitations when using the DTRM in FLUENT: • The DTRM assumes that all surfaces are diffuse. This means that the reflection of incident radiation at the surface is isotropic with respect to solid angle. • The effect of scattering is not included. • The implementation assumes gray radiation. • Solving a problem with a large number of rays is CPU-intensive.

Advantages and Limitations of the P-1 Model The P-1 model has several advantages over the DTRM. For the P-1 model, the RTE (Equation 11.3-1) is a diffusion equation, which is easy to solve with little CPU demand. The model includes the effect of scattering. For combustion applications where the optical thickness is large, the P-1 model works reasonably well. In addition, the P-1 model can easily be applied to complicated geometries with curvilinear coordinates. You should be aware of the following limitations when using the P-1 radiation model: • The P-1 model assumes that all surfaces are diffuse. This means that the reflection of incident radiation at the surface is isotropic with respect to the solid angle. • The implementation assumes gray radiation. • There may be a loss of accuracy, depending on the complexity of the geometry, if the optical thickness is small. • The P-1 model tends to overpredict radiative fluxes from localized heat sources or sinks.

Advantages and Limitations of the Rosseland Model The Rosseland model has two advantages over the P-1 model. Since it does not solve an extra transport equation for the incident radiation (as the P-1 model does), the Rosseland model is faster than the P-1 model and requires less memory. The Rosseland model can only be used for optically thick media. It is recommended for use when the optical thickness exceeds 3. Note also that the Rosseland model is not available when one of the coupled solvers is being used; it is available only with the segregated solver.


11-17


Advantages and Limitations of the DO Model The DO model spans the entire range of optical thicknesses, and allows you to solve problems ranging from surface-to-surface radiation to participating radiation in combustion problems. It also allows the solution of radiation in semi-transparent media. Computational cost is moderate for typical angular discretizations, and memory requirements are modest. The current implementation is restricted to either gray radiation or non-gray radiation using a gray-band model. Solving a problem with a fine angular discretization may be CPU-intensive. The non-gray implementation in FLUENT is intended for use with participating media with a spectral absorption coefficient aλ that varies in a stepwise fashion across spectral bands, but varies smoothly within the band. Glass, for example, displays banded behavior of this type. The current implementation does not model the behavior of gases such as carbon dioxide or water vapor, which absorb and emit energy at distinct wave numbers [174]. The modeling of non-gray gas radiation is still an evolving field. However, some researchers [75] have used gray-band models to model gas behavior by approximating the absorption coefficients within each band as a constant. The implementation in FLUENT can be used in this fashion if desired. The non-gray implementation in FLUENT is compatible with all the models with which the gray implementation of the DO model can be used. Thus, it is possible to include scattering, anisotropy, semi-transparent media, and particulate effects. However, the nongray implementation assumes a constant absorption coefficient within each wavelength band. The weighted sum of gray gases model (WSGGM) cannot be used to specify the absorption coefficient in each band. The implementation allows the specification of spectral emissivity at walls. The emissivity is assumed to be constant within each band.

Advantages and Limitations of the S2S Model The surface-to-surface radiation model is good for modeling the enclosure radiative transfer without participating media (e.g., spacecraft heat rejection system, solar collector systems, radiative space heaters, and automotive underhood cooling). In such cases, the methods for participating radiation may not always be efficient. As compared to the DTRM and the DO radiation model, the S2S model has a much faster time per iteration, although the view factor calculation itself is CPU-intensive. You should be aware of the following limitations when using the S2S radiation model: • The S2S model assumes that all surfaces are diffuse. • The implementation assumes gray radiation.

11-18



• The storage and memory requirements increase very rapidly as the number of surface faces increases. This can be minimized by using a cluster of surface faces, although the CPU time is independent of the number of clusters that are used. • The S2S model cannot be used to model participating radiation problems. • The surface clustering method does not work with sliding meshes or hanging nodes. • The S2S model cannot be used if your model contains periodic or symmetry boundary conditions. • The S2S model cannot be used with 2d axisymmetric geometries. • The S2S model cannot be used for models with multiple enclosures. Only single enclosure geometries can be treated using the S2S model.

11.3.3

The Discrete Transfer Radiation Model (DTRM)

The main assumption of the DTRM is that the radiation leaving the surface element in a certain range of solid angles can be approximated by a single ray. This section provides details about the equations used in the DTRM.

The DTRM Equations The equation for the change of radiant intensity, dI, along a path, ds, can be written as dI aσT 4 + aI = ds π where

a I T σ

= = = =

(11.3-2)

gas absorption coefficient intensity gas local temperature Stefan-Boltzmann constant (5.672 × 10−8 W/m2 -K4 )

Here, the refractive index is assumed to be unity. The DTRM integrates Equation 11.3-2 along a series of rays emanating from boundary faces. If a is constant along the ray, then I(s) can be estimated as I(s) =

σT 4 (1 − e−as ) + I0 e−as π

(11.3-3)

where I0 is the radiant intensity at the start of the incremental path, which is determined by the appropriate boundary condition (see the description of boundary conditions, below). The energy source in the fluid due to radiation is then computed by summing the change in intensity along the path of each ray that is traced through the fluid control volume.


11-19


The “ray tracing” technique used in the DTRM can provide a prediction of radiative heat transfer between surfaces without explicit view-factor calculations. The accuracy of the model is limited mainly by the number of rays traced and the computational grid.

Ray Tracing The ray paths are calculated and stored prior to the fluid flow calculation. At each radiating face, rays are fired at discrete values of the polar and azimuthal angles (see Figure 11.3.2). To cover the radiating hemisphere, θ is varied from 0 to π2 and φ from 0 to 2π. Each ray is then traced to determine the control volumes it intercepts as well as its length within each control volume. This information is then stored in the radiation file, which must be read in before the fluid flow calculations begin. n θ

φ P

t

Figure 11.3.2: Angles θ and φ Defining the Hemispherical Solid Angle About a Point P

Clustering DTRM is computationally very expensive when there are too many surfaces to trace rays from and too many volumes crossed by the rays. To reduce the computational time, the number of radiating surfaces and absorbing cells is reduced by clustering surfaces and cells into surface and volume “clusters”. The volume clusters are formed by starting from a cell and simply adding its neighbors and their neighbors until a specified number of cells per volume cluster is collected. Similarly, surface clusters are made by starting from a face and adding its neighbors and their neighbors until a specified number of faces per surface cluster is collected. The incident radiation flux, qin , and the volume sources are calculated for the surface and volume clusters respectively. These values are then distributed to the faces and cells in the clusters to calculate the wall and cell temperatures. Since the radiation source terms are highly non-linear (proportional to the fourth power of temperature), care must be

11-20



taken to calculate the average temperatures of surface and volume clusters and distribute the flux and source terms appropriately among the faces and cells forming the clusters. The surface and volume cluster temperatures are obtained by area and volume averaging as shown in the following equations: !1/4

(11.3-4)

!1/4

(11.3-5)

Af Tf4 P Af

Tsc =

P

Tvc =

P

f

Vc Tc4 P Vc c

where Tsc and Tvc are the temperatures of the surface and volume clusters respectively, Af and Tf are the area and temperature of face f , and Vc and Tc are the volume and temperature of cell c. The summations are carried over all faces of a surface cluster and all cells of a volume cluster.

Boundary Condition Treatment for the DTRM at Walls The radiation intensity approaching a point on a wall surface is integrated to yield the incident radiative heat flux, qin , as qin =

Z

~s·~ n>0

Iin~s · ~ndΩ

(11.3-6)

where Ω is the hemispherical solid angle, Iin is the intensity of the incoming ray, ~s is the ray direction vector, and ~n is the normal pointing out of the domain. The net radiative heat flux from the surface, qout , is then computed as a sum of the reflected portion of qin and the emissive power of the surface: qout = (1 − w )qin + w σTw4

(11.3-7)

where Tw is the surface temperature of the point P on the surface and w is the wall emissivity which you input as a boundary condition. FLUENT incorporates the radiative heat flux (Equation 11.3-7) in the prediction of the wall surface temperature. Equation 11.3-7 also provides the surface boundary condition for the radiation intensity I0 of a ray emanating from the point P , as I0 =


qout π

(11.3-8)

11-21


Boundary Condition Treatment for the DTRM at Flow Inlets and Exits The net radiative heat flux at flow inlets and outlets is computed in the same manner as at walls, as described above. FLUENT assumes that the emissivity of all flow inlets and outlets is 1.0 (black body absorption) unless you choose to redefine this boundary treatment. FLUENT includes an option that allows you to use different temperatures for radiation and convection at inlets and outlets. This can be useful when the temperature outside the inlet or outlet differs considerably from the temperature in the enclosure. See Section 11.3.16 for details.

11.3.4

The P-1 Radiation Model

The P-1 radiation model is the simplest case of the more general P-N model, which is based on the expansion of the radiation intensity I into an orthogonal series of spherical harmonics [38, 234]. This section provides details about the equations used in the P-1 model.

The P-1 Model Equations As mentioned above, the P-1 radiation model is the simplest case of the P-N model. If only four terms in the series are used, the following equation is obtained for the radiation flux qr : qr = −

1 ∇G 3(a + σs ) − Cσs

(11.3-9)

where a is the absorption coefficient, σs is the scattering coefficient, G is the incident radiation, and C is the linear-anisotropic phase function coefficient, described below. After introducing the parameter 1 (3(a + σs ) − Cσs )

(11.3-10)

qr = −Γ∇G

(11.3-11)

∇ (Γ∇G) − aG + 4aσT 4 = SG

(11.3-12)

Γ= Equation 11.3-9 simplifies to

The transport equation for G is

11-22



where σ is the Stefan-Boltzmann constant and SG is a user-defined radiation source. FLUENT solves this equation to determine the local radiation intensity when the P-1 model is active. Combining Equations 11.3-11 and 11.3-12, the following equation is obtained: − ∇qr = aG − 4aσT 4

(11.3-13)

The expression for −∇qr can be directly substituted into the energy equation to account for heat sources (or sinks) due to radiation.

Anisotropic Scattering Included in the P-1 radiation model is the capability for modeling anisotropic scattering. FLUENT models anisotropic scattering by means of a linear-anisotropic scattering phase function: Φ(~s 0 · ~s) = 1 + C~s 0 · ~s

(11.3-14)

Here, ~s is the unit vector in the direction of scattering, and ~s 0 is the unit vector in the direction of the incident radiation. C is the linear-anisotropic phase function coefficient, which is a property of the fluid. C ranges from −1 to 1. A positive value indicates that more radiant energy is scattered forward than backward, and a negative value means that more radiant energy is scattered backward than forward. A zero value defines isotropic scattering (i.e., scattering that is equally likely in all directions), which is the default in FLUENT. You should modify the default value only if you are certain of the anisotropic scattering behavior of the material in your problem.

Particulate Effects in the P-1 Model When your FLUENT model includes a dispersed second phase of particles, you can include the effect of particles in the P-1 radiation model. Note that when particles are present, FLUENT ignores scattering in the gas phase. (That is, Equation 11.3-15 assumes that all scattering is due to particles.) For a gray, absorbing, emitting, and scattering medium containing absorbing, emitting, and scattering particles, the transport equation for the incident radiation can be written as σT 4 + Ep − (a + ap )G = 0 ∇ · (Γ∇G) + 4π a π !

(11.3-15)

where Ep is the equivalent emission of the particles and ap is the equivalent absorption coefficient. These are defined as follows:


11-23


4 σTpn Ep = lim pn Apn V →0 πV n=1 N X

(11.3-16)

and

ap = lim

V →0

N X

pn

n=1

Apn V

(11.3-17)

In Equations 11.3-16 and 11.3-17, pn , Apn , and Tpn are the emissivity, projected area, and temperature of particle n. The summation is over N particles in volume V . These quantities are computed during particle tracking in FLUENT. The projected area Apn of particle n is defined as Apn =

πd2pn 4

(11.3-18)

where dpn is the diameter of the nth particle. The quantity Γ in Equation 11.3-15 is defined as Γ=

1 3(a + ap + σp )

(11.3-19)

where the equivalent particle scattering factor is defined as

σp = lim

V →0

N X

(1 − fpn )(1 − pn )

n=1

Apn V

(11.3-20)

and is computed during particle tracking. In Equation 11.3-20, fpn is the scattering factor associated with the nth particle. Heat sources (sinks) due to particle radiation are included in the energy equation as follows: σT 4 − ∇qr = −4π a + Ep + (a + ap )G π !

11-24

(11.3-21)



Boundary Condition Treatment for the P-1 Model at Walls To get the boundary condition for the incident radiation equation, the dot product of the outward normal vector ~n and Equation 11.3-11 is computed:

qr · ~n = −Γ∇G · ~n ∂G qr,w = −Γ ∂n

(11.3-22) (11.3-23)

Thus the flux of the incident radiation, G, at a wall is −qr,w . The wall radiative heat flux is computed using the following boundary condition:

Iw (~r, ~s) = fw (~r, ~s) σT 4 fw (~r, ~s) = w w + ρw I(~r, −~s) π

(11.3-24) (11.3-25)

where ρw is the wall reflectivity. The Marshak boundary condition is then used to eliminate the angular dependence [188]: Z

0

2π

Iw (~r, ~s) ~n · ~s dΩ =

Z

0

2π

fw (~r, ~s) ~n · ~s dΩ

(11.3-26)

Substituting Equations 11.3-24 and 11.3-25 into Equation 11.3-26 and performing the integrations yields 4

qr,w

4πw σTπw − (1 − ρw )Gw =− 2(1 + ρw )

(11.3-27)

If it is assumed that the walls are diffuse gray surfaces, then ρw = 1 − w , and Equation 11.3-27 becomes qr,w = −

w 4σTw4 − Gw 2 (2 − w )

(11.3-28)

Equation 11.3-28 is used to compute qr,w for the energy equation and for the incident radiation equation boundary conditions.


11-25


Boundary Condition Treatment for the P-1 Model at Flow Inlets and Exits The net radiative heat flux at flow inlets and outlets is computed in the same manner as at walls, as described above. FLUENT assumes that the emissivity of all flow inlets and outlets is 1.0 (black body absorption) unless you choose to redefine this boundary treatment. FLUENT includes an option that allows you to use different temperatures for radiation and convection at inlets and outlets. This can be useful when the temperature outside the inlet or outlet differs considerably from the temperature in the enclosure. See Section 11.3.16 for details.

11.3.5

The Rosseland Radiation Model

The Rosseland or diffusion approximation for radiation is valid when the medium is optically thick ((a + σs )L 1), and is recommended for use in problems where the optical thickness is greater than 3. It can be derived from the P-1 model equations, with some approximations. This section provides details about the equations used in the Rosseland model.

The Rosseland Model Equations As with the P-1 model, the radiative heat flux vector in a gray medium can be approximated by Equation 11.3-11: qr = −Γ∇G

(11.3-29)

where Γ is given by Equation 11.3-10. The Rosseland radiation model differs from the P-1 model in that the Rosseland model assumes that the intensity is the black-body intensity at the gas temperature. (The P-1 model actually calculates a transport equation for G.) Thus G = 4σT 4 . Substituting this value for G into Equation 11.3-29 yields qr = −16σΓT 3 ∇T

(11.3-30)

Since the radiative heat flux has the same form as the Fourier conduction law, it is possible to write

q = qc + qr = −(k + kr )∇T kr = 16σΓT 3

11-26

(11.3-31) (11.3-32) (11.3-33)



where k is the thermal conductivity and kr is the radiative conductivity. Equation 11.3-31 is used in the energy equation to compute the temperature field.

Anisotropic Scattering The Rosseland model allows for anisotropic scattering, using the same phase function (Equation 11.3-14) described for the P-1 model in Section 11.3.4.

Boundary Condition Treatment for the Rosseland Model at Walls Since the diffusion approximation is not valid near walls, it is necessary to use a temperature slip boundary condition. The radiative heat flux at the wall boundary, qr,w , is defined using the slip coefficient ψ:

qr,w = −

σ Tw4 − Tg4

ψ

(11.3-34)

where Tw is the wall temperature, Tg is the temperature of the gas at the wall, and the slip coefficient ψ is approximated by a curve fit to the plot given in [234]:

ψ=

   1/2 3  

2x +3x2 −12x+7 54

0

Nw < 0.01 0.01 ≤ Nw ≤ 10 Nw > 10

(11.3-35)

where Nw is the conduction to radiation parameter at the wall: Nw =

k(a + σs ) 4σTw3

(11.3-36)

and x = log10 Nw .

Boundary Condition Treatment for the Rosseland Model at Flow Inlets and Exits No special treatment is required at flow inlets and outlets for the Rosseland model. The radiative heat flux at these boundaries can be determined using Equation 11.3-31. FLUENT includes an option that allows you to use different temperatures for radiation and convection at inlets and outlets. This can be useful when the temperature outside the inlet or outlet differs considerably from the temperature in the enclosure. See Section 11.3.16 for details.


11-27


11.3.6

The Discrete Ordinates (DO) Radiation Model

The discrete ordinates (DO) radiation model solves the radiative transfer equation (RTE) for a finite number of discrete solid angles, each associated with a vector direction ~s fixed in the global Cartesian system (x, y, z). The fineness of the angular discretization is controlled by you, analogous to choosing the number of rays for the DTRM. Unlike the DTRM, however, the DO model does not perform ray tracing. Instead, the DO model transforms Equation 11.3-1 into a transport equation for radiation intensity in the spatial coordinates (x, y, z). The DO model solves for as many transport equations as there are directions ~s. The solution method is identical to that used for the fluid flow and energy equations. The implementation in FLUENT uses a conservative variant of the discrete ordinates model called the finite-volume scheme [41, 203], and its extension to unstructured meshes [179].

The DO Model Equations The DO model considers the radiative transfer equation (RTE) in the direction ~s as a field equation. Thus, Equation 11.3-1 is written as

∇ · (I(~r, ~s)~s) + (a + σs )I(~r, ~s) = an2

σT 4 σs Z 4π + I(~r, ~s 0 ) Φ(~s · ~s 0 ) dΩ0 π 4π 0

(11.3-37)

FLUENT also allows the modeling of non-gray radiation using a gray-band model. The RTE for the spectral intensity Iλ (~r, ~s) can be written as σs Z 4π ∇ · (Iλ (~r, ~s)~s) + (aλ + σs )Iλ (~r, ~s) = aλ n Ibλ + Iλ (~r, ~s 0 ) Φ(~s · ~s 0 ) dΩ0 (11.3-38) 4π 0 2

Here λ is the wavelength, aλ is the spectral absorption coefficient, and Ibλ is the black body intensity given by the Planck function. The scattering coefficient, the scattering phase function, and the refractive index n are assumed independent of wavelength. The non-gray DO implementation divides the radiation spectrum into N wavelength bands, which need not be contiguous or equal in extent. The wavelength intervals are supplied by you, and correspond to values in vacuum (n = 1). The RTE is integrated over each wavelength interval, resulting in transport equations for the quantity Iλ ∆λ, the radiant energy contained in the wavelength band ∆λ. The behavior in each band is assumed gray. The black body emission in the wavelength band per unit solid angle is written as [F (0 → nλ2 T ) − F (0 → nλ1 T )]n

11-28

2 σT

π

4

(11.3-39)



where F (0 → nλT ) is the fraction of radiant energy emitted by a black body [174] in the wavelength interval from 0 to λ at temperature T in a medium of refractive index n. λ2 and λ1 are the wavelength boundaries of the band. The total intensity I(~r, ~s) in each direction ~s at position ~r is computed using I(~r, ~s) =

X

Iλk (~r, ~s)∆λk

(11.3-40)

k

where the summation is over the wavelength bands. Boundary conditions for the non-gray DO model are applied on a band basis. The treatment within a band is the same as that for the gray DO model.

Angular Discretization and Pixelation Each octant of the angular space 4π at any spatial location is discretized into Nθ × Nφ solid angles of extent ωi , called control angles. The angles θ and φ are the polar and azimuthal angles respectively, and are measured with respect to the global Cartesian system (x, y, z) as shown in Figure 11.3.3. The θ and φ extents of the control angle, ∆θ and ∆φ, are constant. In two-dimensional calculations, only four octants are solved due to symmetry, making a total of 4Nθ Nφ directions in all. In three-dimensional calculations, a total of 8Nθ Nφ directions are solved. In the case of the non-gray model, 4Nθ Nφ or 8Nθ Nφ equations are solved for each band.

z

s

θ φ

y x Figure 11.3.3: Angular Coordinate System When Cartesian meshes are used, it is possible to align the global angular discretization with the control volume face, as shown in Figure 11.3.4. For generalized unstructured


11-29


meshes, however, control volume faces do not in general align with the global angular discretization, as shown in Figure 11.3.5, leading to the problem of control angle overhang [179].

incoming directions C0

●

n

●

C1

outgoing directions face f Figure 11.3.4: Face with No Control Angle Overhang

overhanging control angle incoming directions C0

n

● ● C1 outgoing directions face f

Figure 11.3.5: Face with Control Angle Overhang Essentially, control angles can straddle the control volume faces, so that they are partially incoming and partially outgoing to the face. Figure 11.3.6 shows a 3D example of a face with control angle overhang. The control volume face cuts the sphere representing the angular space at an arbitrary angle. The line of intersection is a great circle. Control angle overhang may also occur as a result of reflection and refraction. It is important in these cases to correctly account for the overhanging fraction. This is done through the use of pixelation [179].

11-30


11.3 Radiative Heat Transfer outgoing directions z overhanging control angle

y x

incoming directions

control volume face

Figure 11.3.6: Face with Control Angle Overhang (3D)

Each overhanging control angle is divided into Nθp ×Nφp pixels, as shown in Figure 11.3.7. The energy contained in each pixel is then treated as incoming or outgoing to the face. The influence of overhang can thus be accounted for within the pixel resolution. FLUENT allows you to choose the pixel resolution. For problems involving gray-diffuse radiation, the default pixelation of 1×1 is usually sufficient. For problems involving symmetry, periodic, specular, or semi-transparent boundaries, a pixelation of 3×3 is recommended. You should be aware, however, that increasing the pixelation adds to the cost of computation.

Anisotropic Scattering The DO implementation in FLUENT admits a variety of scattering phase functions. You can choose an isotropic phase function, a linear anisotropic phase function, a DeltaEddington phase function, or a user-defined phase function. The linear anisotropic phase function is described in Equation 11.3-14. The Delta-Eddington function takes the following form: Φ(~s · ~s 0 ) = 2f δ(~s · ~s 0 ) + (1 − f )(1 + C~s · ~s 0 )

(11.3-41)

Here, f is the forward-scattering factor and δ(~s · ~s 0 ) is the Dirac delta function. The f term essentially cancels a fraction f of the out-scattering; thus, for f = 1, the DeltaEddington phase function will cause the intensity to behave as if there is no scattering at all. C is the asymmetry factor. When the Delta-Eddington phase function is used, you will specify values for f and C. When a user-defined function is used to specify the scattering phase function, FLUENT assumes the phase function to be of the form


11-31


control angle ω i

si

control volume face

pixel

Figure 11.3.7: Pixelation of Control Angle

Φ(~s · ~s 0 ) = 2f δ(~s · ~s 0 ) + (1 − f )Φ∗ (~s · ~s 0 )

(11.3-42)

The user-defined function will specify Φ∗ and the forward-scattering factor f . The scattering phase functions available for gray radiation can also be used for non-gray radiation. However, the scattered energy is restricted to stay within the band.

Particulate Effects in the DO Model The DO model allows you to include the effect of a discrete second phase of particulates on radiation. In this case, FLUENT will neglect all other sources of scattering in the gas phase. The contribution of the particulate phase appears in the RTE as:

∇ · (I~s) + (a + ap + σp )I(~r, ~s) = an

4

σp Z 4π + Ep + I(~r, ~s 0 ) Φ(~s · ~s 0 ) dΩ0 (11.3-43) π 4π 0

2 σT

where ap is the equivalent absorption coefficient due to the presence of particulates, and is given by Equation 11.3-17. The equivalent emission Ep is given by Equation 11.3-16. The equivalent particle scattering factor σp , defined in Equation 11.3-20, is used in the scattering terms.

11-32



For non-gray radiation, absorption, emission, and scattering due to the particulate phase are included in each wavelength band for the radiation calculation. Particulate emission and absorption terms are also included in the energy equation.

Boundary Condition Treatment at Gray-Diffuse Walls For gray radiation, the incident radiative heat flux, qin , at the wall is qin =

Z

~s·~ n>0

Iin~s · ~ndΩ

(11.3-44)

The net radiative flux leaving the surface is given by qout = (1 − w )qin + n2 w σTw4

(11.3-45)

where n is the refractive index of the medium next to the wall. The boundary intensity for all outgoing directions ~s at the wall is given by I0 =

qout π

(11.3-46)

For non-gray radiation, the incident radiative heat flux qin,λ in the band ∆λ at the wall is qin,λ = ∆λ

Z

~s·~ n>0

Iin,λ~s · ~ndΩ

(11.3-47)

The net radiative flux leaving the surface in the band ∆λ is given by qout,λ = (1 − wλ )qin,λ + wλ [F (0 → nλ2 Tw ) − F (0 → nλ1 Tw )]n2 σTw4

(11.3-48)

where wλ is the wall emissivity in the band. The boundary intensity for all outgoing directions ~s in the band ∆λ at the wall is given by I0λ =


qout,λ π∆λ

(11.3-49)

11-33


The Diffuse Fraction FLUENT allows you to specify the fraction of incoming radiation that is treated as diffuse at diffuse boundaries. If qin is the amount of radiative energy incident on the wall, then • emission from the wall = fd w qin • diffusely reflected energy = fd (1 − w )qin • specularly reflected energy = (1 − fd )qin where fd is the diffuse fraction and w is the wall emissivity. See below for more information about specular walls. For non-gray radiation, you can specify the diffuse fraction separately for each band.

Boundary Condition Treatment at Semi-Transparent Walls FLUENT allows the specification of both diffusely and specularly reflecting semi-transparent walls. You can prescribe the fraction of the incoming radiation at the semi-transparent wall which is to be reflected and transmitted diffusely; the rest is treated specularly. For non-gray radiation, this treatment is applied on a band basis. The radiant energy within a band ∆λ is transmitted, reflected, and refracted as in the gray case; there is no transmission, reflection, or refraction of radiant energy from one band to another. Specular Semi-Transparent Walls Consider a ray traveling from a semi-transparent medium a with refractive index na to a semi-transparent medium b with a refractive index nb in the direction ~s, as shown in Figure 11.3.8. Side a of the interface is the side that faces medium a; similarly, side b faces medium b. The interface normal ~n is assumed to point into side a. We distinguish between the intensity Ia (~s), the intensity in the direction ~s on side a of the interface, and the corresponding quantity on the side b, Ib (~s). A part of the energy incident on the interface is reflected, and the rest is transmitted. The reflection is specular, so that the direction of reflected radiation is given by ~sr = ~s − 2 (~s · ~n) ~n

(11.3-50)

The radiation transmitted from medium a to medium b undergoes refraction. The direction of the transmitted energy, ~st , is given by Snell’s law: sin θb =

11-34

na sin θa nb

(11.3-51)



s’

st θb

medium b

medium a

θa sr

n

s

n b > na Figure 11.3.8: Reflection and Refraction of Radiation at the Interface Between Two Semi-Transparent Media

where θa is the angle of incidence and θb is the angle of transmission, as shown in Figure 11.3.8. We also define the direction ~s 0 = ~st − 2 (~st · ~n) ~n

(11.3-52)

shown in Figure 11.3.8. The interface reflectivity on side a [174] 1 ra (~s) = 2

na cos θb − nb cos θa na cos θb + nb cos θa

!2

1 + 2

na cos θa − nb cos θb na cos θa + nb cos θb

!2

(11.3-53)

represents the fraction of incident energy transferred from ~s to ~sr . The boundary intensity Iw,a (~sr ) in the outgoing direction ~sr on side a of the interface is determined from the reflected component of the incoming radiation and the transmission from side b. Thus Iw,a (~sr ) = ra (~s)Iw,a (~s) + τb (~s 0 )Iw,b (~s 0 )

(11.3-54)

where τb (~s 0 ) is the transmissivity of side b in direction ~s0 . Similarly, the outgoing intensity in the direction ~st on side b of the interface, Iw,b (~st ), is given by


11-35


Iw,b (~st ) = rb (~s 0 )Iw,b (~s 0 ) + τa (~s)Iw,a (~s)

(11.3-55)

For the case na < nb , the energy transmitted from medium a to medium b in the incoming solid angle 2π must be refracted into a cone of apex angle θc (see Figure 11.3.9) where θc = sin−1

medium b

medium a

θc

na nb

(11.3-56)

θb

θa

n

n b > na Figure 11.3.9: Critical Angle θc Similarly, the transmitted component of the radiant energy going from medium b to medium a in the cone of apex angle θc is refracted into the outgoing solid angle 2π. For incident angles greater than θc , total internal reflection occurs and all the incoming energy is reflected specularly back into medium b. When medium b is external to the domain, Iw,b (~s 0 ) is given in Equation 11.3-54 as a part of the problem specification. This boundary specification is usually made by providing the incoming radiative flux and the solid angle over which the radiative flux is to be applied. The refractive index of the external medium is assumed to be unity. Diffuse Semi-Transparent Walls In many engineering problems, the semi-transparent interface may be a diffuse reflector. For such a case, the interfacial reflectivity r(~s) is assumed independent of ~s, and equal to the hemispherically averaged value rd . For n = na /nb > 1, rd,a and rd,b are given by [235]

11-36



(1 − rd,b ) n2 n−1 1 (3n + 1)(n − 1) n2 (n2 − 1)2 = + + ln − 2 6(n + 1)2 (n2 + 1)3 n+1 2n3 (n2 + 2n − 1) 8n4 (n4 + 1) + ln(n) (n2 + 1)(n4 − 1) (n2 + 1)(n4 − 1)2

rd,a = 1 − rd,b

(11.3-57)

(11.3-58)

The boundary intensity for all outgoing directions on side a of the interface is given by Iw,a =

rd,a qin,a + τd,b qin,b π

(11.3-59)

Iw,b =

rd,b qin,b + τd,a qin,a π

(11.3-60)

Similarly for side b,

where

qin,a = − qin,b =

Z

Z

4π

4π

Iw,a~s · ~ndΩ, ~s · ~n < 0

Iw,b~s · ~ndΩ, ~s · ~n ≥ 0

(11.3-61) (11.3-62)

As before, if medium b is external to the domain, qin,b is given as a part of the boundary specification. Beam Irradiation As mentioned above, FLUENT allows the specification of the irradiation at semi-transparent boundaries. The irradiation is specified in terms of an incident radiant heat flux (W/m2 ). You can specify the solid angle over which the irradiation is distributed, as well as the vector of the centroid of the solid angle. To indicate whether the irradiation is reflected specularly or diffusely, you can specify the diffuse fraction. For non-gray radiation, FLUENT allows you to specify the irradiation at semi-transparent boundaries on a band basis. The irradiation is specified as an incident heat flux (W/m2 ) for each wavelength band. As in the gray case, you can specify the solid angle over which the irradiation is distributed, as well as the vector of the centroid of the solid angle.


11-37


The Diffuse Fraction At semi-transparent boundaries, FLUENT allows you to specify the fraction of the incoming radiation that is treated as diffuse. The diffuse fraction is reflected diffusely, using the treatment described above; the transmitted portion is also treated diffusely. The remainder of the incoming energy is treated in a specular fashion. For non-gray radiation, you can specify the diffuse fraction separately for each band.

Boundary Condition Treatment at Specular Walls and Symmetry Boundaries At specular walls and symmetry boundaries, the direction of the reflected ray ~sr corresponding to the incoming direction ~s is given by Equation 11.3-50. Furthermore, Iw (~sr ) = Iw (~s)

(11.3-63)

Boundary Condition Treatment at Periodic Boundaries When rotationally periodic boundaries are used, it is important to use pixelation in order to ensure that radiant energy is correctly transferred between the periodic and shadow faces. A pixelation between 3 × 3 and 10 × 10 is recommended.

Boundary Condition Treatment at Flow Inlets and Exits The treatment at flow inlets and exits is described in Section 11.3.3.

11.3.7

The Surface-to-Surface (S2S) Radiation Model

The surface-to-surface radiation model can be used to account for the radiation exchange in an enclosure of gray-diffuse surfaces. The energy exchange between two surfaces depends in part on their size, separation distance, and orientation. These parameters are accounted for by a geometric function called a “view factor”. The main assumption of the S2S model is that any absorption, emission, or scattering of radiation can be ignored; therefore, only “surface-to-surface” radiation need be considered for analysis.

Gray-Diffuse Radiation FLUENT’s S2S radiation model assumes the surfaces to be gray and diffuse. Emissivity and absorptivity of a gray surface are independent of the wavelength. Also, by Kirchoff’s law [174], the emissivity equals the absorptivity ( = α). For a diffuse surface, the reflectivity is independent of the outgoing (or incoming) directions.

11-38



The gray-diffuse model is what is used in FLUENT. Also, as stated earlier, for applications of interest, the exchange of radiative energy between surfaces is virtually unaffected by the medium that separates them. Thus, according to the gray-body model, if a certain amount of radiant energy (E) is incident on a surface, a fraction (ρE) is reflected, a fraction (αE) is absorbed, and a fraction (τ E) is transmitted. Since for most applications the surfaces in question are opaque to thermal radiation (in the infrared spectrum), the surfaces can be considered opaque. The transmissivity, therefore, can be neglected. It follows, from conservation of energy, that α + ρ = 1, since α = (emissivity), and ρ = 1 − .

The S2S Model Equations The energy flux leaving a given surface is composed of directly emitted and reflected energy. The reflected energy flux is dependent on the incident energy flux from the surroundings, which then can be expressed in terms of the energy flux leaving all other surfaces. The energy reflected from surface k is qout,k = k σTk4 + ρk qin,k

(11.3-64)

where qout,k is the energy flux leaving the surface, k is the emissivity, σ is Boltzmann’s constant, and qin,k is the energy flux incident on the surface from the surroundings. The amount of incident energy upon a surface from another surface is a direct function of the surface-to-surface “view factor,” Fjk . The view factor Fjk is the fraction of energy leaving surface k that is incident on surface j. The incident energy flux qin,k can be expressed in terms of the energy flux leaving all other surfaces as

Ak qin,k =

N X

Aj qout,j Fjk

(11.3-65)

j=1

where Ak is the area of surface k and Fjk is the view factor between surface k and surface j. For N surfaces, using the view factor reciprocity relationship gives Aj Fjk = Ak Fkj for j = 1, 2, 3, . . . N

(11.3-66)

so that

qin,k =

N X

Fkj qout,j

(11.3-67)

j=1

Therefore,


11-39


qout,k =

k σTk4

+ ρk

N X

Fkj qout,j

(11.3-68)

j=1

which can be written as

Jk = Ek + ρk

N X

Fkj Jj

(11.3-69)

j=1

where Jk represents the energy that is given off (or radiosity) of surface k, and Ek represents the emissive power of surface k. This represents N equations, which can be recast into matrix form as KJ = E

(11.3-70)

where K is an N × N matrix, J is the radiosity vector, and E is the emissive power vector. Equation 11.3-70 is referred to as the radiosity matrix equation. The view factor between two finite surfaces i and j is given by 1 Z Z cos θi cos θj Fij = δij dAi dAj Ai Ai Aj πr2

(11.3-71)

where δij is determined by the visibility of dAj to dAi . δij = 1 if dAj is visible to dAi and 0 otherwise.

Clustering The S2S radiation model is computationally very expensive when there are a large number of radiating surfaces. To reduce the computational time as well as the storage requirement, the number of radiating surfaces is reduced by creating surface “clusters”. The surface clusters are made by starting from a face and adding its neighbors and their neighbors until a specified number of faces per surface cluster is collected. The radiosity, J, is calculated for the surface clusters. These values are then distributed to the faces in the clusters to calculate the wall temperatures. Since the radiation source terms are highly non-linear (proportional to the fourth power of temperature), care must be taken to calculate the average temperature of the surface clusters and distribute the flux and source terms appropriately among the faces forming the clusters. The surface cluster temperature is obtained by area averaging as shown in the following equation:

11-40



Af Tf4 P Af

P

f

Tsc =

!1/4

(11.3-72)

where Tsc is the temperature of the surface cluster, and Af and Tf are the area and temperature of face f . The summation is carried over all faces of a surface cluster.

Smoothing Smoothing can be performed on the view factor matrix to enforce the reciprocity relationship and conservation. The reciprocity relationship is represented by Ai Fij = Ai Fji

(11.3-73)

where Ai is the area of surface i, Fij is the view factor between surfaces i and j, and Fji is the view factor between surfaces j and i. Once the reciprocity relationship has been enforced, a least-squares smoothing method [135] can be used to ensure that conservation is satisfied, i.e., X

11.3.8

Fij = 1.0

(11.3-74)

Radiation in Combusting Flows

The Weighted-Sum-of-Gray-Gases Model The weighted-sum-of-gray-gases model (WSGGM) is a reasonable compromise between the oversimplified gray gas model and a complete model which takes into account particular absorption bands. The basic assumption of the WSGGM is that the total emissivity over the distance s can be presented as

=

I X

a,i (T )(1 − e−κi ps )

(11.3-75)

i=0

where a,i are the emissivity weighting factors for the ith fictitious gray gas, the bracketed quantity is the ith fictitious gray gas emissivity, κi is the absorption coefficient of the ith gray gas, p is the sum of the partial pressures of all absorbing gases, and s is the path length. For a,i and κi FLUENT uses values obtained from [45] and [244]. These values depend on gas composition, and a,i also depend on temperature. When the total pressure is not equal to 1 atm, scaling rules for κi are used (see Equation 11.3-81).


11-41


The absorption coefficient for i = 0 is assigned a value of zero to account for windows in P the spectrum between spectral regions of high absorption ( Ii=1 a,i < 1) and the weighting factor for i = 0 is evaluated from [244]:

a,0 = 1 −

I X

a,i

(11.3-76)

i=1

The temperature dependence of a,i can be approximated by any function, but the most common approximation is J X

a,i =

b,i,j T j−1

(11.3-77)

j=1

where b,i,j are the emissivity gas temperature polynomial coefficients. The coefficients b,i,j and κi are estimated by fitting Equation 11.3-75 to the table of total emissivities, obtained experimentally [45, 54, 244]. The absorptivity α of the radiation from the wall can be approximated in a similar way [244], but, to simplify the problem, it is assumed that = α [173]. This assumption is justified unless the medium is optically thin and the wall temperature differs considerably from the gas temperature. Since the coefficients b,i,j and κi are slowly varying functions of ps and T , they can be assumed constant for a wide range of these parameters. In [244] these constant coefficients are presented for different relative pressures of the CO2 and H2 O vapor, assuming that the total pressure pT is 1 atm. The values of the coefficients shown in [244] are valid for 0.001 ≤ ps ≤ 10.0 atm-m and 600 ≤ T ≤ 2400 K. For T > 2400 K, coefficient values suggested by [45] are used. If κi ps 1 for all i, Equation 11.3-75 simplifies to =

I X

a,i κi ps

(11.3-78)

i=0

Comparing Equation 11.3-78 with the gray gas model with absorption coefficient a, it can be seen that the change of the radiation intensity over the distance s in the WSGGM is exactly the same as in the gray gas model with the absorption coefficient

a=

I X

a,i κi p

(11.3-79)

i=0

which does not depend on s. In the general case, a is estimated as a=−

11-42

ln(1 − ) s

(11.3-80)



where the emissivity for the WSGGM is computed using Equation 11.3-75. a as defined by Equation 11.3-80 depends on s, reflecting the non-gray nature of the absorption of thermal radiation in molecular gases. In FLUENT, Equation 11.3-79 is used when s ≤ 10−4 m and Equation 11.3-80 is used for s > 10−4 m. Note that for s ≈ 10−4 m, the values of a predicted by Equations 11.3-79 and 11.3-80 are practically identical (since Equation 11.3-80 reduces to Equation 11.3-79 in the limit of small s). FLUENT allows you to specify s as the characteristic cell size or the mean beam length. The model based on the mean beam length is appropriate if you have a nearly homogeneous medium and you are interested mainly in the radiation exchange between the walls of the enclosure. You can specify the mean beam length or have FLUENT compute it. If you are primarily interested in the radiation heat exchange between neighboring cells (e.g., the distribution of radiation in the vicinity of a heater), which is very common for the optically thick media for which the P-1 model is primarily designed, using the characteristic cell size as s is more appropriate. Note that the values of a predicted by the WSGGM based on the characteristic cell size can be somewhat grid-dependent, if s is small. This grid dependence, however, will not necessarily affect the predicted temperature distribution, since the radiation energy is proportional to T 4 . The characteristic-cellsize approach may give a better temperature distribution, while the mean-beam-length approach can give more accurate fluxes at the boundaries. See Section 7.6.1 for details about setting properties for the WSGGM.

! The WSGGM cannot be used to specify the absorption coefficient in each band when using the non-gray DO model. If the WSGGM is used with the non-gray DO model, the absorption coefficient will be the same in all bands. When ptot 6= 1 atm The WSGGM, as described above, assumes that ptot —the total (static) gas pressure—is equal to 1 atm. In cases where ptot is not unity (e.g., combustion at high temperatures), scaling rules suggested in [67] are used to introduce corrections. When ptot < 0.9 atm or ptot > 1.1 atm, the values for κi in Equations 11.3-75 and 11.3-79 are rescaled: κi → κi pm tot

(11.3-81)

where m is a nondimensional value obtained from [67], which depends on the partial pressures and temperature T of the absorbing gases, as well as on ptot .

The Effect of Soot on the Absorption Coefficient When soot formation is computed, FLUENT can include the effect of the soot concentration on the radiation absorption coefficient. The generalized soot model estimates the effect of the soot on radiative heat transfer by determining an effective absorption coefficient for soot. The absorption coefficient of a mixture of soot and an absorbing


11-43


(radiating) gas is then calculated as the sum of the absorption coefficients of pure gas and pure soot: as+g = ag + as

(11.3-82)

where ag is the absorption coefficient of gas without soot (obtained from the WSGGM) and as = b1 ρm [1 + bT (T − 2000)]

(11.3-83)

with b1 = 1232.4 m2 /kg and bT ≈ 4.8 × 10−4 K−1 ρm is the soot density in kg/m3 . The coefficients b1 and bT were obtained [222] by fitting Equation 11.3-83 to data based on the Taylor-Foster approximation [266] and data based on the Smith et al. approximation [244]. See Sections 7.6 and 18.2.3 for information about including the soot-radiation interaction effects.

The Effect of Particles on the Absorption Coefficient FLUENT can also include the effect of discrete phase particles on the radiation absorption coefficient, provided that you are using either the P-1 or the DO model. When the P-1 or DO model is active, radiation absorption by particles can be enabled. The particle emissivity, reflectivity, and scattering effects are then included in the calculation of the radiative heat transfer. See Section 21.11 for more details on the input of radiation properties for the discrete phase.

11.3.9

Overview of Using the Radiation Models

The procedure for setting up and solving a radiation problem is outlined below, and described in detail in Sections 11.3.10–11.3.18. Steps that are relevant only for a particular radiation model are noted as such. Remember that only the steps that are pertinent to radiation modeling are shown here. For information about inputs related to other models that you are using in conjunction with radiation, see the appropriate sections for those models.

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1. Select the radiation model, as described in Section 11.3.10. 2. If you are using the DTRM, define the ray tracing as described in Section 11.3.11. If you are using the S2S model, compute or read the view factors as described in Section 11.3.12. If you are using the DO model, define the angular discretization as described in Section 11.3.13 and, if relevant, define the non-gray radiation parameters as described in Section 11.3.14. 3. Define the material properties, as described in Section 11.3.15. 4. Define the boundary conditions, as described in Section 11.3.16. If your model contains a semi-transparent medium, see the information below on setting up semitransparent media. 5. Set the solution parameters (DTRM, DO, S2S, and P-1 only). See Section 11.3.17 for details. 6. Solve the problem, as described in Section 11.3.18.

Setup of Semi-Transparent Media As part of step 4 above, you will take the following steps in order to set up a semitransparent medium such as glass in your domain. 1. If your semi-transparent material is a solid, enable the calculation of radiation in the solid cell zone, as described in Section 11.3.16. (If your semi-transparent material is a fluid, this step is not necessary.) 2. At internal boundaries between the semi-transparent medium and adjacent fluids (or between adjacent semi-transparent media), set the two-sided wall to be semitransparent, as described in Section 11.3.16. This will enable radiation to pass through the internal boundary and will account for effects such as reflection and refraction. 3. At external semi-transparent boundaries, set the external wall radiation boundary condition to be semi-transparent, as described in Section 11.3.16. This will allow the externally specified radiative flux to enter the domain, and also allow the transmission of radiation from the interior to the outside. Both the radiation from the exterior of the domain and the radiation being transmitted from the interior to the outside will be reflected and refracted at the boundary appropriately. 4. Specify the degree to which interior and exterior walls reflect diffusely or specularly by setting the diffuse fraction, as described in Section 11.3.16. 5. Specify the appropriate refractive index for the material associated with the solid cell zone (in the Materials panel).


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If you are not interested in the detailed temperature distribution inside your semitransparent medium, you can use a thin semi-transparent wall instead of a semi-transparent solid zone, as described in Section 11.3.16.

11.3.10

Selecting the Radiation Model

You can enable radiative heat transfer by selecting a radiation model in the Radiation Model panel (Figure 11.3.10). Define −→ Models −→Radiation...

Figure 11.3.10: The Radiation Model Panel (DO Model) Select Rosseland, P1, Discrete Transfer (DTRM), Surface to Surface (S2S), or Discrete Ordinates as the Model. To disable radiation, select Off. Note that when the DTRM or the DO or S2S model is activated, the Radiation Model panel will expand to show additional parameters (described in Sections 11.3.12, 11.3.13, 11.3.14, and 11.3.17). These parameters will not appear if you select one of the other radiation models.

! The Rosseland model can be used only with the segregated solver. When the radiation model is active, the radiation fluxes will be included in the solution of the energy equation at each iteration. If you set up a problem with the radiation model turned on, and you then decide to turn it off completely, you must select the Off button in the Radiation Model panel.

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Note that, when you enable a radiation model, FLUENT will automatically turn on solution of the energy equation; you need not turn on the energy equation first.

11.3.11

Defining the Ray Tracing for the DTRM

When you select the Discrete Transfer model and click OK in the Radiation Model panel, the Ray Tracing panel (Figure 11.3.11) will open automatically. (Should you need to modify the current settings later in the problem setup or solution procedure, you can open this panel manually using the Define/Ray Tracing... menu item.)

Figure 11.3.11: The Ray Tracing Panel

In this panel you will set parameters for and create the rays and clusters discussed in Section 11.3.3. The procedure is as follows: 1. To control the number of radiating surfaces and absorbing cells, set the Cells Per Volume Cluster and Faces Per Surface Cluster. (See the explanation below.) 2. To control the number of rays being traced, set the number of Theta Divisions and Phi Divisions. (Guidelines are provided below.) 3. When you click OK in the Ray Tracing panel, a Select File dialog box will open, prompting you for the name of the “ray file”. After you have specified the file name and written the ray file, FLUENT will read the file back in again for use in the calculation. See below for details.

! If you cancel the Ray Tracing panel without writing and reading the ray file, the DTRM will be disabled.


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Controlling the Clusters Your inputs for Cells Per Volume Cluster and Faces Per Surface Cluster will control the number of radiating surfaces and absorbing cells. By default, each is set to 1, so the number of surface clusters (radiating surfaces) will be the number of boundary faces, and the number of volume clusters (absorbing cells) will be the number of cells in the domain. For small 2D problems, these are acceptable numbers, but for larger problems you will want to reduce the number of surface and/or volume clusters in order to reduce the ray-tracing expense. (See Section 11.3.3 for details about clustering.)

Controlling the Rays Your inputs for Theta Divisions and Phi Divisions will control the number of rays being traced from each surface cluster (radiating surface). Theta Divisions defines the number of discrete divisions in the angle θ used to define the solid angle about a point P on a surface. The solid angle is defined as θ varies from 0 to 90 degrees (Figure 11.3.2), and the default setting of 2 for the number of discrete settings implies that each ray traced from the surface will be located at a 45◦ angle from the other rays. Phi Divisions defines the number of discrete divisions in the angle φ used to define the solid angle about a point P on a surface. The solid angle is defined as φ varies from 0 to 180 degrees in 2D and from 0 to 360 degrees in 3D (Figure 11.3.2). The default setting of 2 implies that each ray traced from the surface will be located at a 90◦ angle from the other rays in 2D calculations, and in combination with the default setting for Theta Divisions, above, implies that 4 rays will be traced from each surface control volume in your 2D model. Note that the Phi Divisions should be increased to 4 for equivalent accuracy in 3D models. In many cases, it is recommended that you at least double the number of divisions in θ and φ.

Writing and Reading the DTRM Ray File After you have activated the DTRM and defined all of the parameters controlling the ray tracing, you must create a ray file which will be read back in and used during the radiation calculation. The ray file contains a description of the ray traces (path lengths, cells traversed by each ray, etc.). This information is stored in the ray file, instead of being recomputed, in order to speed up the calculation process. By default, a binary ray file will be written. You can also create text (formatted) ray files by turning off the Write Binary Files option in the Select File dialog box.

! Do not write or read a compressed ray file, because FLUENT will not be able to access the ray tracing information properly from a compressed ray file.

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The ray filename must be specified to FLUENT only once. Thereafter, the filename is stored in your case file and the ray file will be automatically read into FLUENT whenever the case file is read. FLUENT will remind you that it is reading the ray file after it finishes reading the rest of the case file by reporting its progress in the text (console) window. Note that the ray filename stored in your case file may not contain the full name of the directory in which the ray file exists. The full directory name will be stored in the case file only if you initially read the ray file through the GUI (or if you typed in the directory name along with the filename when using the text interface). In the event that the full directory name is absent, the automatic reading of the ray file may fail (since FLUENT does not know in which directory to look for the file), and you will need to manually specify the ray file, using the File/Read/Rays... menu item. The safest approaches are to use the GUI when you first read the ray file or to supply the full directory name when using the text interface.

! You should recreate the ray file whenever you do anything that changes the grid, such as: • change the type of a boundary zone • adapt or reorder the grid • scale the grid You can open the Ray Tracing panel directly with the Define/Ray Tracing... menu item.

Displaying the Clusters Once a ray file has been created or read in manually, you can click on the Display Clusters button in the Ray Tracing panel to graphically display the clusters in the domain. See Section 11.3.20 for additional information about displaying rays and clusters.

11.3.12

Computing or Reading the View Factors for the S2S Model

When you select the Surface to Surface (S2S) model, the Radiation Model panel will expand (see Figure 11.3.12). In this section of the panel, you will compute the view factors for your problem or read previously computed view factors into FLUENT. The S2S radiation model is computationally very expensive when there are a large number of radiating surfaces. To reduce the memory requirement for the calculation, the number of radiating surfaces is reduced by creating surface clusters. The surface cluster information (coordinates and connectivity of the nodes, surface cluster IDs) is used by FLUENT to compute the view factors for the surface clusters.

! You should recreate the surface cluster information whenever you do anything that


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Figure 11.3.12: The Radiation Model Panel (S2S Model)

changes the grid, such as: • change the type of a boundary zone • reorder the grid • scale the grid Note that you do not need to recalculate view factors after shell conduction at any wall has been enabled or disabled. See Section 6.13.1 for more information about shell conduction.

Computing View Factors FLUENT can compute the view factors for your problem in the current session and save them to a file for use in the current session and future sessions. Alternatively, you can save the surface cluster information and view factor parameters to a file, calculate the view factors outside FLUENT, and then read the view factors into FLUENT. These methods for computing view factors are described below.

! For large meshes or complex models, it is recommended that you calculate the view factors outside FLUENT and then read them into FLUENT before starting your simulation.

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Computing View Factors Inside FLUENT To compute view factors in your current FLUENT session, you must first set the parameters for the view factor calculation in the View Factor and Cluster Parameters panel (see below for details). When you have set the view factor and surface cluster parameters, click Compute/Write... under Methods in the Radiation Model panel. A Select File dialog box will open, prompting you for the name of the file in which FLUENT should save the surface cluster information and the view factors. After you have specified the file name, FLUENT will write the surface cluster information to the file. FLUENT will use the surface cluster information to compute the view factors, save the view factors to the same file, and then automatically read the view factors. The FLUENT console window will report the status of the view factor calculation. For example: Completed 25% calculation of viewfactors Completed 50% calculation of viewfactors Completed 75% calculation of viewfactors Completed 100% calculation of viewfactors

Computing View Factors Outside FLUENT To compute view factors outside FLUENT, you must save the surface cluster information and view factor parameters to a file. File −→ Write −→Surface Clusters... FLUENT will open the View Factor and Cluster Parameters panel, where you will set the view factor and surface cluster parameters (see below for details). When you click OK in the View Factor and Cluster Parameters panel, a Select File dialog box will open, prompting you for the name of the file in which FLUENT should save the surface cluster information and view factor parameters. After you have specified the file name, FLUENT will write the surface cluster information and view factor parameters to the file. If the specified Filename ends in .gz or .Z, appropriate file compression will be performed. (See Section 3.1.5 for details about file compression.) To calculate the view factors outside FLUENT, enter one of the following commands: • For the serial solver: utility viewfac inputfile where inputfile is the filename, or the correct path to the filename, for the surface cluster information and view factor parameters file that you saved from FLUENT. You can then read the view factors into FLUENT, as described below.


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• For the network parallel solver: utility viewfac -p -tn -cnf=host1,host2,. . .,hostn inputfile where n is the number of compute nodes, and host1, host2,. . . are the names of the machines being used.

!

Note that host1 must be a host machine. • For a dedicated parallel machine with multiple processors: utility viewfac -tn inputfile

! Note that for parallel runs (dedicated or network) using n processors, the problem is duplicated for each processor. For example, if the view factor calculation requires 100 MB of RAM using a single CPU, it will require 100n MB of RAM to run the calculation on n processors.

Reading View Factors into FLUENT If the view factors for your problem have already been computed (either inside or outside FLUENT) and saved to a file, you can read them into FLUENT. To read in the view factors, click Read... under Methods in the Radiation Model panel. A Select File dialog box will open where you can specify the name of the file containing the view factors. You can also manually specify the view factors file, using the File/Read/View Factors... menu item.

Setting View Factor and Surface Cluster Parameters You will use the View Factor and Cluster Parameters panel (Figure 11.3.13) to set view factor and cluster parameters for the S2S model. To open this panel, click Set... under Parameters in the Radiation Model panel or use the File/Write/Surface Clusters... menu item. Controlling the Clusters Your input for Faces Per Surface Cluster will control the number of radiating surfaces. By default, it is set to 1, so the number of surface clusters (radiating surfaces) will be the number of boundary faces. For small 2D problems, this is an acceptable number. For larger problems, you may want to reduce the number of surface clusters to reduce both the size of the view-factor file and the memory requirement. Such a reduction in the number of clusters, however, comes at the cost of some accuracy. (See Section 11.3.7 for details about clustering.) In some cases, you may wish to modify the cutoff or “split” angle between adjacent face normals for the purpose of controlling surface clustering. The split angle sets the

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Figure 11.3.13: The View Factor and Cluster Parameters Panel

limit for which adjacent surfaces are clustered. A smaller split angle allows for a better representation of the view factor. By default, no surface cluster will contain any face that has a face normal greater than 20◦ . To modify the value of this parameter, you can use the split-angle text command: define −→ models −→ radiation −→ s2s-parameters −→split-angle or file −→ write-surface-clusters −→split-angle Specifying the Orientation of Surface Pairs View factor calculations depend on the geometric orientations of surface pairs with respect to each other. Two situations may be encountered when examining surface pairs: • If there is no obstruction between the surface pairs under consideration, then they are referred to as “non-blocking” surfaces. • If there is another surface blocking the views between the surfaces under consideration, then they are referred to as “blocking” surfaces. Blocking will change the view factors between the surface pairs and require additional checks to compute the correct value of the view factors.


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For cases with blocking surfaces, select Blocking under Surfaces in the View Factor and Cluster Parameters panel. For cases with non-blocking surfaces, you can choose either Blocking or Nonblocking without affecting the accuracy. However, it is better to choose Nonblocking for such cases, as it takes less time to compute. Selecting the Method for Smoothing In order to enforce reciprocity and conservation (see Section 11.3.7), smoothing can be performed on the view factor matrix. To use the least-squares method for smoothing of the view factor matrix, select Least Square under Smoothing in the View Factor and Cluster Parameters panel. If you do not wish to smooth the view factor matrix, select None under Smoothing. Selecting the Method for Computing View Factors FLUENT provides two methods for computing view factors: the hemicube method and the adaptive method. The hemicube method is available only for 3D cases. The adaptive method calculates the view factors on a pair-by-pair basis using a variety of algorithms (analytic or Gauss quadrature) that are chosen adaptively depending on the proximity of the surfaces. To maintain accuracy, the order of the quadrature increases the closer the faces are together. For surfaces that are very close to each other, the analytic method is used. FLUENT determines the method to use by performing a visibility calculation. The Gaussian quadrature method is used if none of the rays from a surface are blocked by the other surface. If some of the rays are blocked by the other surface, then either a Monte Carlo integration method or a quasi-Monte Carlo integration method is used. To use the adaptive method to compute the view factors, select Adaptive in the View Factor and Cluster Parameters panel. It is recommended that you use the adaptive method for simple models, because it is faster than the hemicube method for these types of models. The hemicube method uses a differential area-to-area method and calculates the view factors on a row-by-row basis. The view factors calculated from the differential areas are summed to provide the view factor for the whole surface. This method originated from the use of the radiosity approach in the field of computer graphics [44]. To use the hemicube method to compute the view factors, select Hemicube in the View Factor and Cluster Parameters panel. It is recommended that you use the hemicube method for large complex models, because it is faster than the adaptive method for these types of models. The hemicube method is based upon three assumptions about the geometry of the surfaces: aliasing, visibility, and proximity. To validate these assumptions, you can specify three different hemicube parameters, which can help you obtain better accuracy in calculating view factors. In most cases, however, the default settings will be sufficient.

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• Aliasing—The true projection of each visible face onto the hemicube can be accurately accounted for by using a finite-resolution hemicube. As described above, the faces are projected onto a hemicube. Because of the finite resolution of the hemicube, the projected areas and resulting view factors may be over- or underestimated. Aliasing effects can be reduced by increasing the value of the Resolution of the hemicube under Hemicube Parameters. • Visibility—The visibility between any two faces does not change. In some cases, face i has a complete view of face k from its centroid, but some other face j occludes much of face k from face i. In such a case, the hemicube method will overestimate the view factor between face i and face k calculated from the centroid of face i. This error can be reduced by subdividing face i into smaller subfaces. You can specify the number of subfaces by entering a value for Subdivision under Hemicube Parameters. • Proximity—The distance between faces is great compared to the effective diameter of the faces. The proximity assumption is violated whenever faces are close together in comparison to their effective diameter or are adjacent to one another. In such cases, the distances between the centroid of one face and all points on the other face vary greatly. Since the view factor dependence on distance is non-linear, the result is a poor estimate of the view factor. Under Hemicube Parameters, you can set a limit for the Normalized Separation Distance, which is the ratio of the minimum face separation to the effective diameter of the face. If the computed normalized separation distance is less than the specified value, the face will then be divided into a number of subfaces until the normalized distances of the subfaces are greater than the specified value. Alternatively, you can specify the number of subfaces to create for such faces by entering a value for Subdivision.

11.3.13

Defining the Angular Discretization for the DO Model

When you select the Discrete Ordinates model, the Radiation Model panel will expand to show inputs for Angular Discretization (see Figure 11.3.10). In this section, you will set parameters for the angular discretization and pixelation described in Section 11.3.6. Theta Divisions (Nθ ) and Phi Divisions (Nφ ) will define the number of control angles used to discretize each octant of the angular space (see Figure 11.3.3). For a 2D model, FLUENT will solve only 4 octants (due to symmetry); thus, a total of 4Nθ Nφ directions ~s will be solved. For a 3D model, 8 octants are solved, resulting in 8Nθ Nφ directions ~s. By default, the number of Theta Divisions and the number of Phi Divisions are both set to 2. For most practical problems, these settings are adequate. A finer angular discretization can be specified to better resolve the influence of small geometric features or strong spatial variations in temperature, but larger numbers of Theta Divisions and Phi Divisions will add to the cost of the computation.


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Theta Pixels and Phi Pixels are used to control the pixelation that accounts for any control volume overhang (see Figure 11.3.7 and the figures and discussion preceding it). For problems involving gray-diffuse radiation, the default pixelation of 1 × 1 is usually sufficient. For problems involving symmetry, periodic, specular, or semi-transparent boundaries, a pixelation of 3 × 3 is recommended. You should be aware, however, that increasing the pixelation adds to the cost of computation.

11.3.14

Defining Non-Gray Radiation for the DO Model

If you want to model non-gray radiation using the DO model, you can specify the Number Of Bands (N ) under Non-Gray Model in the expanded Radiation Model panel (Figure 11.3.14). For a 2D model, FLUENT will solve 4Nθ Nφ N directions. For a 3D model, 8Nθ Nφ N directions will be solved. By default, the Number of Bands is set to zero, indicating that only gray radiation will be modeled. Because the cost of computation increases directly with the number of bands, you should try to minimize the number of bands used. In many cases, the absorption coefficient or the wall emissivity is effectively constant for the wavelengths of importance in the temperature range of the problem. For such cases, the gray DO model can be used with little loss of accuracy. For other cases, non-gray behavior is important, but relatively few bands are necessary. For typical glasses, for example, two or three bands will frequently suffice. When a non-zero Number Of Bands is specified, the Radiation Model panel will expand once again to show the Wavelength Intervals (Figure 11.3.14). You can specify a Name for each wavelength band, as well as the Start and End wavelength of the band in µm. Note that the wavelength bands are specified for vacuum (n = 1). FLUENT will automatically account for the refractive index in setting band limits for media with n different from unity. The frequency of radiation remains constant as radiation travels across a semi-transparent interface. The wavelength, however, changes such that nλ is constant. Thus, when radiation passes from a medium with refractive index n1 to one with refractive index n2 , the following relationship holds: n 1 λ1 = n 2 λ2

(11.3-84)

Here λ1 and λ2 are the wavelengths associated with the two media. It is conventional to specify the wavelength rather than frequency. FLUENT requires you to specify wavelength bands for an equivalent medium with n = 1. For example, consider a typical glass with a step jump in the absorption coefficient at a cut-off wavelength of λc . The absorption coefficient is a1 for λ ≤ λc µm and a2 for λ > λc µm. The refractive index of the glass is ng . Since nλ is constant across a semitransparent interface, the equivalent cut-off wavelength for a medium with n = 1 is ng λc using Equation 11.3-84. You should choose two bands in this case, with the limits 0 to ng λc and ng λc to 100. Here, the upper wavelength limit has been chosen to be a large

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Figure 11.3.14: The Radiation Model Panel (Non-Gray DO Model)

number, 100, in order to ensure that the entire spectrum is covered by the bands. When multiple materials exist, you should convert all the cut-off wavelengths to equivalent cut-off wavelengths for an n = 1 medium, and choose the band boundaries accordingly. The bands can have different widths and need not be contiguous. You can ensure that the entire spectrum is covered by your bands by choosing λmin = 0 and nλmax Tmin ≥ 50, 000. Here λmin and λmax are the minimum and maximum wavelength bounds of your wavelength bands, and Tmin is the minimum expected temperature in the domain.

11.3.15

Defining Material Properties for Radiation

When you are using the P-1, DO, or Rosseland radiation model in FLUENT, you should be sure to define both the absorption and scattering coefficients of the fluid in the Materials panel. If you are modeling semi-transparent media using the DO model, you should also define the refractive index for the semi-transparent fluid or solid material. For the DTRM, you need to define only the absorption coefficient. Define −→Materials...


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If your model includes gas phase species such as combustion products, absorption and/or scattering in the gas may be significant. The scattering coefficient should be increased from the default of zero if the fluid contains dispersed particles or droplets which contribute to scattering. FLUENT provides the facility for input of a composition-dependent absorption coefficient for CO2 and H2 O mixtures, using the WSGGM. The method for computing a variable absorption coefficient is described in Section 11.3.8. Section 7.6 provides a detailed description of the procedures used for input of radiation properties.

Absorption Coefficient for a Non-Gray DO Model If you are using the non-gray DO model, you can specify a different constant absorption coefficient for each of the bands used by the gray-band model, as described in Section 7.6. You cannot, however, compute a composition-dependent absorption coefficient in each band. If you use the WSGGM to compute a variable absorption coefficient, the value will be the same for all bands.

Refractive Index for a Non-Gray DO Model If you are using the non-gray DO model, you can specify a different constant refractive index for each of the bands used by the gray-band model, as described in Section 7.6. You cannot, however, compute a composition-dependent refractive index in each band.

11.3.16

Setting Radiation Boundary Conditions

When you set up a problem that includes radiation, you will set additional boundary conditions at walls, inlets, and exits. Define −→Boundary Conditions...

Inlet and Exit Boundary Conditions Emissivity When radiation is active, you can define the emissivity at each inlet and exit boundary when you are defining boundary conditions in the associated inlet or exit boundary panel (Pressure Inlet panel, Velocity Inlet panel, Pressure Outlet panel, etc.). Enter the appropriate value for Internal Emissivity. The default value for all boundary types is 1. For non-gray DO models, the specified constant emissivity will be used for all wavelength bands.

! The Internal Emissivity boundary condition is not available with the Rosseland model.

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Black Body Temperature FLUENT includes an option that allows you to take into account the influence of the temperature of the gas and the walls beyond the inlet/exit boundaries, and specify different temperatures for radiation and convection at inlets and exits. This is useful when the temperature outside the inlet or exit differs considerably from the temperature in the enclosure. For example, if the temperature of the walls beyond the inlet is 2000 K and the temperature at the inlet is 1000 K, you can specify the outside-wall temperature to be used for computing radiative heat flux, while the actual temperature at the inlet is used for calculating convective heat transfer. To do this, you would specify a radiation temperature of 2000 K as the black body temperature. Although this option allows you to account for both cooler and hotter outside walls, you must use caution in the case of cooler walls, since the radiation from the immediate vicinity of the hotter inlet or outlet almost always dominates over the radiation from cooler outside walls. If, for example, the temperature of the outside walls is 250 K and the inlet temperature is 1500 K, it might be misleading to use 250 K for the radiation boundary temperature. This temperature might be expected to be somewhere between 250 K and 1500 K; in most cases it will be close to 1500 K. (Its value depends on the geometry of the outside walls and the optical thickness of the gas in the vicinity of the inlet.) In the flow inlet or exit panel (Pressure Inlet panel, Velocity Inlet panel, etc.), select Specified External Temperature in the External Black Body Temperature Method drop-down list, and then enter the value of the radiation boundary temperature as the Black Body Temperature.

! If you want to use the same temperature for radiation and convection, retain the default selection of Boundary Temperature as the External Black Body Temperature Method.

! The Black Body Temperature boundary condition is not available with the Rosseland model.

Wall Boundary Conditions for the DTRM, and the P-1, S2S and Rosseland Models The DTRM and the P-1, S2S, and Rosseland models assume all walls to be gray and diffuse. The only radiation boundary condition required in the Wall panel is the emissivity. For the Rosseland model, the internal emissivity is 1. For the DTRM and the P-1 and S2S models, you can enter the appropriate value for Internal Emissivity in the Thermal section of the Wall panel. The default value is 1. Partial Enclosure Wall Boundary Condition for the S2S Model When the S2S model is used, you also have the option to define a “partial enclosure”; i.e., you can disable view factor calculations for walls that are not participating in the


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radiative heat transfer calculation. This feature allows you to save time computing the view factors and also reduce the memory required to store the view factor file during the FLUENT calculation. To make use of this feature, turn off the Participates in S2S Radiation option in the Thermal section of the Wall panel for each relevant wall. You can specify the Temperature of the partial enclosure under Partial Enclosure in the Radiation Model panel (Figure 11.3.12). The partial enclosure is treated like a black body with the specified temperature.

! If you change the definition of the partial enclosure by including or excluding some of the boundary zones, you will need to recompute the view factors.

! The Flux Reports panel will not show the exact balance of the Radiation Heat Transfer Rate because the radiative heat transfer to the partial enclosure is not included.

Wall Boundary Conditions for the DO Model When the DO model is used, you can model opaque (diffuse or specular) and semitransparent walls, as discussed in Section 11.3.6. You can use a diffuse wall to model wall boundaries in many industrial applications since, for the most part, surface roughness makes the reflection of incident radiation diffuse. For highly polished surfaces, such as reflectors or mirrors, the specular boundary condition is appropriate. The semi-transparent boundary condition is appropriate for modeling glass panes in air, for example. Opaque Wall Boundary Conditions for the DO Model In the Radiation section of the Wall panel, select opaque in the BC Type drop-down list to specify an opaque wall. Opaque walls are treated as gray if gray radiation is being computed, or non-gray if the non-gray DO model is being used. Once you have selected opaque as the BC Type, you can specify the fraction of the irradiation that is to be treated as diffuse. By default, the Diffuse Fraction is set to 1, indicating that all of the irradiation is diffuse. If you specify a value less than 1, the diffuse fraction will be reflected diffusely (as described in Section 11.3.6) and the remainder will be reflected specularly. If the non-gray DO model is being used, the Diffuse Fraction can be specified for each band. Additionally, you will be required to specify the emissivity in the Thermal section of the Wall panel. For gray-radiation DO models, enter the appropriate value for Internal Emissivity. (The default value is 1.) For non-gray DO models, specify a constant Internal Emissivity for each wavelength band in the Radiation tab. (The default value in each band is 1.)

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Semi-Transparent Wall Boundary Conditions for the DO Model In the Radiation section of the Wall panel, select semi-transparent in the BC Type dropdown list to specify a semi-transparent wall. For an external semi-transparent wall, you can define an external irradiation flux in the Wall panel (see Figure 11.3.15). For an internal semi-transparent wall, see the discussion on multiple-zone domains, below.

Figure 11.3.15: The Wall Panel for a Semi-Transparent Wall

The inputs for an external semi-transparent wall are as follows: 1. Specify the value of the irradiation flux under Irradiation. If the non-gray DO model is being used, a constant Irradiation can be specified for each band. 2. Define the Beam Width by specifying the beam Theta and Phi extents. 3. Specify the (X,Y,Z) vector that defines the Beam Direction. 4. Specify the fraction of the irradiation that is to be treated as diffuse. By default, the Diffuse Fraction is set to 1, indicating that all of the irradiation is diffuse. If you specify a value less than 1, the diffuse fraction will be reflected diffusely (as


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described in Section 11.3.6), the transmitted portion will also be reflected diffusely, and the remainder will be reflected specularly. If the non-gray DO model is being used, the Diffuse Fraction can be specified for each band.

! Note that the refractive index of the external medium is assumed to be 1. ! If Heat Flux conditions are specified in the Thermal section of the Wall panel, the specified heat flux is considered to be only the conduction and convection portion of the boundary flux. The given irradiation specifies the incoming exterior radiative flux; the radiative flux transmitted from the domain interior to the outside is computed as a part of the calculation by FLUENT.

Enabling Radiation in Specific Cell Zones (DO Model Only) With the DO model, you can specify whether or not you want to solve for radiation in each cell zone in the domain. By default, the DO equations are solved in all fluid zones, but not in any solid zones. If you want to model semi-transparent media, for example, you can enable radiation in the solid zone(s). To do so, turn on the Participates In Radiation option in the Solid panel (Figure 11.3.16).

Figure 11.3.16: The Solid Panel

! In general, you should not turn off the Participates In Radiation option for any fluid zones.

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Two-Sided-Wall Boundary Conditions for the DO Model in Multiple-Zone Domains For the DO model, you can specify the boundary condition on each side of a two-sided wall independently to be either diffuse or specular. Note that the two fluid zones bordering the wall will not be radiatively coupled (although you can choose them to be thermally coupled.) You can also choose to couple the contiguous fluid or solid zones radiatively by making the two-sided wall between them semi-transparent. In this case, radiation will pass through the wall. You can specify the two-sided wall to be semi-transparent only if both the neighboring cell zones participate in radiation; both sides of the wall will be semitransparent if you define one side to be semi-transparent. You can, however, specify a different diffuse fraction for each side. It is also possible to associate a thickness with the two-sided wall. In this case, the refraction due to the wall thickness is accounted for as radiation travels through the boundary. You can specify a Wall Thickness and a wall Material Name in the Wall panel (as described in Section 6.13.1). The refractive index and the absorption coefficient are those of the specified wall material. Only a constant absorption coefficient is allowed for a solid material. The effective reflectivity and transmissivity of the wall are computed assuming a planar layer of the given thickness with absorption but no emission. The refractive indices of the surrounding media correspond to those of the surrounding fluid materials. (When an external wall is specified to be semi-transparent, the refractive index of the external medium is assumed to be 1.)

Thermal Boundary Conditions In general, any well-posed combination of thermal boundary conditions can be used when any of the radiation models is active. The radiation model will be well-posed in combination with fixed temperature walls, conducting walls, and/or walls with set external heat transfer boundary conditions (Section 6.13.1). You can also use any of the radiation models with heat flux boundary conditions defined at walls, in which case the heat flux you define will be treated as the sum of the convective and radiative heat fluxes. The exception to this is the case of semi-transparent walls for the DO model. Here, FLUENT allows you to specify the convective and radiative portions of the heat flux separately, as explained above.

11.3.17

Setting Solution Parameters for Radiation

For the DTRM and the DO, S2S, and P-1 radiation models, there are several parameters that control the radiation calculation. You can use the default solution parameters for most problems, or you can modify these parameters to control the convergence and accuracy of the solution. There are no solution parameters to be set for the Rosseland model, since it impacts the solution only through the energy equation.


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DTRM Solution Parameters When the DTRM is active, FLUENT updates the radiation field during the calculation and computes the resulting energy sources and heat fluxes via the ray-tracing technique described in Section 11.3.3. FLUENT provides several solution parameters that control the solver and the solution accuracy. These parameters appear in the expanded portion of the Radiation Model panel (Figure 11.3.17).

Figure 11.3.17: The Radiation Model Panel (DTRM)

You can control the maximum number of sweeps of the radiation calculation during each global iteration by changing the Number of DTRM Sweeps. The default setting of 1 sweep implies that the radiant intensity will be updated just once. If you increase this number, the radiant intensity at the surfaces will be updated multiple times, until the tolerance criterion is met or the number of radiation sweeps is exceeded. The Tolerance parameter (0.001 by default) determines when the radiation intensity update is converged. It is defined as the maximum normalized change in the surface intensity from one DTRM sweep to the next (see Equation 11.3-85). You can also control the frequency with which the radiation field is updated as the continuous phase solution proceeds. The Flow Iterations Per Radiation Iteration parameter is set to 10 by default. This implies that the radiation calculation is performed once every 10 iterations of the solution process. Increasing the number can speed the calculation process, but may slow overall convergence.

S2S Solution Parameters For the S2S model, as for the DTRM, you can control the frequency with which the radiosity is updated as the continuous-phase solution proceeds. See the description of Flow Iterations Per Radiation Iteration for the DTRM, above.

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If you are using the segregated solver and you first solve the flow equations with the energy equation turned off, you should reduce the Flow Iterations Per Radiation Iteration from 10 to 1 or 2. This will ensure the convergence of the radiosity. If the default value of 10 is kept in this case, it is possible that the flow and energy residuals may converge and the solution will terminate before the radiosity is converged. See Section 11.3.18 for more information about residuals for the S2S model. You can control the maximum number of sweeps of the radiation calculation during each global iteration by changing the Number of S2S Sweeps. The default setting of 1 sweep implies that the radiosity will be updated just once. If you increase this number, the radiosity at the surfaces will be updated multiple times, until the tolerance criterion is met or the number of radiation sweeps is exceeded. The Tolerance parameter (0.001 by default) determines when the radiosity update is converged. It is defined as the maximum normalized change in the radiosity from one S2S sweep to the next (see Equation 11.3-86).

DO Solution Parameters For the discrete ordinates model, as for the DTRM, you can control the frequency with which the surface intensity is updated as the continuous phase solution proceeds. See the description of Flow Iterations Per Radiation Iteration for the DTRM, above. For most problems, the default under-relaxation of 1.0 for the DO equations is adequate. For problems with large optical thicknesses (aL > 10), you may experience slow convergence or solution oscillation. For such cases, under-relaxing the energy and DO equations is useful. Under-relaxation factors between 0.9 and 1.0 are recommended for both equations.

P-1 Solution Parameters For the P-1 radiation model, you can control the convergence criterion and underrelaxation factor. You should also pay attention to the optical thickness, as described below. The default convergence criterion for the P-1 model is 10−6 , the same as that for the energy equation, since the two are closely linked. See Section 24.16.1 for details about convergence criteria. You can set the Convergence Criterion for p1 in the Residual Monitors panel. Solve −→ Monitors −→Residual... The under-relaxation factor for the P-1 model is set with those for other variables, as described in Section 24.9. Note that since the equation for the radiation temperature (Equation 11.3-12) is a relatively stable scalar transport equation, in most cases you can safely use large values of under-relaxation (0.9–1.0).


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For optimal convergence with the P-1 model, the optical thickness (a + σs )L must be between 0.01 and 10 (preferably not larger than 5). Smaller optical thicknesses are typical for very small enclosures (characteristic size of the order of 1 cm), but for such problems you can safely increase the absorption coefficient to a value for which (a + σs )L = 0.01. Increasing the absorption coefficient will not change the physics of the problem because the difference in the level of transparency of a medium with optical thickness = 0.01 and one with optical thickness < 0.01 is indistinguishable within the accuracy level of the computation.

11.3.18

Solving the Problem

Once the radiation problem has been set up, you can proceed as usual with the calculation. Note that while the P-1 and DO models will solve additional transport equations and report residuals, the DTRM and the Rosseland and S2S models will not (since they impact the solution only through the energy equation). Residuals for the DTRM and S2S model sweeps are reported by FLUENT every time a DTRM or S2S model iteration is performed, as described below.

Residual Reporting for the P-1 Model The residual for radiation as calculated by the P-1 model is updated after each iteration and reported with the residuals for all other variables. FLUENT reports the normalized P-1 radiation residual as defined in Section 24.16.1 for the other transport equations.

Residual Reporting for the DO Model After each DO iteration, the DO model reports a composite normalized residual for all the DO transport equations. The definition of the residuals is similar to that for the other transport equations (see Section 24.16.1).

Residual Reporting for the DTRM FLUENT does not include a DTRM residual in its usual residual report that is issued after each iteration. The effect of radiation on the solution can be gathered, instead, via its impact on the energy field and the energy residual. However, each time a DTRM iteration is performed, FLUENT will print out the normalized radiation error for each DTRM sweep. The normalized radiation error is defined as X

E=

(Inew all radiating surfaces N (σT 4 /π)

− Iold ) (11.3-85)

where the error E is the maximum change in the intensity (I) at the current sweep, normalized by the maximum surface emissive power, and N is the total number of ra-

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diating surfaces. Note that the default radiation convergence criterion, as noted in Section 11.3.17, defines the radiation calculation to be converged when E decreases to 10−3 or less.

Residual Reporting for the S2S Model FLUENT does not include an S2S residual in its usual residual report that is issued after each iteration. The effect of radiation on the solution can be gathered, instead, via its impact on the energy field and the energy residual. However, each time an S2S iteration is performed, FLUENT will print out the normalized radiation error for each S2S sweep. The normalized radiation error is defined as X

E=

(Jnew − Jold )

all radiating surface clusters N σT 4

(11.3-86)

where the error E is the maximum change in the radiosity (J) at the current sweep, normalized by the maximum surface emissive power, and N is the total number of radiating surface clusters. Note that the default radiation convergence criterion, as noted in Section 11.3.17, defines the radiation calculation to be converged when E decreases to 10−3 or less.

Disabling the Update of the Radiation Fluxes Sometimes, you may wish to set up your FLUENT model with the radiation model active and then disable the radiation calculation during the initial calculation phase. For the P1 and DO models, you can turn off the radiation calculation temporarily by deselecting P1 or Discrete Ordinates in the Equations list in the Solution Controls panel. For the DTRM and the S2S model, there is no item in the Equations list. You can instead set a very large number for Flow Iterations Per Radiation Iteration in the expanded portion of the Radiation Model panel. If you turn off the radiation calculation, FLUENT will skip the update of the radiation field during subsequent iterations, but will leave in place the influence of the current radiation field on energy sources due to absorption, wall heat fluxes, etc. Turning the radiation calculation off in this way can thus be used to initiate your modeling work with the radiation model inactive and/or to focus the computational effort on the other equations if the radiation model is relatively well converged.

11.3.19

Reporting and Displaying Radiation Quantities

FLUENT provides several additional reporting options when your model includes solution of radiative heat transfer. You can generate graphical plots or alphanumeric reports of the following variables/functions:


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• Absorption Coefficient (DTRM, P-1, DO, and Rosseland models only) • Scattering Coefficient (P-1, DO, and Rosseland models only) • Refractive Index (DO model only) • Radiation Temperature (P-1 and DO models only) • Incident Radiation (P-1 and DO models only) • Incident Radiation (Band n) (non-gray DO model only) • Surface Cluster ID (S2S model only) • Radiation Heat Flux • Surface Incident Radiation (DO model only) • Transmitted Radiation Flux (Band n) (DO model only) • Reflected Radiation Flux (Band n) (DO model only) • Absorbed Radiation Flux (Band n) (DO model only) The first seven variables are contained in the Radiation... category of the variable selection drop-down list that appears in postprocessing panels, and the last five are contained in the Wall Fluxes... category. The final three variables are available only for semi-transparent walls. See Chapter 29 for their definitions.

! Note the sign convention on the radiative heat flux: heat flux from the wall surface is a positive quantity. Note that it is possible to export heat flux data on wall zones (including radiation) to a generic file that you can examine or use in an external program. See Section 11.2.5 for details.

Reporting Radiative Heat Transfer Through Boundaries You can use the Flux Reports panel to compute the radiative heat transfer through each boundary of the domain, or to sum the radiative heat transfer through all boundaries. Report −→Fluxes... See Section 28.2 for details about generating flux reports.

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Overall Heat Balances When Using the DTRM The DTRM yields a global heat balance and a balance of radiant heat fluxes only in the limit of a sufficient number of rays. In any given calculation, therefore, if the number of rays is insufficient you may find that the radiant fluxes do not obey a strict balance. Such imbalances are the inevitable consequence of the discrete ray tracing procedure and can be minimized by selecting a larger number of rays from each wall boundary.

11.3.20

Displaying Rays and Clusters for the DTRM

When you use the DTRM, FLUENT allows you to display surface or volume clusters, as well as the rays that emanate from a particular surface cluster. You will use the DTRM Graphics panel (Figure 11.3.18) for all of these displays. Display −→DTRM Graphics...

Figure 11.3.18: The DTRM Graphics Panel

Displaying Clusters To view clusters, select Cluster under Display Type and then select either Surface or Volume under Cluster Type. To display all of the surface or volume clusters, select the Display All Clusters option under Cluster Selection and click the Display button.


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To display only the cluster (surface or volume) nearest to a specified point, deselect the Display All Clusters option and specify the coordinates under Nearest Point. You may also use the mouse to choose the nearest point. Click on the Select Point With Mouse button and then right-click on a point in the graphics window.

Displaying Rays To display the rays emanating from the surface cluster nearest to the specified point, select Ray under Display Type. Set the appropriate values for Theta and Phi Divisions under Ray Parameters (see Section 11.3.11 for details), and then click on the Display button. Figure 11.3.19 shows a ray plot for a simple 2D geometry.

DTRM Rays

Figure 11.3.19: Ray Display

Including the Grid in the Display For some problems, especially complex 3D geometries, you may want to include portions of the grid in your ray or cluster display as spatial reference points. For example, you may want to show the location of an inlet and an outlet along with displaying the rays. This is accomplished by turning on the Draw Grid option in the DTRM Graphics panel. The Grid Display panel will appear automatically when you turn on the Draw Grid option, and you can set the grid display parameters there. When you click on Display in the DTRM Graphics panel, the grid display, as defined in the Grid Display panel, will be included in the ray or cluster display.

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11.4 Periodic Heat Transfer

11.4

Periodic Heat Transfer

FLUENT is able to predict heat transfer in periodically repeating geometries, such as compact heat exchangers, by including only a single periodic module for analysis. This section discusses streamwise-periodic heat transfer. The treatment of streamwiseperiodic flows is discussed in Section 8.3, and a description of no-pressure-drop periodic flow is provided in Section 6.15. Information about streamwise-periodic heat transfer is presented in the following sections: • Section 11.4.1: Overview and Limitations • Section 11.4.2: Theory • Section 11.4.3: Modeling Periodic Heat Transfer • Section 11.4.4: Solution Strategies for Periodic Heat Transfer • Section 11.4.5: Monitoring Convergence • Section 11.4.6: Postprocessing for Periodic Heat Transfer

11.4.1


Overview As discussed in Section 8.3.1, streamwise-periodic flow conditions exist when the flow pattern repeats over some length L, with a constant pressure drop across each repeating module along the streamwise direction. Periodic thermal conditions may be established when the thermal boundary conditions are of the constant wall temperature or wall heat flux type. In such problems, the temperature field (when scaled in an appropriate manner) is periodically fully-developed [190]. As for periodic flows, such problems can be analyzed by restricting the numerical model to a single module or periodic length.

Constraints for Periodic Heat Transfer Predictions In addition to the constraints for streamwise-periodic flow discussed in Section 8.3.1, the following constraints must be met when periodic heat transfer is to be considered: • The segregated solver must be used.


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• The thermal boundary conditions must be of the specified heat flux or constant wall temperature type. Furthermore, in a given problem, these thermal boundary types cannot be combined: all boundaries must be either constant temperature or specified heat flux. (You can, however, include constant-temperature walls and zero-heat-flux walls in the same problem.) For the constant-temperature case, all walls must be at the same temperature (profiles are not allowed) or zero heat flux. For the heat flux case, profiles and/or different values of heat flux may be specified at different walls. • When constant-temperature wall boundaries are used, you cannot include viscous heating effects or any volumetric heat sources. • In cases that involve solid regions, the regions cannot straddle the periodic plane. • The thermodynamic and transport properties of the fluid (heat capacity, thermal conductivity, viscosity, and density) cannot be functions of temperature. (You cannot, therefore, model reacting flows.) Transport properties may, however, vary spatially in a periodic manner, and this allows you to model periodic turbulent flows in which the effective turbulent transport properties (effective conductivity, effective viscosity) vary with the (periodic) turbulence field. Sections 11.4.2 and 11.4.3 provide more detailed descriptions of the input requirements for periodic heat transfer.

11.4.2

Theory

Streamwise-periodic flow with heat transfer from constant-temperature walls is one of two classes of periodic heat transfer that can be modeled by FLUENT. A periodic fullydeveloped temperature field can also be obtained when heat flux conditions are specified. In such cases, the temperature change between periodic boundaries becomes constant and can be related to the net heat addition from the boundaries as described in this section.

! Periodic heat transfer can be modeled only if you are using the segregated solver. Definition of the Periodic Temperature for ConstantTemperature Wall Conditions For the case of constant wall temperature, as the fluid flows through the periodic domain, its temperature approaches that of the wall boundaries. However, the temperature can be scaled in such a way that it behaves in a periodic manner. A suitable scaling of the temperature for periodic flows with constant-temperature walls is [190] θ=

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T (~r) − Twall Tbulk,inlet − Twall

(11.4-1)



The bulk temperature, Tbulk,inlet , is defined by R

Tbulk,inlet = RA

~ T |ρ~v · dA| ~ |ρ~v · dA|

(11.4-2)

A

where the integral is taken over the inlet periodic boundary (A). It is the scaled temperature, θ, which obeys a periodic condition across the domain of length L.

Definition of the Periodic Temperature Change σ for Specified Heat Flux Conditions When periodic heat transfer with heat flux conditions is considered, the form of the unscaled temperature field becomes analogous to that of the pressure field in a periodic flow: ~ − T (~r) ~ − T (~r + L) ~ T (~r + L) T (~r + 2L) = = σ. L L

(11.4-3)

~ is the periodic length vector of the domain. This temperature gradient, σ, can where L be written in terms of the total heat addition within the domain, Q, as σ=

Q Tbulk,exit − Tbulk,inlet = mc ˙ pL L

(11.4-4)

where m ˙ is the specified or calculated mass flow rate.

11.4.3

Modeling Periodic Heat Transfer

Overview of Streamwise-Periodic Flow and Heat Transfer Modeling Procedures A typical calculation involving both streamwise-periodic flow and periodic heat transfer is performed in two parts. First, the periodic velocity field is calculated (to convergence) without consideration of the temperature field. Next, the velocity field is frozen and the resulting temperature field is calculated. These periodic flow calculations are accomplished using the following procedure: 1. Set up a grid with translationally periodic boundary conditions. 2. Input constant thermodynamic and molecular transport properties. 3. Specify either the periodic pressure gradient or the net mass flow rate through the periodic boundaries.


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4. Compute the periodic flow field, solving momentum, continuity, and (optionally) turbulence equations. 5. Specify the thermal boundary conditions at walls as either heat flux or constant temperature. 6. Define an inlet bulk temperature. 7. Solve the energy equation (only) to predict the periodic temperature field. These steps are detailed below.

User Inputs for Periodic Heat Transfer In order to model the periodic heat transfer, you will need to set up your periodic model in the manner described in Section 8.3.3 for periodic flow models with the segregated solver, noting the restrictions discussed in Sections 8.3.1 and 11.4.1. In addition, you will need to provide the following inputs related to the heat transfer model: 1. Activate solution of the energy equation in the Energy panel. Define −→ Models −→Energy... 2. Define the thermal boundary conditions according to one of the following procedures: Define −→Boundary Conditions... • If you are modeling periodic heat transfer with specified-temperature boundary conditions, set the wall temperature Twall for all wall boundaries in their respective Wall panels. Note that all wall boundaries must be assigned the same temperature and that the entire domain (except the periodic boundaries) must be “enclosed” by this fixed-temperature condition, or by symmetry or adiabatic (q=0) boundaries. • If you are modeling periodic heat transfer with specified-heat-flux boundary conditions, set the wall heat flux in the Wall panel for each wall boundary. You can define different values of heat flux on different wall boundaries, but you should have no other types of thermal boundary conditions active in the domain. 3. Define solid regions, if appropriate, according to one of the following procedures: Define −→Boundary Conditions... • If you are modeling periodic heat transfer with specified-temperature conditions, conducting solid regions can be used within the domain, provided that on the perimeter of the domain they are enclosed by the fixed-temperature condition. Heat generation within the solid regions is not allowed when you are solving periodic heat transfer with fixed-temperature conditions.

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• If you are modeling periodic heat transfer with specified-heat-flux conditions, you can define conducting solid regions at any location within the domain, including volumetric heat addition within the solid, if desired. 4. Set constant material properties (density, heat capacity, viscosity, thermal conductivity), not temperature-dependent properties, using the Materials panel. Define −→Materials... 5. Specify the Upstream Bulk Temperature in the Periodicity Conditions panel. Define −→Periodic Conditions...

!

If you are modeling periodic heat transfer with specified-temperature conditions, the bulk temperature should not be equal to the wall temperature, since this will give you the trivial solution of constant temperature everywhere.

11.4.4

Solution Strategies for Periodic Heat Transfer

After completing the inputs described in Section 11.4.3, you can solve the flow and heat transfer problem to convergence. The most efficient approach to the solution, however, is a sequential one in which the periodic flow is first solved without heat transfer and then the heat transfer is solved leaving the flow field unaltered. This sequential approach is accomplished as follows: 1. Disable solution of the energy equation under Equations in the Solution Controls panel. Solve −→ Controls −→Solution... 2. Solve the remaining equations (continuity, momentum, and, optionally, turbulence parameters) to convergence to obtain the periodic flow field.

!

When you initialize the flow field before beginning the calculation, use the mean value between the inlet bulk temperature and the wall temperature for the initialization of the temperature field. 3. Return to the Solution Controls panel and turn off solution of the flow equations and turn on the energy solution. 4. Solve the energy equation to convergence to obtain the periodic temperature field of interest. While you can solve your periodic flow and heat transfer problems by considering both the flow and heat transfer simultaneously, you will find that the procedure outlined above is more efficient.


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11.4.5

Monitoring Convergence

If you are modeling periodic heat transfer with specified-temperature conditions, you can monitor the value of the bulk temperature ratio θ=

Twall − Tbulk,inlet Twall − Tbulk,exit

(11.4-5)

during the calculation using the Statistic Monitors panel to ensure that you reach a converged solution. Select per/bulk-temp-ratio as the variable to be monitored. See Section 24.16.2 for details about using this feature.

11.4.6

Postprocessing for Periodic Heat Transfer

The actual temperature field predicted by FLUENT in periodic models will not be periodic, and viewing the temperature results during postprocessing will display this actual temperature field (T (~r) of Equation 11.4-1). The displayed temperature may exhibit values outside the range defined by the inlet bulk temperature and the wall temperature. This is permissible since the actual temperature profile at the inlet periodic face will have temperatures that are higher or lower than the inlet bulk temperature. Static Temperature is found in the Temperature... category of the variable selection dropdown list that appears in postprocessing panels. Figure 11.4.1 shows the temperature field in a periodic heat exchanger geometry.

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4.00e+02 3.87e+02 3.74e+02 3.61e+02 3.48e+02 3.35e+02 3.22e+02 3.09e+02 2.96e+02 2.83e+02 2.70e+02

Contours of Static Temperature (k)

Figure 11.4.1: Temperature Field in a 2D Heat Exchanger Geometry With Fixed Temperature Boundary Conditions


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11.5

Buoyancy-Driven Flows

When heat is added to a fluid and the fluid density varies with temperature, a flow can be induced due to the force of gravity acting on the density variations. Such buoyancy-driven flows are termed natural-convection (or mixed-convection) flows and can be modeled by FLUENT.

11.5.1

Theory

The importance of buoyancy forces in a mixed convection flow can be measured by the ratio of the Grashof and Reynolds numbers: Gr gβ∆T L 2 = v2 Re

(11.5-1)

When this number approaches or exceeds unity, you should expect strong buoyancy contributions to the flow. Conversely, if it is very small, buoyancy forces may be ignored in your simulation. In pure natural convection, the strength of the buoyancy-induced flow is measured by the Rayleigh number: Ra =

gβ∆T L3 ρ µα

(11.5-2)

where β is the thermal expansion coefficient: 1 β=− ρ

∂ρ ∂T

!

(11.5-3)

p

and α is the thermal diffusivity: α=

k ρcp

(11.5-4)

Rayleigh numbers less than 108 indicate a buoyancy-induced laminar flow, with transition to turbulence occurring over the range of 108 < Ra < 1010 .

11.5.2

Modeling Natural Convection in a Closed Domain

When you model natural convection inside a closed domain, the solution will depend on the mass inside the domain. Since this mass will not be known unless the density is known, you must model the flow in one of the following ways:

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11.5 Buoyancy-Driven Flows

• Perform a transient calculation. In this approach, the initial density will be computed from the initial pressure and temperature, so the initial mass is known. As the solution progresses over time, this mass will be properly conserved. If the temperature differences in your domain are large, you must follow this approach. • Perform a steady-state calculation using the Boussinesq model (described in Section 11.5.3). In this approach, you will specify a constant density, so the mass is properly specified. This approach is valid only if the temperature differences in the domain are small; if not, you must use the transient approach.

! For a closed domain, you can use the incompressible ideal gas law only with a fixed operating pressure. It cannot be used with a floating operating pressure. You can use the compressible ideal gas law with either floating or fixed operating pressure. See Section 8.5.4 for more information about the floating operating pressure option.

11.5.3

The Boussinesq Model

For many natural-convection flows, you can get faster convergence with the Boussinesq model than you can get by setting up the problem with fluid density as a function of temperature. This model treats density as a constant value in all solved equations, except for the buoyancy term in the momentum equation: (ρ − ρ0 )g ≈ −ρ0 β(T − T0 )g

(11.5-5)

where ρ0 is the (constant) density of the flow, T0 is the operating temperature, and β is the thermal expansion coefficient. Equation 11.5-5 is obtained by using the Boussinesq approximation ρ = ρ0 (1−β∆T ) to eliminate ρ from the buoyancy term. This approximation is accurate as long as changes in actual density are small; specifically, the Boussinesq approximation is valid when β(T − T0 ) 1.

Limitations of the Boussinesq Model The Boussinesq model should not be used if the temperature differences in the domain are large. In addition, it cannot be used with species calculations, combustion, or reacting flows.

11.5.4

User Inputs for Buoyancy-Driven Flows

You must provide the following inputs to include buoyancy forces in the simulation of mixed or natural convection flows: 1. Turn on solution of the energy equation in the Energy panel. Define −→ Models −→Energy...


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2. Turn on Gravity in the Operating Conditions panel (Figure 11.5.1) and set the Gravitational Acceleration in each Cartesian coordinate direction by entering the appropriate values in the X, Y, and (for 3D) Z fields. Define −→Operating Conditions

Figure 11.5.1: The Operating Conditions Panel Note that the default gravitational acceleration in FLUENT is zero. 3. If you are using the incompressible ideal gas law, check that the Operating Pressure is set to an appropriate (non-zero) value in the Operating Conditions panel. 4. Depending on whether or not you use the Boussinesq approximation, specify the appropriate parameters described below: • If you are not using the Boussinesq model, the inputs are as follows: (a) If necessary, enable the Specified Operating Density option in the Operating Conditions panel, and specify the Operating Density. See below for details. (b) Define the fluid density as a function of temperature, as described in Sections 7.1.3 and 7.2. Define −→Materials...

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• If you are using the Boussinesq model (described in Section 11.5.3), the inputs are as follows: (a) Specify the Operating Temperature (T0 in Equation 11.5-5) in the Operating Conditions panel. (b) Select boussinesq as the method for Density in the Materials panel, as described in Sections 7.1.3 and 7.2. (c) Also in the Materials panel, set the Thermal Expansion Coefficient (β in Equation 11.5-5) for the fluid material and specify a constant density. Note that, if your model involves multiple fluid materials, you can choose whether or not to use the Boussinesq model for each material. As a result, you may have some materials using the Boussinesq model and others not. In such cases, you will need to set all the parameters described above in this step. 5. The boundary pressures that you input at pressure inlet and outlet boundaries are the redefined pressures as given by Equation 11.5-6. In general you should input equal pressures, p0 , at the inlet and exit boundaries of your FLUENT model if there are no externally-imposed pressure gradients. Define −→Boundary Conditions... 6. Select Body Force Weighted or Second Order as the Discretization method for Pressure in the Solution Controls panel. Solve −→ Controls −→Solution... You may also want to add cells near the walls to resolve boundary layers. If you are using the segregated solver, selecting PRESTO! as the Discretization method for Pressure is another recommended approach. See also Section 11.2.2 for information on setting up heat transfer calculations.

Definition of the Operating Density When the Boussinesq approximation is not used, the operating density, ρ0 , appears in the body-force term in the momentum equations as (ρ − ρ0 )g. This form of the body-force term follows from the redefinition of pressure in FLUENT as p0s = ps − ρ0 gx

(11.5-6)

The hydrostatic pressure in a fluid at rest is then p0s = 0

(11.5-7)

The definition of the operating density is thus important in all buoyancy-driven flows.


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Setting the Operating Density By default, FLUENT will compute the operating density by averaging over all cells. In some cases, you may obtain better results if you explicitly specify the operating density instead of having the solver compute it for you. For example, if you are solving a naturalconvection problem with a pressure boundary, it is important to understand that the pressure you are specifying is p0s in Equation 11.5-6. Although you will know the actual pressure ps , you will need to know the operating density ρ0 in order to determine p0s from ps . Therefore, you should explicitly specify the operating density rather than use the computed average. The specified value should, however, be representative of the average value. In some cases, the specification of an operating density will improve convergence behavior, rather than the actual results. For such cases, use the approximate bulk density value as the operating density, and be sure that the value you choose is appropriate for the characteristic temperature in the domain. Note that, if you are using the Boussinesq approximation for all fluid materials, the operating density is not used, so you need not specify it.

11.5.5

Solution Strategies for Buoyancy-Driven Flows

For high-Rayleigh-number flows, you may want to consider the solution guidelines below. In addition, the guidelines presented in Section 11.2.3 for solving other heat transfer problems can also be applied to buoyancy-driven flows. Note, however, that for some laminar, high-Rayleigh-number flows, no steady-state solution exists.

Guidelines for Solving High-Rayleigh-Number Flows When you are solving a high-Rayleigh-number flow (Ra > 108 ), you should follow one of the procedures outlined below for best results. The first procedure uses a steady-state approach: 1. Start the solution with a lower value of Rayleigh number (e.g., 107 ) and run to convergence using the first-order scheme. 2. To change the effective Rayleigh number, change the value of gravitational acceleration (e.g., from 9.8 to 0.098 to reduce the Rayleigh number by two orders of magnitude). 3. Use the resulting data file as an initial guess for the higher Rayleigh number, and start the higher-Rayleigh-number solution using the first-order scheme. 4. After you obtain a solution with the first-order scheme, you may continue the calculation with a higher-order scheme.

11-82



The second procedure uses a time-dependent approach to obtain a steady-state solution [100]: 1. Start the solution from a steady-state solution obtained for the same or a lower Rayleigh number. 2. Estimate the time constant as [18] τ=

L L2 L ∼ (PrRa)−1/2 = √ U α gβ∆T L

(11.5-8)

where L and U are the length and velocity scales, respectively. Use a time step ∆t such that ∆t ≈

τ 4

(11.5-9)

Using a larger time step ∆t may lead to divergence. 3. After oscillations with a typical frequency of f τ = 0.05–0.09 have decayed, the solution reaches steady state. Note that τ is the time constant estimated in Equation 11.5-8 and f is the oscillation frequency in Hz. In general, this solution process may take as many as 5000 time steps to reach steady state.

11.5.6

Postprocessing for Buoyancy-Driven Flows

The postprocessing reports of interest for buoyancy-driven flows are the same as for other heat transfer calculations. See Section 11.2.4 for details.


11-83


11-84


Chapter 12. Introduction to Modeling Species Transport and Reacting Flows FLUENT provides several models for chemical species transport and chemical reactions. This chapter provides an overview of the species transport and reaction models available in FLUENT. Details about the models are provided in Chapters 13–17. Models for pollutant formation are described in Chapter 18. • Section 12.1: Overview of Species and Reaction Modeling • Section 12.2: Approaches to Reaction Modeling • Section 12.3: Choosing a Reaction Model

12.1

Overview of Species and Reaction Modeling

FLUENT can model species transport with or without chemical reactions. For information about modeling species transport without chemical reactions, see Section 13.4. Chemical reactions that can be modeled in FLUENT include the following: • Gas phase reactions that may involve NOx and other pollutant formation, etc. • Surface reactions (e.g., chemical vapor deposition) in which the reaction occurs at a solid (wall) boundary. • Particle surface reactions (e.g., coal char combustion) in which the reaction occurs at the surface of a discrete-phase particle. Additional information on modeling of droplet/particle reactions is presented in Section 21.3.

12.2

Approaches to Reaction Modeling

FLUENT provides five approaches to modeling gas phase reacting flows: • Generalized finite-rate model • Non-premixed combustion model


12-1

Introduction to Modeling Species Transport and Reacting Flows

• Premixed combustion model • Partially premixed combustion model • Composition PDF Transport model A brief overview of each model is provided in Sections 12.2.1–12.2.5. See Section 12.3 for guidelines on choosing a model.

12.2.1

Generalized Finite-Rate Model

This approach is based on the solution of transport equations for species mass fractions, with the chemical reaction mechanism defined by you. The reaction rates that appear as source terms in the species transport equations are computed from Arrhenius rate expressions, from the eddy dissipation model of Magnussen and Hjertager [162], or from the EDC model [161]. Models of this type are suitable for a wide range of applications including premixed, partially premixed, and non-premixed turbulent combustion. See Chapter 13 for details.

12.2.2

Non-Premixed Combustion Model

In this approach individual species transport equations are not solved. Instead, transport equations for one or two conserved scalars (the mixture fractions) are solved and individual component concentrations are derived from the predicted mixture fraction distribution. This approach has been specifically developed for the simulation of turbulent diffusion flames and offers many benefits over the finite-rate formulation. In the conserved scalar approach, turbulence effects are accounted for with the help of an assumed shape probability density function or PDF. Reaction mechanisms are not defined by you; instead the reacting system is treated using a flame sheet (mixed-is-burned) approach or chemical equilibrium calculations. See Chapter 14 for details. The laminar flamelet model is an extension of the non-premixed combustion model to account for aerodynamic strain-induced departure from chemical equilibrium. See Section 14.4 for details.

12.2.3

Premixed Combustion Model

This model has been specifically developed for turbulent combustion systems that are of the purely premixed type. In these problems perfectly mixed reactants and burned products are separated by a flame front. The “reaction progress variable” is solved to predict the position of this front. The influence of turbulence is accounted for by means of a turbulent flame speed. See Chapter 15 for details.

12-2


12.3 Choosing a Reaction Model

12.2.4

Partially Premixed Combustion Model

The partially premixed combustion model has been developed for turbulent reacting flows that have a combination of non-premixed and premixed combustion. The mixture fraction equations and the reaction progress variable are solved to determine the species concentrations and position of the flame front, respectively. See Chapter 16 for details.

12.2.5

Composition PDF Transport Combustion Model

The composition PDF transport model simulates realistic finite-rate chemistry in turbulent flames. Arbitrary chemical mechanisms can be imported into FLUENT, and kinetic effects such as non-equilibrium species and ignition/extinction can be captured. This model is applicable to premixed, non-premixed, and partially premixed flames. Note that the model is computationally expensive. See Chapter 17 for details.

12.3

Choosing a Reaction Model

The first step in solving any problem involving species transport and reacting flow is to determine which model is appropriate. Consider the following guidelines: • For cases involving the mixing, transport, or reaction of chemical species, or reactions on the surface of a wall or particle (e.g., chemical vapor deposition), use the generalized finite-rate model. See Chapter 13 for more information about the generalized finite-rate model. • For reacting systems involving turbulent diffusion flames that are near chemical equilibrium where the fuel and oxidizer enter the domain in two or three distinct streams, use the non-premixed combustion model. See Chapter 14 for more information about non-premixed combustion. • For cases with a single, perfectly premixed reactant stream, use the premixed combustion model. See Chapter 15 for more information about premixed combustion. • For cases involving premixed flames with varying equivalence ratio in the domain, use the partially premixed combustion model. See Chapter 16 for more information about partially premixed combustion. • For turbulent flames where finite-rate chemistry is important, use the laminar flamelet model (see Chapter 14), the EDC model (see Chapter 13), or the composition PDF transport model (see Chapter 17).


12-3

Introduction to Modeling Species Transport and Reacting Flows

12-4


Chapter 13. Modeling Species Transport and Finite-Rate Chemistry FLUENT can model the mixing and transport of chemical species by solving conservation equations describing convection, diffusion, and reaction sources for each component species. Multiple simultaneous chemical reactions can be modeled, with reactions occurring in the bulk phase (volumetric reactions) and/or on wall or particle surfaces, and in the porous region. Species transport modeling capabilities, both with and without reactions, and the inputs you provide when using the model are described in this chapter. Note that you may also want to consider modeling your turbulent reacting flame using the mixture fraction approach (for non-premixed systems, described in Chapter 14), the reaction progress variable approach (for premixed systems, described in Chapter 15), the partially premixed approach (described in Chapter 16), or the composition PDF Transport approach (described in Chapter 17). See Chapter 12 for an overview of the reaction modeling approaches available in FLUENT. Information is divided into the following sections: • Section 13.1: Volumetric Reactions • Section 13.2: Wall Surface Reactions and Chemical Vapor Deposition • Section 13.3: Particle Surface Reactions • Section 13.4: Species Transport Without Reactions


13-1

Modeling Species Transport and Finite-Rate Chemistry

13.1

Volumetric Reactions

Information about species transport and finite-rate chemistry as related to volumetric reactions is presented in the following subsections: • Section 13.1.1: Theory • Section 13.1.2: Overview of User Inputs for Modeling Species Transport and Reactions • Section 13.1.3: Enabling Species Transport and Reactions and Choosing the Mixture Material • Section 13.1.4: Defining Properties for the Mixture and Its Constituent Species • Section 13.1.5: Defining Boundary Conditions for Species • Section 13.1.6: Defining Other Sources of Chemical Species • Section 13.1.7: Solution Procedures for Chemical Mixing and Finite-Rate Chemistry • Section 13.1.8: Postprocessing for Species Calculations • Section 13.1.9: Importing a Chemical Mechanism from CHEMKIN

13.1.1

Theory

Species Transport Equations When you choose to solve conservation equations for chemical species, FLUENT predicts the local mass fraction of each species, Yi , through the solution of a convection-diffusion equation for the ith species. This conservation equation takes the following general form: ∂ (ρYi ) + ∇ · (ρ~v Yi ) = −∇ · J~i + Ri + Si ∂t

(13.1-1)

where Ri is the net rate of production of species i by chemical reaction (described later in this section) and Si is the rate of creation by addition from the dispersed phase plus any user-defined sources. An equation of this form will be solved for N − 1 species where N is the total number of fluid phase chemical species present in the system. Since the mass fraction of the species must sum to unity, the N th mass fraction is determined as one minus the sum of the N − 1 solved mass fractions. To minimize numerical error, the N th species should be selected as that species with the overall largest mass fraction, such as N2 when the oxidizer is air.

13-2


13.1 Volumetric Reactions

Mass Diffusion in Laminar Flows In Equation 13.1-1, J~i is the diffusion flux of species i, which arises due to concentration gradients. By default, FLUENT uses the dilute approximation, under which the diffusion flux can be written as J~i = −ρDi,m ∇Yi

(13.1-2)

Here Di,m is the diffusion coefficient for species i in the mixture. For certain laminar flows, the dilute approximation may not be acceptable, and full multicomponent diffusion is required. In such cases, the Maxwell-Stefan equations can be solved; see Section 7.7.2 for details. Mass Diffusion in Turbulent Flows In turbulent flows, FLUENT computes the mass diffusion in the following form: µt J~i = − ρDi,m + ∇Yi Sct

(13.1-3)

µt where Sct is the turbulent Schmidt number ( ρD where µt is the turbulent viscosity t and Dt is the turbulent diffusivity). The default Sct is 0.7. Note that turbulent diffusion generally overwhelms laminar diffusion, and the specification of detailed laminar diffusion properties in turbulent flows is generally not warranted.

Treatment of Species Transport in the Energy Equation For many multicomponent mixing flows, the transport of enthalpy due to species diffusion ∇·

"

n X

hi J~i

#

i=1

can have a significant effect on the enthalpy field and should not be neglected. In particular, when the Lewis number Lei =

k ρcp Di,m

(13.1-4)

for any species is far from unity, neglecting this term can lead to significant errors. FLUENT will include this term by default. In Equation 13.1-4, k is the thermal conductivity.


13-3


Diffusion at Inlets For the segregated solver in FLUENT, the net transport of species at inlets consists of both convection and diffusion components. (For the coupled solvers, only the convection component is included.) The convection component is fixed by the inlet species mass fraction specified by you. The diffusion component, however, depends on the gradient of the computed species field at the inlet. Thus the diffusion component (and therefore the net inlet transport) is not specified a priori. See Section 13.1.5 for information about specifying the net inlet transport of species.

The Generalized Finite-Rate Formulation for Reaction Modeling The reaction rates that appear as source terms in Equation 13.1-1 are computed in FLUENT by one of three models: • Laminar finite-rate model: The effect of turbulent fluctuations are ignored, and reaction rates are determined by Arrhenius expressions. • Eddy-dissipation model: Reaction rates are assumed to be controlled by the turbulence, so expensive Arrhenius chemical kinetic calculations can be avoided. The model is computationally cheap, but, for realistic results, only one or two step heat-release mechanisms should be used. • Eddy-dissipation-concept (EDC) model: Detailed Arrhenius chemical kinetics can be incorporated in turbulent flames. Note that detailed chemical kinetic calculations are computationally expensive. The generalized finite-rate formulation is suitable for a wide range of applications including laminar or turbulent reaction systems, and combustion systems with premixed, non-premixed, or partially-premixed flames. The Laminar Finite-Rate Model The laminar finite-rate model computes the chemical source terms using Arrhenius expressions, and ignores the effects of turbulent fluctuations. The model is exact for laminar flames, but is generally inaccurate for turbulent flames due to highly non-linear Arrhenius chemical kinetics. The laminar model may, however, be acceptable for combustion with relatively slow chemistry and small turbulent fluctuations, such as supersonic flames. The net source of chemical species i due to reaction Ri is computed as the sum of the Arrhenius reaction sources over the NR reactions that the species participate in:

Ri = Mw,i

NR X

ˆ i,r R

(13.1-5)

r=1

13-4


13.1 Volumetric Reactions ˆ i,r is the Arrhenius molar rate of where Mw,i is the molecular weight of species i and R creation/destruction of species i in reaction r. Reaction may occur in the continuous phase between continuous-phase species only, or at wall surfaces resulting in the surface deposition or evolution of a continuous-phase species. Consider the rth reaction written in general form as follows: N X

N kf,r X

0 νi,r Mi * )

kb,r

i=1

00 νi,r Mi

(13.1-6)

i=1

where N 0 νi,r 00 νi,r Mi kf,r kb,r

= = = = = =

number of chemical species in the system stoichiometric coefficient for reactant i in reaction r stoichiometric coefficient for product i in reaction r symbol denoting species i forward rate constant for reaction r backward rate constant for reaction r

Equation 13.1-6 is valid for both reversible and non-reversible reactions. (Reactions in FLUENT are non-reversible by default.) For non-reversible reactions, the backward rate constant, kb,r , is simply omitted. The summations in Equation 13.1-6 are for all chemical species in the system, but only species that appear as reactants or products will have non-zero stoichiometric coefficients. Hence, species that are not involved will drop out of the equation. ˆ i,r in Equation 13.1-5) The molar rate of creation/destruction of species i in reaction r (R is given by

ˆ i,r = Γ R

00 νi,r

−

0 νi,r



kf,r

Nr Y

j=1

0 ηj,r

[Cj,r ]

− kb,r

Nr Y

j=1



00 ηj,r 

[Cj,r ]

(13.1-7)

where Nr Cj,r 0 ηj,r 00 ηj,r

= number of chemical species in reaction r = molar concentration of each reactant and product species j in reaction r (kgmol/m3 ) = forward rate exponent for each reactant and product species j in reaction r = backward rate exponent for each reactant and product species j in reaction r

See Section 13.1.4 for information about inputting the stoichiometric coefficients and rate exponents for both global forward (non-reversible) reactions and elementary (reversible) reactions.


13-5


Γ represents the net effect of third bodies on the reaction rate. This term is given by

Γ=

Nr X

γj,r Cj

(13.1-8)

j

where γj,r is the third-body efficiency of the jth species in the rth reaction. By default, FLUENT does not include third-body effects in the reaction rate calculation. You can, however, opt to include the effect of third-body efficiencies if you have data for them. The forward rate constant for reaction r, kf,r , is computed using the Arrhenius expression kf,r = Ar T βr e−Er /RT

(13.1-9)

where Ar βr Er R

= = = =

pre-exponential factor (consistent units) temperature exponent (dimensionless) activation energy for the reaction (J/kgmol) universal gas constant (J/kgmol-K)

0 00 0 00 You (or the database) will provide values for νi,r , νi,r , ηj,r , ηj,r , βr , Ar , Er , and, optionally, γj,r during the problem definition in FLUENT.

If the reaction is reversible, the backward rate constant for reaction r, kb,r , is computed from the forward rate constant using the following relation: kb,r =

kf,r Kr

(13.1-10)

where Kr is the equilibrium constant for the rth reaction, computed from

∆Sr0 ∆Hr0 Kr = exp − R RT

!

patm RT

NR X

00 0 (νj,r − νj,r )

r=1

(13.1-11)

where patm denotes atmospheric pressure (101325 Pa). The term within the exponential function represents the change in Gibbs free energy, and its components are computed as follows:

13-6

N S0 ∆Sr0 X i 00 0 = νi,r − νi,r R R i=1

(13.1-12)

N h0 ∆Hr0 X i 00 0 = νi,r − νi,r RT RT i=1

(13.1-13)



where Si0 and h0i are the standard-state entropy and standard-state enthalpy (heat of formation). These values are specified in FLUENT as properties of the mixture material. Pressure-Dependent Reactions FLUENT can use one of three methods to represent the rate expression in pressuredependent (or pressure fall-off) reactions. A “fall-off” reaction is one in which the temperature and pressure are such that the reaction occurs between Arrhenius high-pressure and low-pressure limits, and thus is no longer solely dependent on temperature. There are three methods of representing the rate expressions in this fall-off region. The simplest one is the Lindemann [153] form. There are also two other related methods, the Troe method [87] and the SRI method [256], that provide a more accurate description of the fall-off region. Arrhenius rate parameters are required for both the high- and low-pressure limits. The rate coefficients for these two limits are then blended to produce a smooth pressuredependent rate expression. In Arrhenius form, the parameters for the high-pressure limit (k) and the low-pressure limit (klow ) are as follows:

k = AT β e−E/RT klow = Alow T βlow e−Elow /RT

(13.1-14) (13.1-15)

The net rate constant at any pressure is then taken to be

knet

!

pr F =k 1 + pr

(13.1-16)

klow [M ] k

(13.1-17)

where pr is defined as pr =

and [M ] is the concentration of the bath gas, which can include third-body efficiencies. If the function F in Equation 13.1-16 is unity, then this is the Lindemann form. FLUENT provides two other forms to describe F , namely the Troe method and the SRI method. In the Troe method, F is given by  

"

#2 −1 

log pr + c log F = 1 + n − d(log pr + c) 

log Fcent

(13.1-18)

where


13-7


c = −0.4 − 0.67 log Fcent n = 0.75 − 1.27 log Fcent d = 0.14

(13.1-19) (13.1-20) (13.1-21)

Fcent = (1 − α)e−T /T3 + αe−T /T1 + e−T2 /T

(13.1-22)

and

The parameters α, T3 , T2 , and T1 are specified as inputs. In the SRI method, the blending function F is approximated as "

!

−b −T F = d a exp + exp T c

# X

Te

(13.1-23)

where X=

1 1 + log2 pr

(13.1-24)

In addition to the three Arrhenius parameters for the low-pressure limit (klow ) expression, you must also supply the parameters a, b, c, d, and e in the F expression.

! Chemical kinetic mechanisms are usually highly non-linear and form a set of stiff coupled equations. See Section 13.1.7 for solution procedure guidelines. Also, if you have a chemical mechanism in CHEMKIN [125] format, you can import this mechanism into FLUENT as described in Section 13.1.9. The Eddy-Dissipation Model Most fuels are fast burning, and the overall rate of reaction is controlled by turbulent mixing. In non-premixed flames, turbulence slowly convects/mixes fuel and oxidizer into the reaction zones where they burn quickly. In premixed flames, the turbulence slowly convects/mixes cold reactants and hot products into the reaction zones, where reaction occurs rapidly. In such cases, the combustion is said to be mixing-limited, and the complex, and often unknown, chemical kinetic rates can be safely neglected. FLUENT provides a turbulence-chemistry interaction model, based on the work of Magnussen and Hjertager [162], called the eddy-dissipation model. The net rate of production of species i due to reaction r, Ri,r , is given by the smaller (i.e., limiting value) of the two expressions below:

13-8



Ri,r =

0 νi,r Mw,i Aρ

Ri,r = where

YP YR A B

is is is is

YR min 0 k R νR,r Mw,R

0 νi,r Mw,i ABρ

k

!

P

P YP 00 j νj,r Mw,j

PN

(13.1-25)

(13.1-26)

the mass fraction of any product species, P the mass fraction of a particular reactant, R an empirical constant equal to 4.0 an empirical constant equal to 0.5

In Equations 13.1-25 and 13.1-26, the chemical reaction rate is governed by the largeeddy mixing time scale, k/, as in the eddy-breakup model of Spalding [252]. Combustion proceeds whenever turbulence is present (k/ > 0), and an ignition source is not required to initiate combustion. This is usually acceptable for non-premixed flames, but in premixed flames, the reactants will burn as soon as they enter the computational domain, upstream of the flame stabilizer. To remedy this, FLUENT provides the finite-rate/eddydissipation model, where both the Arrhenius (Equation 13.1-7), and eddy-dissipation (Equations 13.1-25 and 13.1-26) reaction rates are calculated. The net reaction rate is taken as the minimum of these two rates. In practice, the Arrhenius rate acts as a kinetic “switch”, preventing reaction before the flame holder. Once the flame is ignited, the eddy-dissipation rate is generally smaller than the Arrhenius rate, and reactions are mixing-limited.

! Although FLUENT allows multi-step reaction mechanisms (number of reactions > 2) with the eddy-dissipation and finite-rate/eddy-dissipation models, these will likely produce incorrect solutions. The reason is that multi-step chemical mechanisms are based on Arrhenius rates, which differ for each reaction. In the eddy-dissipation model, every reaction has the same, turbulent rate, and therefore the model should be used only for one-step (reactant → product), or two-step (reactant → intermediate, intermediate → product) global reactions. The model cannot predict kinetically controlled species such as radicals. To incorporate multi-step chemical kinetic mechanisms in turbulent flows, use the EDC model (described below).

! The eddy-dissipation model requires products to initiate reaction (see Equation 13.1-26). When you initialize the solution, FLUENT sets the product mass fractions to 0.01, which is usually sufficient to start the reaction. However, if you converge a mixing solution first, where all product mass fractions are zero, you may then have to patch products into the reaction zone to ignite the flame. See Section 13.1.7 for details. The Eddy-Dissipation Model for LES When the LES turbulence model is used, the turbulent mixing rate, /k in Equations 13.1-25 and 13.1-26, is replaced by the subgrid-scale mixing rate. This is calculated as


13-9


−1 τsgs =

q

2Sij Sij

(13.1-27)

where −1 τsgs Sij

−1 = subgrid-scale mixing rate (s ) ∂ui j = 12 ∂x = strain rate tensor (s−1 ) + ∂u ∂xi j

The Eddy-Dissipation-Concept (EDC) Model The eddy-dissipation-concept (EDC) model is an extension of the eddy-dissipation model to include detailed chemical mechanisms in turbulent flows [161]. It assumes that reaction occurs in small turbulent structures, called the fine scales. The volume fraction of the fine scales is modeled as [90] ξ ∗ = Cξ where Cξ ν

∗

ν k2

3/4

(13.1-28)

denotes fine-scale quantities and = =

volume fraction constant = 2.1377 kinematic viscosity

Species are assumed to react in the fine structures over a time scale τ ∗ = Cτ

1/2

ν

(13.1-29)

where Cτ is a time scale constant equal to 0.4082. In FLUENT, combustion at the fine scales is assumed to occur as a constant pressure reactor, with initial conditions taken as the current species and temperature in the cell. Reactions proceed over the time scale τ ∗ , governed by the Arrhenius rates of Equation 13.1-7, and are integrated numerically using the ISAT algorithm [201]. ISAT can accelerate the chemistry calculations by two to three orders of magnitude, offering substantial reductions in run-times. Details about the ISAT algorithm may be found in Sections 17.2.4 and 17.2.5. ISAT is very powerful, but requires some care. See Section 17.3.7 for details on using ISAT efficiently. The source term in the conservation equation for the mean species i, Equation 13.1-1, is modeled as ρ(ξ ∗ )2 ∗ Ri = ∗ 3 (Yi − Yi ) ∗ τ [1 − (ξ ) ]

(13.1-30)

where Yi∗ is the fine-scale species mass fraction after reacting over the time τ ∗ .

13-10



The EDC model can incorporate detailed chemical mechanisms into turbulent reacting flows. However, typical mechanisms are invariably stiff and their numerical integration is computationally costly. Hence, the model should be used only when the assumption of fast chemistry is invalid, such as modeling the slow CO burnout in rapidly quenched flames, or the NO conversion in selective non-catalytic reduction (SNCR). See Section 13.1.7 for guidelines on obtaining a solution using the EDC model.

13.1.2

Overview of User Inputs for Modeling Species Transport and Reactions

The basic steps for setting up a problem involving species transport and reactions are listed below, and the details about performing each step are presented in Sections 13.1.3– 13.1.5. Additional information about setting up and solving the problem is provided in Sections 13.1.6–13.1.8. 1. Enable species transport and volumetric reactions, and specify the mixture material. See Section 13.1.3. (The mixture material concept is explained below.) 2. If you are also modeling wall or particle surface reactions, turn on wall surface and/or particle surface reactions as well. See Sections 13.2 and 13.3 for details. 3. Check and/or define the properties of the mixture. (See Section 13.1.4.) Mixture properties include the following: • species in the mixture • reactions • other physical properties (e.g., viscosity, specific heat) 4. Check and/or set the properties of the individual species in the mixture. (See Section 13.1.4.) 5. Set species boundary conditions. (See Section 13.1.5.) In many cases, you will not need to modify any physical properties because the solver gets species properties, reactions, etc. from the materials database when you choose the mixture material. Some properties, however, may not be defined in the database. You will be warned when you choose your material if any required properties need to be set, and you can then assign appropriate values for these properties. You may also want to check the database values of other properties to be sure that they are correct for your particular application. For details about modifying an existing mixture material or creating a new one from scratch, see Section 13.1.4. Modifications to the mixture material can include the following:


13-11


• Addition or removal of species • Changing the chemical reactions • Modifying other material properties for the mixture • Modifying material properties for the mixture’s constituent species If you are solving a reacting flow, you will usually want to define the mixture’s specific heat as a function of composition, and the specific heat of each species as a function of temperature. You may want to do the same for other properties as well. By default, constant properties are used, but for the properties of some species, there is a piecewisepolynomial function of temperature that exists in the database and is available for your use. You may also choose to specify a different temperature-dependent function if you know of one that is more suitable for your problem.

Mixture Materials The concept of mixture materials has been implemented in FLUENT to facilitate the setup of species transport and reacting flow. A mixture material may be thought of as a set of species and a list of rules governing their interaction. The mixture material carries with it the following information: • A list of the constituent species, referred to as “fluid” materials • A list of mixing laws dictating how mixture properties (density, viscosity, specific heat, etc.) are to be derived from the properties of individual species if compositiondependent properties are desired • A direct specification of mixture properties if composition-independent properties are desired • Diffusion coefficients for individual species in the mixture • Other material properties (e.g., absorption and scattering coefficients) that are not associated with individual species • A set of reactions, including a reaction type (finite-rate, eddy-dissipation, etc.) and stoichiometry and rate constants Both mixture materials and fluid materials are stored in the FLUENT materials database. Many common mixture materials are included (e.g., methane-air, propane-air). Generally, one/two-step reaction mechanisms and many physical properties of the mixture and its constituent species are defined in the database. When you indicate which mixture

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material you want to use, the appropriate mixture material, fluid materials, and properties are loaded into the solver. If any necessary information about the selected material (or the constituent fluid materials) is missing, the solver will inform you that you need to specify it. In addition, you may choose to modify any of the predefined properties. See Section 7.1.2 for information about the sources of FLUENT’s database property data. For example, if you plan to model combustion of a methane-air mixture, you do not need to explicitly specify the species involved in the reaction or the reaction itself. You will simply select methane-air as the mixture material to be used, and the relevant species (CH4 , O2 , CO2 , H2 O, and N2 ) and reaction data will be loaded into the solver from the database. You can then check the species, reactions, and other properties and define any properties that are missing and/or modify any properties for which you wish to use different values or functions. You will generally want to define a composition- and temperature-dependent specific heat, and you may want to define additional properties as functions of temperature and/or composition. The use of mixture materials gives you the flexibility to use one of the many predefined mixtures, modify one of these mixtures, or create your own mixture material. Customization of mixture materials is performed in the Materials panel, as described in Section 13.1.4.

13.1.3

Enabling Species Transport and Reactions and Choosing the Mixture Material

The problem setup for species transport and volumetric reactions begins in the Species Model panel (Figure 13.1.1). Define −→ Models −→Species... 1. Under Model, select Species Transport. 2. Under Reactions, turn on Volumetric Reactions. 3. In the Mixture Material drop-down list under Mixture Properties, choose which mixture material you want to use in your problem. The drop-down list will include all of the mixtures that are currently defined in the database. To check the properties of a mixture material, select it and click the View... button. If the mixture you want to use is not in the list, choose the mixture-template material, and see Section 13.1.4 for details on setting your mixture’s properties. If there is a mixture material listed that is similar to your desired mixture, you may choose that material and see Section 13.1.4 for details on modifying properties of an existing material. When you choose the Mixture Material, the Number of Volumetric Species in the mixture will be displayed in the panel for your information.

!

Note that if you re-open the Species Model panel after species transport has already


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Figure 13.1.1: The Species Model Panel

been enabled, only the mixture materials available in your case will appear in the list. You can add more mixture materials to your case by copying them from the database, as described in Section 7.1.2, or by creating a new mixture, as described in Sections 7.1.2 and 13.1.4. As mentioned in Section 13.1.2, modeling parameters for the species transport and (if relevant) reactions will automatically be loaded from the database. If any information is missing, you will be informed of this after you click on OK in the Species Model panel. If you want to check or modify any properties of the mixture material, you will use the Materials panel, as described in Section 13.1.4. 4. Choose the Turbulence-Chemistry Interaction model. Four models are available: Laminar Finite-Rate computes only the Arrhenius rate (see Equation 13.1-7) and neglects turbulence-chemistry interaction. Eddy-Dissipation (for turbulent flows) computes only the mixing rate (see Equations 13.1-25 and 13.1-26). Finite-Rate/Eddy-Dissipation (for turbulent flows) computes both the Arrhenius rate and the mixing rate and uses the smaller of the two.

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EDC (for turbulent flows) models turbulence-chemistry interaction with detailed chemical mechanisms (see Equations 13.1-25 and 13.1-26). 5. If you selected EDC, you have the option to modify the Volume Fraction Constant and the Time Scale Constant (Cξ in Equation 13.1-28 and Cτ in Equation 13.1-29), although the default values are recommended. Further, to reduce the computational expense of the chemistry calculations, you can increase the number of Flow Its. Per Chem. Update. By default, FLUENT will update the chemistry one per 10 flow iterations. For details about using the Integration Parameters options, see Section 17.3. 6. (optional) If you want to model full multicomponent diffusion or thermal diffusion, turn on the Full Multicomponent Diffusion or Thermal Diffusion option. See Section 7.7.2 for details.

13.1.4

Defining Properties for the Mixture and Its Constituent Species

As discussed in Section 13.1.2, if you use a mixture material from the database, most mixture and species properties will already be defined. You may follow the procedures in this section to check the current properties, modify some of the properties, or set all properties for a brand-new mixture material that you are defining from scratch. Remember that you will need to define properties for the mixture material and also for its constituent species. It is important that you define the mixture properties before setting any properties for the constituent species, since the species property inputs may depend on the methods you use to define the properties of the mixture. The recommended sequence for property inputs is as follows: 1. Define the mixture species, and reaction(s), and define physical properties for the mixture. Remember to click on the Change/Create button when you are done setting properties for the mixture material. 2. Define physical properties for the species in the mixture. Remember to click on the Change/Create button after defining the properties for each species. These steps, all of which are performed in the Materials panel, are described in detail in this section. Define −→Materials...


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Defining the Species in the Mixture If you are using a mixture material from the database, the species in the mixture will already be defined for you. If you are creating your own material or modifying the species in an existing material, you will need to define them yourself. In the Materials panel (Figure 13.1.2), check that the Material Type is set to mixture and your mixture is selected in the Mixture Materials list. Click on the Edit... button to the right of Mixture Species to open the Species panel (Figure 13.1.3).

Figure 13.1.2: The Materials Panel (showing a mixture material)

Overview of the Species Panel In the Species panel, the Selected Species list shows all of the fluid-phase species in the mixture. If you are modeling wall or particle surface reactions, the Selected Solid Species list will show all of the bulk solid species in the mixture. Solid species are species that are created or evolved from wall boundaries or discrete-phase particles (e.g., Si(s)) and do not exist as fluid-phase species.

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Figure 13.1.3: The Species Panel

If you are modeling wall surface reactions, the Selected Site Species list will show all of the site species in the mixture. Site species are species that are adsorbed to a wall boundary. The use of solid and site species with wall surface reactions is described in Section 13.2. See Section 13.3 for information about particle surface reactions.

! The order of the species in the Selected Species list is very important. FLUENT considers the last species in the list to be the bulk species. You should therefore be careful to retain the most abundant species (by mass) as the last species when you add species to or delete species from a mixture material. The Available Materials list shows materials that are available but not in the mixture. Generally you will see air in this list, since air is always available by default. Adding Species to the Mixture If you are creating a mixture from scratch or starting from an existing mixture and adding some missing species, you will first need to load the desired species from the database (or create them, if they are not present in the database) so that they will be available to the solver. The procedure for adding species is listed below. (You will need to close the Species panel before you begin, since it is a “modal” panel that will not allow you to do anything else when it is open.) 1. In the Materials panel, click on the Database... button to open the Database Materials


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panel and copy the desired species, as described in Section 7.1.2. Remember that the constituent species of the mixture are fluid materials, so you should select fluid as the Material Type in the Database Materials panel to see the correct list of choices. Note that available solid species (for surface reactions) are also contained in the fluid list.

!

If you do not see the species you are looking for in the database, you can create a new fluid material for that species, following the instructions in Section 7.1.2, and then continue with step 2, below. 2. Re-open the Species panel, as described above. You will see that the fluid materials you copied from the database (or created) are listed in the Available Materials list. 3. To add a species to the mixture, select it in the Available Materials list and click on the Add button below the Selected Species list (or below the Selected Site Species or Selected Solid Species list, to define a site or solid species). The species will be added to the end of the relevant list and removed from the Available Materials list. 4. Repeat the previous step for all the desired species. When you are finished, click on the OK button.

! Adding a species to the list will alter the order of the species. You should be sure that the last species in the list is the bulk species, and you should check any boundary conditions, under-relaxation factors, or other solution parameters that you have set, as described in detail below. Removing Species from the Mixture To remove a species from the mixture, simply select it in the Selected Species list (or the Selected Site Species or Selected Solid Species list) and click on the Remove button below the list. The species will be removed from the list and added to the Available Materials list.

! Removing a species from the list will alter the order of the species. You should be sure that the last species in the list is the bulk species, and you should check any boundary conditions, under-relaxation factors, or other solution parameters that you have set, as described in detail below. Reordering Species If you find that the last species in the Selected Species list is not the most abundant species (as it must be), you will need to rearrange the species to obtain the proper order. 1. Remove the bulk species from the Selected Species list. It will now appear in the Available Species list.

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2. Add the species back in again. It will automatically be placed at the end of the list. The Naming and Ordering of Species As discussed above, you must retain the most abundant species as the last one in the Selected Species list when you add or remove species. Additional considerations you should be aware of when adding and deleting species are presented here. There are three characteristics of a species that identify it to the solver: name, chemical formula, and position in the list of species in the Species panel. Changing these characteristics will have the following effects: • You can change the Name of a species (using the Materials panel, as described in Section 7.1.2) without any consequences. • You should never change the given Chemical Formula of a species. • You will change the order of the species list if you add or remove any species. When this occurs, all boundary conditions, solver parameters, and solution data for species will be reset to the default values. (Solution data, boundary conditions, and solver parameters for other flow variables will not be affected.) Thus, if you add or remove species you should take care to redefine species boundary conditions and solution parameters for the newly defined problem. In addition, you should recognize that patched species concentrations or concentrations stored in any data file that was based on the original species ordering will be incompatible with the newly defined problem. You can use the data file as a starting guess, but you should be aware that the species concentrations in the data file may provide a poor initial guess for the newly defined model.

Defining Reactions If your FLUENT model involves chemical reactions, you can next define the reactions in which the defined species participate. This will be necessary only if you are creating a mixture material from scratch, you have modified the species, or you want to redefine the reactions for some other reason. Depending on which turbulence-chemistry interaction model you selected in the Species Model panel (see Section 13.1.3), the appropriate reaction model will be displayed in the Reaction drop-down list in the Materials panel. If you are using the laminar finite-rate or EDC model, the reaction model will be finite-rate; if you are using the eddy-dissipation model, the reaction model will be eddy-dissipation; if you are using the finite-rate/eddydissipation model, the reaction model will be finite-rate/eddy-dissipation.


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Inputs for Reaction Definition To define the reactions, click on the Edit... button to the right of Reaction. The Reactions panel (Figure 13.1.4) will open.

Figure 13.1.4: The Reactions Panel The steps for defining reactions are as follows: 1. Set the total number of reactions (volumetric reactions, wall surface reactions, and particle surface reactions) in the Total Number of Reactions field. (Use the arrows to change the value, or type in the value and press RETURN.) Note that if your model includes discrete-phase combusting particles, you should include the particulate surface reaction(s) (e.g., char burnout, multiple char oxidation) in the number of reactions only if you plan to use the multiple surface reactions model for surface combustion.

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2. Specify the Reaction Name of the reaction you want to define. 3. Set the Reaction ID of the reaction you want to define. (Again, if you type in the value be sure to press RETURN.) 4. If this is a fluid-phase reaction, keep the default selection of Volumetric as the Reaction Type. If this is a wall surface reaction (described in Section 13.2) or a particle surface reaction (described in Section 13.3), select Wall Surface or Particle Surface as the Reaction Type. See Section 13.3.2 for further information about defining particle surface reactions. 5. Specify how many reactants and products are involved in the reaction by increasing the value of the Number of Reactants and the Number of Products. Select each reactant or product in the Species drop-down list and then set its stoichiometric coefficient and rate exponent in the appropriate Stoich. Coefficient and Rate Exponent 0 00 fields. (The stoichiometric coefficient is the constant νi,r or νi,r in Equation 13.1-6 and the rate exponent is the exponent on the reactant or product concentration, 0 00 ηj,r or ηj,r in Equation 13.1-7.) There are two general classes of reactions that can be handled by the Reactions panel, so it is important that the parameters for each reaction are entered correctly. The classes of reactions are as follows: • Global forward reaction (no reverse reaction): Product species generally do 00 not affect the forward rate, so the rate exponent for all products (ηj,r ) should 0 be 0. For reactant species, set the rate exponent (ηj,r ) to the desired value. If such a reaction is not an elementary reaction, the rate exponent will generally 0 not be equal to the stoichiometric coefficient (νi,r ) for that species. An example of a global forward reaction is the combustion of methane: CH4 + 2O2 −→ CO2 + 2H2 O 0 0 0 00 00 where νCH = 1, ηCH = 0.2, νO0 2 = 2, ηO = 1.3, νCO = 1, ηCO = 0, νH00 2 O = 2, 4 4 2 2 2 and ηH00 2 O = 0.

Figure 13.1.4 shows the coefficient inputs for the combustion of methane. (See also the methane-air mixture material in the Database Materials panel.) Note that, in certain cases, you may wish to model a reaction where product species affect the forward rate. For such cases, set the product rate exponent 00 (ηj,r ) to the desired value. An example of such a reaction is the gas-shift reaction (see the carbon-monoxide-air mixture material in the Database Materials panel), in which the presence of water has an effect on the reaction rate: CO + 12 O2 + H2 O −→ CO2 + H2 O In the gas-shift reaction, the rate expression may be defined as:


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k[CO][O2 ]1/4 [H2 O]1/2 0 0 0 00 00 where νCO = 1, ηCO = 1, νO0 2 = 0.5, ηO = 0.25, νCO = 1, ηCO = 0, νH00 2 O = 0, 2 2 2 and ηH00 2 O = 0.5.

• Reversible reaction: An elementary chemical reaction that assumes the rate exponent for each species is equivalent to the stoichiometric coefficient for that species. An example of an elementary reaction is the oxidation of SO2 to SO3 : SO2 + 12 O2 * ) SO3 0 0 0 00 00 where νSO = 1, ηSO = 1, νO0 2 = 0.5, ηO = 0.5, νSO = 1, and ηSO = 1. 2 2 2 3 3

See step 6 below for information about how to enable reversible reactions. 6. If you are using the laminar finite-rate, finite-rate/eddy-dissipation, or EDC model for the turbulence-chemistry interaction, enter the following parameters for the Arrhenius rate under the Arrhenius Rate heading: Pre-exponential Factor (the constant Ar in Equation 13.1-9). The units of Ar must ˆ i,r in Equabe specified such that the units of the molar reaction rate, R 3 tion 13.1-5, are moles/volume-time (e.g., kgmol/m -s) and the units of the volumetric reaction rate, Ri in Equation 13.1-5, are mass/volume-time (e.g., kg/m3 -s).

!

It is important to note that if you have selected the British units system, the Arrhenius factor should still be input in SI units. This is because FLUENT applies no conversion factor to your input of Ar (the conversion factor is 1.0) when you work in British units, as the correct conversion factor depends on 0 your inputs for νi,r , βr , etc. Activation Energy (the constant Er in the forward rate constant expression, Equation 13.1-9). Temperature Exponent (the value for the constant βr in Equation 13.1-9). Third Body Efficiencies (the values for γj,r in Equation 13.1-8). If you have accurate data for the efficiencies and want to include this effect on the reaction rate (i.e., include Γ in Equation 13.1-7), turn on the Third Body Efficiencies option and click on the Specify... button to open the Reaction Parameters panel (Figure 13.1.5). For each Species in the panel, specify the Third-body Efficiency.

!

It is not necessary to include the third-body efficiencies. You should not enable the Third Body Efficiencies option unless you have accurate data for these parameters. Pressure Dependent Reaction (if relevant) If you are using the laminar finite-rate or EDC model for turbulence-chemistry interaction, or have enabled the composition PDF transport model (see Chapter 17), and the reaction is a pressure fall-off reaction (see Section 13.1.1), turn on the Pressure Dependent Reaction

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Figure 13.1.5: The Reaction Parameters Panel option for the Arrhenius Rate and click on the Specify... button to open the Pressure-Dependent Reaction panel (Figure 13.1.6). Under Reaction Parameters, select the appropriate Reaction Type (lindemann, troe, or sri). See Section 13.1.1 for details about the three methods. Next, you must specify if the Bath Gas Concentration ([M ] in Equation 13.1-17) is to be defined as the concentration of the mixture, or as the concentration of one of the mixture’s constituent species, by selecting the appropriate item in the drop-down list. The parameters you specified under Arrhenius Rate in the Reactions panel represent the high-pressure Arrhenius parameters. You can, however, specify values for the following parameters under Low Pressure Arrhenius Rate: ln(Pre-exponential Factor) (Alow in Equation 13.1-15) The pre-exponential factor Alow is often an extremely large number, so you will input the natural logarithm of this term. Activation Energy (Elow in Equation 13.1-15) Temperature Exponent (βlow in Equation 13.1-15) If you selected troe for the Reaction Type, you can specify values for Alpha, T1, T2, and T3 (α, T1 , T2 , and T3 in Equation 13.1-22) under Troe parameters. If you selected sri for the Reaction Type, you can specify values for a, b, c, d, and e (a, b, c, d, and e in Equation 13.1-23) under SRI parameters. 7. If you are using the laminar finite-rate or EDC model for turbulence-chemistry interaction, and the reaction is reversible, turn on the Include Backward Reaction


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Figure 13.1.6: The Pressure-Dependent Reaction Panel option for the Arrhenius Rate. When this option is enabled, you will not be able to edit the Rate Exponent for the product species, which instead will be set to be equivalent to the corresponding product Stoich. Coefficient. If you do not wish to use FLUENT’s default values, or if you are defining your own reaction, you will also need to specify the standard-state enthalpy and standard-state entropy, to be used in the calculation of the backward reaction rate constant (Equation 13.1-10). Note that the reversible reaction option is not available for either the eddy-dissipation or the finite-rate/eddy-dissipation turbulence-chemistry interaction model. 8. If you are using the eddy-dissipation or finite-rate/eddy-dissipation model for turbulence-chemistry interaction, you can enter values for A and B under the Mixing Rate heading. Note, however, that these values should not be changed unless you have reliable data. In most cases you will simply use the default values. A is the constant A in the turbulent mixing rate (Equations 13.1-25 and 13.1-26) when it is applied to a species that appears as a reactant in this reaction. The default setting of 4.0 is based on the empirically derived values given by Magnussen et al. [162]. B is the constant B in the turbulent mixing rate (Equation 13.1-26) when it is

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applied to a species that appears as a product in this reaction. The default setting of 0.5 is based on the empirically derived values given by Magnussen et al. [162]. 9. Repeat steps 2–8 for each reaction you need to define. When you are finished defining all reactions, click OK. Defining Species and Reactions for Fuel Mixtures Quite often, combustion systems will include fuel that is not easily described as a pure species (such as CH4 or C2 H6 ). Complex hydrocarbons, including fuel oil or even wood chips, may be difficult to define in terms of such pure species. However, if you have available the heating value and the ultimate analysis (elemental composition) of the fuel, you can define an equivalent fuel species and an equivalent heat of formation for this fuel. Consider, for example, a fuel known to contain 50% C, 6% H, and 44% O by weight. Dividing by atomic weights, you can arrive at a “fuel” species with the molecular formula C4.17 H6 O2.75 . You can start from a similar, existing species or create a species from scratch, and assign it a molecular weight of 100.04 (4.17 × 12 + 6 × 1 + 2.75 × 16). The chemical reaction would be considered to be C4.17 H6 O2.75 + 4.295O2 −→ 4.17CO2 + 3H2 O You will need to set the appropriate stoichiometric coefficients for this reaction. The heat of formation (or standard-state enthalpy) for the fuel species can be calculated from the known heating value ∆H since

∆H =

N X

00 0 h0i νi,r − νi,r

(13.1-31)

i=1

where h0i is the standard-state enthalpy on a molar basis. Note the sign convention in Equation 13.1-31: ∆H is negative when the reaction is exothermic.

Defining Zone-Based Reaction Mechanisms If your FLUENT model involves reactions that are confined to a specific area of the domain, you can define “reaction mechanisms” to enable different reactions selectively in different geometrical zones. You can create reaction mechanisms by selecting reactions from those defined in the Reactions panel and grouping them. You can then assign a particular mechanism to a particular zone.


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Figure 13.1.7: The Reaction Mechanisms Panel

Inputs for Reaction Mechanism Definition To define a reaction mechanism, click on the Edit... button to the right of Mechanism. The Reaction Mechanisms panel (Figure 13.1.7) will open. The steps for defining a reaction mechanism are as follows: 1. Set the total number of mechanisms in the Number of Mechanisms field. (Use the arrows to change the value, or type the value and press RETURN.) 2. Set the Mechanism ID of the mechanism you want to define. (Again, if you type in the value, be sure to press RETURN.) 3. Specify the Name of the mechanism. 4. Select the type of reaction to add to the mechanism under Reaction Type. If you select Volumetric, the Reactions list will display all available fluid-phase reactions. If you select Wall Surface or Particle Surface, the Reactions list will display all available wall surface reactions (described in Section 13.2) or particle surface reactions (described in Section 13.3). If you select All, the Reactions list will display all available reactions. (This option is meant for backward compatibility with FLUENT 6.0 or earlier cases.) 5. Select the reactions to be included in the mechanism.

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• For Volumetric or Particle Surface reactions, select available reactions for the mechanism in the Reactions list. • For Wall Surface reactions, use the following procedure: (a) Select available wall surface reactions for the mechanism in the Reactions list. (b) If any site species appear in the selected reaction(s), set the number of sites in the Number of Sites field. (Use the arrows to change the value, or type the value and press RETURN.) See Section 13.2.2 for details about site species in wall surface reactions. (c) If you specify a Number of Sites that is greater than zero, specify the properties of the site. Site Name (optional) Site Density (in kgmol/m2 ) This value is typically in the range of 10−8 to 10−6 . Click on the Define... button. This will open the Site Parameters panel (Figure 13.1.8), where you will define the parameters of the site species.

Figure 13.1.8: The Site Parameters Panel Site Name is the optional name of the site that was specified in the Reaction Mechanisms panel. Total Number of Site Species is the number of adsorbed species that are to be modeled at the site. (Use the arrows to change the value, or type the value and press RETURN.)


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Under Site Species, select the appropriate species from the drop-down list(s) and specify the fractional Initial Site Coverage for each species. For steady-state calculations, it is recommended (though not strictly required) that the initial values of Initial Site Coverage sum to unity. For transient calculations, it is required that these values sum to unity. Click Apply in the Site Parameters panel to store the new values. 6. Repeat steps 2–5 for each reaction mechanism you need to define. When you are finished defining all reaction mechanisms, click OK.

Defining Physical Properties for the Mixture When your FLUENT model includes chemical species, the following physical properties must be defined, either by you or by the database, for the mixture material: • density, which you can define using the gas law or as a volume-weighted function of composition • viscosity, which you can define as a function of composition • thermal conductivity and specific heat (in problems involving solution of the energy equation), which you can define as functions of composition. • mass diffusion coefficients and Schmidt number, which govern the mass diffusion fluxes (Equations 13.1-2 and 13.1-3) Detailed descriptions of these property inputs are provided in Chapter 7.

! Remember to click on the Change/Create button when you are done setting the properties of the mixture material. The properties that appear for each of the constituent species will depend on your settings for the properties of the mixture material. If, for example, you specify a composition-dependent viscosity for the mixture, you will need to define viscosity for each species.

Defining Physical Properties for the Species in the Mixture For each of the fluid materials in the mixture, you (or the database) must define the following physical properties: • molecular weight, which is used in the gas law and/or in the calculation of reaction rates and mole-fraction inputs or outputs • standard-state (formation) enthalpy and reference temperature (in problems involving solution of the energy equation)

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• viscosity, if you defined the viscosity of the mixture material as a function of composition • thermal conductivity and specific heat (in problems involving solution of the energy equation), if you defined these properties of the mixture material as functions of composition • standard-state entropy, if you are modeling reversible reactions • thermal and momentum accommodation coefficients, if you have enabled the lowpressure boundary slip model. Detailed descriptions of these property inputs are provided in Chapter 7.

! Global reaction mechanisms with one or two steps inevitably neglect the intermediate species. In high-temperature flames, neglecting these dissociated species may cause the temperature to be overpredicted. A more realistic temperature field can be obtained by increasing the specific heat capacity for each species. Rose and Cooper [279] have created a set of specific heat polynomials as a function of temperature. The specific heat capacity for each species is calculated as cp (T ) =

m X

ak T k

(13.1-32)

k=0

The modified cp polynomial coefficients from [279] are provided in Table 13.1.1.

a0 a1 a2 a3 a4 a0 a1 a2 a3 a4 a5 a6

Table 13.1.1: Modified cp Polynomial Coefficients [279] N2 CH4 CO H2 1.02705e+03 2.00500e+03 1.04669e+03 1.4147e+04 2.16182e−02 −6.81428e−01 −1.56841e−01 1.7372e−01 1.48638e−04 7.08589e−03 5.39904e−04 6.9e−04 −4.48421e−08 −4.71368e−06 −3.01061e−07 —– —– 8.51317e−10 5.05048e−11 —– CO2 H2 O O2 5.35446e+02 1.93780e+03 8.76317e+02 1.27867e+00 −1.18077e+00 1.22828e−01 −5.46776e−04 3.64357e−03 5.58304e−04 −2.38224e−07 −2.86327e−06 −1.20247e−06 1.89204e−10 7.59578e−10 1.14741e−09 —– —– −5.12377e−13 —– —– 8.56597e−17


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13.1.5

Defining Boundary Conditions for Species

You will need to specify the inlet mass fraction for each species in your simulation. In addition, for pressure outlets you will set species mass fractions to be used in case of backflow at the exit. At walls, FLUENT will apply a zero-gradient (zero-flux) boundary condition for all species unless you have defined a surface reaction at that wall (see Section 13.2), you have defined a reaction mechanism at that wall (see Section 13.1.4), or you choose to specify species mass fractions at the wall. For fluid zones, you also have the option of specifying a reaction mechanism. Input of boundary conditions is described in Chapter 6.

! Note that you will explicitly set mass fractions only for the first N − 1 species. The solver will compute the mass fraction of the last species by subtracting the total of the specified mass fractions from 1. If you want to explicitly specify the mass fraction of the last species, you must reorder the species in the list (in the Materials panel), as described in Section 13.1.4.

Diffusion at Inlets with the Segregated Solver As noted in Section 13.1.1, the species diffusion component at inlets (and therefore the net inlet transport) is not specified when the segregated solver is used. In some cases, you may wish to include only the convective transport of species through the inlets of your domain. You can do this by disabling inlet species diffusion. By default, FLUENT includes the diffusion flux of species at inlets. To turn off inlet diffusion, use the define/models/species-transport/inlet-diffusion? text command.

13.1.6

Defining Other Sources of Chemical Species

You can define a source or sink of a chemical species within the computational domain by defining a source term in the Fluid panel. You may choose this approach when species sources exist in your problem but you do not want to model them through the mechanism of chemical reactions. Section 6.28 describes the procedures you follow to define species sources in your FLUENT model. If the source is not a constant, you can use a user-defined function. See the separate UDF Manual for details about user-defined functions.

13.1.7

Solution Procedures for Chemical Mixing and Finite-Rate Chemistry

While many simulations involving chemical species may require no special procedures during the solution process, you may find that one or more of the solution techniques noted in this section helps to accelerate the convergence or improve the stability of more complex simulations. The techniques outlined below may be of particular importance if your problem involves many species and/or chemical reactions, especially when modeling combusting flows.

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Stability and Convergence in Reacting Flows Obtaining a converged solution in a reacting flow can be difficult for a number of reasons. First, the impact of the chemical reaction on the basic flow pattern may be strong, leading to a model in which there is strong coupling between the mass/momentum balances and the species transport equations. This is especially true in combustion, where the reactions lead to a large heat release and subsequent density changes and large accelerations in the flow. All reacting systems have some degree of coupling, however, when the flow properties depend on the species concentrations. These coupling issues are best addressed by the use of a two-step solution process, as described below, and by the use of underrelaxation as described in Section 24.9. A second convergence issue in reacting flows involves the magnitude of the reaction source term. When your FLUENT model involves very rapid reaction rates (i.e., much more rapid than the rates of convection and diffusion), the solution of the species transport equations becomes numerically difficult. Such systems are termed “stiff” systems and are created when you define models that involve very rapid kinetic rates, especially when these rates describe reversible or competing reactions. In the eddy-dissipation model, the fast reaction rates are removed by using the slower turbulent rates. For non-premixed systems, reaction rates are eliminated from the model. For stiff systems with laminar chemistry, the coupled solver is recommended instead of the segregated solver. For a turbulent finite-rate mechanism (which can be stiff), the EDC model, which uses a stiff ODE integrator for the chemistry, is recommended. See below for additional guidelines for solving stiff chemistry systems.

Two-Step Solution Procedure (Cold Flow Simulation) Solving a reacting flow as a two-step process can be a practical method for reaching a stable converged solution to your FLUENT problem. In this process, you begin by solving the flow, energy, and species equations with reactions disabled (the “cold-flow”, or unreacting flow). When the basic flow pattern has thus been established, you can reenable the reactions and continue the calculation. The cold-flow solution provides a good starting solution for the calculation of the combusting system. This two-step approach to combustion modeling can be accomplished using the following procedure: 1. Set up the problem including all species and reactions of interest. 2. Temporarily disable reaction calculations by turning off Volumetric Reactions in the Species Model panel. Define −→ Models −→Species... 3. Turn off calculation of the product species in the Solution Controls panel. Solve −→ Controls −→Solution...


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4. Calculate an initial (cold-flow) solution. (Note that it is generally not productive to obtain a fully converged cold-flow solution unless the non-reacting solution is also of interest to you.) 5. Enable the reaction calculations by turning on Volumetric Reactions again in the Species Model panel. 6. Turn on all equations. If you are using the laminar finite-rate, finite-rate/eddydissipation, or EDC model for turbulence-chemistry interaction, you may need to patch an ignition source (as described below).

Density Under-Relaxation One of the main reasons a combustion calculation can have difficulty converging is that large changes in temperature cause large changes in density, which can, in turn, cause instabilities in the flow solution. When you use the segregated solver, FLUENT allows you to under-relax the change in density to alleviate this difficulty. The default value for density under-relaxation is 1, but if you encounter convergence trouble you may wish to reduce this to a value between 0.5 and 1 (in the Solution Controls panel).

Ignition in Combustion Simulations If you introduce fuel to an oxidant, spontaneous ignition does not occur unless the temperature of the mixture exceeds the activation energy threshold required to maintain combustion. This physical issue manifests itself in a FLUENT simulation as well. If you are using the laminar finite-rate, finite-rate/eddy-dissipation, or EDC model for turbulence-chemistry interaction, you have to supply an ignition source to initiate combustion. This ignition source may be a heated surface or inlet mass flow that heats the gas mixture above the required ignition temperature. Often, however, it is the equivalent of a spark: an initial solution state that causes combustion to proceed. You can supply this initial spark by patching a hot temperature into a region of the FLUENT model that contains a sufficient fuel/air mixture for ignition to occur. Solve −→ Initialize −→Patch... Depending on the model, you may need to patch both the temperature and the fuel/ oxidant/product concentrations to produce ignition in your model. The initial patch has no impact on the final steady-state solution—no more than the location of a match determines the final flow pattern of the torch that it lights. See Section 24.13.2 for details about patching initial values.

Solution of Stiff Laminar Chemistry Systems When modeling laminar reaction systems with the laminar finite-rate model, you will likely need to use the coupled solver when the chemical mechanism is stiff. (See the

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above discussion on solution convergence in reacting flows. Note that you can use the laminar finite-rate model for turbulent flames, which implies that turbulence-chemistry interactions are neglected.) In addition, you can provide further solution stability for the coupled solver by using the stiff-chemistry text command. solve −→ set −→stiff-chemistry This option allows a larger Courant (CFL) number specification, although additional calculations are required to calculate the eigenvalues of the chemical Jacobian [285]. When you enable the stiff-chemistry solver, you will be asked to specify the following: • Positivity rate limit for temperature: limits new temperature changes by this factor multiplied by the old temperature. Its default value is 0.2. • Temperature time-step reduction factor: limits the local CFL number when the temperature is changing too rapidly. Its default value is 0.25. • Maximum allowable time-step/chemical-time-scale ratio: limits the local CFL number when the chemical time scales (eigenvalues of the chemical Jacobian) become too large to maintain a well-conditioned matrix. Its default value is 0.9. The default values of these parameters are applicable in most cases. Note that the stiff-chemistry option is not available with the segregated solver; it can be used only with the coupled solver (either implicit or explicit).

EDC Model Solution Procedure Due to the high computational expense of the EDC model, it is recommended that you use the following procedure to obtain a solution using the segregated solver: 1. Calculate an initial solution using the equilibrium non-premixed or partially premixed model (see Chapters 14 and 16). Remember to include all the species in your EDC chemical mechanism in prePDF. 2. Import a CHEMKIN [125] format mechanism (see Section 13.1.9). 3. Enable the reaction calculations by turning on Volumetric Reactions in the Species Model panel and selecting EDC under Turbulence-Chemistry Interaction. Select the mechanism that you just imported as the Mixture Material. Define −→ Models −→Species... 4. Set the species boundary conditions. Define −→Boundary Conditions... 5. Calculate a solution.


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13.1.8

Postprocessing for Species Calculations

FLUENT can report chemical species as mass fractions, mole fractions, and molar concentrations. You can also display laminar and effective mass diffusion coefficients. The following variables are available for postprocessing of species transport and reaction simulations: • Mass fraction of species-n • Mole fraction of species-n • Concentration of species-n • Lam Diff Coef of species-n • Eff Diff Coef of species-n • Thermal Diff Coef of species-n • Enthalpy of species-n (segregated solver calculations only) • species-n Source Term (coupled solver calculations only) • Relative Humidity • Time Step Scale (stiff-chemistry solver only) • Fine Scale Mass fraction of species-n (EDC model only) • Fine Scale Transfer Rate (EDC model only) • 1-Fine Scale Volume Fraction (EDC model only) • Fine Scale Temperature (EDC model only) • Rate of Reaction-n • Arrhenius Rate of Reaction-n • Turbulent Rate of Reaction-n These variables are contained in the Species..., Temperature..., and Reactions... categories of the variable selection drop-down list that appears in postprocessing panels. See Chapter 29 for a complete list of flow variables, field functions, and their definitions. Chapters 27 and 28 explain how to generate graphics displays and reports of data.

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Averaged Species Concentrations Averaged species concentrations at inlets and exits, and across selected planes (i.e., surfaces that you have created using the Surface menu items) within your model can be obtained using the Surface Integrals panel, as described in Section 28.5. Report −→Surface Integrals... Select the Concentration of species-n for the appropriate species in the Field Variable dropdown list.

13.1.9

Importing a Chemical Mechanism from CHEMKIN

If you have a gas-phase chemical mechanism in CHEMKIN [125] format, you can import the mechanism files into FLUENT using the Chemkin Import panel (Figure 13.1.9). File −→ Import −→CHEMKIN Mechanism...

Figure 13.1.9: The Chemkin Import Panel In the Chemkin Import panel, enter the path to the CHEMKIN file (e.g., path/file.che) under Chemkin Mechanism File and specify the location of the Thermodynamic Data File (THERMO.DB). See Section 14.3.1 for more information about this database. When you have specified the correct path for both files, enter a name for the chemical mechanism under Material Name and click the Import button. FLUENT will create a material with the specified name, which will contain the CHEMKIN data for the species and reactions, and add it to the list of available Mixture Materials in the Materials panel.


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13.2

Wall Surface Reactions and Chemical Vapor Deposition

For gas-phase reactions, the reaction rate is defined on a volumetric basis and the rate of creation and destruction of chemical species becomes a source term in the species conservation equations. The rate of deposition is governed by both chemical kinetics and the diffusion rate from the fluid to the surface. Wall surface reactions thus create sources (and sinks) of chemical species in the bulk phase and determine the rate of deposition of surface species. Information about wall surface reactions and chemical vapor deposition is presented in the following subsections: • Section 13.2.1: Overview of Surface Species and Wall Surface Reactions • Section 13.2.2: Theory • Section 13.2.3: User Inputs for Wall Surface Reactions • Section 13.2.4: Solution Procedures for Wall Surface Reactions • Section 13.2.5: Postprocessing for Wall Surface Reactions

13.2.1

Overview of Surface Species and Wall Surface Reactions

FLUENT treats chemical species deposited on surfaces as distinct from the same chemical species in the gas. Similarly, reactions involving surface deposition are defined as distinct surface reactions and hence treated differently than bulk phase reactions involving the same chemical species. Surface reactions can be limited so that they occur on only some of the wall boundaries (while the other wall boundaries remain free of surface reaction). The surface reaction rate is defined and computed per unit surface area, in contrast to the fluid-phase reactions, which are based on unit volume.

13.2.2

Theory

Consider the rth wall surface reaction written in general form as follows: Ng X i=1

0 gi,r Gi

+

Nb X i=1

b0i,r Bi

+

Ns X i=1

Kr s0i,r Si * )

Ng X i=1

00 gi,r Gi

+

Nb X i=1

b00i,r Bi

+

Ns X

s00i,r Si

(13.2-1)

i=1

where Gi , Bi , and Si represent the gas-phase species, the bulk (or solid) species, and the surface-adsorbed (or site) species, respectively. Ng , Nb , and Ns are the total numbers of 0 these species. gi,r , b0i,r , and s0i,r are the stoichiometric coefficients for each reactant species

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13.2 Wall Surface Reactions and Chemical Vapor Deposition

00 i, and gi,r , b00i,r , and s00i,r are the stoichiometric coefficients for each product species i. Kr is the overall reaction rate constant.

The summations in Equation 13.2-1 are for all chemical species in the system, but only species involved as reactants or products will have non-zero stoichiometric coefficients. Hence, species that are not involved will drop out of the equation. The rate of the rth reaction is

Rr = kf,r

Ng Y

g0

s0

i,r i,r [Gi ]wall [Si ]wall

(13.2-2)

i=1

where [ ]wall represents molar concentrations on the wall. It is assumed that the reaction rate does not depend on concentrations of the bulk (solid) species. From this, the net molar rate of production or consumption of each species i is given by

ˆ i,gas = R ˆ i,bulk = R ˆ i,site = R

N rxn X

r=1 N rxn X

r=1 N rxn X

00 0 (gi,r − gi,r )Rr

i = 1, 2, 3, . . . , Ng

(13.2-3)

(b00i,r − b0i,r )Rr

i = 1, 2, 3, . . . , Nb

(13.2-4)

(s00i,r − s0i,r )Rr

i = 1, 2, 3, . . . , Ns

(13.2-5)

r=1

The forward rate constant for reaction r (kf,r ) is computed using the Arrhenius expression. For example, kf,r = Ar T βr e−Er /RT where

Ar βr Er R

= = = =

(13.2-6)

pre-exponential factor (consistent units) temperature exponent (dimensionless) activation energy for the reaction (J/kgmol) universal gas constant (J/kgmol-K)

0 00 You (or the database) will provide values for gi,r , gi,r , b0i,r , b00i,r , s0i,r , s00i,r , βr , Ar , and Er .

Wall Surface Reaction Boundary Conditions As shown in Equations 13.2-2–13.2-5, the goal of surface reaction modeling is to compute concentrations of gas species and site species at the wall; i.e., [Gi ]wall and [Si ]wall . Assuming that, on a reacting surface, the mass flux of each gas species is balanced with its rate of production/consumption, then


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ρwall Di

∂Yi,wall ˆ i,gas −m ˙ dep Yi,wall = Mw,i R ∂n ∂ [Si ]wall ˆ i,site = R ∂t

i = 1, 2, 3, . . . , Ng

(13.2-7)

i = 1, 2, 3, . . . , Ns

(13.2-8)

The mass fraction Yi,wall is related to concentration by [Gi ]wall =

ρwall Yi,wall Mw,i

(13.2-9)

m ˙ dep is the net rate of mass deposition or etching as a result of surface reaction; i.e.,

m ˙ dep =

Nb X

ˆ i,bulk Mw,i R

(13.2-10)

i=1

[Si ]wall is the site species concentration at the wall, and is defined as [Si ]wall = ρsite zi

(13.2-11)

where ρsite is the site density and zi is the site coverage of species i. Using Equations 13.2-7 and 13.2-8, expressions can be derived for the mass fraction of species i at the wall and for the net rate of creation of species i per unit area. These expressions are used in FLUENT to compute gas-phase species concentrations, and if applicable, site coverages, at reacting surfaces using a point-by-point coupled stiff solver.

Including Mass Transfer To Surfaces in Continuity In the surface reaction boundary condition described above, the effects of the wall normal velocity or bulk mass transfer to the wall are not included in the computation of species transport. The momentum of the net surface mass flux from the surface is also ignored because the momentum flux through the surface is usually small in comparison with the momentum of the flow in the cells adjacent to the surface. However, you can include the effect of surface mass transfer in the continuity equation by activating the Mass Deposition Source option in the Species Model panel.

Wall Surface Mass Transfer Effects in the Energy Equation Species diffusion effects in the energy equation due to wall surface reactions are included in the normal species diffusion term described in Section 13.1.1. If you are using the segregated solver, you can neglect this term by turning off the Diffusion Energy Source option in the Species Model panel. (For the coupled solvers, this term is

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always included; you cannot turn it off.) Neglecting the species diffusion term implies that errors may be introduced to the prediction of temperature in problems involving mixing of species with significantly different heat capacities, especially for components with a Lewis number far from unity. While the effect of species diffusion should go to zero at Le = 1, you may see subtle effects due to differences in the numerical integration in the species and energy equations.

Modeling the Heat Release Due to Wall Surface Reactions The heat release due to a wall surface reaction is, by default, ignored by FLUENT. You can, however, choose to include the heat of surface reaction by activating the Heat of Surface Reactions option in the Species Model panel and setting appropriate formation enthalpies in the Materials panel.

Slip Boundary Formulation for Low-Pressure Gas Systems Most semiconductor fabrication devices operate far below atmospheric pressure, typically only a few millitorrs. At such low pressures, the fluid flow is in the slip regime and the normally used no-slip boundary conditions for velocity and temperature are no longer valid. Knudsen number, Kn, which is defined as the ratio of mean free path to a characteristic length scale of the system, is used to describe various flow regimes. Since the mean free path increases as the pressure is lowered, the high end of Kn values represents free molecular flow and the low end the continuum regime. The range in between these two extremes is called the slip regime (0.001 < Kn < 0.1). In the slip regime, the gas phase velocity at a solid surface differs from the velocity at which the wall moves, and the gas temperature at the surface differs from the wall temperature. Maxwell’s models are adopted for these physical phenomena in FLUENT for their simplicity and effectiveness. • velocity slip 2 − αv ∂U 2 − αv Uw − Ug = Kn ≈ αv ∂n αv

Vg ≡ (V~ · ~n)g = Vw

λ (Ug − Uc ) δ

(13.2-12) (13.2-13)

Here, U and V represents the velocity component that is parallel and normal to the wall, respectively. The subscripts g, w and c indicate gas, wall and cell-center velocities. δ is the distance from cell center to the wall. αv is the momentum accommodation coefficient of the gas mixture and its value is calculated as massfraction weighted average of each gas species in the system.


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αv =

Ng X

Yi αi

(13.2-14)

i=1

The mean free path, λ, is computed as follows: kB T λ = √ 2πσ 2 p Ng X

σ =

(13.2-15)

Yi σi

(13.2-16)

i=1

σi is the Lennard-Jones characteristic length of species i. kB is the Boltzmann constant, 1.38066 × 10−23 J/K. Equations 13.2-12 and 13.2-13 indicate that while the gas velocity component normal to the wall is the same as the wall normal velocity, the tangential components slip. The values lie somewhere between the cell-center and the wall values. These two equations can be combined to give a generalized formulation: V~w + kδ [(V~w · ~n)~n + V~c − (V~c · ~n)~n] ~ Vg = 1 + kδ

(13.2-17)

where k≡λ

2 − αv αv

(13.2-18)

• temperature jump Tw − Tg = 2

2 − αT αT

Kn

∂T 2 − αT ≈2 ∂n αT

λ (Tg − Tc ) δ

(13.2-19)

or equivalently Tg =

Tw + βTc 1+β

(13.2-20)

β=

2(2 − αT ) αT δ

(13.2-21)

where

αT is the thermal accommodation coefficient of the gas mixture and is calculated P as αT = Yi αT,i .

! The low-pressure slip boundary formulation is available only with the segregated solver.

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13.2.3

User Inputs for Wall Surface Reactions

The basic steps for setting up a problem involving wall surface reactions are the same as those presented in Section 13.1.2 for setting up a problem with only fluid-phase reactions, with a few additions: 1. In the Species Model panel: Define −→ Models −→Species... (a) Enable Species Transport, select Volumetric and Wall Surface under Reactions, and specify the Mixture Material. See Section 13.1.3 for details about this procedure, and Section 13.1.2 for an explanation of the mixture material concept. (b) (optional) If you want to model the heat release due to wall surface reactions, turn on the Heat of Surface Reactions option. (c) (optional) If you want to include the effect of surface mass transfer in the continuity equation, turn on the Mass Deposition Source option. (d) (optional) If you are using the segregated solver and you do not want to include species diffusion effects in the energy equation, turn off the Diffusion Energy Source option. See Section 13.2.2 for details. (e) (optional, but recommended for CVD) If you want to model full multicomponent diffusion or thermal diffusion, turn on the Full Multicomponent Diffusion or Thermal Diffusion option. See Section 7.7.2 for details. 2. Check and/or define the properties of the mixture. (See Section 13.1.4.) Define −→Materials... Mixture properties include the following: • species in the mixture • reactions • other physical properties (e.g., viscosity, specific heat)

!

You will find all species (including the solid/bulk and site species) in the list of Fluid Materials. For a species such as Si, you will find both Si(g) and Si(s) in the materials list for the fluid material type. If you were modeling the silicon deposition reactions in the example at the beginning of Section 13.2.1, you would need to include both Si species (gas and solid) in the mixture.

!

Note that the final gas-phase species named in the Selected Species list should be the carrier gas if your model includes species in dilute mixtures. (This is because FLUENT will not solve the transport equation for the final species.) Note also that any reordering, adding or deleting of species should be handled with caution, as described in Section 13.1.4.


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3. Check and/or set the properties of the individual species in the mixture. (See Section 13.1.4.) Note that if you are modeling the heat of surface reactions, you should be sure to check (or define) the formation enthalpy for each species. 4. Set species boundary conditions. Define −→Boundary Conditions... In addition to the boundary conditions described in Section 13.1.5, you will first need to indicate whether or not surface reactions are in effect on each wall. If so, you will then need to assign a reaction mechanism to the wall. To enable the effect of surface reaction on a wall, turn on the Surface Reactions option in the Species section of the Wall panel.

!

If you have enabled the global Low-Pressure Boundary Slip option in the Viscous Model panel, the Shear Condition for each wall will be reset to No Slip even though the slip model will be in effect. Note that the Low-Pressure Boundary Slip option is available only when the Laminar model is selected in the Viscous Model panel. See Section 6.13.1 for details about boundary condition inputs for walls. See Section 6.19.6 for details about boundary condition inputs for porous media.

13.2.4

Solution Procedures for Wall Surface Reactions

As in all CFD simulations, your surface reaction modeling effort may be more successful if you start with a simple problem description, adding complexity as the solution proceeds. For wall surface reactions, you can follow the same guidelines presented for fluid-phase reactions in Section 13.1.7. In addition, if you are modeling the heat release due to surface reactions and you are having convergence trouble, you should try temporarily turning off the Heat of Surface Reactions and Mass Deposition Source options in the Species Model panel.

13.2.5

Postprocessing for Surface Reactions

In addition to the variables listed in Section 13.1.8, for surface reactions you can also display/report the surface coverage as well as the deposition rate of the solid species deposited on a surface. Select Surface Coverage of species-n or Surface Deposition Rate of species-n in the Species... category of the variable selection drop-down list.

! For surface reactions involving porous media, you can display/report the surface reaction rates using the Arrhenius Rate of Reaction-n in the Reactions... category of the variable selection drop-down list.

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13.3 Particle Surface Reactions

13.3

Particle Surface Reactions

As described in Section 21.3.6, it is possible to define multiple particle surface reactions to model the surface combustion of a combusting discrete-phase particle. Information about particle surface reactions is provided in the following subsections: • Section 13.3.1: Theory • Section 13.3.2: User Inputs for Particle Surface Reactions • Section 13.3.3: Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion

13.3.1

Theory

General Description The relationships for calculating char particle burning rates are presented and discussed in detail by Smith [243]. The particle reaction rate, R (kg/m2 -s), can be expressed as R = D0 (Cg − Cs ) = Rc (Cs )N

(13.3-1)

where D0 Cg Cs Rc N

= bulk diffusion coefficient (m/s) = mean reacting gas species concentration in the bulk (kg/m3 ) = mean reacting gas species concentration at the particle surface (kg/m3 ) = chemical reaction rate coefficient (units vary) = apparent reaction order (dimensionless)

In Equation 13.3-1, the concentration at the particle surface, Cs , is not known, so it should be eliminated, and the expression is recast as follows:

R = Rc Cg −

R D0

N

(13.3-2)

This equation has to be solved by an iterative procedure, with the exception of the cases when N = 1 or N = 0. When N = 1, Equation 13.3-2 can be written as R=

Cg Rc D0 D0 + R c

(13.3-3)

In the case of N = 0, if there is a finite concentration of reactant at the particle surface, the solid depletion rate is equal to the chemical reaction rate. If there is no reactant at the surface, the solid depletion rate changes abruptly to the diffusion-controlled rate.


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In this case, however, FLUENT will always use the chemical reaction rate for stability reasons.

FLUENT Model Formulation A particle undergoing an exothermic reaction in the gas phase is shown schematically in Figure 13.3.1. Tp and T∞ are the temperatures in Equation 21.3-78.

Cd,b

Tp Ck

T∞

Temperature

Concentration

Cd,s

Distance

Figure 13.3.1: A Reacting Particle in the Multiple Surface Reactions Model Based on the analysis above, FLUENT uses the following equation to describe the rate of reaction r of a particle surface species j with the gas phase species n. The reaction stoichiometry of reaction r in this case is described by particle species j(s) + gas phase species n → products and the rate of reaction is given as Rj,r = Ap ηr Yj Rj,r

Rj,r = Rkin,r

Rj,r pn − D0,r

(13.3-4) !Nr

(13.3-5)

where

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13.3 Particle Surface Reactions Rj,r Ap Yj ηr Rj,r pn D0,r Rkin,r Nr

= = = = = = = = =

rate of particle surface species depletion (kg/s) particle surface area (m2 ) mass fraction of surface species j in the particle effectiveness factor (dimensionless) rate of particle surface species reaction per unit area (kg/m2 -s) bulk partial pressure of the gas phase species (Pa) diffusion rate coefficient for reaction r kinetic rate of reaction r (units vary) apparent order of reaction r

The effectiveness factor, ηr , is related to the surface area, and can be used in each reaction in the case of multiple reactions. D0,r is given by

D0,r = C1,r

[(Tp + T∞ )/2]0.75 dp

(13.3-6)

The kinetic rate of reaction r is defined as Rkin,r = Ar T βr e−(Er /RT )

(13.3-7)

The rate of the particle surface species depletion for reaction order Nr = 1 is given by Rj,r = Ap ηr Yj pn

Rkin,r D0,r D0,r + Rkin,r

(13.3-8)

For reaction order Nr = 0, Rj,r = Ap ηr Yj Rkin,r

(13.3-9)

Extension for Stoichiometries with Multiple Gas-Phase Reactants When more than one gas-phase reactant takes part in the reaction, the reaction stoichiometry must be extended to account for this case: particle species j(s) + gas phase species 1 + gas phase species 2 + . . . + gas phase species nmax → products To describe the rate of reaction r of a particle surface species j in the presence of nmax gas phase species n, it is necessary to define the diffusion-limited species for each solid particle reaction, i.e., the species for which the concentration gradient between the bulk and the particle surface is the largest. For the rest of the species, the surface and the bulk concentrations are assumed to be equal. The concentration of the diffusion-limited


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species is shown as Cd,b and Cd,s in Figure 13.3.1, and the concentrations of all other species are denoted as Ck . For stoichiometries with multiple gas-phase reactants, the bulk partial pressure pn in Equations 13.3-4 and 13.3-8 is the bulk partial pressure of the diffusion-limited species, pr,d for reaction r. The kinetic rate of reaction r is then defined as Rkin,r =

max Ar T βr e−(Er /RT ) nY r,n pN n (pr,d )Nr,d n=1

(13.3-10)

where pn Nr,n

= =

bulk partial pressure of gas species n reaction order in species n

When this model is enabled, the constant C1,r (Equation 13.3-6) and the effectiveness factor ηr (Equation 13.3-4) are entered in the Reactions panel, as described in Section 13.3.2.

Solid-Solid Reactions Reactions involving only particle surface reactants can be modeled, provided that the particle surface reactants and products exist on the same particle. particle species 1(s) + particle species 2(s) + . . . → products The reaction rate for this case is given by Equation 13.3-9.

Solid Decomposition Reactions The decomposition reactions of particle surface species can be modeled. particle species 1(s) + particle species 2(s) + . . . + particle species nmax (s) → gas species j + products The reaction rate for this case is given by Equations 13.3-4–13.3-10, where the diffusionlimited species is now the gaseous product of the reaction. If there are more than one gaseous product species in the reaction, it is necessary to define the diffusion-limited species for the particle reaction as the species for which the concentration gradient between the bulk and the particle surface is the largest.

Solid Deposition Reactions The deposition reaction of a solid species on a particle can be modeled with the following assumptions: gas species 1 + gas species 2 + . . . + gas species nmax → solid species j(s) + products

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13.3 Particle Surface Reactions

The theoretical analysis and Equations 13.3-4–13.3-10 are applied for the surface reaction rate calculation, with the mass fraction of the surface species set to unity in Equations 13.3-4, 13.3-8, and 13.3-9. In FLUENT, for the particle surface species to be deposited on a particle, a finite mass of the species must already exist in the particle. This allows for activation of the deposition reaction selectively to particular injection particles. It follows that, to initiate the solid species deposition reaction on a particle, the particle must be defined in the Set Injection Properties panel (or Set Multiple Injection Properties panel) to contain a small mass fraction of the solid species to be deposited. See Section 13.3.3 for details on defining the particle surface species mass fractions.

Gaseous Solid Catalyzed Reactions on the Particle Surface Reactions of gaseous species catalyzed on the particle surface can also be modeled following Equations 13.3-4–13.3-10 for the surface reaction rate calculation, with the mass fraction of the surface species set to unity in Equations 13.3-4, 13.3-8, and 13.3-9. The catalytic particle surface reaction option is enabled in FLUENT when Particle Surface is selected as the Reaction Type in the Reactions panel and there are no solid species in the reaction stoichiometry. The solid species acting as a catalyst for the reaction is defined in the Reactions panel. The catalytic particle surface reaction will proceed only on those particles containing the catalyst species. See Section 13.3.3 for details on defining the particle surface species mass fractions.

13.3.2

User Inputs for Particle Surface Reactions

The setup procedure for particle surface reactions requires only a few inputs in addition to the procedure for volumetric reactions described in Sections 13.1.2–13.1.6. These additional inputs are as follows: • In the Species Model panel, turn on the Particle Surface option under Reactions. Define −→ Models −→Species... • When you specify the species involved in the particle surface reaction, be sure to identify the surface species, as described in Section 13.1.4.

!

You will find all species (including the surface species) in the list of Fluid Materials. If, for example, you are modeling coal gasification, you will find solid carbon, C(s), in the materials list for the fluid material type. • For each particle surface reaction, select Particle Surface as the Reaction Type in the Reactions panel, and specify the following parameters (in addition to those described in Section 13.1.4):


13-47


Diffusion Limited Species When there is more than one gaseous reactant taking part in the particle surface reaction, the diffusion-limited species is the species for which the concentration gradient between the bulk and the particle surface is the largest. See Figure 13.3.1 for an illustration of this concept. In most cases, there is a single gas-phase reactant and the diffusion-limited species does not need to be defined. Catalyst Species This option is available only when there are no solid species defined in the stoichiometry of the particle surface reaction. In such a case, you will need to specify the solid species that acts as a catalyst for the reaction. The reaction will proceed only on the particles that contain this solid species. See Section 13.3.3 for details on defining the particle surface species mass fractions. Diffusion Rate Constant (C1,r in Equation 13.3-6) Effectiveness Factor (ηr in Equation 13.3-4)

13.3.3

Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion

When you use the multiple surface reactions model, the procedure for setting up a problem involving a discrete phase is slightly different from that outlined in Section 21.6. The revised procedure is as follows: 1. Enable any of the discrete phase modeling options, if relevant, as described in Section 21.7. 2. Specify the initial conditions, as described in Section 21.9. 3. Define the boundary conditions, as described in Section 21.10. 4. Define the material properties, as described in Section 21.11.

!

You must select multiple-surface-reactions in the Combustion Model drop-down list in the Materials panel before you can proceed to the next step. 5. If you have defined more than one particle surface species, for example, carbon (C) and sulfur (S), you will need to return to the Set Injection Properties panel (or Set Multiple Injection Properties panel) to specify the mass fraction of each particle surface species in the combusting particle. Click the Multiple Reactions tab, and enter the Species Mass Fractions. These mass fractions refer to the combustible fraction of the combusting particle, and should sum to 1. If there is only one surface species in the mixture material, the mass fraction of that species will be set to 1, and you will not specify anything under Multiple Surface Reactions. 6. Set the solution parameters and solve the problem, as described in Section 21.12.

13-48


13.4 Species Transport Without Reactions

7. Examine the results, as described in Section 21.13.

! Unsteady particle tracking cannot be performed when the multiple surface reactions model is used.

13.4

Species Transport Without Reactions

In addition to the volumetric and surface reactions described in the previous sections, you can also use FLUENT to solve a species mixing problem without reactions. The species transport equations that FLUENT will solve are described in Section 13.1.1, and the procedure you will follow to set up the non-reacting species transport problem is the same as that described in Sections 13.1.2–13.1.6, with some simplifications. The basic steps are listed below: 1. Enable Species Transport in the Species Model panel and select the appropriate Mixture Material. Define −→ Models −→Species... See Section 13.1.2 for information about the mixture material concept, and Section 13.1.3 for more details about using the Species Model panel. 2. (optional) If you want to model full multicomponent diffusion or thermal diffusion, turn on the Full Multicomponent Diffusion or Thermal Diffusion option. See Section 7.7.2 for details. 3. Check and/or define the properties of the mixture and its constituent species. Define −→Materials... Mixture properties include the following: • species in the mixture • other physical properties (e.g., viscosity, specific heat) See Section 13.1.4 for details. 4. Set species boundary conditions, as described in Section 13.1.5. No special solution procedures are usually required for a non-reacting species transport calculation. Upon completion of the calculation, you can display or report the following quantities: • Mass fraction of species-n • Mole fraction of species-n


13-49


• Concentration of species-n • Lam Diff Coef of species-n • Eff Diff Coef of species-n • Enthalpy of species-n (segregated solver calculations only) • Relative Humidity • Mean Molecular Weight These variables are contained in the Species... and Properties... categories of the variable selection drop-down list that appears in postprocessing panels. See Chapter 29 for a complete list of flow variables, field functions, and their definitions. Chapters 27 and 28 explain how to generate graphics displays and reports of data.

13-50


Chapter 14. Combustion

Modeling Non-Premixed

In non-premixed combustion, fuel and oxidizer enter the reaction zone in distinct streams. This is in contrast to premixed systems, in which reactants are mixed at the molecular level before burning. Examples of non-premixed combustion include methane combustion, pulverized coal furnaces, and diesel (compression) internal-combustion engines. Under certain assumptions, the thermochemistry can be reduced to a single parameter: the mixture fraction. The mixture fraction, denoted by f , is the mass fraction that originated from the fuel stream. In other words, it is the local mass fraction of burnt and unburnt fuel stream elements (C, H, etc.) in all the species (CO2 , H2 O, O2 , etc.). The approach is elegant because atomic elements are conserved in chemical reactions. In turn, the mixture fraction is a conserved scalar quantity, and therefore its governing transport equation does not have a source term. Combustion is simplified to a mixing problem, and the difficulties associated with closing non-linear mean reaction rates are avoided. Once mixed, the chemistry can be modeled as in chemical equilibrium, or near chemical equilibrium with the laminar flamelet model. These models are presented in the following sections: • Section 14.1: Description of the Equilibrium Mixture Fraction/PDF Model • Section 14.2: Modeling Approaches for Non-Premixed Equilibrium Chemistry • Section 14.3: User Inputs for the Non-Premixed Equilibrium Model • Section 14.4: The Laminar Flamelet Model • Section 14.5: Adding New Species to the prePDF Database

14.1

Description of the Equilibrium Mixture Fraction/ PDF Model

The non-premixed modeling approach involves the solution of transport equations for one or two conserved scalars (the mixture fractions). Equations for individual species are not solved. Instead, species concentrations are derived from the predicted mixture fraction fields. The thermochemistry calculations are preprocessed in prePDF and tabulated for look-up in FLUENT. Interaction of turbulence and chemistry is accounted for with a probability density function (PDF).


14-1

Modeling Non-Premixed Combustion

Information about the non-premixed mixture fraction/PDF model is presented in the following subsections: • Section 14.1.1: Benefits and Limitations of the Non-Premixed Approach • Section 14.1.2: Details of the Non-Premixed Approach • Section 14.1.3: Restrictions and Special Cases for Non-Premixed Modeling See Section 14.2 for an overview of modeling and solution procedures, and Section 14.3 for instructions on using the model.

14.1.1

Benefits and Limitations of the Non-Premixed Approach

Advantages of the Non-Premixed Approach The non-premixed modeling approach has been specifically developed for the simulation of turbulent diffusion flames with fast chemistry. For such systems, the method offers many benefits over the finite rate formulation described in Chapter 13. The non-premixed model allows intermediate (radical) species prediction, dissociation effects, and rigorous turbulence-chemistry coupling. The method is computationally efficient in that it does not require the solution of a large number of species transport equations. When the underlying assumptions are valid, the non-premixed approach is preferred over the finite rate formulation.

Limitations of the Non-Premixed Approach As detailed in Section 14.1.2, the non-premixed approach can be used only when your reacting flow system meets several requirements. First, the FLUENT implementation requires that the flow be turbulent. Second, the reacting system includes a fuel stream, an oxidant stream, and, optionally, a secondary stream (another fuel or oxidant, or a non-reacting stream). Finally, the chemical kinetics must be rapid so that the flow is near chemical equilibrium. These issues are detailed in Sections 14.1.2 and 14.1.3.

! Note that the non-premixed model can be used only with the segregated solver; it is not available with the coupled solvers.

14.1.2

Details of the Non-Premixed Approach

Definition of the Mixture Fraction The basis of the non-premixed modeling approach is that under a certain set of simplifying assumptions, the instantaneous thermochemical state of the fluid is related to a conserved scalar quantity known as the mixture fraction f . The mixture fraction can be written in terms of the atomic mass fraction as [238]

14-2


14.1 Description of the Equilibrium Mixture Fraction/ PDF Model

f=

Zi − Zi,ox Zi,fuel − Zi,ox

(14.1-1)

where Zi is the elemental mass fraction for some element, i. The subscript ox denotes the value at the oxidizer stream inlet and the subscript fuel denotes the value at the fuel stream inlet. If the diffusion coefficients for all species are equal, then Equation 14.1-1 is identical for all elements, and the mixture fraction definition is unique. The mixture fraction is thus the elemental mass fraction that originated from the fuel stream. Note that this mass fraction includes all elements from the fuel stream, including inert species such as N2 , and any oxidizing species mixed with the fuel, such as O2 . If a secondary stream (another fuel or oxidant, or a non-reacting stream) is included, the fuel and secondary mixture fractions are simply the mass fractions of the fuel and secondary streams. The sum of all three mixture fractions in the system (fuel, secondary stream, and oxidizer) is always equal to 1: ffuel + fsec + fox = 1

(14.1-2)

This indicates that only points on the plane ABC (shown in Figure 14.1.1) in the mixture fraction space are valid. Consequently, the two mixture fractions, ffuel and fsec , cannot vary independently; their values are valid only if they are both within the triangle OBC shown in Figure 14.1.2.

fox

1

fsec

A 1 C

O 0

B 1

ffuel

Figure 14.1.1: Relationship of ffuel , fsec , and fox FLUENT discretizes the triangle OBC as shown in Figure 14.1.2. Essentially, the primary mixture fraction, ffuel , is allowed to vary between zero and one, as for the single mixture fraction case, while the secondary mixture fraction lies on lines with the following equation:


14-3


C

1

p

sec

f sec

B

O 0

f fuel

1

Figure 14.1.2: Relationship of ffuel , fsec , and psec

fsec = psec × (1 − ffuel )

(14.1-3)

where psec is the normalized secondary mixture fraction and is the value at the intersection of a line with the secondary mixture fraction axis. Note that unlike fsec , psec is bounded between zero and one, regardless of the ffuel value. An important characteristic of the normalized secondary mixture fraction, psec , is its assumed statistical independence from the fuel mixture fraction, ffuel . Note that unlike fsec , psec is not a conserved scalar. The normalized mixture fraction definition for the second scalar variable is used everywhere except when defining the rich limit for a secondary fuel stream, which is defined in terms of fsec . Transport Equations for the Mixture Fraction Under the assumption of equal diffusivities, the species equations can be reduced to a single equation for the mixture fraction, f . The reaction source terms in the species equations cancel, and thus f is a conserved quantity. While the assumption of equal diffusivities is problematic for laminar flows, it is generally acceptable for turbulent flows where turbulent convection overwhelms molecular diffusion. The mean (time-averaged) mixture fraction equation is ∂ µt (ρf ) + ∇ · (ρ~v f ) = ∇ · ∇f + Sm + Suser ∂t σt

(14.1-4)

The source term Sm is due solely to transfer of mass into the gas phase from liquid fuel droplets or reacting particles (e.g., coal). Suser is any user-defined source term.

14-4



In addition to solving for the mean mixture fraction, FLUENT solves a conservation equation for the mean mixture fraction variance, f 0 2 [118]:

∂ 02 µt ρf + ∇ · ρ~v f 0 2 = ∇ · ∇f 0 2 + Cg µt ∇2 f − Cd ρ f 0 2 + Suser ∂t σt k

(14.1-5)

where f 0 = f − f . The constants σt , Cg , and Cd take the values 0.85, 2.86, and 2.0, respectively, and Suser is any user-defined source term. The mixture fraction variance is used in the closure model describing turbulence-chemistry interactions (see below). 0

2 For a two-mixture-fraction problem, ffuel and ffuel are obtained from Equations 14.1-4 and 02 02 14.1-5 by substituting ffuel for f and ffuel for f . fsec is obtained from Equation 14.1-4 by 2 is obtained substituting fsec for f . psec is then calculated using Equation 14.1-3, and p0sec 02 02 by solving Equation 14.1-5 with psec substituted for f . Solution for psec instead of fsec is justified by the fact that the amount of the secondary stream is relatively small compared with the total mass flow rate. To a first-order approximation, the variances in psec and 2 is essentially the same as f 0 2 . fsec are relatively insensitive to ffuel , and therefore p0sec sec

The Non-Premixed Model for LES For large eddy simulations (LES), an equation for the mean mixture fraction is solved, which is identical in form to Equation 14.1-4 except that µt is the subgrid-scale viscosity. A transport equation is not solved for the mixture fraction variance. Instead, it is modeled as 2

f 0 2 = Cvar L2sgs |∇f |

(14.1-6)

where Cvar Lsgs

= =

user-adjustable constant subgrid length scale

Mixture Fraction vs. Equivalence Ratio The mixture fraction definition can be understood in relation to common measures of reacting systems. Consider a simple combustion system involving a fuel stream (F), an oxidant stream (O), and a product stream (P) symbolically represented at stoichiometric conditions as F + r O → (1 + r) P


(14.1-7)

14-5


where r is the air-to-fuel ratio on a mass basis. Denoting the equivalence ratio as φ, where φ=

(fuel/air)actual (fuel/air)stoichiometric

(14.1-8)

the reaction in Equation 14.1-7, under more general mixture conditions, can then be written as φ F + r O → (φ + r) P

(14.1-9)

Looking at the left side of this equation, the mixture fraction for the system as a whole can then be deduced to be f=

φ φ+r

(14.1-10)

Equation 14.1-10 is an important result, allowing the computation of the mixture fraction at stoichiometric conditions (φ = 1) or at fuel-rich conditions (e.g., φ > 1). Relationship of f to Species Mass Fraction, Density, and Temperature The power of the mixture fraction modeling approach is that the chemistry is reduced to one or two conserved mixture fractions. All thermochemical scalars (species mass fraction, density, and temperature) are uniquely related to the mixture fraction(s). Given a description of the reacting system chemistry, and certain other restrictions on the system (see Section 14.1.3), the instantaneous mixture fraction value at each point in the flow field can be used to compute the instantaneous values of individual species mole fractions, density, and temperature. If, in addition, the reacting system is adiabatic, the instantaneous values of mass fractions, density, and temperature depend solely on the instantaneous mixture fraction, f : φi = φi (f )

(14.1-11)

for a single fuel-oxidizer system. If a secondary stream is included, the instantaneous values will depend on the instantaneous fuel mixture fraction, ffuel , and the secondary partial fraction, psec : φi = φi (ffuel , psec )

14-6

(14.1-12)



In Equations 14.1-11 and 14.1-12, φi represents the instantaneous species mass fraction, density, or temperature. In the case of non-adiabatic systems, this relationship generalizes to φi = φi (f, H ∗ )

(14.1-13)

for a single mixture fraction system, where H ∗ is the instantaneous enthalpy (identical to H as defined in Equation 11.2-7): ∗

H =

X

m j Hj =

j

X j

mj

"Z

T

Tref,j

cp,j dT +

#

h0j (Tref,j )

(14.1-14)

If a secondary stream is included, φi = φi (ffuel , psec , H ∗ )

(14.1-15)

Examples of non-adiabatic flows include systems with radiation, heat transfer through walls, heat transfer to/from discrete phase particles or droplets, and multiple inlets at different temperatures. Additional detail about the mixture fraction approach in such non-adiabatic systems is provided on page 14-13. The details of the functional relationship between φi (species mass fraction, density, and temperature) and mixture fraction (Equations 14.1-11 through 14.1-15) depend on the description of the system chemistry. You can choose to describe this relationship using the flame sheet (mixed-is-burned), equilibrium chemistry, or non-equilibrium chemistry (flamelet) model, as described below.

Models Describing the System Chemistry FLUENT provides three options for description of the system chemistry when you use the non-premixed modeling approach. These options are: • The Flame Sheet Approximation (Mixed-is-Burned): The simplest reaction scheme is the flame sheet or “mixed-is-burned” approximation. This approach assumes that the chemistry is infinitely fast and irreversible, with fuel and oxidant species never coexisting in space and complete one-step conversion to final products. This description allows species mass fractions to be determined directly from the given reaction stoichiometry, with no reaction rate or chemical equilibrium information required. This simple system description yields straight line relationships between the species mass fractions and the mixture fraction, as shown in Figure 14.1.3. Because no reaction rate or equilibrium calculations are required, the flame sheet approximation is easily computed and yields a rapid calculation. However, the


14-7


flame sheet model is limited to the prediction of single-step reactions and cannot predict intermediate species formation or dissociation effects. This often results in a serious overprediction of peak flame temperature, especially in those systems that involve very high temperature (e.g., systems using pre-heat or oxygen-enrichment). • Equilibrium Assumption: The equilibrium model assumes that the chemistry is rapid enough for chemical equilibrium to always exist at the molecular level. An algorithm based on the minimization of Gibbs free energy [132] is used to compute species mole fractions from f . Figure 14.1.4 shows the resulting mole fractions for a reacting system that includes 10 species in the combustion of methane in air. The equilibrium model is powerful since it can predict the formation of intermediate species and it does not require a knowledge of detailed chemical kinetic rate data. Instead of defining a specific multi-step reaction mechanism (see Chapter 13), you simply define the important chemical species that will be present in the system. FLUENT then predicts the mole fraction of each species based on chemical equilibrium. FLUENT allows you to restrict the full equilibrium calculation to those situations in which the instantaneous mixture fraction is below a specified rich limit, frich . In fuel-rich regions (e.g., equivalence ratio greater than 1.5 ) when the instantaneous mixture fraction exceeds frich , FLUENT assumes that the combustion reaction is extinguished and that unburned fuel coexists with reacted material. In such fuel-rich regions the composition at a given value of mixture fraction is computed from the composition of the limiting mixture (f =frich ) and that of the fuel inlet stream (f =1) based on a known stoichiometry. The stoichiometry is either supplied by you or determined automatically from chemical equilibrium at the rich limit (f =frich ). This approach, known as the partial equilibrium approach, allows you to bypass complex equilibrium calculations in the rich flame region. The latter are time-consuming to compute and may not be representative of the real combustion process. When a full equilibrium approach is required, you can simply define the rich limit as frich = 1.0. Guidelines on the choice of which species to include in the equilibrium calculation are provided in Section 14.3. The species you include must exist in the chemical database accessed by prePDF. Note that the species included in the equilibrium calculation should probably not include NOx species, as the NOx reaction rates are slow and should not be treated using an equilibrium assumption. Instead, NOx concentration is predicted most accurately using the FLUENT NOx postprocessor where finite rate chemical kinetics are incorporated. • Non-Equilibrium Chemistry (Flamelet Model): In combustion models where nonequilibrium effects are important, the assumption of local chemical equilibrium can lead to unrealistic results. Typical cases in which the equilibrium assumption breaks down are modeling the rich side of hydrocarbon flames, predicting the intermediate

14-8



species that govern NOx formation, and modeling lift-off and blow-off phenomena in jet flames.

Mass Fraction, Y and Enthalpy, h

Several approaches are available to overcome these modeling difficulties on a caseby-case basis; in FLUENT the partial-equilibrium/rich-limit approximation (described above) can be used to model the fuel-rich side of the hydrocarbon flames. Flamelet models have been proposed as a more general solution to the problem of moderate non-equilibrium flame chemistry. See Section 14.4 for details about the laminar flamelet model in FLUENT.

h

Y

F

Y

O

Y

P

0

f st

1 Mixture Fraction, f

Figure 14.1.3: Species Mass Fractions and Enthalpy Derived Using the Flame Sheet Approximation

PDF Modeling of Turbulence-Chemistry Interaction Equations 14.1-11 through 14.1-15 describe the instantaneous relationships between mixture fraction and species mass fraction, density, and temperature as given by the equilibrium, flamelet, or mixed-is-burned chemistry model. The FLUENT prediction of the turbulent reacting flow, however, is concerned with prediction of the time-averaged values of these fluctuating scalars. How these time-averaged values are related to the instantaneous values depends on the turbulence-chemistry interaction model. FLUENT applies the assumed shape probability density function (PDF) approach as its closure model when the non-premixed modeling approach is used. The PDF closure model is described in this section.


14-9


KEY 1.00E+00

CH4 O2 CO2 H2O N2 CO H2

8.00E-01

M o l e F r a c t i o n

6.00E-01

4.00E-01

2.00E-01

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

Mixture Fraction F

CHEMICAL EQUILIBRIUM INSTANTANEOUS SPECIES COMPOSITION

prePDF V4.00

Fluent Inc.

Figure 14.1.4: Species Mole Fractions Computed Based on Chemical Equilibrium

Description of the Probability Density Function The probability density function, written as p(f ), can be thought of as the fraction of time that the fluid spends at the state f . Figure 14.1.5 illustrates this concept. The fluctuating value of f , plotted on the right side of the figure, spends some fraction of time in the range denoted as ∆f . p(f ), plotted on the left side of the figure, takes on values such that the area under its curve in the band denoted, ∆f , is equal to the fraction of time that f spends in this range. Written mathematically, 1X τi T →∞ T i

p(f ) ∆f = lim

(14.1-16)

where T is the time scale and τi is the amount of time that f spends in the ∆f band. The shape of the function p(f ) depends on the nature of the turbulent fluctuations in f . In practice, p(f ) is expressed as a mathematical function that approximates the PDF shapes that have been observed experimentally. Derivation of Mean Scalar Values from the Instantaneous Mixture Fraction The probability density function p(f ), describing the temporal fluctuations of f in the turbulent flow, has the very beneficial property that it can be used to compute timeaveraged values of variables that depend on f . Time-averaged values of species mole fractions and temperature can be computed (in adiabatic systems) as

14-10



Figure 14.1.5: Graphical Description of the Probability Density Function, p(f )

φi =

Z

0

1

p(f )φi (f )df

(14.1-17)

for a single mixture fraction system. When a secondary stream exists, the average values are calculated as φi =

Z

1

0

Z

0

1

p1 (ffuel )p2 (psec )φi (ffuel , psec )dffuel dpsec

(14.1-18)

where p1 is the PDF of ffuel and p2 is the PDF of psec . Here, statistical independence of ffuel and psec is assumed, so that p(ffuel , psec ) = p1 (ffuel )p2 (psec ). Similarly, the true time-averaged fluid density, ρ, can be computed as 1 Z 1 p(f ) = df ρ 0 ρ(f )

(14.1-19)

for a single mixture fraction system, and 1 Z 1 Z 1 p1 (ffuel )p2 (psec ) = dffuel dpsec ρ ρ(ffuel , psec ) 0 0

(14.1-20)

when a secondary stream exists. ρ(f ) or ρ(ffuel , psec ) is the instantaneous density obtained using the instantaneous species mole fractions and temperature in the gas law equation. Equations 14.1-19 and 14.1-20 provide a more accurate description of the time-averaged density than the alternate approach of applying the gas law using time-averaged species and temperature.


14-11


Using Equations 14.1-17 and 14.1-19 (or Equations 14.1-18 and 14.1-20), it remains only to specify the shape of the function p(f ) (or p1 (ffuel ) and p2 (psec )) in order to determine the local time-averaged state of the fluid at all points in the flow field. The PDF Shape The shape of the assumed PDF, p(f ), is described in FLUENT by one of two mathematical functions: • the double delta function • the β-function The double delta function is the most easily computed, while the β-function most closely represents experimentally observed PDFs. The shape produced by these functions depends solely on the mean mixture fraction, f , and its variance, f 0 2 . The choice of these functions (and others, such as the clipped Gaussian) have their basis in experimental measurements of concentration fluctuations [19, 118]. A detailed description of each function follows. The Double Delta Function PDF The double delta function is given by     0.5,

p(f ) =  0.5,   0,

q

f = f − qf 0 2 f = f + f 02 elsewhere

(14.1-21)

with suitable bounding near f = 1 and f = 0. One example of the double delta function is illustrated in Figure 14.1.6. As noted above, the double delta function PDF is very easy to compute but is invariably less accurate than the alternate β-function PDF. For this reason, it should be employed only in special circumstances. The β-Function PDF The β-function PDF shape is given by the following function of f and f 0 2 :

p(f ) = R

f α−1 (1 − f )β−1 f α−1 (1 − f )β−1 df

(14.1-22)

where

14-12



p(f)

0.5

0

f

0

f

Figure 14.1.6: Example of the Double Delta Function PDF Shape

"

#

f (1 − f ) −1 α=f f 02

(14.1-23)

and "

#

f (1 − f ) β = (1 − f ) −1 f 02

(14.1-24)

Figures 14.1.7 and 14.1.8 show the form of the β function for two conditions of f and f 02. Importantly, the PDF shape p(f ) can be computed at all points in the flow in terms of its first two moments, namely mean, f , and variance, f 0 2 . Thus, given FLUENT’s prediction of f and f 0 2 at each point in the flow field (Equations 14.1-4 and 14.1-5), the known PDF shape can be computed and used as the weighting function to determine the time-averaged mean values of species mass fraction, density, and temperature using, Equations 14.1-17 and 14.1-19 (or, for a system with a secondary stream, Equations 14.1-18 and 14.1-20). This logical dependence is depicted visually in Figure 14.1.9 for a single mixture fraction. (When a secondary stream is included, the PDF shape will be computed for the fuel mixture fraction, ffuel , and the secondary partial fraction, psec , and the order of the calculations is different, as shown in Figure 14.2.2.)

Non-Adiabatic Extensions of the Non-Premixed Model Many reacting systems involve heat transfer to wall boundaries, droplets, and/or particles by convective and radiative heat transfer. In such flows the local thermochemical state is no longer related only to f , but also to the enthalpy H ∗ . The system enthalpy impacts the


14-13


KEY 5.53E+00

4.43E+00 P r o b a b i l i t y D e n s i t y

3.32E+00

2.21E+00

p 1.11E+00

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

Mixture Fraction F

BETA PROBABILITY DENSITY FUNCTION F-Bar = 3.00E-01, F-Fluc = 5.00E-03.

prePDF V4.00

Fluent Inc.

Figure 14.1.7: β-Function PDF Shapes for f = 0.3 and f 0 2 = 0.005

KEY 1.63E+01

1.30E+01 P r o b a b i l i t y D e n s i t y

9.78E+00

6.52E+00

p 3.26E+00

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

Mixture Fraction F

BETA PROBABILITY DENSITY FUNCTION F-Bar = 1.00E-01, F-Fluc = 1.00E-02.

prePDF V4.00

Fluent Inc.

Figure 14.1.8: β-Function PDF Shapes for f = 0.1 and f 0 2 = 0.01

14-14



PDF Shape p(f ) = p (f , f ’ 2 )

Chemistry Model φ i (f )

1

φ i = ∫ p(f ) φ i (f ) df o

Look-up Table φi = φi (f , f

’2)

Figure 14.1.9: Logical Dependence of Averaged Scalars φi on f , f 0 2 , and the Chemistry Model (Adiabatic, Single-Mixture-Fraction Systems)

chemical equilibrium calculation and the temperature of the reacted flow. Consequently, changes in enthalpy due to heat loss must be considered when computing scalars from the mixture fraction. Thus, the scalar dependence becomes φi = φi (f, H ∗ )

(14.1-25)

where H ∗ is given by Equation 14.1-14. In such non-adiabatic systems, turbulent fluctuations should be accounted for by means of a joint PDF p(f, H ∗ ). The computation of p(f, H ∗ ) is not practical for most engineering applications, however. The problem can be simplified significantly by assuming that the enthalpy fluctuations are independent of the enthalpy level (i.e., heat losses do not significantly impact the turbulent enthalpy fluctuations). When this is assumed, we again have p = p(f ) and φi =

Z

0

1

φi (f, H ∗ )p(f )df

(14.1-26)

Determination of φi in the non-adiabatic system thus requires solution of the modeled transport equation for time-averaged enthalpy: ∂ kt (ρH ∗ ) + ∇ · (ρ~v H ∗ ) = ∇ · ∇H ∗ ∂t cp

!

(14.1-27)

where Sh accounts for source terms due to radiation, heat transfer to wall boundaries, and heat exchange with the second phase. Figure 14.1.10 depicts the logical dependence


14-15


of mean scalar values (species mass fraction, density, and temperature) on FLUENT’s prediction of f , f 0 2 , and H ∗ in non-adiabatic single-mixture-fraction systems.

PDF Shape p(f ) = p (f , f ’ 2 )

Chemistry Model φ i (f , H * )

1

φ i = ∫ p(f ) φ i (f ,H*)d f o

Look-up Table φi = φi (f , f ’ 2,H*)

Figure 14.1.10: Logical Dependence of Averaged Scalars φi on f , f 0 2 , H ∗ , and the Chemistry Model (Non-Adiabatic, Single-Mixture-Fraction Systems)

When a secondary stream is included, the scalar dependence becomes φi = φi (ffuel , psec , H ∗ )

(14.1-28)

and the mean values are calculated from φi =

Z

0

1

Z

0

1

φi (ffuel , psec , H ∗ )p1 (ffuel )p2 (psec )dffuel dpsec

(14.1-29)

As noted above, the non-adiabatic extensions to the PDF model are required in systems involving heat transfer to walls and in systems with radiation included. In addition, the non-adiabatic model is required in systems that include multiple fuel or oxidizer inlets with different inlet temperatures or that include flue gas recycle. Finally, the non-adiabatic model is required in particle-laden flows (e.g., liquid fuel systems or coal combustion systems) since such flows include heat transfer to the dispersed phase. Figure 14.1.11 illustrates several systems that must include the non-adiabatic form of the PDF model. Note that even if your system is non-adiabatic, you may want to perform the much simpler adiabatic calculation as an initial exercise. This will allow you to bound the non-adiabatic analysis in an efficient manner, as described in Section 14.3.

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Q wall or Q radiation

Fuel Oxidant

f=1 f=0

(a) Heat Transfer to Domain Boundaries and/or Radiation Heat Transfer

Oxidant T = T1 Fuel Oxidant T = T2 (b) Multiple Fuel or Oxidant Inlets at Different Temperatures

Oxidant

Liquid Fuel or Pulverized Coal

(c) Dispersed Phase Heat or Mass Transfer (e.g., Liquid Fuel or Coal Combustion)

Figure 14.1.11: Reacting Systems Requiring Non-Adiabatic Non-Premixed Model Approach


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14.1.3

Restrictions and Special Cases for the Non-Premixed Model

Restrictions on the Mixture Fraction Approach The unique dependence of φi (species mass fractions, density, or temperature) on f (Equation 14.1-11 or 14.1-13) requires that the reacting system meet the following conditions: • The chemical system must be of the diffusion type with discrete fuel and oxidizer inlets (spray combustion and pulverized fuel flames may also fall into this category). • The Lewis number must be unity. (This implies that the diffusion coefficients for all species and enthalpy are equal, a good approximation in turbulent flow). • When a single mixture fraction is used, the following conditions must be met: – Only one type of fuel is involved. The fuel may be made up of a burnt mixture of reacting species (e.g., 90% CH4 and 10% CO) and you may include multiple fuel inlets. The multiple fuel inlets must have the same composition, however. Two or more fuel inlets with different fuel composition are not allowed (e.g., one inlet of CH4 and one inlet of CO). Similarly, in spray combustion systems or in systems involving reacting particles, only one off-gas is permitted. – Only one type of oxidizer is involved. The oxidizer may consist of a mixture of species (e.g., 21% O2 and 79% N2 ) and you may have multiple oxidizer inlets. The multiple oxidizer inlets must, however, have the same composition. Two or more oxidizer inlets with different composition are not allowed (e.g., one inlet of air and a second inlet of pure oxygen). • When two mixture fractions are used, three streams can be involved in the system. Valid systems are as follows: – Two fuel streams with different compositions and one oxidizer stream. Each fuel stream may be made up of a mixture of reacting species (e.g., 90% CH4 and 10% CO). You may include multiple inlets of each fuel stream, but each fuel inlet must have one of the two defined compositions (e.g., one inlet of CH4 and one inlet of CO). – Mixed fuel systems including gas-liquid, gas-coal, or liquid-coal fuel mixtures with a single oxidizer. In systems with a gas-coal or liquid-coal fuel mixture, the coal volatiles and char are treated as a single composite fuel stream. – Coal combustion in which volatiles and char are tracked separately. – Two oxidizer streams with different compositions and one fuel stream. Each oxidizer stream may consist of a mixture of species (e.g. 21% O2 and 79% N2 ). You may have multiple inlets of each oxidizer stream, but each oxidizer

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inlet must have one of the two defined compositions (e.g., one inlet of air and a second inlet of pure oxygen). – A fuel stream, an oxidizer stream, and a non-reacting secondary stream. • The flow must be turbulent. It is important to emphasize that these restrictions eliminate the use of the non-premixed approach for directly modeling premixed combustion. This is because the unburned premixed stream is far from chemical equilibrium. Note, however, that an extended mixture fraction formulation, described in Chapter 16, can be applied to premixed and partially premixed flames. Figures 14.1.12 and 14.1.13 illustrate typical reacting system configurations that can be handled by the non-premixed model in FLUENT. Figure 14.1.14 shows a premixed configuration that cannot be modeled using the non-premixed model.

Using the Non-Premixed Model for Liquid Fuel or Coal Combustion You can use the non-premixed model if your FLUENT simulation includes liquid droplets and/or coal particles. In this case, fuel enters the gas phase within the computational domain at a rate determined by the evaporation, devolatilization, and char combustion laws governing the dispersed phase. In the case of coal, the volatiles and the products of char can be defined as two different types of fuel (using two mixture fractions) or as a single composite off-gas (using one mixture fraction), as described in Section 14.3.5.

Using the Non-Premixed Model with Flue Gas Recycle While most problems you solve using the non-premixed model will involve inlets that contain either pure oxidant or pure fuel (f = 0 or 1), you can include an inlet that has an intermediate value of mixture fraction (0 < f < 1) provided that this inlet represents a completely reacted mixture. Such cases arise when there is flue gas recirculation, as depicted schematically in Figure 14.1.15. Since f is a conserved quantity, the mixture fraction at the flue gas recycle inlet can be computed as m ˙ fuel + m ˙ recyc fexit = (m ˙ fuel + m ˙ ox + m ˙ recyc )fexit

(14.1-30)

or fexit =


m ˙ fuel m ˙ fuel + m ˙ ox

(14.1-31)

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60% CH4 40% CO

f=1

21% O2 79% N2

f=0

(a) Simple Fuel/Oxidant Diffusion Flame 35% O 2 65% N 2 f=0 60% CH 4 40% CO 35% O2

f=1

f=0

65% N 2

(b) Diffusion System Using Multiple Oxidant Inlets 60% CH 4 20% CO 10% C3H8 10% CO2

f=1

21% O2 79% N2

f=0

60% CH 4 20% CO 10% C3H8 10% CO2

f=1

(c) System Using Multiple Fuel Inlets

Figure 14.1.12: Chemical Systems That Can Be Modeled Using a Single Mixture Fraction

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CH 4/CO/C 3H 8 Oxidant CH 4/C 3H

8

(a) System Containing Two Dissimilar Fuel Inlets

21% O2 Fuel 35% O2

(b) System Containing Two Dissimilar Oxidant Inlets

Figure 14.1.13: Chemical System Configurations That Can Be Modeled Using Two Mixture Fractions

CH 4 O 2 N 2

Figure 14.1.14: Premixed Systems CANNOT Be Modeled Using the Non-Premixed Model


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where fexit is the exit mixture fraction (and the mixture fraction at the flue gas recycle inlet), m ˙ ox is the mass flow rate of the oxidizer inlet, m ˙ fuel is the mass flow rate of the fuel inlet, m ˙ recyc is the mass flow rate of the recycle inlet. If a secondary stream is included, ffuel,exit =

m ˙ fuel

m ˙ fuel +m ˙ sec + m ˙ ox

(14.1-32)

and psec,exit =

m ˙ sec m ˙ sec + m ˙ ox

(14.1-33)

. m R

fexit . m F

f=1

. m O

f=0

fexit

Figure 14.1.15: Using the Non-Premixed Model with Flue Gas Recycle

14.2

Modeling Approaches for Non-Premixed Equilibrium Chemistry

The FLUENT software package offers two different ways to model non-premixed equilibrium chemistry. You can choose either a single- or two-mixture-fraction approach depending on how many streams you have. prePDF stores information about the streams in “look-up tables”, which are then used by FLUENT to solve for the mixture fraction, enthalpy, and scalar quantities. For more information about prePDF, see Section 14.3.

14.2.1

Single-Mixture-Fraction Approach

To keep computation time to a minimum, much of the calculation required for the nonpremixed model is performed outside of the FLUENT simulation by preprocessing the chemistry calculations and PDF integrations in a separate code, called prePDF. Figure 14.2.1 illustrates how the computational effort is divided between the preprocessor

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14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry

(prePDF) and the solver (FLUENT). In prePDF, the chemistry model (mixed-is-burned, equilibrium chemistry, or laminar flamelet) is used in conjunction with the assumed shape of the PDF to perform the integrations given in Equations 14.1-17, 14.1-19, and/or 14.1-26. These integrations are performed within prePDF and stored in look-up tables that relate the mean thermochemical variables φi (temperature, density and species mass fractions) to the values of f , fs0 2 , and H ∗ . Note that the scaled mixture fraction variance is used for tabulation, where fs0 2 is defined as 02

fs

f 02 = 0.25f (1 − f )

(14.2-1)

Equations 14.1-4, 14.1-5, and 14.1-27 (for non-adiabatic systems) are solved in FLUENT to obtain local values of f , f 0 2 , and H ∗ .

prePDF:

1 Integration: φ = ∫ p(ƒ ) φ ( ƒ, H*)d ƒ i i o

Look-up Table

φ i = φi ( ƒ, ƒs ′ , H*) 2

FLUENT:

1. Solve ƒ, ƒ ′ , H* 2. Look up Scalars φi 2

Figure 14.2.1: Separation of Computational Tasks Between FLUENT and prePDF for a Single-Mixture-Fraction Case

14.2.2

Two-Mixture-Fraction Approach

For the two-mixture-fraction (secondary stream) case, the preprocessor prePDF calculates the instantaneous values for the temperature, density, and species mass fractions (Equation 14.1-12 or 14.1-15) and stores them in the look-up tables. For the adiabatic case with two mixture fractions, the look-up tables contain ρ, T , and Yi as functions of the fuel mixture fraction and the secondary partial fraction. For the non-adiabatic case


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with two mixture fractions, the 3D look-up table contains the physical properties as functions of the fuel mixture fraction, the secondary partial fraction, and the instantaneous enthalpy. The PDFs p1 and p2 of the fuel mixture fraction and the secondary partial fraction, respectively, are calculated inside FLUENT from the values of the solved mixture fractions and their variances. The PDF integrations for calculating the mean values for the properties are also performed inside FLUENT (using Equation 14.1-18 or 14.1-29, together with Equation 14.1-20 or its non-adiabatic equivalent). The instantaneous values required in the integrations are obtained from the look-up tables.

! Note that the computation time in FLUENT for a two-mixture-fraction case will be much greater than for a single-mixture-fraction problem since the PDF integrations are being performed in FLUENT rather than in prePDF. This expense should be carefully considered before choosing the two-mixture-fraction model. Also, it is usually expedient to start a two-mixture-fraction simulation from a converged single-mixture-fraction solution. Figure 14.2.2 illustrates the division of labor between prePDF and FLUENT for the twomixture-fraction case. prePDF: Calculation: φ = φ (f fuel ,p ,H*) sec i i

Look-up Table φ = φ (f fuel ,p ,H*) sec i i

FLUENT: Š2

Š2 1. Solve ffuel ,ffuel ,psec ,psec ,H* 2. Look up scalars φ i 3. Compute p1 (f fuel)

4. Compute p2 (psec ) 5. Compute φi

Figure 14.2.2: Separation of Computational Tasks Between FLUENT and prePDF for a Two-Mixture-Fraction Case

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14.2.3

The Look-Up Table Concept

Look-Up Tables for Adiabatic Systems Figure 14.2.3 illustrates the concept of the look-up tables generated by prePDF for a single-mixture-fraction system. Given FLUENT’s predicted value for f and f 0 2 at a point in the flow domain, the time-averaged mean value of mass fractions, density, or temperature (φi ) at that point can be obtained from the table. FLUENT first uses Equation 14.2-1 to compute the scaled mixture fraction variance fs0 2 because the single-mixture-fraction look-up tables contain property data as a function of f and fs0 2 , rather than f and f 0 2 . The table, Figure 14.2.3, is the mathematical result of the integration of Equation 14.1-17. There is one look-up table of this type for each scalar of interest (species mass fractions, density, temperature). In adiabatic systems, where the instantaneous enthalpy is a function only of the instantaneous mixture fraction, a two-dimensional look-up table, like that in Figure 14.2.3, is all that is required. Scalar Value

Scaled Variance

Mean Mixture Fraction

Figure 14.2.3: Visual Representation of a Look-Up Table for the Scalar φi as a Function of f and f 0 2 in Adiabatic Single-Mixture-Fraction Systems

For a system with two mixture fractions, there will be a look-up table for each instantaneous scalar property φi as a function of the fuel mixture fraction ffuel and the secondary partial fraction psec (Equation 14.1-12), as shown in Figure 14.2.4. The look-up table structure is summarized in Table 14.2.1.

3D Look-Up Tables for Non-Adiabatic Systems In non-adiabatic systems, where the enthalpy is not linearly related to the mixture fraction, but depends also on wall heat transfer and/or radiation, a look-up table is required for each possible enthalpy value in the system. The result is a three-dimensional look-up


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Instantaneous Scalar Value

Secondary Partial Fraction

Fuel Mixture Fraction

Figure 14.2.4: Visual Representation of a Look-Up Table for the Scalar φi as a Function of ffuel and psec in Adiabatic Two-Mixture-Fraction Systems

table, as illustrated in Figure 14.2.5, which consists of layers of two-dimensional tables, each one corresponding to the normalized heat loss or gain. The first layer or slice corresponds to the maximum heat loss for the system, where all the points in the look-up table are at the minimum temperature defined in the problem setup. The maximum slice corresponds to the heat gain that occurs when all points have reached the maximum temperature defined. The zero heat loss/gain slice corresponds to adiabatic operation. Slices interpolated between the adiabatic and maximum slices correspond to heat gain, and those interpolated between the adiabatic and minimum slices correspond to heat loss. The three-dimensional look-up table allows FLUENT to determine the value of each mass fraction, density, and temperature from calculated values of f , f 0 2 , and H ∗ . This threedimensional table is the visual representation of the integral in Equation 14.1-26. For two-mixture-fraction problems, the 3D look-up table allows FLUENT to determine the instantaneous values for the scalar properties from instantaneous values of ffuel , psec , and H ∗ . The three-dimensional table is the visual representation of Equation 14.1-28. These instantaneous values are used to perform the integration of Equation 14.1-29. See Table 14.2.1 for a summary of the look-up table structure.

Summary of Look-Up Table Formats Table 14.2.1 summarizes the look-up table format for different types of non-premixed models.

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normalized heat loss/gain

n+1

normalized heat loss/gainn

normalized heat loss/gainn-1

Scalar Value

Scaled Variance

Mean Mixture Fraction

Figure 14.2.5: Visual Representation of a Look-Up Table for the Scalar φi as a Function of f and f 0 2 and Normalized Heat Loss/Gain in Non-Adiabatic Single-Mixture-Fraction Systems


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Instantaneous Scalar Value

n+1

normalized heat loss/gain n


n-1

Secondary Partial Fraction Fuel Mixture Fraction

Figure 14.2.6: Visual Representation of a Look-Up Table for the Scalar φi as a Function of ffuel , psec , and Normalized Heat Loss/Gain in Non-Adiabatic Two-Mixture-Fraction Systems

Table 14.2.1: Look-Up Table Formats Type of Model Adiabatic Non-Adiabatic single mixture fraction f , fs0 2 f , fs0 2 , H ∗ two mixture fractions ffuel , psec ffuel , psec , H ∗

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14.3 User Inputs for the Non-Premixed Equilibrium Model

14.3

User Inputs for the Non-Premixed Equilibrium Model

A description of the user inputs (in prePDF and FLUENT) for the non-premixed equilibrium model is provided in the following sections: • Section 14.3.1: Problem Definition Procedure in prePDF • Section 14.3.2: Informational Messages and Errors Reported by prePDF • Section 14.3.3: Non-Premixed Model Input and Solution Procedures in FLUENT • Section 14.3.4: Modeling Liquid Fuel Combustion • Section 14.3.5: Modeling Coal Combustion

14.3.1

Problem Definition Procedure in prePDF

As illustrated in Figures 14.2.1 and 14.2.2, the solution of chemically reacting flows using the non-premixed equilibrium approach begins with the problem definition in prePDF. For a single-mixture-fraction problem, you will perform the following steps in prePDF: 1. Define the chemical species to be considered in the reacting system model and choose the chemical description of the system. The default equilibrium chemistry option should invariably be used. If you are modeling a mixing problem without reaction, or if a solution cannot be obtained with the equilibrium option and alternate species components are not acceptable, you may want to use the infinitely fast chemistry option. 2. Indicate whether or not the problem is adiabatic. 3. Choose the PDF (probability density function) shape that will be used to describe the turbulent fluctuations in the mixture fraction. The default Beta PDF should be selected unless you have a special reason to use the double-delta PDF. 4. Compute the look-up table, containing mean (time-averaged) values of species mass fractions, density, and temperature as a function of mean mixture fraction, mixture fraction variance, and enthalpy. The contents of this look-up table will reflect your preceding inputs describing the turbulent reacting system. The look-up table is the output of prePDF. It is the stored result of the integration of Equations 14.1-17 (or 14.1-26) and 14.1-19. The look-up table will be used in FLUENT to determine mean species mass fractions, density, and temperature from the values of mixture fraction (f ), mixture fraction variance (f 0 2 ), and enthalpy (H ∗ ) as they are computed during the FLUENT calculation of the reacting flow. See Section 14.2 and Figures 14.2.3 and 14.2.5.


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For a problem that includes a secondary stream (and, therefore, a second mixture fraction), you will perform the first three steps listed above for the single-mixture-fraction approach, and then prepare a look-up table of instantaneous properties using Equation 14.1-12 or 14.1-15. The following step-by-step procedure explains how to use prePDF, taking you through the problem definition procedure and explaining how your inputs are used.

Step 1: Start prePDF The way you start prePDF will be different for UNIX and Windows systems. The installation process (described in the separate installation instructions for your computer type) is designed to ensure that the prePDF program is launched when you follow the appropriate instructions. If it is not, consult your computer systems manager or your Fluent support engineer. Starting prePDF on a UNIX System On a UNIX machine, type prepdf at the command prompt. Starting prePDF on a Windows System For a Windows system, there are two ways to start prePDF: • Click on the Start button, select the Programs menu, select the Fluent.Inc menu, and then select the prePDF program item. (Note that if the default Fluent.Inc program group name was changed when prePDF was installed, you will find the prePDF menu item in the program group with the new name that was assigned, rather than in the Fluent.Inc program group.) • Start from an MS-DOS Command Prompt window by typing prepdf at the prompt. Before doing so, however, you must first modify your user environment so that the MS-DOS Command utility will find prepdf. You can do this by selecting the program item “Set Environment”, which is also found in the Fluent.Inc program group. This program will add the Fluent.Inc directory to your command search path.

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The Thermodynamic Database prePDF uses a thermodynamic database [125] and must be able to access the database file, THERMO.DB. This file must be present in the directory where you run prePDF, or it must be accessed through an environment variable, THERMODB, which points to the location of this file. In most installations, you will be running prePDF using procedures supplied by Fluent Inc. and these procedures will set this environment variable for you.

Step 2: Allocate Memory The amount of memory used by prePDF cannot be changed once it has been allocated, without restarting the application. You must, therefore, take care to allocate enough memory for the maximum number of points in the PDF table, species, and flamelets that you are planning to use. The parameters for which you can modify memory allocation are as follows: Maximum Number of Species is the maximum number of species in the PDF table. The default value is 20, and this parameter can be increased up to a value of 65. Maximum Number of f-mean Points is the maximum number of mixture fraction points in the PDF table. The default value is 45, and this parameter can be increased up to a value of 100. Maximum Number of f-var Points is the maximum number of mixture fraction variance points in the PDF table. The default value is 22, and this parameter can be increased up to a value of 30. Maximum Number of Enthalpy Points is the maximum number of enthalpy points in the PDF table. The default value is 45, and this parameter can be increased up to a value of 100. Maximum Number of Flamelets is the maximum number of flamelets in the flamelet model. The default value is 20, and this parameter can be increased up to a value of 30. You can set these parameters in the Memory Allocation panel (Figure 14.3.1). Setup −→Memory Allocation... When you click Apply, memory will be allocated for these parameters. If you need to allocate more memory later in the setup process, you will need to save an input file, exit prePDF, and restart. Then, allocate the appropriate amount of memory, read the input file into prePDF, and continue the problem setup. Note that, if you read an input file or PDF file without first allocating memory, prePDF will allocate memory based on the number of species and points specified in the file. If


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Figure 14.3.1: The Memory Allocation Panel in prePDF

the number is less than the default allocation, the default memory will be allocated. If it is more, memory adequate for the number of species and points in the file will be allocated.

! Note that memory allocation in prePDF is not available on Linux platforms. Step 3: Initialize the Problem Definition Once you have allocated memory, your first task in prePDF is to define the type of reaction system and reaction model that you intend to use. This includes selection of the following options: • Addition of a secondary stream • Partially premixed model option (see Chapter 16) • Adiabatic or non-adiabatic modeling options (see Section 14.1.2) • Equilibrium chemistry model or stoichiometric reaction (mixed-is-burned) model (see Section 14.1.2)

!

Procedures for setting up flamelet PDF models are described in Section 14.4.6. • Beta PDF or Double-Delta PDF (see Section 14.1.2) • Empirically defined fuel and/or secondary stream composition Your subsequent inputs and the inputs that prePDF will expect from you depend on these choices.

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You can make these model selections using the Define Case panel (Figure 14.3.2). Setup −→ Case...

Figure 14.3.2: The Define Case Panel in prePDF Each of these modeling choices is described in detail below. Be sure to click Apply after completing your inputs. Enabling a Secondary Inlet Stream If you are modeling a system consisting of a single fuel and a single oxidizer stream, you do not need to enable a secondary stream in your PDF calculation. As discussed in Section 14.1.2, a secondary stream should be enabled if your PDF reaction model will include any of the following: • two dissimilar gaseous fuel streams: In these simulations, the fuel stream defines one of the fuels and the secondary stream defines the second fuel. • mixed fuel systems of dissimilar gaseous and liquid fuel: In these simulations, the fuel stream defines the gaseous fuel and the secondary stream defines the liquid fuel (or vice versa). • mixed fuel systems of dissimilar gaseous and coal fuels: In these simulations, you can use the fuel stream or the secondary stream to define either the coal or the


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gaseous fuel. See Section 14.3.5 regarding coal combustion simulations with the non-premixed combustion model. • mixed fuel systems of coal and liquid fuel: In these simulations, you can use the fuel stream or the secondary stream to define either the coal or the liquid fuel. See Section 14.3.5 regarding coal combustion simulations with the non-premixed combustion model. • coal combustion: Coal combustion can be more accurately modeled by using a secondary stream. The fuel stream must define the char and the secondary stream must define the volatile components of the coal. See Section 14.3.5 regarding coal combustion simulations with the non-premixed combustion model. • a single fuel with two dissimilar oxidizer streams: In these simulations, the fuel stream defines the fuel, the oxidizer stream defines one of the oxidizers, and the secondary stream defines the second oxidizer.

! Using a secondary stream substantially increases the calculation time for your simulation since the multi-dimensional PDF integrations are performed in FLUENT at run-time. Choosing Adiabatic or Non-Adiabatic Options You should use the non-adiabatic modeling option if your problem definition in FLUENT will include one or more of the following: • radiation or wall heat transfer • multiple fuel inlets at different temperatures • multiple oxidant inlets at different temperatures • flue gas recycle • liquid fuel, coal particles, and/or heat transfer to inert particles Note that the adiabatic model is a simpler model involving a two-dimensional look-up table in which scalars depend only on f and f 0 2 (or on ffuel and psec ). If your model is defined as adiabatic, you will not need to solve the enthalpy equation in FLUENT and the system temperature will be determined directly from the mixture fraction and the fuel and oxidant inlet temperatures. The non-adiabatic case will be more complex and more time-consuming to compute, requiring the generation of three-dimensional look-up tables in prePDF. However, the non-adiabatic model option allows you to include the types of reacting systems described above. Select Adiabatic or Non-Adiabatic under Heat transfer options in the Define Case panel.

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Using the Adiabatic Calculation to Determine Inputs to the Non-Adiabatic Model Even if your FLUENT model will ultimately need to include non-adiabatic effects, you may benefit from starting the analysis with an adiabatic calculation in prePDF. This simpler calculation can be used to fine-tune the inputs to the non-adiabatic model, identifying the peak temperature that needs to be considered in the non-adiabatic case and identifying which chemical species are significant and need to be considered. Thus the adiabatic prePDF calculation provides you with an understanding of the system that can help you to develop an efficient non-adiabatic model. Choosing the Chemistry Model In general, the equilibrium chemistry model is recommended over the stoichiometric reaction model. In this approach the concentration of species of interest are determined from the mixture fraction using the assumption of chemical equilibrium (see Section 14.1.2). With this model, you can include the effects of intermediate species and dissociation reactions, producing more realistic predictions of flame temperatures in combustion models. In contrast, the stoichiometric reaction (mixed-is-burned) modeling option provides a less accurate single-step description of the system chemistry. When you choose the equilibrium chemistry option, you will have the opportunity, in Step 8, to use a “partial equilibrium” model. Select Equilibrium Chemistry or Stoichiometric Reaction under Chemistry models in the Define Case panel.

! If you want to model non-equilibrium chemistry, you should use the flamelet modeling approach described in Section 14.4. Procedures for using this model is presented in Section 14.4.6. Choosing the Chemistry Model for Non-Reacting Systems If you are using the non-premixed combustion model to consider a non-reacting system, choose the Stoichiometric Reaction option in the Define Case panel. When you are prompted to input the stoichiometric coefficients for each species (Step 7, below), simply input zeros for all species. Choosing the PDF Shape The shape of the PDF you select will have some impact on the results you obtain. In general, the default β-function PDF shape matches experimental observations of f fluctuations much better than the double-delta function, and should be the one used. The double-delta function, on the other hand, is more efficient computationally during the generation of look-up tables in prePDF. Since the look-up table generation is a preprocessing step, the double-delta PDF should be used only in special circumstances.


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When a secondary stream is included, you will not choose the PDF type in prePDF. This step will occur in FLUENT instead. Select Delta PDF or Beta PDF under PDF models in the Define Case panel. Empirical Definition of the Fuel Stream(s) The empirical definition option provides an alternative method for defining the composition of the fuel or secondary stream. When you do not select this option, you will define which chemical species are present in each stream and the mass or mole fraction of each species, as described below, in Step 5. When an empirically defined fuel or secondary stream is used, you will follow a different procedure for determining the chemical composition of the stream: 1. Define the list of chemical species present in the stream (following the suggestions below, in Step 4), using the Define Species panel. The choice of species is not altered by your use of the empirical definition option, except that you must also include atomic elements (C, H, N, S, and O) and combustion products (CO2 and H2 O) which are used for the calculation of the lower heating value of the fuel. 2. In the Composition panel (Step 5, below), you will not input mass or mole fractions for each species. Instead, you will input the atomic composition of the stream (atom mole fractions of C, H, N, S, and O), its lower heating value, and its mean specific heat. prePDF will compute the mole fraction of each chemical species from these inputs. The heat of formation of an empirical fuel stream is calculated from the heating value and the atomic composition. The fuel inlet temperature and fuel specific heat are used to calculate the sensible enthalpy. prePDF performs an equilibrium calculation, using the atomic composition and enthalpy, and returns the equilibrium molar species composition and temperature of the fuel. Note that the empirical definition option is available only with the full equilibrium chemistry model. It cannot be used with the stoichiometric or partial equilibrium models, since equilibrium calculations are required for the determination of the fuel composition. If your empirically defined fuel is a gaseous fuel, you should be aware of the modeling issues related to gas-phase fuel inlet temperature in full equilibrium systems (see Step 8, below). The option for defining an empirical fuel stream is particularly useful for coal combustion simulations (see Section 14.3.5) or for simulations involving other complex hydrocarbon mixtures. Because empirical fuels use the full equilibrium model, which impacts your flow boundary conditions at gas-phase fuel inlets, the empirical definition option is not generally recommended for gaseous fuels.

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Turn on Fuel stream or Secondary stream under Empirically Defined Streams in the Define Case panel to define a fuel or secondary stream empirically.

Step 4: Define the Chemical Species to be Considered One of your most important modeling inputs will be the selection of species to be included in the description of the reacting system. All species that you include must exist in the chemical database and you must enter their names in the same format used in the database. You can include a maximum of the number of species you entered in the Memory Allocation panel (see Step 2 above) when you use the non-premixed model. (Note the additional requirements mentioned below for defining species when you have an empirically defined fuel stream.) The number of species and their names are entered using the Define Species panel (Figure 14.3.3). Setup −→ Species −→ Define...

Figure 14.3.3: The Define Species Panel in prePDF The steps for defining your species are as follows: 1. Specify the number of species you will define in the Maximum # of Species field. (You can change the maximum number of species at any time by incrementing the counter.) 2. Define your first species by selecting it in the Database Species drop-down list. This list contains a complete listing of the species in the database. The species name will appear in the Defined Species list.


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3. Increase the Species # field (either use the counter arrow or type in the new value and press ) and select the next species from the Database Species list. Continue in this manner until all of the species you want to include are shown in the Defined Species list. 4. When you are satisfied with your selections, click Apply and close the panel. If you need to alter a species selection, click on the species name in the Defined Species list and then select a new species from the Database Species drop-down list. Choosing Species for Empirically Defined Streams For an empirically defined fuel or secondary stream, you must choose the constituent elements in addition to the species that make up the chemical system. The elements allowed are C, H, N, S, and O. Also, the species CO2 and H2 O must be selected since they are the combustion products for the calculation of the lower caloric (heating) value of the fuel. If you are considering S (sulfur), you will also need to add SO2 in the species list. Including Solid and Liquid Species Solid and liquid species can be included in the thermodynamic calculations as well as gases. They are indicated by an L or an S in parentheses after the species name. If you select a solid or liquid species, you must define the species density in the Condensed Species Densities panel (Figure 14.3.4). Setup −→ Species −→Density...

Figure 14.3.4: The Condensed Species Densities Panel in prePDF In the panel, choose each solid or liquid species in the Defined Species list and enter its Density. Note that this density should be the density of the condensed phase species and

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not the apparent density of the particles as defined in FLUENT. For example, in coal combustion, you should enter the density of C(s) and not the apparent density of the coal. When you have set the density for all solid and liquid species, click Apply and close the panel. Guidelines on Choosing the Species to Include In the combustion of simple hydrocarbons, many species and radicals have been identified. Although you could, in principle, define an equilibrium system that includes a large number of species, you should limit your system description to those species that are of the most significance. The following suggestions may be helpful in the definition of the system chemistry: • In high-temperature flames (i.e., T > 2000 K) include radicals such as H, O, and OH. These radicals are produced in dissociation reactions at high temperatures and can have a significant impact on peak flame temperatures. • For heavy hydrocarbon fuels (e.g., fuel oils), lighter hydrocarbons (CH4 , C2 H4 , etc.) will be formed in the rich mixture as a result of pyrolysis and gasification reactions. • For coal combustion, volatiles may be represented by a mixture of CH4 (or a heavier hydrocarbon) and CO. Char in the coal should be represented by C(s). Follow the other general guidelines outlined here to determine the other species that should be included in the combustion system. • If you want to consider the water content in a coal fuel, include H2 O(l). Include the liquid water content as part of the fuel composition. Alternately, the water content can be included using vapor phase H2 O. (See Section 14.3.5 for additional information.) • If soot formation is of interest, C(s) can be included in the fuel stream definition. However, you should note that the equilibrium model will not represent the complex finite rate chemistry which is usually associated with soot formation.

!

Care should be taken to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should be selected only if you are using the empirically-defined input method. • Combustion products should always include CO2 and H2 O. In addition, you may want to include CO and H2 . Note that H2 should not be included alone as it is produced in the water-gas shift reaction, CO + H2 O −→ CO2 + H2 . • If your fuel composition is known empirically (e.g., C0.9 H3 O0.2 ), use the option for an empirically-defined stream (see Step 3). • For hydrocarbon combustion systems, it is recommended that you include C(s) and H2 O(l).


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• If you wish to include the sulfur that may be present in a hydrocarbon fuel, note that this may hinder the convergence of the equilibrium solver, especially if the concentration of sulfur is small. It is therefore recommended that you include sulfur in the calculation only if it is present in considerable quantities. The simplest way to model sulfur is to represent it as SO2 and S(l), where SO2 will be formed in oxygen-rich mixtures and S(l) will be formed in fuel-rich mixtures. A more elaborate description of a sulfur-containing fuel-oxidizer system could include SO2 , H2 S, COS, S(l), CS2 , and S2 . It is extremely important that your choice of species provide a sensible description of the system chemistry. If this is not the case, the equilibrium calculation may fail to converge or may produce incorrect results. The species included in the equilibrium calculation should probably not include NOx species, as the NOx reaction rates are slow and should not be treated using an equilibrium assumption. Instead, the NOx concentration is predicted most accurately using the FLUENT NOx postprocessor, where finite-rate kinetics are included. (See Section 18.1.) Note that it is not important to include NOx predictions with the combustion simulation since the NOx species are present at low concentrations and have little impact on the combustion process. Modifying the Database If you want to include a new species in your reacting system that is not available in the chemical database, you can add it to the database files, THERMO.DB (used by prePDF) and thermodb.scm (used by FLUENT). The format for THERMO.DB is detailed in [125]. You can generate the thermodb.scm file in prePDF using the File/Write/Thermodb... menu item. File −→ Write −→ Thermodb... FLUENT will recognize the new species if the thermodb.scm file is in the directory where FLUENT is started. To permanently store the new species in the standard database, copy the new species data from the generated thermodb.scm file to the default thermodb.scm file, as described in Section 14.5. If you choose to modify the standard database files, you should create copies of the original files.

Step 5: Define the Fuel and Oxidizer (and Secondary-Stream) Compositions After defining the species that will be considered in the reaction system, you must define their mole or mass fractions at the fuel and oxidizer inlets and at the secondary inlet, if one exists. (If you choose to define the fuel or secondary stream composition empirically, you will instead enter the parameters described at the end of this step.) For the

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example shown in Figure 14.1.12c, for example, the fuel inlet consists of 60% CH4 , 20% CO, 10% CO2 , and 10% C3 H8 . This information is input using the Composition panel (Figure 14.3.5). Setup −→ Species −→ Composition...

Figure 14.3.5: The Composition Panel in prePDF The procedure for defining mole or mass fractions is as follows: 1. Under Stream, select the Fuel, Oxidiser, or Secondary option. 2. Under Specify Composition In..., indicate whether you want to enter Mole Fractions or Mass Fractions. 3. Select a species from the Defined Species list and then enter its mole or mass fraction in the selected stream (fuel, oxidizer, or secondary) by typing in the Species Fraction field. Repeat this process for all species in the Defined Species list until you have set all mole or mass fractions for the selected stream.


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4. Input the mole or mass fractions for each of the other streams by selecting the appropriate option (i.e., one that you did not choose in step 1) and repeating step 3. 5. When you are satisfied with all the settings, click the Apply button and close the panel. You can check the current setting for a species in a particular stream by selecting the stream and choosing the species name in the Defined Species list. Un-Normalized Mole or Mass Fraction Inputs If you input un-normalized mole or mass fractions when you are defining the compositions, prePDF will scale your inputs so that they sum to unity, and inform you (in an Information dialog box) that the mole or mass fractions will be normalized. Defining the Fuel Composition for Liquid Fuels If your FLUENT model considers combustion of fuel that is evaporated from liquid droplets, the composition of the vaporized fuel should be defined in prePDF. Defining the Fuel Composition for Coal Combustion If your FLUENT model involves coal combustion, the fuel and secondary stream compositions can be input in one of several ways. You can use a single mixture fraction (fuel stream) to represent the coal, defining the fuel composition as a mixture of volatiles and char (solid carbon). Alternately, you can use two mixture fractions (fuel and secondary streams), defining the volatiles and char separately. In two-mixture-fraction models for coal combustion, the fuel stream represents the char and the secondary stream represents volatiles. See Section 14.3.5 for more detailed descriptions of modeling options and input procedures for coal combustion. Composition Inputs for Empirically-Defined Fuel Streams As mentioned in Step 3, you can define the composition of a fuel stream (i.e., the standard fuel or a secondary fuel) empirically instead of by specifying mole or mass fractions. For an empirically-defined stream, you will enter atom fractions, the lower caloric (heating) value of the fuel (with the combustion product assumed to be water vapor and CO2 ), and the mean specific heat of the fuel. The steps are as follows: 1. Enable the Fuel (or Secondary) option under Stream. 2. Select each element in the Defined Species list and enter its Atom Fraction. 3. Enter the Lower Caloric Value and Specific Heat of the Fuel (or Secondary) stream.

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4. When you are satisfied with all the settings, click the Apply button and close the panel. Equilibrium Corrections to Fuel Composition Note that for the full equilibrium option (i.e., when the fuel rich limit set in Step 8 is 1), prePDF will also perform an equilibrium calculation for the fuel stream inputs (e.g., at f = 1). As a result, you may find that prePDF will modify your inputs of fuel composition and temperature if the fuel system, as defined by your inputs, is not at equilibrium. For example, if you define the fuel as 0.5 CO and 0.5 CH4 at 300 K, prePDF will correct the fuel to 0.35 C(S), 0.14 CH4 , 0.009 CO, 0.1552 CO2 , and 0.3596 H2 at 751 K, which is the corresponding equilibrium composition. Equilibrium calculations will always be used when you define your fuel empirically, since only the full equilibrium method is available for such cases. If you define the fuel using species mole or mass fractions, the correction will occur only when the full equilibrium option is used. If your fuel is a liquid or solid (coal) fuel, the equilibrium correction will have no impact on your model setup.

! For gas-phase fuels, the effect of the equilibrium calculation on the fuel composition and temperature is an important modeling issue that impacts your flow boundary conditions at gas-phase fuel inlets in FLUENT. If you are modeling a gaseous fuel, and you are using the full equilibrium model or empirical definition of the fuel, you should review the additional information on this topic that is included under Step 8, below.

Step 6: Define Operating Conditions The thermodynamic operating conditions of your reacting system are required for construction of the look-up table and computation of the equilibrium chemistry model. These conditions are input using the Operating Conditions panel (Figure 14.3.6). Setup −→ Operating Conditions... Each of these inputs is described below. Remember to click the Apply button when you are done. Absolute Pressure is used to extract appropriate property data from the database and in the calculation of chemical equilibrium via the minimization of the Gibbs free energy. Min. Temperature is used to determine the lowest temperature for which the look-up tables are generated (see Figure 14.2.5). Your input should correspond to the minimum temperature expected in the domain (e.g., an inlet or wall temperature). The minimum temperature should be set 10–20 K below the minimum system temperature. This option is available only when the Equilibrium Chemistry model is selected in the Define Case panel.


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Figure 14.3.6: The Operating Conditions Panel in prePDF

Max. Temperature is used to determine the highest temperature for which the look-up tables are generated (see Figure 14.2.5). It should be set to a value about 100 K above the peak temperature predicted by prePDF for the adiabatic system calculation. Note that if your input of the peak temperature is too low, prePDF’s calculation of the look-up tables will fail. This option is available only when the Equilibrium Chemistry model is selected in the Define Case panel. Inlet Temperature contains temperature inputs for the fuel, oxidant, and secondary stream inlets: Fuel is the temperature of the fuel inlet in your model. In adiabatic simulations, this input (together with the oxidizer inlet temperature) determines the inlet stream temperatures that will be used by FLUENT. In non-adiabatic systems, this input should match the inlet thermal boundary condition that you will use in FLUENT (although you will enter this boundary condition again in the FLUENT session). If your FLUENT model will use liquid fuel or coal combustion, define the inlet fuel temperature as the temperature at which vaporization/devolatilization begins (i.e., the Vaporization Temperature specified for the discrete-phase material—see Section 21.11). For such non-adiabatic

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systems, the inlet temperature will be used in prePDF only to adjust the lookup table grid (e.g., the discrete enthalpy values for which the look-up table is computed). Note that if you have more than one fuel inlet, and these inlets are not at the same temperature, you must define your system as non-adiabatic. In this case, you should enter the fuel inlet temperature as the value at the dominant fuel inlet.

!

prePDF uses your input of fuel and oxidizer inlet temperatures to determine the fuel and oxidizer enthalpies. When the full equilibrium model is used (rich limit of 1.0), the equilibrium calculation performed at f = 1 may result in a modified fuel composition and temperature. If you are using the full equilibrium model for a gaseous fuel (or if you are using an empirically defined gaseous fuel), you should be aware of how this equilibrium adjustment of the fuel temperature impacts your fuel inlet boundary conditions in FLUENT. See Step 8, below. Oxidiser is the temperature of the oxidizer inlet in your model. The issues raised in the discussion of the input of the fuel inlet temperature (directly above) pertain to this input as well. Secondary is the temperature of the secondary stream inlet in your model. (This item will appear only when you have defined a secondary inlet.) The issues raised in the discussion of the input of the fuel inlet temperature (directly above) pertain to this input as well. Nonadiabatic Flamelet Temperature Limits contains inputs for the temperature limits of a non-adiabatic flamelet system. These inputs are required only if you are using the laminar flamelet model and you have defined your case as non-adiabatic. See Section 14.4.6 for more information on flamelet inputs.

Step 7: Define the Reaction Stoichiometry The input of the reaction stoichiometry is required when you choose to use the stoichiometric reaction (mixed-is-burned) chemistry model. If you are using the partial equilibrium approach (rich limit defined) you may also choose to define the system stoichiometry at the rich limit (see below). In either case, your input of reaction stoichiometry defines a simple one-step reaction between fuel species and oxidant species. Consider, for example, the following very simple system: CH4 + 2O2 → CO2 + 2H2 O prePDF requires that you input the molar stoichiometric coefficients as follows for this simple system: 1 for CH4 , 2 for O2 , −1 for CO2 , and −2 for H2 O. Note the convention that the product stoichiometry is entered with a negative number.


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You can input the coefficients using the Stoichiometric Coefficients panel (Figure 14.3.7). Setup −→ Species −→ Stoichiometry...

Figure 14.3.7: The Stoichiometric Coefficients Panel in prePDF Select each species in the Defined Species list and enter its stoichiometric coefficient in the Coefficient field. When you have set the coefficients for all species, click Apply and close the panel. Input of Stoichiometry for Fuel Mixtures If your fuel stream consists of more than one species, you will need to input the stoichiometry for the composite reaction. Suppose, for example that your fuel contains 40% CH4 and 60% CO by volume. Two moles of O2 are required for each CH4 and 0.5 moles of O2 are required for each mole of CO. The molar stoichiometric coefficient for O2 would thus be input as (0.4 × 2) + (0.6 × 0.5) = 1.1. The molar stoichiometry for each product species would be determined in a similar fashion. The final stoichiometry would then be (0.4CH4 + 0.6CO) + 1.1O2 → CO2 + 0.8H2 O

(14.3-1)

Input of Stoichiometry for Two Fuel or Oxidant Streams Defining stoichiometry for a two-mixture-fraction problem is similar to that for a singlemixture-fraction problem with a single, mixed fuel stream (described above). Consider, for example, the following two-fuel system: one inlet of CO, one inlet of CH4 , and one inlet of O2 . A single reaction will be defined: CH4 + CO + 2.5O2 → 2CO2 + 2H2 O

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(14.3-2)



Input of Stoichiometry for Partial Equilibrium Calculations As described in Section 14.1.2, you can define a rich limit on the mixture fraction when the equilibrium chemistry option is used. Input of the rich limit is accomplished using the Solution Parameters panel, described below. For mixture fraction values above this limit, prePDF will suspend the equilibrium chemistry calculation and will compute the composition based on mixing of the fuel with the composition at the rich limit. When you choose this partial equilibrium approach, you can let prePDF compute the composition at the rich limit using equilibrium or you can input the stoichiometry to be assumed at the rich limit. Generally, you should choose to use the equilibrium calculation of the composition at the rich limit unless you have experimental data (e.g., laminar flame data) that you want to represent through the input of stoichiometric coefficients.

Step 8: Define Parameters Used in Creation of the Look-Up Table prePDF requires several inputs that are used in the creation of the look-up tables. Several of these inputs control the number and distribution of discrete values for which the lookup tables will be computed. These parameters are input using the Solution Parameters panel (Figure 14.3.8). Setup −→ Solution Parameters...

Figure 14.3.8: The Solution Parameters Panel in prePDF


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The solution parameters are as follows: Non-Adiabatic Model contains parameters related to non-adiabatic models Enthalpy Points is the number of discrete values of enthalpy at which the threedimensional look-up tables will be computed. This input is required only if you are modeling a non-adiabatic system. In general, you should choose the number of enthalpy points to be one and a half to two times the number of mean mixture fraction points considered. The default value of 31 enthalpy points may be sufficient for your model, or you may want to increase this number (up to a maximum of 45). The number of points required will depend on the chemical system that you are considering, with more points required in high heat release systems (e.g., hydrogen/oxygen flames). Fuel Mixture Fraction contains parameters related to the fuel mixture fraction: Fuel Mixture Fraction Points is the number of discrete values of f at which the lookup tables will be computed. For a two-mixture-fraction model, this value will also be the number of points used by FLUENT to compute the PDF if you select beta for the Probability Density Function in the Species Model panel (see Section 14.3.3). Increasing the number of points will yield a more accurate PDF shape, but the calculation will take longer. Automatic Distribution enables the automatic discretization of the fuel mixture fraction and its variance. This feature optimizes the distribution of the discrete mixture fraction values by clustering them around the peak temperature value. The automatic discretization is recommended in most cases. Distribution Center Point (available only when Automatic Distribution is disabled) determines the distribution of the requested number of discrete values of f . The requested number of points will be distributed on either side of the center point with more points concentrated near the center point and fewer at the endpoints. If the center point is defined as 0.5 (the default), the values will be distributed uniformly over the range between 0 and 1. Generally, you should choose this value to be on the rich side of the stoichiometric value of f . This will create more points (and hence better resolution and accuracy) in the stoichiometric range and below—where the calculation is most critical. Determination of the stoichiometric value of f is discussed below. Note that you should not set the center point above 0.8 or below 0.2. Mixture Fraction Variance Points is the number of discrete values of fs0 2 at which the look-up tables will be computed. The number of mixture fraction variance points should be roughly one-half the number of mean mixture fraction points requested. Lower resolution is required because the variation along the fs0 2 axis is, in general, slower than the variation along the f axis of the look-up tables.

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Secondary Partial Fraction contains parameters related to the (optional) secondary partial fraction: Secondary Partial Fraction Points is the number of discrete values of psec at which the look-up tables will be computed. Like Fuel Mixture Fraction Points, FLUENT will use the Secondary Partial Fraction Points to compute the PDF if you choose the beta PDF option (see Section 14.3.3) for a two-mixture-fraction model. A larger number of points will give a more accurate shape for the PDF, but with a longer calculation time. Automatic Distribution enables the automatic discretization of the secondary partial fraction and its variance. The automatic discretization is recommended in most cases. Distribution Center Point (available only when Automatic Distribution is disabled) determines the distribution of the requested number of discrete values of psec . The requested number of points will be distributed on either side of the center point with more points concentrated near the center point and fewer at the endpoints. If the center point is defined as 0.5 (the default), the values will be distributed uniformly over the range between 0 and 1. For an oxidant or non-reacting secondary stream, you should keep this default value. For a secondary fuel stream, you should generally choose this value to be on the rich side of the stoichiometric value of psec . This will create more points (and hence better resolution and accuracy) in the stoichiometric range and below—where the calculation is most critical. Determination of the stoichiometric value of fsec is discussed below. You can then use Equation 14.1-3 to determine the corresponding value for psec . Note that you should not set the center point above 0.8 or below 0.2. Equilibrium Chemistry Model contains parameters related to the equilibrium chemistry model (see Section 14.1.2). You will not set these if you have chosen the stoichiometry chemistry model or if you have used the empirical definition option for fuel composition. Fuel Rich Flamability Limit controls the equilibrium calculation for the fuel mixture fraction. A value of 1.0 for the rich limit implies that equilibrium calculations will be performed over the full range of mixture fraction. When you use a rich limit that is less than 1.0, equilibrium calculations are suspended whenever f or ffuel exceeds the limit. This “partial equilibrium” model is a useful approach in hydrocarbon combustion calculations, allowing you to bypass complex equilibrium calculations in the fuel-rich region. The efficiency of partial equilibrium will be especially important when your model is nonadiabatic, speeding up the preparation of the look-up tables. If you use a rich limit below 1.0, prePDF will ask if you want to define the reaction stoichiometry at the rich limit or if you would like the program to compute the rich limit composition using equilibrium chemistry:


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If you choose the automatic calculation, prePDF will determine the composition at the rich limit using the equilibrium calculation. If you do not choose the automatic calculation, you must input the molar stoichiometry at the rich limit using the Stoichiometric Coefficients panel (see Step 7, above). Secondary Rich Flamability Limit controls the equilibrium calculation for the secondary mixture fraction. If your secondary stream is not a fuel, you should keep the default value of 1. For a secondary fuel stream, you can consider modifying the value to use the “partial equilibrium model.” A value of 1.0 for the rich limit implies that equilibrium calculations will be performed over the full range of mixture fraction. When you input a rich limit that is less than 1.0, equilibrium calculations are suspended whenever fsec exceeds the limit. (Note that it is the secondary mixture fraction fsec and not the partial fraction psec that is used here.) See the description of the Fuel Rich Flamability Limit above for details. Equilibrium Calculations in Fuel Rich Mixtures Experimental studies and reviews [25, 238] have shown that although the fuel lean flame region approximates thermodynamic equilibrium, chemical kinetics will prevail under fuel rich conditions. Therefore, when using prePDF for non-empirically defined fuels, the partial equilibrium model is strongly recommended. As described above, this approach suspends the equilibrium calculations in the rich mixture. Guidelines on how to set the rich limit values are given below. If you are using the full equilibrium approach (rich limit of 1 or empirically defined fuel), you should be aware that prePDF will perform an equilibrium calculation for the fuel (e.g., at f = 1). The resulting equilibrium fuel composition and temperature will, in most cases, differ from your original inputs defining the fuel. This indicates that the fuel composition and temperature, as defined by you, were not at equilibrium conditions. When prePDF adjusts the fuel composition and temperature to new equilibrium values, you will receive a warning message:

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The purpose of this warning is to alert you that the fuel inlet temperature and composition have been modified to new equilibrium values. This information is important because it impacts how you will define gaseous fuel inlet boundary conditions in FLUENT, as follows. The new equilibrium fuel temperature and composition define the fuel density at gasphase fuel inlet boundaries in FLUENT. This equilibrium density should be used to compute the appropriate inlet velocity, preserving the desired mass flow rate of the fuel. You can determine the equilibrium fuel density using the VIEW-ALPHA/DENSITY text command in prePDF at the final discrete F-MEAN point (f = 1). In non-adiabatic systems, the density you should use is that on the enthalpy slice corresponding to your fuel inlet temperature. If your fuel inlet temperature is equal to the temperature you input in the Operating Conditions panel in prePDF, you should examine the density on the adiabatic enthalpy slice. If you have multiple fuel inlets at different inlet temperatures, you can perform an adiabatic calculation at each temperature to determine the equilibrium density.

! Although prePDF will compute a new equilibrium temperature for the fuel, you should use your original prePDF input of fuel inlet temperature when you define a gas-phase fuel inlet in FLUENT. FLUENT uses this original, non-equilibrium fuel temperature to compute the inlet fuel enthalpy. (This enthalpy is the same as that used in the prePDF equilibrium calculation.) Based on this inlet enthalpy, FLUENT will determine the equilibrium temperature, composition, and density at the fuel inlet. If you are modeling a liquid or coal fuel using the discrete phase model, the modified equilibrium fuel temperature and composition do not impact your inputs in FLUENT. Determining the Stoichiometric and Rich Limit Values of Mixture Fraction Determination of the rich limit mixture fraction is an important part of your inputs in the Solution Parameters panel. Generally, you should choose the rich limit to be equal to 1.5 to 2 times the stoichiometric mixture fraction: frich ≈ 2.0fs

(14.3-3)

The stoichiometric mixture fraction, in turn, can be computed from the air-to-fuel mass ratio, r, as described in Section 14.1.2 (Equation 14.1-10). Alternately, you can estimate


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the stoichiometric mixture fraction by examining the instantaneous temperature vs. mixture fraction predicted by prePDF for your adiabatic system. The maximum temperature will occur near the stoichiometric mixture fraction. The combustion of methanol in air provides an example of how you can compute the stoichiometric mixture fraction. Written in terms of molar stoichiometry, the reaction is CH3 OH + 1.5(O2 + 3.76N2 ) → CO2 + 2H2 O + 5.64N2

(14.3-4)

To compute the stoichiometric mixture fraction, first write the reaction on a mass basis, in terms of the stoichiometric air-to-fuel ratio, r, and the equivalence ratio, φ. The reaction becomes φ CH3 OH + r(O2 + 3.76N2 ) → (φ + r) Products

(14.3-5)

where r = 6.435. Using Equation 14.1-10, the stoichiometric mixture fraction (φ = 1.0) is then fs =

φ 1 = = 0.134 φ+r 7.435

(14.3-6)

and the fuel rich mixture fraction, taken at φ = 2.0, is frich =

2 = 0.237 8.435

(14.3-7)

Extension of this exercise to a fuel consisting of a mixture of hydrocarbons is straightforward, with Equation 14.3-4 simply taking on a more general form. Consider, for example, a fuel-air system in which the fuel is comprised of 60% CH4 and 40% CO: (0.6CH4 + 0.4CO) + z(O2 + 3.76N2 ) → xCO2 + yH2 O + 3.76zN2

(14.3-8)

After balancing this equation and solving for z, you can compute the air-to-fuel mass ratio and then compute the stoichiometric mixture fraction as described above. Rich Limit Values for Secondary Streams If the secondary stream is an oxidizer or an inert, the rich limit for the secondary stream should be set to 1. If it is a second fuel, the single fuel system analysis above applies, since the secondary rich limit is defined in terms of secondary mixture fraction, fsec (not secondary partial fraction, psec ).

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Step 9: Save Your Inputs When all of the preceding procedures are complete, you should save your inputs to an “input” file: File −→ Write −→ Input... This file contains all of your inputs defining the reaction system in prePDF. You will have the option to save either a binary (unformatted) file or a formatted (ASCII, or text) file. You can read and edit a formatted file, but it will require more storage space than the same file in binary format. Binary files take up less space and can be read and written by prePDF more quickly, but they cannot be transferred between all machine types.

Step 10: Compute the Look-Up Tables After saving your inputs, you can initiate the computation of the look-up tables by prePDF: Calculate −→PDF Table The computations performed in prePDF for a single-mixture-fraction calculation culminate in the discrete integration of Equation 14.1-17 (or 14.1-26) as represented in Figure 14.1.9 (or Figure 14.1.10). For a two-mixture-fraction calculation, prePDF will calculate the physical properties using Equation 14.1-28 or its adiabatic equivalent. These computations may take only a few moments for simple systems or they may require up to an hour for a complex system (e.g., non-adiabatic systems with 10 or more species). prePDF reports progress as the calculation proceeds. Below, sample output is shown for an adiabatic, single-mixture-fraction calculation:


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(*)- INITIALIZING AT ADIABATIC ENTHALPY LINE .................ADIABATIC CALCULATION...................... POINTS TO-GO EQUILIBRIUM DELTA-PDF 0 375 16 359 T(K) = 2004. F-MEAN = 0.04 F-VAR = .000 17 358 T(K) = 1386. F-MEAN = 0.04 F-VAR = .018 18 357 T(K) = 1108. F-MEAN = 0.04 F-VAR = .036 19 356 T(K) = 1053. F-MEAN = 0.04 F-VAR = .040 20 355 T(K) = 1053. F-MEAN = 0.04 F-VAR = .040 21 354 T(K) = 1053. F-MEAN = 0.04 F-VAR = .040 . . . 356 19 T(K) = 467. F-MEAN = 0.96 F-VAR = .040 357 18 T(K) = 467. F-MEAN = 0.96 F-VAR = .040 358 17 T(K) = 467. F-MEAN = 0.96 F-VAR = .040 359 16 T(K) = 467. F-MEAN = 0.96 F-VAR = .040 360 15 T(K) = 467. F-MEAN = 0.96 F-VAR = .040 . . . (*)- CALCULATION SUCCEEDED

After completing the equilibrium calculation at the specified number of mixture fraction points, prePDF reports that the calculation succeeded. The resulting look-up tables take the form illustrated in Figure 14.2.3 (or Figure 14.2.5, for non-adiabatic systems). These look-up tables can be plotted using the graphics tools available in prePDF, as described below in Step 12. Note that in non-adiabatic calculations, the report includes information on the enthalpy point currently considered:

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(*)- INITIALIZING ENTHALPY AT TEMPERATURE LIMITS

.................NON-ADIABATIC CALCULATION...................... POINTS TO-GO H-POINT EQUILIBRIUM DELTA-PDF 0 15375 8 15367 8 T(K) = 298. F-MEAN = 0.00 F-VAR = .000 9 15366 9 T(K) = 334. F-MEAN = 0.00 F-VAR = .000 10 15365 10 T(K) = 888. F-MEAN = 0.00 F-VAR = .000 11 15364 11 T(K) = 1391. F-MEAN = 0.00 F-VAR = .000 12 15363 12 T(K) = 1869. F-MEAN = 0.00 F-VAR = .000 13 15362 13 T(K) = 2334. F-MEAN = 0.00 F-VAR = .000 14 15361 14 T(K) = 2792. F-MEAN = 0.00 F-VAR = .000 15 15360 15 T(K) = 3243. F-MEAN = 0.00 F-VAR = .000

You may notice that non-adiabatic calculations terminate before the tabulated number of points under TO-GO is zero. This is simply because the final calculations, at mixture fraction equal to 1.0, do not include multiple variance points. For a two-mixture-fraction calculation, prePDF will print the following information during the calculation: (*)- INITIALIZING AT ADIABATIC ENTHALPY ...........ADIABATIC CALCULATION POINTS TO-GO EQUILIBRIUM 0 725 1 724 T(K) = 600. 2 723 T(K) = 1134. 3 722 T(K) = 1622. 4 721 T(K) = 2064. 5 720 T(K) = 2357. 6 719 T(K) = 2216. 7 718 T(K) = 1954. 8 717 T(K) = 1690. 9 716 T(K) = 1432.

/ SECONDARY STREAM............. PROGRESS-VARIABLES F-FUEL F-FUEL F-FUEL F-FUEL F-FUEL F-FUEL F-FUEL F-FUEL F-FUEL

= = = = = = = = =

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

P-SECND P-SECND P-SECND P-SECND P-SECND P-SECND P-SECND P-SECND P-SECND

= = = = = = = = =

0.000 0.014 0.029 0.045 0.062 0.081 0.100 0.121 0.143

The resulting look-up tables take the form illustrated in Figure 14.2.4 (or Figure 14.2.6, for non-adiabatic systems). These look-up tables can be plotted using the graphics tools available in prePDF, as described below. For a non-adiabatic calculation, the current enthalpy point will be shown as in the example output listed above for the non-adiabatic single-mixture-fraction calculation.


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Stability Issues in prePDF Complex chemistry and non-adiabatic effects may make the equilibrium calculation more time-consuming and difficult. In some instances the equilibrium calculation may even fail. You may be able to eliminate any difficulties that you encounter using one of the following techniques: • Try the calculation as an adiabatic system. Adiabatic system calculations are generally quite straightforward and can provide valuable insight into the optimal inputs to the non-adiabatic calculation. Using the adiabatic results, you can determine the maximum temperature expected and correct this important input to the non-adiabatic case. You can determine which species are important to the reacting system, and eliminate those that are unimportant. This information can be obtained by a simple review of the look-up tables generated by the adiabatic calculation. Selecting an appropriate temperature range and an appropriate list of chemical species to include will greatly simplify the non-adiabatic calculation. You might also simplify the non-adiabatic calculation by a better choice of the rich cut-off limit, as described in Step 8, and adjust the mixture fraction center point to capture the adiabatic temperature curve more adequately. • Try reducing the number of species considered. Simplify your model of the reacting system. If your system includes heavy hydrocarbons, be sure that you are including basic hydrocarbons such as CH4 in the system. Additional stability issues may arise for solid or heavy liquid fuels that have been defined using the empirical fuel approach. You may find that for rich fuel mixtures the equilibrium calculation produces very low temperatures and eventually fails. This indicates that strong endothermic reactions are taking place and the mixture is not able to sustain them. In this situation, you may need to raise the heating value of the fuel until prePDF produces acceptable results. Provided that your fuel will be treated as a liquid or solid (coal) fuel, you can maintain the desired heating value in your FLUENT simulation. This is accomplished by defining the difference between the desired and the adjusted heating values as latent heat (in the case of combusting solid fuel) or heat of pyrolysis (in the case of liquid fuel). Informational Messages and Errors Reported During the prePDF Calculation prePDF may report a variety of error messages or informational reports as it computes the equilibrium chemistry and generates the look-up tables. These messages are detailed in Section 14.3.2.

Step 11: Save the Look-Up Tables The look-up tables computed by prePDF are stored in a file that you will read into FLUENT. FLUENT will use the tables to extract the species, density, and temperature

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fields from the mixture fraction field that it predicts as part of the flow-field calculation. The look-up tables must be saved before you exit from prePDF. File −→ Write −→ PDF... The file can be saved as formatted (ASCII, or text) or binary (unformatted), for either FLUENT 4 or FLUENT 6.

! Be sure to save a PDF file for the appropriate solver. In addition to reading the PDF file into FLUENT for the flow analysis, you can read it back into prePDF at a later date if you want to examine the look-up tables using the graphics tools described below, in Step 12. (All types of PDF files can be read back into prePDF.)

Step 12: Graphics and Alphanumeric Reports in prePDF prePDF supplies a number of utilities that allow you to examine the result of the look-up table computations. Reviewing the Beta PDF Shape You can plot the shape of the beta PDF using the Beta-Pdf panel (Figure 14.3.9). Display −→Beta PDF...

Figure 14.3.9: The Beta-Pdf Panel in prePDF

This utility simply plots the function, Equation 14.1-22, for any value of f (Mean Mixture Fraction) and f 0 2 (Mixture Fraction Variance) that you define in the panel. Figure 14.1.7 illustrates two of the many forms that the beta PDF shape may take. Note that none of your inputs in prePDF will change the beta PDF shape for a given pair of f and f 0 2 . (Since the β PDF plots are just for general informational purposes, you can plot them even when you are working on a two-mixture-fraction problem, for which the PDFs will be calculated in FLUENT.)


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Reviewing Instantaneous Values in Adiabatic Single-Mixture-Fraction Systems You can plot the variation of instantaneous species concentration, density, or temperature with the instantaneous mixture fraction using the Property Curves panel (Figure 14.3.10). Display −→Property Curves...

Figure 14.3.10: The Adiabatic Property Curves Panel in prePDF You can select temperature, density, species, or enthalpy as the variable to be plotted using the Plot Variable drop-down list. The resulting displays show how these quantities vary with mixture fraction and can be used to determine the stoichiometric value of mixture fraction, the peak temperature expected, and the most important species in the system. Figures 14.3.11 and 14.3.12 show instantaneous values derived for a very simple hydrocarbon system. For adiabatic systems, you can also write property data to a file in the format used by the XY plotter in FLUENT. To write an XY plot file containing property data, use the WRITE-XY-FILE text command in prePDF: VIEW-GRAPHICS −→ PROPERTY-CURVES −→WRITE-XY-FILE When you select this command, you will be asked to select the property to be written and specify a name for the file:

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KEY 1.00E+00

CH4 O2 CO2 H2O N2 CO H2

8.00E-01

M o l e F r a c t i o n

6.00E-01

4.00E-01

2.00E-01

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

Mixture Fraction F

CHEMICAL EQUILIBRIUM INSTANTANEOUS SPECIES COMPOSITION

prePDF V4.00

Fluent Inc.

Figure 14.3.11: Instantaneous Species Mole Fractions Derived From the Equilibrium Chemistry Calculation

KEY 3.28E+03

2.62E+03

T e m p e r a t u r e

1.97E+03

1.31E+03

6.56E+02

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

Mixture Fraction F

CHEMICAL EQUILIBRIUM INSTANTANEOUS TEMPERATURE (KELVIN)

prePDF V4.00

Fluent Inc.

Figure 14.3.12: Instantaneous Temperature Derived From the Equilibrium Chemistry Calculation


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COMMANDS AVAILABLE FROM PROPERTY-CURVES: PLOT WRITE-XY-FILE QUIT (PROPERTY-CURVES)wxy COMMANDS AVAILABLE FROM WRITE-XY-FILE: TEMPERATURE DENSITY SPECIES QUIT (WRITE-XY-FILE)te ENTER NAME OF XY PLOT FILE (S)- DEFAULT- sample.xy

ENTHALPY

Later, during your FLUENT session, you can read and plot this data using the File XY Plot panel. Plot −→File... Reviewing Instantaneous Values in Adiabatic Two-Mixture-Fraction Systems If your problem includes a secondary stream, in addition to choosing the variable to be plotted, you must also specify a constant value of the fuel mixture fraction or the secondary partial fraction at which the property curve should be drawn. Choose either fraction under Constant Value of and specify its Value. The selected variable will be plotted as a function of the fraction that is not held constant. In Figure 14.3.13, the secondary partial fraction is held constant at 0.05, and the plot shows how temperature varies with fuel mixture fraction. Reviewing Instantaneous Values in Non-Adiabatic Systems If your single-mixture-fraction system is non-adiabatic, you can still review the variation of instantaneous scalar values with the instantaneous mixture fraction. In the nonadiabatic case, because the instantaneous results depend on the mean enthalpy value, you will specify the mean mixture fraction, its variance, and the mean enthalpy value at which the variable will be displayed. The Property Curves panel (Figure 14.3.14) contains the fields required to input these parameters in non-adiabatic systems. Display −→Property Curves... Select temperature, density, species mass fraction, or enthalpy as the variable to be plotted using the Plot Variable drop-down list. Then enter the Mean Mixture Fraction, Mixture Fraction Variance, and Mean Enthalpy at which to display the selected variable. Click Display to generate the graphical display.

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KEY 3.28E+03

2.62E+03

T e m p e r a t u r e

1.97E+03

1.31E+03

6.56E+02

0.00E+00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F Fuel CONSTANT SECONDARY PARTIAL FRACTION 0.050

prePDF V4.00

INSTANTANEOUS TEMPERATURE (KELVIN)

Fluent Inc.

Figure 14.3.13: Instantaneous Temperature Plotted for a Two-Mixture-Fraction Case

Figure 14.3.14: The Non-Adiabatic Property Curves Panel in prePDF


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! Note that you cannot plot instantaneous property curves for a non-adiabatic two-mixturefraction case. You will instead plot the look-up tables of instantaneous values using the Nonadiabatic-Table panel.

! Note also the following important difference in the Property Curves display for adiabatic and non-adiabatic cases. For adiabatic cases, the instantaneous property curves correspond to the values of the look-up tables at fs0 2 = 0. In non-adiabatic systems, however, the property curves represent only the intermediate values of the properties prior to the PDF integrations, and therefore do not correspond to any of the values in the PDF lookup tables. In order to examine the values stored in the look-up tables for a non-adiabatic case you should use the Nonadiabatic-Table panel. Reviewing the 2D Look-Up Tables Computed by prePDF for a Single Mixture Fraction You can use either graphics or alphanumerics to display the 2D PDF look-up tables generated for single-mixture-fraction adiabatic systems. To plot the tables, use the PdfTable panel (Figure 14.3.15). Display −→PDF Table...

Figure 14.3.15: The Pdf-Table Panel in prePDF Using the Plot Variable drop-down list, you can display the look-up table for temperature, density, or any individual species fraction (defined in the Species Selection panel that appears when you choose SPECIES). Figure 14.3.16 illustrates the look-up table generated for temperature in a simple hydrocarbon combustion model. Similarly, you can use the VIEW-ALPHA command, available in the text interface, to display the look-up table in tabular form at each point in the discrete mean/variance matrix: MAIN −→ VIEW-ALPHA

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VIEW ALPHA: TEMPERATURE (K) F-VAR F-MEAN= 1 2 15 1.5E+03 1.5E+03 14 1.5E+03 1.5E+03 13 1.5E+03 1.5E+03 12 1.5E+03 1.5E+03 11 1.5E+03 1.5E+03 . . 4 1.5E+03 1.6E+03 3 1.5E+03 1.6E+03 2 1.5E+03 1.7E+03 1 1.5E+03 1.8E+03

3 1.5E+03 1.5E+03 1.5E+03 1.5E+03 1.5E+03

4 1.5E+03 1.5E+03 1.5E+03 1.5E+03 1.5E+03

5 1.5E+03 1.5E+03 1.5E+03 1.5E+03 1.5E+03

1.7E+03 1.7E+03 1.8E+03 2.1E+03

1.7E+03 1.8E+03 2.0E+03 2.4E+03

1.8E+03 1.9E+03 2.1E+03 2.7E+03

2.3E+03

1.9E+03 T E M P E R A T U R E

1.5E+03

2.50E-01 2.00E-01

1.1E+03 1.50E-01 SCALED-F-VARIANCE

K

1.00E-01

7.0E+02 5.00E-02

3.0E+02

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

PDF TABLE - CHEMICAL EQUILIBRIUM MEAN FLAME TEMPERATURE

prePDF V4.00

Fluent Inc.

Figure 14.3.16: Two-Dimensional Look-Up Table for Temperature Generated by prePDF for a Simple Hydrocarbon System (Single-Mixture-Fraction, Adiabatic System)

Reviewing the 2D Look-Up Tables Computed by prePDF for Two Mixture Fractions

! It is important for you to view your temperature and species tables in prePDF to ensure that they are adequately but not excessively resolved. Inadequate resolution will lead to inaccuracies, and excessive resolution will lead to unnecessarily slow calculation times in FLUENT.


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You can use either graphics or alphanumerics to display the 2D look-up tables of instantaneous properties generated for two-mixture-fraction adiabatic systems. To plot the tables, use the Property-Table panel: Display −→Property Table...

Figure 14.3.17: The Property-Table Panel You will use this panel exactly as described above for the Pdf-Table panel, but the resulting plot will show the selected variable as a function of instantaneous fuel mixture fraction and secondary partial fraction (instead of as a function of mean fuel mixture fraction and variance). Alphanumeric reports are generated in the same way as for single-mixture-fraction calculations, but the report will list the ffuel , psec points instead of the mean/variance matrix. VIEW ALPHA: TEMPERATURE (K) P-SEC F-FUEL= 1 2 7 1.954E+03 1.773E+03 6 2.216E+03 2.020E+03 5 2.357E+03 2.263E+03 4 2.064E+03 2.339E+03 3 1.622E+03 2.043E+03 2 1.134E+03 1.630E+03 1 6.000E+02 1.180E+03

3 1.593E+03 1.824E+03 2.055E+03 2.279E+03 2.339E+03 2.071E+03 1.696E+03

4 1.420E+03 1.631E+03 1.845E+03 2.059E+03 2.267E+03 2.357E+03 2.145E+03

5 1.273E+03 1.442E+03 1.638E+03 1.836E+03 2.032E+03 2.225E+03 2.366E+03

Reviewing the 3D Look-Up Tables for Single-Mixture-Fraction Non-Adiabatic Systems The look-up tables generated for single-mixture-fraction non-adiabatic systems contain the mean temperature, density, and species concentrations as a function of three quantities: mean mixture fraction, mixture fraction variance, and mean enthalpy. Consequently,

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when you ask to display the look-up tables in alphanumerics or graphics, you will be displaying them slice-by-slice. The graphical display begins with the Nonadiabatic-Table panel (Figure 14.3.18). Display −→ Nonadiabatic-Table...

Figure 14.3.18: The Nonadiabatic-Table Panel in prePDF In this panel, you can select the variable to be plotted in the Plot Variable drop-down list. Next, you must define how the three-dimensional array of data points available in the look-up table are to be sliced: which discrete independent variable (either f or H ∗ ) is to be held constant and whether the constant value is to be selected as a numerical value (choose Value as the Plot type) or by discretization index (choose Slice as the Plot type). If you choose the latter approach, click the Slice... button to select the discretization index slice that you want.

Figure 14.3.19: The Slice Panel in prePDF


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In the Slice panel (Figure 14.3.19), select which discretized variable is to be constant (Enthalpy or F-Mean) and then pick the Slice # (discretization index). For example, in the panel in Figure 14.3.19, a look-up table generated at the tenth discrete value of mean enthalpy has been requested. As discussed in Section 14.2, each slice actually corresponds to a normalized heat loss or gain. The enthalpy slice index corresponding to the adiabatic case is displayed in the Adiabatic Slice # field. To generate the plot, click Apply and close the Slice panel, and then click Display in the Nonadiabatic-Table panel. A sample plot is shown in Figure 14.3.20.

2.4E+03


1.6E+03

2.50E-01 2.00E-01


K

1.00E-01

7.2E+02 5.00E-02

3.0E+02

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

MEAN ENTHALPY SLICE NUMBER 23

prePDF V4.00

MEAN FLAME TEMPERATURE FROM 3D-PDF-TABLE

Fluent Inc.

Figure 14.3.20: Display of a Single Slice of the Three-Dimensional Look-Up Table in a Non-Adiabatic System (Single Mixture Fraction) Alternately, you may want to define a slice of the 3D look-up table based on a specific value of one of the independent quantities. When this is the case, select the Value option under Plot type in the Nonadiabatic-Table panel. To set the slice, click the Value... button to open the Lookup Points panel (Figure 14.3.21). In this panel, you can select a slice of the 3D table that corresponds to: • constant value of mean enthalpy (Enthalpy Values and Constant Enthalpy options) • constant value of mean mixture fraction (Constant F-Mean Value) • adiabatic enthalpy (Enthalpy Values and Adiabatic Relationship options) In addition, you supply the physical value of the selected quantity in the Value field. When the adiabatic enthalpy option is selected, you must supply the Fuel and Oxidiser

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Figure 14.3.21: The Lookup Points Panel in prePDF

Inlet Temperature instead of the fixed value. prePDF uses this information to construct the adiabatic relationship between enthalpy and mixture fraction that is used to slice the table. The adiabatic enthalpy option is very useful, as it allows you to generate adiabatic (2D) look-up tables for various combinations of fuel and oxidizer inlet temperatures from your 3D look-up table generated for the non-adiabatic system. Finally, you can set the Refinement Factor, which determines the resolution of the plotted curve. A refinement factor of 1.0 (the default) implies that the plot will use the same number of discrete points that you requested in the Solution Parameters panel. Increasing this factor will cause prePDF to compute and display additional data points, yielding a smoother plot but requiring some time to compute. To generate the plot, click Apply and close the Lookup Points panel, and then click Display in the Nonadiabatic-Table panel. Reviewing the 3D Look-Up Tables for Two-Mixture-Fraction Non-Adiabatic Systems The look-up tables generated for two-mixture-fraction non-adiabatic systems contain the instantaneous temperature, density, and species concentrations as a function of three instantaneous quantities: fuel mixture fraction, secondary partial fraction, and enthalpy. As for the single-mixture-fraction case described above, you will use the Nonadiabatic-


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Table panel to display the look-up table. The procedure is exactly the same as that described above, except that you can choose only enthalpy slices or values on which to display the look-up table.

14.3.2

Informational Messages and Errors Reported by prePDF

The following messages may be issued by prePDF during the case setup, the calculation of the look-up tables, or postprocessing. The source of the message and the action required by you, if any, are detailed here. BOTTOM TEMPERATURE TOO HIGH

From: Solver Cause: The minimum temperature defined for the non-adiabatic calculation is higher than the inlet temperatures. Action: Correct the minimum temperature value. CALCULATIONS INTERRUPTED CONTINUE ? (ELSE RETURN TO MAIN MENU)

From: Solver Cause: Ctrl-C has been pressed. Action: Typing N will cause the solver to abort to the main menu and all previous equilibrium iterations will be lost. Typing Y or RETURN will cause the calculations to continue. ENTHALPY CURVE GENERATION FAILED

From: Graphics Cause: For the non-adiabatic single-mixture-fraction case, prePDF was unable to construct the instantaneous enthalpy curve required for the calculation of the instantaneous property curves. Action: Modify your input of mixture fraction, variance, or enthalpy for the property curve plot. ENTHALPY HIGHER THAN ENTHALPY CEILING

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From: Graphics Cause: For the non-adiabatic single-mixture-fraction case the enthalpy input for the calculation of the instantaneous property curves is too high. Action: Decrease the enthalpy value for the property curve plot. ENTHALPY LOWER THAN ENTHALPY FLOOR

From: Graphics Cause: For the non-adiabatic single-mixture-fraction case the enthalpy input for the calculation of the instantaneous property curves is too low. Action: Increase the enthalpy value for the property curve plot. ERROR: NO ATOMS EXIST TO DEFINE THE EMPIRICAL STREAM

From: Setup Cause: The empirical fuel stream option has been selected but no elements have been defined from which to construct the fuel. Elements allowed are C, H, O, S, and N. Action: Add the elements C, H, O, S, and N in the species list. ERROR: NO CARBON DIOXIDE SPECIES EXISTS

From: Setup Cause: The empirical fuel stream option has been selected but CO2 species has not been defined. CO2 is needed to calculate the heat of formation of the empirical fuel from its heating value Action: Add CO2 in the species list. ERROR: NO WATER VAPOR SPECIES EXISTS

From: Setup Cause: The empirical fuel stream option has been selected but H2 O species has not been defined. H2 O is needed to calculate the heat of formation of the empirical fuel from its heating value.


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Action: Add H2 O in the species list. ERROR OPENING TEMPORARY LINKING FILE

From: Files or Setup Cause: prePDF was unable to open the file DBLINK used for temporary storage of thermodynamic data. Action: Make sure you have write permission in the working directory. ERROR WRITING TEMPORARY LINKING FILE

From: Files or Setup Cause: prePDF was unable to write the file DBLINK used for temporary storage of thermodynamic data. Action: Make sure there is space on the disk. FAULT AT STOICHIOMETRIC REACTION CALCULATION FOR F-MEAN = xx

From: Solver Cause: This message may appear for one of the following reasons: • the temperature limits are not sufficient • the stoichiometry defined is incorrect. • the rich flammability limit with the automatic stoichiometry calculation has been used and the value of rich flammability limit has been set too low. Action: Check inputs of temperature limits. Check inputs of stoichiometry. Check the setting of rich flammability limit. INCORRECT STOICHIOMETRY DEFINED

From: Solver Cause: The stoichiometry defined does not satisfy the element balance. Action: Check inputs of stoichiometry.

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SETTING UP DATA BASE LINK FILE FAILED

From: Files or Setup Cause: prePDF was unable to access the thermodynamic properties database. Action: Make sure the instructions for installation of prePDF have been followed and all the environment variables are set correctly. TOP TEMPERATURE TOO LOW

From: Solver Cause: The maximum temperature defined for the non-adiabatic calculation is lower than the adiabatic flame temperature for this mixture. Action: Increase the maximum temperature limit. It is recommended that this is set at Tadiabatic + 100 K. The adiabatic flame temperature Tadiabatic can be calculated by performing an adiabatic calculation and reviewing the instantaneous temperature vs. mixture fraction curves predicted by prePDF. UNABLE TO CALCULATE COMPOSITION AT F-MEAN xx AND TEMPERATURE xxxx K

From: Solver Cause: The equilibrium calculation has failed. This may happen for the following reasons: • The species list defined is not adequate. • The mixture is liquid for the conditions the equilibrium solver has entered. Action: Try using better temperature limits. Experiment with the species list, using an adiabatic calculation, adding or removing species based on the amount formed over the mixture fraction range. Try moving the rich flammability limit closer to the stoichiometric mixture fraction. UNABLE TO CALCULATE ENTHALPY CURVE AT I-FMEAN = xx J-FVAR = xx K-ENTH = xx

From: Solver Cause: For the non-adiabatic calculation, prePDF was unable to construct the instantaneous enthalpy curve required for the PDF calculation. Action: This message should not appear. Contact Fluent customer support.


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14.3.3

Non-Premixed Model Input and Solution Procedures in FLUENT

The non-premixed model setup and solution procedure in FLUENT differs slightly for single- and two-mixture-fraction problems. Below, an overview of each approach is provided. Note that your FLUENT case file must always meet the restrictions listed for the non-premixed modeling approach in Section 14.1.3. In this section, details are provided regarding the problem definition and calculation procedures you follow in FLUENT.

Single-Mixture-Fraction Approach For a single-mixture-fraction system, when you have completed the calculation of the mixture fraction/PDF look-up tables in prePDF, you are ready to begin your reacting flow simulation in FLUENT. In FLUENT, you will solve the flow field and predict the spatial distribution of f and f 0 2 (and H ∗ if the system is non-adiabatic or χst,d if the system is based on laminar flamelets). FLUENT will obtain the implied values of temperature and individual chemical species mass fractions from the look-up tables.

Two-Mixture-Fraction Approach When a secondary stream is included, FLUENT will solve transport equations for the mean secondary partial fraction (psec ) and its variance in addition to the mean fuel mixture fraction and its variance. FLUENT will then look up the instantaneous values for temperature, density, and individual chemical species in the look-up tables, compute the PDFs for the fuel and secondary streams, and calculate the mean values for temperature, density, and species. Note that in order to avoid both inaccuracies and unnecessarily slow calculation times, it is important for you to view your temperature and species tables in prePDF to ensure that they are adequately but not excessively resolved.

Step 1: Start FLUENT and Read a Grid File Start your FLUENT session in the usual way, as described in Section 1.5, and then read in a grid file. The number and types of inlets in your model must meet the constraints of the non-premixed modeling approach, as discussed in Section 14.1.3 and illustrated in Figures 14.1.12, 14.1.13, and 14.1.14. Starting a Non-Premixed Calculation From a Previous Case File You can read a previously defined FLUENT case file as a starting point for your nonpremixed combustion modeling. If this case file contains inputs that are incompatible with the current non-premixed combustion model, FLUENT will alert you when the nonpremixed model is turned on and it will turn off those incompatible models. For example,

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if the case file includes species that differ from those included in the PDF file created by prePDF, these species will be disabled. If the case file contains property descriptions that conflict with the property data in the chemical database, these property inputs will be ignored.

! See Step 2, below, for important information about PDF files created by previous versions of prePDF.

Step 2: Activate the Non-Premixed Combustion Model Preliminaries Before turning on the non-premixed combustion model, you must enable turbulence calculations in the Viscous Model panel. Define −→ Models −→Viscous... If your model is non-adiabatic, you should also enable heat transfer (and radiation, if required). Define −→ Models −→Energy... Define −→ Models −→Radiation... Figure 14.1.11 illustrates the types of problems that must be treated as non-adiabatic. Note, however, that the decision to include non-adiabatic effects is made in prePDF. FLUENT will turn off the energy equation if your prePDF inputs are for an adiabatic system. Enabling Non-Premixed Combustion Before any other modeling inputs (e.g., setting of boundary conditions or properties) you should turn on the non-premixed combustion model, because activating this model will impact how other inputs are requested during your subsequent work. The non-premixed combustion model is enabled in the Species Model panel. Define −→ Models −→Species... Select Non-Premixed Combustion under the Model heading. When you click OK in the Species Model panel, a Select File dialog box will immediately appear, prompting you for the name of the PDF file containing the look-up tables created in prePDF. (The PDF file is the file you saved using the File/Write/PDF... menu item in prePDF after computing the look-up tables.) FLUENT will indicate that it has successfully read the specified PDF file:


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Figure 14.3.22: The Species Model Panel in FLUENT

Reading "/home/mydirectory/adiabatic.pdf"... read 5 species (binary c, adiabatic prepdf) pdf file successfully read. Done.

After you read in the PDF file, FLUENT will inform you that some material properties have changed. You can accept this information; you will be updating properties later on. You can read in an altered PDF file at any time by using the File/Read/Pdf... menu item.

! Recall that the non-premixed combustion model is available only when you used the segregated solver; it cannot be used with the coupled solvers. Also, the non-premixed combustion model is available only when turbulence modeling is active. If you are modeling a non-adiabatic system and you wish to include the effects of compressibility, re-open the Species Model panel (Figure 14.3.23) and turn on Compressibility Effects under PDF Options. This option tells FLUENT to update the density, temperature, species mass fraction, and enthalpy from the PDF tables to account for the varying pressure of the system. When the non-premixed combustion model is active, you can enable compressibility effects only in the Species Model panel. For other models, you will specify compressible flow (ideal-gas, boussinesq, etc.) in the Materials panel. Using PDF Files Created by Previous Releases of prePDF PDF files created by prePDF 1 cannot be read into FLUENT or into prePDF 4 (the current version). If you have prePDF 1 files, read the input file into prePDF 4, recalculate the lookup tables, and save a new PDF file to be read into FLUENT. As noted in Section 14.3.5, prePDF 1 input files that were created for coal combustion systems must be modified before computing the PDF look-up tables in prePDF 4.

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Figure 14.3.23: The Species Model Panel With Available PDF Options

PDF files created by prePDF 2 can be read into FLUENT, but it is recommended that you recalculate the look-up tables in prePDF 4. In these versions of prePDF, the mixture fraction variance was not scaled to its maximum value while building the PDF table. This resulted in a lower-resolution table, especially for lower mixture fraction values, and at mixture fraction values close to 0 and 1. To take advantage of a more advanced PDF table look-up scheme, you can read a PDF or input file created by prePDF 2 into prePDF 4 and recalculate the look-up table. Two-mixture-fraction PDF files created in prePDF 2 should be read into prePDF 4 and written out in FLUENT 6 format. (Two-mixture-fraction PDF files written by prePDF 2 cannot be read directly into FLUENT.) Table 14.3.1 summarizes the recommended procedures for using old PDF files in FLUENT. Retrieving the PDF File During Case File Reads The PDF filename is specified to FLUENT only once. Thereafter, the filename is stored in your FLUENT case file and the PDF file will be automatically read into FLUENT whenever the case file is read. FLUENT will remind you that it is reading the PDF file after it finishes reading the rest of the case file by reporting its progress in the text (console) window. Note that the PDF filename stored in your case file may not contain the full name of the directory in which the PDF file exists. The full directory name will be stored in the case file only if you initially read the PDF file through the GUI (or if you typed in the directory name along with the filename when using the text interface). In the event that the full directory name is absent, the automatic reading of the PDF file may fail (since


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Table 14.3.1: Using Old PDF Files in FLUENT PDF file type

Readable in prePDF 4? input files only

Readable in FLUENT? no

yes

yes

prePDF 2 (two yes mixture fractions)

no

prePDF 3

yes

prePDF 1

prePDF 2 (single mixture fraction)

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yes

Recommended Procedure Read input file into prePDF 4, recalculate PDF table, and write a PDF file in FLUENT 6 format. Read input or PDF file into prePDF 4, recalculate PDF table, and write a PDF file in FLUENT 6 format. Read PDF file into prePDF 4 and write a PDF file in FLUENT 6 format. prePDF 3 files are compatible with both prePDF 4 and FLUENT 6.



FLUENT does not know which directory to look in for the file), and you will need to manually specify the PDF file. The safest approaches are to use the GUI when you first read the PDF file or to supply the full directory name when using the text interface.

Step 3: Define Boundary Conditions Input of Mixture Fraction Boundary Conditions When the non-premixed combustion model is used, flow boundary conditions at inlets and exits (i.e., velocity or pressure, turbulence intensity) are defined in the usual way. Species mass fractions at inlets are not required. Instead, you define values for the mean mixture fraction, f , and the mixture fraction variance, f 0 2 , at inlet boundaries. (For problems that include a secondary stream, you will define boundary conditions for the mean secondary partial fraction and its variance as well as the mean fuel mixture fraction and its variance.) These inputs provide boundary conditions for the conservation equations you will solve for these quantities. The inlet values are supplied in the boundary conditions panel for the selected inlet boundary (e.g., Figure 14.3.24). Define −→ Boundary Conditions... Input the Mean Mixture Fraction and Mixture Fraction Variance (and the Secondary Mean Mixture Fraction and Secondary Mixture Fraction Variance, if you are using two mixture fractions). In general, the inlet value of the mean fractions will be 1.0 or 0.0 at flow inlets: the mean fuel mixture fraction will be 1.0 at fuel stream inlets and 0.0 at oxidizer or secondary stream inlets; the mean secondary mixture fraction will be 1.0 at secondary stream inlets and 0.0 at fuel or oxidizer inlets. The fuel or secondary mixture fraction will lie between 0.0 and 1.0 only if you are modeling flue gas recycle, as illustrated in Figure 14.1.15 and discussed in Section 14.1.2. The fuel or secondary mixture fraction variance can usually be taken as zero at inlet boundaries. Diffusion at Inlets In some cases, you may wish to include only the convective transport of mixture fraction through the inlets of your domain. You can do this by disabling inlet mixture-fraction diffusion. By default, FLUENT includes the diffusion flux of mixture fraction at inlets. To turn off inlet diffusion, use the define/models/species-transport/inlet-diffusion? text command. Input of Thermal Boundary Conditions and Fuel Inlet Velocities If your model is non-adiabatic, you should input the Temperature at the flow inlets. While the inlet temperatures were requested in prePDF (as the Fuel Inlet Temperature, Oxidiser Inlet Temperature, and (if applicable) Secondary Inlet Temperature in the Operating Conditions panel), these inputs were used only in the construction of the look-up tables. The inlet temperatures for each fuel, oxidizer, and secondary inlet in your non-adiabatic


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Figure 14.3.24: The Velocity Inlet Panel Showing Mixture Fraction Boundary Conditions

model should be defined, in addition, as boundary conditions in FLUENT. It is acceptable for the inlet temperature boundary conditions defined in FLUENT to differ slightly from those you input in prePDF. If the inlet temperatures differ significantly from those in prePDF, however, your look-up tables may provide less accurate interpolation. This is because the discrete points in the look-up tables were selected based on the inlet temperatures as defined in prePDF. When you are using the full equilibrium model (rich limit of 1.0), prePDF will in most cases predict a modified equilibrium fuel temperature and composition. As detailed in Section 14.3.1, your inlet velocity at gas-phase fuel inlets should be based on the density corresponding to this adjusted temperature and composition. The temperature at the gas-phase fuel inlet, however, should be retained at the value you used to define the fuel inlet in prePDF. Similar equilibrium adjustments may occur, under unusual circumstances, at oxidizer inlets and your inputs should be determined in the same way. Wall thermal boundary conditions should also be defined for non-adiabatic non-premixed combustion calculations. You can use any of the standard conditions available in FLU-

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ENT, including specified wall temperature, heat flux, external heat transfer coefficient, or external radiation. If radiation is to be included within the domain, the wall emissivity should be defined as well. See Section 6.13.1 for details about thermal boundary conditions at walls.

Step 4: Define Physical Properties When you use the non-premixed combustion model, the material used for all fluid zones is automatically set to pdf-mixture. This material is a special case of the mixture material concept discussed in Section 13.1.2. The constituent species of this mixture are the species that you defined in prePDF; you cannot change them in FLUENT. When the nonpremixed model is used, heat capacities, molecular weights, and enthalpies of formation for each species considered are extracted from the chemical database, so you will not modify any properties for the constituent species in the PDF mixture. For the PDF mixture itself, the density is determined from the look-up tables and the specific heat is determined via the mixing law discussed in Section 7.5.4, using specific heat values for the constituent species obtained from the chemical database (thermodb.scm). The physical property inputs for a non-premixed combustion problem are therefore only the transport properties (viscosity, thermal conductivity, etc.) for the PDF mixture. To set these in the Materials panel, choose mixture as the Material Type, pdf-mixture (the default, and only choice) in the Mixture Materials list, and set the desired values for the transport properties. Define −→Materials... See Chapter 7 for details about setting physical properties. The transport properties in a non-premixed combustion problem can be defined as functions of temperature, if desired, but not as functions of composition. In practice, since turbulence effects will dominate, it will be of little benefit to include even the temperature dependence of these transport properties. If you are modeling radiation heat transfer, you will also input radiation properties, as described in Section 7.6. Composition-dependent absorption coefficients (using the WSGGM) are allowed.

Step 5: Solve the Flow Problem The next step in the non-premixed combustion modeling process in FLUENT is the solution of the mixture fraction and flow equations. First, initialize the flow. By default, the mixture fraction and its variance have initial values of zero, which is the recommended value; you should generally not set non-zero initial values for these variables. See Section 24.13 for details about solution initialization. Solve −→ Initialize −→Initialize...


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Next, begin calculations in the usual manner. Solve −→ Iterate... During the calculation process, FLUENT reports residuals for the mixture fraction and its variance in the fmean and fvar columns of the residual report: iter cont x-vel y-vel k 28 1.57e-3 4.92e-4 4.80e-4 2.68e-2 29 1.42e-3 4.43e-4 4.23e-4 2.48e-2 30 1.28e-3 3.98e-4 3.75e-4 2.29e-2

epsilon fmean fvar 2.59e-3 9.09e-1 1.17e+0 2.30e-3 8.89e-1 1.15e+0 2.04e-3 8.88e-1 1.14e+0

(For two-mixture-fraction calculations, columns for psec and pvar will also appear.) Under-Relaxation Factors for PDF Equations The transport equations for the mean mixture fraction and mixture fraction variance are quite stable and high under-relaxation can be used when solving them. By default, an under-relaxation factor of 1 is used for the mean mixture fraction (and secondary partial fraction) and 0.9 for the mixture fraction variance (and secondary partial fraction variance). If the residuals for these equations are increasing, you should consider decreasing these under-relaxation factors, as discussed in Section 24.9. Density Under-Relaxation One of the main reasons a combustion calculation can have difficulty converging is that large changes in temperature cause large changes in density, which can, in turn, cause instabilities in the flow solution. FLUENT allows you to under-relax the change in density to alleviate this difficulty. The default value for density under-relaxation is 1, but if you encounter convergence trouble you may wish to reduce this to a value between 0.5 and 1 (in the Solution Controls panel). Tuning the PDF Parameters for Two-Mixture-Fraction Calculations For cases that include a secondary stream, the PDF integrations are performed inside FLUENT. The parameters for these integrations are defined in the Species Model panel (Figure 14.3.25). Define −→ Models −→Species... The parameters are as follows: Compressibility Effects (non-adiabatic systems only) tells FLUENT to update the density, temperature, species mass fraction, and enthalpy from the PDF tables to account for the varying pressure of the system.

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Figure 14.3.25: The Species Model Panel for a Two-Mixture-Fraction Calculation

Probability Density Function specifies which type of PDF should be used. You can pick either double delta (the default) or beta in the drop-down list. These choices are the same as what you saw in prePDF for the single-mixture-fraction case. (See Section 14.1.2.) The double delta PDF has the advantage of being faster than the beta PDF, and it is the default. The beta function, however, may be a more accurate representation of the PDF. Number of Flow Iterations Per Property Update specifies how often the density, temperature, and specific heats are updated from the look-up table. Remember that when you are calculating two mixture fractions, the updating of properties includes computation of the PDFs and can be quite CPU-intensive. You should generally not reduce the Number of Flow Iterations Per Property Update below the default value of 10, unless you are experiencing convergence difficulties. For simulations involving non-adiabatic multiple strained flamelets, looking up the four-dimensional PDF tables can be CPU-intensive if a large number of species exist in the flamelet files. In such cases, the Number of Flow Iterations Per Property Update controls the updating of the mean molecular weight, which involves looking up the PDF tables for the species mass fractions.


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Step 6: Postprocessing the Non-Premixed Model Results in FLUENT The final step in the non-premixed combustion modeling process is the postprocessing of species concentrations and temperature data from the mixture fraction and flow-field solution data. The following variables are of particular interest: • Mean Mixture Fraction (in the Pdf... category) • Secondary Mean Mixture Fraction (in the Pdf... category) • Mixture Fraction Variance (in the Pdf... category) • Secondary Mixture Fraction Variance (in the Pdf... category) • Fvar Prod (in the Pdf... category) • Fvar2 Prod (in the Pdf... category) • Mass fraction of (species-n) (in the Species... category) • Mole fraction of (species-n) (in the Species... category) • Molar Concentration of (species-n) (in the Species... category) • Static Temperature (in the Temperature... category) • Enthalpy (in the Temperature... category) These quantities can be selected for display in the indicated category of the variableselection drop-down list that appears in postprocessing panels. See Chapter 29 for their definitions. In all cases, the species concentrations are derived from the mixture fraction/variance field using the look-up tables. Note that temperature and enthalpy can be postprocessed even when your FLUENT model is an adiabatic non-premixed combustion simulation in which you have not solved the energy equation. In both the adiabatic and non-adiabatic cases, the temperature is derived from the look-up table created in prePDF. Figures 14.3.26 and 14.3.27 illustrate typical results for a methane diffusion flame modeled using the non-premixed approach.

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1.00e+00 9.00e-01 8.00e-01 7.00e-01 6.00e-01 5.00e-01 4.00e-01 3.00e-01 2.00e-01 1.00e-01 0.00e+00

Contours of Mean Mixture Fraction

Figure 14.3.26: Predicted Contours of Mixture Fraction in a Methane Diffusion Flame

1.35e-01 1.22e-01 1.08e-01 9.48e-02 8.12e-02 6.77e-02 5.42e-02 4.06e-02 2.71e-02 1.35e-02 0.00e+00

Contours of Mass fraction of co2

Figure 14.3.27: Predicted Contours of CO2 Mass Fraction Using the Non-Premixed Combustion Model


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14.3.4

Modeling Liquid Fuel Combustion Using the Non-Premixed Model

Liquid fuel combustion can be modeled with the non-premixed model. In prePDF, the fuel vapor, which is produced by evaporation of the liquid fuel, is defined as the fuel stream, and the oxidizer (e.g., air) inlet composition is defined as the oxidizer stream. (See Section 14.3.1.) The liquid fuel that evaporates within the domain appears as a source of the fuel mixture fraction, f , when the non-premixed model is used. Within FLUENT, you define the liquid fuel model in the usual way. The gas phase (oxidizer) flow inlet is modeled using an inlet mixture fraction of zero and the fuel droplets are introduced as discrete-phase injections (see Section 21.9). The property inputs for the liquid fuel droplets are unaltered by the non-premixed model, and should be input as usual (see Section 21.11). Note that when you are requested to input the gas phase species destination for the evaporating liquid, you should input the species that comprises the fuel stream as defined in prePDF. Note that if the fuel stream was defined as a mixture of components in prePDF, you should simply select one of these components as the “evaporating species”. FLUENT will ensure that the mass evaporated from the liquid droplet enters the gas phase as a source of the fuel mixture that you defined in prePDF. The evaporating species you select here is used only to compute the diffusion controlled driving force in the evaporation rate.

14.3.5

Modeling Coal Combustion Using the Non-Premixed Model

Coal combustion can be modeled with the non-premixed approach, using either a single mixture fraction (fuel stream) or using two mixture fractions (fuel stream and secondary stream). This section describes the modeling options and special input procedures for coal combustion models using the non-premixed approach.

! Note that prePDF 4 uses a different formulation for coal combustion than that used in prePDF 1. If you have a coal combustion system defined in a prePDF 1 input file, you can read that input file into prePDF 4 but you will have to modify the definition of the coal composition before computing the new prePDF 4 PDF look-up tables. Using a prePDF 1 input file in prePDF 4, without making the required modifications to the definition of coal composition, will result in an incorrect PDF look-up table. The correct prePDF 4 procedures for definition of the fuel composition are described in this section. PDF files created by prePDF 2 or 3 will have the correct inputs for coal composition, so you need not change them. You may however, want to consider recomputing the look-up tables in prePDF 4, as described in Section 14.3.3. If you have a two-mixture-fraction PDF file from prePDF 2 or 3, you will need to read it into prePDF 4 and write it out in FLUENT 6 format.

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Non-Premixed Modeling Options for Coal Combustion There are three basic non-premixed modeling options for coal combustion: • When coal is the only fuel in the system, you can model the coal using two mixture fractions. When this approach is used, one stream is used to represent the char and the other stream is used to represent volatiles. Generally, the char stream composition is represented as 100% C(s). The volatile stream composition is defined by selecting appropriate species and setting their mole or mass fractions. Alternately, you can use the empirical method (input of atom fractions) for defining these compositions.

!

Using two mixture fractions to model coal combustion is more accurate than using one mixture fraction as the volatile and char streams are modeled separately. However, the two-mixture-fraction model incurs significant additional computational expense since the multi-dimensional PDF integrations are performed at run-time. • When coal is the only fuel in the system, you can choose to model the coal using a single mixture fraction (the fuel stream). When this approach is adopted, the fuel composition you define includes both volatiles species and char. Char is typically represented by including C(s) in the species list. You can define the fuel stream composition by selecting appropriate species and setting their mole fractions, or by using the empirical method (input of atom fractions). Definition of the composition is described in detail below.

!

Using a single mixture fraction for coal combustion is less accurate than using two mixture fractions. However, convergence in FLUENT should be substantially faster than the two-mixture-fraction model. • When coal is used with another (gaseous or liquid) fuel, you must model the coal with one mixture fraction and use a second mixture fraction to represent the second (gaseous or liquid) fuel. The stream associated with the coal composition is defined as detailed below for single-mixture-fraction models.

Defining the Coal Composition in prePDF: Single-Mixture-Fraction Models When coal is modeled using a single mixture fraction (the fuel stream), the fuel stream composition can be input using one of the following two methods: • Conventional approach: Define the mixture of species in the coal and their mole or mass fractions in the fuel stream: 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C3 H8 , CH4 , CO, CO2 , H2 O(l), H2 O, H2 , OH, H, O, C(s), O2 , and N2 ).


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2. Using the Composition panel, select the fuel stream and then define the mole or mass fractions of each of the species that are present in the coal fuel. Note that C(s) is used to represent the char content of the coal. For example, consider a coal that has a molar composition of 40% volatiles and 60% char on a dry ash free (DAF) basis. Assuming the volatiles can be represented by an equimolar mixture of C3 H8 and CO, the fuel stream composition defined in the Composition panel would be C3 H8 =0.2, CO = 0.2, and C(s)=0.60. Note that the coal composition should always be defined in prePDF on an ash free basis, even if ash will be considered in the FLUENT calculation. The following table illustrates the conversion from a typical mass-based proximate analysis to the species fraction inputs required by prePDF. Note that the conversion requires that you make an assumption regarding the species representing the volatiles. Here, the volatiles are assumed to exist as an equimolar mix of propane and carbon monoxide. Proximate Analysis

Weight %

Volatiles 30 C 3 H8 CO Fixed Carbon (C(s)) 60 Ash 10 (Total)

kg (DAF)

Moles (DAF)

Mole Fraction (DAF)

0.1833 0.1167 0.6 -

.00417 .00417 0.050 .05834

0.0715 0.0715 0.8570 1.0

Moisture in the coal can be considered by adding it in the fuel composition as liquid water, H2 O(l). The moisture can also be defined as water vapor, H2 O, provided that the corresponding latent heat is included in the discrete phase material inputs in FLUENT. • Empirical fuel approach: Use the Empirically Defined Streams option for the fuel stream. This method is ideal if you have an elemental analysis of the coal. 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C3 H8 , CH4 , CO, CO2 , H2 O(l), H2 O, H2 , OH, C(s), O2 , and N2 ). In addition, you must select atomic C, H, N, S, and O. 2. In the Composition panel, select the fuel stream and then define the molar atom fractions of C, H, N, S, and O in the fuel stream. In addition, you will input the lower heating value and mean specific heat of the coal. prePDF will use these inputs to determine the mole fractions of the chemical species you have included in the system.

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Note that for both of these composition input methods, you should take care to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should only be selected if you are using the empirical fuel input method.

Defining the Coal Composition in prePDF: Two-Mixture-Fraction Models If your FLUENT model will represent the coal using both the fuel stream and the secondary stream, one stream is used to represent char and the other stream is used to represent volatiles. (In the procedures below, it is assumed that the fuel stream represents the char and the secondary stream represents the volatiles.) The fuel stream and secondary stream compositions can be input using one of the following two methods: • Conventional approach: Define the mixture of species in the coal and their mole or mass fractions in the fuel and secondary streams: 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C3 H8 , CH4 , CO, CO2 , H2 O(l), H2 O, H2 , OH, H, O, C(s), O2 , and N2 ). 2. Using the Composition panel, select the fuel stream and define the mole or mass fractions of species used to represent the char. Generally, you will input 100% C(s) for the fuel stream. 3. Using the Composition panel, select the secondary stream and define the mole or mass fractions of species used to represent the volatiles. • Empirical fuel approach: Use the Empirically Defined Streams option for the volatile (in this case, secondary) stream. This method is ideal if you have an elemental analysis of the coal. 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C3 H8 , CH4 , CO, CO2 , H2 O(l), H2 O, H2 , OH, C(s), O2 , and N2 ). In addition, you must select atomic C, H, N, S, and O. 2. Using the Composition panel, select the fuel stream and define the mole or mass fractions of species used to represent the char. Generally, you will input 100% C(s) for the fuel stream. This procedure assumes that you are not using an empirical input for the fuel stream (char). 3. Using the Composition panel, select the secondary stream and define the atom fractions of C, H, N, S, and O in the volatiles. In addition, you will input the lower heating value and mean specific heat of the coal. prePDF will use these inputs to determine the mole fractions of the chemical species you have included in the system. For example, consider coal with the following DAF (dry ash free) data and elemental analysis:


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Proximate Analysis Wt % (dry) Volatiles 28 Char (C(s)) 64 Ash 8 Element C H O N S

Wt % (DAF) 30.4 69.6 -

Wt % (DAF) Wt % (DAF) 89.3 89.3 5.0 5.0 3.4 3.4 1.5 2.3 0.8 -

(Note that in the final column, for modeling simplicity, the sulfur content of the coal has been combined into the nitrogen mass fraction.) You can combine the proximate and ultimate analysis data to yield the following elemental composition of the volatile stream: Element C H O N Total

Mass Wt % (89.3 - 69.6) 0.65 5.0 0.16 3.4 0.11 2.3 0.08 30.4

Moles 5.4 16 0.7 0.6 22.7

Mole Fraction 0.24 0.70 0.03 0.03

This adjusted composition is used to define the secondary stream (volatile) composition. The lower heating value of the volatiles can be computed from the known heating value of the coal and the char (DAF): – LCVcoal,DAF = 35.3 MJ/kg – LCVchar,DAF = 32.9 MJ/kg You can compute the heating value of the volatiles as LCVvol =

35.3 MJ/kg − 0.696 × 32.9 MJ/kg 0.304

or LCVvol = 40.795 MJ/kg Note that for both of these composition input methods, you should take care to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should only be selected if you are using the empirical fuel input method.

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Coal Modeling Inputs in FLUENT Within FLUENT, the coal combustion simulation is defined as usual when the nonpremixed combustion model is selected. The air (oxidizer) inlets are defined as having a mixture fraction value of zero. No gas phase fuel inlets will be included and the sole source of fuel will come from the coal devolatilization and char burnout. The coal particles are defined as injections using the Set Injection Properties panel in the usual way, and physical properties for the coal material are specified as described in Section 21.11. You should keep in mind the following issues when defining injections and discrete-phase material properties for coal materials: • In the Set Injection Properties panel, you will specify for the Oxidizing Species one of the components of the oxidizer stream, as defined in prePDF. This species concentration field will be used to calculate the diffusion-controlled driving force in the char burnout law (if applicable). The specification of the char and volatile streams differs depending on the type of model you are defining: – If the coal is modeled using a single mixture fraction, the gas phase species representing the volatiles and the char combustion are represented by the mixture fraction used by the non-premixed combustion model. – If the coal is modeled using two mixture fractions, rather than specifying a destination species for the volatiles and char, you will instead specify the Devolatilizing Stream and Char Stream. – If the coal is modeled using one mixture fraction, and another fuel is modeled using a second mixture fraction, you should specify the stream representing the coal as both the Devolatilizing Stream and the Char Stream. • In the Materials panel, Vaporization Temperature should be set equal to the fuel inlet temperature used in prePDF. This temperature controls the onset of the devolatilization process. Stated inversely, the fuel inlet temperature that you define in prePDF should be set to the temperature at which you want to initiate devolatilization. This way, the look-up tables produced by prePDF will include the appropriate temperature range for your process. • In the Materials panel, Volatile Component Fraction and Combustible Fraction should be set to values that are consistent with the coal composition used to define the fuel stream (and secondary stream) composition in prePDF. • Also in the Materials panel, you will be prompted for the Burnout Stoichiometric Ratio and for the Latent Heat. The Burnout Stoichiometric Ratio is used in the calculation of the diffusion controlled burnout rate but has no other impact on the system chemistry when the non-premixed combustion model is used. The Burnout Stoichiometric Ratio is the mass of oxidant required per mass of char. The default


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value of 1.33 assumes that C(s) is oxidized by O2 to yield CO. The Latent Heat input determines the heat required to generate the vapor phase volatiles defined in the non-premixed system chemistry. You can usually set this value to zero when the non-premixed model is used, since your definition of volatile species will have been based on the overall heating value of the coal. However, if the coal composition defined in prePDF includes water content, the latent heat should be set as follows: – Set latent heat to zero if the water content of the coal has been defined as H2O(L). In this case, the prePDF system chemistry will include the latent heat required to vaporize the liquid water. – Set latent heat to the value for water (2.25 × 106 J/kg), adjusted by the mass loading of water in the volatiles, if the water content of the coal has been defined using water vapor, H2O. In this case, the water content you defined will be evolved along with the other species in the coal but the prePDF system chemistry does not include the latent heat effect. • The Density you define for the coal in the Materials panel should be the apparent density, including ash content. This is to be distinguished from the input of C(s) density in prePDF, where the density of dry ash free char should be used. • You will not be asked to define the Heat of Reaction for Burnout for the char combustion. This quantity is computed based on your inputs to prePDF.

Postprocessing Non-Premixed Models of Coal Combustion FLUENT reports the rate of volatile release from the coal using the DPM Evaporation/Devolatilization postprocessing variable. The rate of char burnout is reported in the DPM Burnout variable.

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14.4 The Laminar Flamelet Model

14.4

The Laminar Flamelet Model

The laminar flamelet approach models a turbulent flame brush as an ensemble of discrete, steady laminar flames, called flamelets. The individual flamelets are assumed to have the same structure as laminar flames in simple configurations, and are obtained by experiments or calculations. Using detailed chemical mechanisms, prePDF can calculate laminar opposed-flow diffusion flamelets for non-premixed combustion. The laminar flamelets are then embedded in a turbulent flame using statistical PDF methods. The advantage of the laminar flamelet approach is that realistic chemical kinetic effects can be incorporated into turbulent flames. As in the equilibrium approach of Section 14.3, the chemistry can be preprocessed and tabulated, offering tremendous computational savings. However, the laminar flamelet model is limited to flames with relatively fast chemistry. The flame is assumed to respond instantaneously to the aerodynamic strain, and thus the model cannot capture deep non-equilibrium effects such as ignition, extinction, and slow chemistry (like NOx ). Information about the flamelet model is presented in the following sections: • Section 14.4.1: Introduction • Section 14.4.2: Restrictions and Assumptions • Section 14.4.3: The Flamelet Concept • Section 14.4.4: Flamelet Generation • Section 14.4.5: Flamelet Import • Section 14.4.6: User Inputs for the Laminar Flamelet Model For general information about the mixture fraction model, see Section 14.1.

14.4.1

Introduction

In a diffusion flame, at the molecular level, fuel and oxidizer diffuse into the reaction zone—where they encounter high temperatures and radical species—and ignite. More heat and radicals are generated in the reaction zone, and some diffuse out. In nearequilibrium flames, the reaction rate is much faster than the diffusion rate. However, as the flame is stretched and strained by the turbulence, species and temperature gradients increase, and radicals and heat more quickly diffuse out of the flame. The species have less time to reach chemical equilibrium, and the local non-equilibrium increases. The laminar flamelet model is suited to predict moderate chemical non-equilibrium in turbulent flames due to aerodynamic straining by the turbulence. The chemistry, however, is assumed to respond rapidly to this strain, so as the strain relaxes, the chemistry relaxes to equilibrium.


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When the chemical time-scale is comparable to the fluid convection time-scale, the species can be considered to be in global chemical non-equilibrium. Such cases include NOx formation and low-temperature CO oxidation. The laminar flamelet model is not suitable for such slow-chemistry flames. Instead, you can model slow chemistry using the trace species assumption (as in the NOx model), or using the EDC model (see Section 13.1.1).

14.4.2

Restrictions and Assumptions

The following restrictions apply to all flamelet models in FLUENT: • Only a single mixture fraction can be modeled; two-mixture-fraction flamelet models are not allowed. • The mixture fraction is assumed to follow the β-function PDF, and the scalar dissipation is assumed to follow the double-delta-function PDF. • Empirically-based streams cannot be used with the flamelet model.

14.4.3

The Flamelet Concept

Overview The flamelet concept views the turbulent flame as an ensemble of thin, laminar, locally one-dimensional flamelet structures embedded within the turbulent flow field [29, 193, 194] (see Figure 14.4.1). A common laminar flame used to represent a flamelet in a turbulent flow is the counterflow diffusion flame. This geometry consists of opposed, axisymmetric fuel and oxidizer jets. As the distance between the jets is decreased and/or the velocity of the jets increased, the flame is strained and increasingly departs from chemical equilibrium until it is eventually extinguished. The species mass fraction and temperature fields can be measured in laminar counterflow diffusion flame experiments, or, most commonly, calculated. For the latter, a self-similar solution exists, and the governing equations can be simplified to one dimension, where complex chemistry calculations can be affordably performed. In the laminar counterflow flame, the mixture fraction, f , (see Section 14.1.2 for definition) decreases monotonically from unity at the fuel jet to zero at the oxidizer jet. If the species mass fraction and temperature along the axis are mapped from physical space to mixture fraction space, they can be uniquely described by two parameters: the mixture fraction and the strain rate (or, equivalently, the scalar dissipation, χ, defined in Equation 14.4-2). Hence, the chemistry is reduced and completely described by the two quantities, f and χ. This reduction of the complex chemistry to two variables allows the flamelet calculations to be preprocessed, and stored in look-up tables. By preprocessing the chemistry, computational costs are reduced considerably.

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turbulent flame laminar flamelet structure (see detail below)

flame

oxidizer

fuel x velocity (u fuel )

velocity (u ox )

velocity gradient (a fuel )

velocity gradient (a ox )

temperature (T fuel )

temperature (Tox )

fuel composition

oxidizer composition

fuel-oxidizer distance

Figure 14.4.1: Laminar Opposed-Flow Diffusion Flamelet


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The balance equations, solution methods, and sample calculations of the counterflow laminar diffusion flame can be found in several references. Comprehensive reviews and analyses are presented in [29, 56].

Strain Rate and Scalar Dissipation A characteristic strain rate for an opposed-flow diffusion flamelet can be defined as as = v/2d, where v is the speed of the fuel and oxidizer jets, and d is the distance between the jet nozzles. Instead of using the strain rate to quantify the departure from equilibrium, it is expedient to use the scalar dissipation, denoted by χ. The scalar dissipation is defined as χ = 2D|∇f |2

(14.4-1)

where D is a representative diffusion coefficient. Note that the scalar dissipation, χ, varies along the axis of the flamelet. For the counterflow geometry, the flamelet strain rate as can be related to the scalar dissipation at the position where f is stoichiometric by [193]:

χst =

as exp −2[erfc−1 (2fst )]2

(14.4-2)

π

where χst as fst erfc−1

= = = =

scalar dissipation at f = fst characteristic strain rate stoichiometric mixture fraction inverse complementary error function

Physically, as the flame is strained, the width of the reaction zone diminishes, and the gradient of f at the stoichiometric position f = fst increases. The instantaneous stoichiometric scalar dissipation, χst , is used as the essential non-equilibrium parameter. It has the dimensions s−1 and may be interpreted as the inverse of a characteristic diffusion time. In the limit χst → 0 the chemistry tends to equilibrium, and as χst increases due to aerodynamic straining, the non-equilibrium increases. Local quenching of the flamelet occurs when χst exceeds a critical value.

Embedding Laminar Flamelets in Turbulent Flames A turbulent flame brush is modeled as an ensemble of discrete laminar flamelets. Since, for adiabatic systems, the species mass fraction and temperature in the laminar flamelets are completely parameterized by f and χst , mean species mass fraction and temperature in the turbulent flame can be determined from the PDF of f and χst as

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φ=

Z Z

φ(f, χst )p(f, χst ) df dχst

(14.4-3)

where φ is a representative scalar, such as a species mass fraction, temperature, or density. In prePDF, f and χst are assumed to be statistically independent, so the joint PDF p(f, χst ) can be simplified as pf (f )pχ (χst ). A β PDF shape is assumed for pf , and transport equations for f and f 0 2 are solved in FLUENT to specify pf . A double-delta PDF is assumed for pχ , which, like the β PDF, is specified by its first two moments. The first moment, namely the mean scalar dissipation, χst , is modeled in FLUENT as

χst =

Cχ f 0 2 k

(14.4-4)

where Cχ is a constant with a default value of 2. The scalar dissipation variance is assumed constant and specified by you in prePDF. According to [29], it has become common practice to ignore the scalar dissipation fluctuations. Note, however, that a non-zero scalar dissipation variance will result in a smoother variation of the physical properties along the scalar dissipation coordinate. To avoid the PDF convolutions at FLUENT run-time, the integrations in Equation 14.4-3 are preprocessed in prePDF and stored in look-up tables. For adiabatic flows, singleflamelet tables have two dimensions: f and f 0 2 . The multiple-flamelet tables have the additional dimension χst . For non-adiabatic laminar flamelets, the additional parameter of enthalpy is required. However, the computational cost of modeling flamelets over a range of enthalpies is prohibitive, so some approximations are made. Heat gain/loss to the system is assumed to have a negligible effect on the species mass fractions, and the flamelet mass fractions at predefined enthalpy levels are used [22, 178]. The temperature is then calculated from Equation 14.1-14 for a range of mean enthalpy gain/loss, H ∗ . Accordingly, mean temperature and density PDF tables have an extra dimension of mean enthalpy. In prePDF, you can either generate your own flamelets, or import them as flamelet files calculated with other stand-alone packages. Such stand-alone codes include OPPDIF [160], RIF [9, 10, 198] and RUN-1DL [196]. prePDF can import flamelet files in OPPDIF format or standard flamelet file format. Instructions for generating and importing flamelets are provided in Section 14.4.4 and Section 14.4.5.

14.4.4

Flamelet Generation

The laminar counterflow diffusion flame equations can be transformed from physical space (with x as the independent variable) to mixture fraction space (with f as the independent


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variable) [199]. In prePDF, a simplified set of the mixture fraction space equations are solved [198]. Here, N equations are solved for the species mass fractions, Yi ,

1 ∂Yi ∂Yi 1 1 ∂ 2 Yi 1 ∂Lei 1 ∂Yi 1 1 ρ = ρχ +S − ρχ − 1 − i 2 ∂t 2 Lei ∂f 2 2 ∂f 2 ∂f 2 Lei Lei ∂f "

#

"

∂ρχ cp ∂(k/cp ) + ρχ ∂f k ∂f (14.4-5)

!#

and one equation for temperature:

X ∂T 1 ∂2T 1 X ∗ 1 ∂cp X 1 ∂Yi ∂T 1 ρ = ρχ 2 − Hi Si + ρχ + cp,i − 4σp Xi ai (T 4 − Tb4 ) ∂t 2 ∂f cp i 2cp ∂f Le ∂f ∂f c i p i i (14.4-6) "

#

"

#

The notation in Equations 14.4-5 and 14.4-6 is as follows: Yi , T , ρ, and f are the ith species mass fraction, temperature, density, and mixture fraction, respectively. Lei is the ith species Lewis number, as defined in Equation 13.1-4. k, cp,i , and cp are the thermal conductivity, ith species specific heat, and mixture-averaged specific heat, respectively. Si is the ith species reaction rate, and Hi∗ is the specific enthalpy of the ith species. The scalar dissipation, χ, must be modeled across the flamelet. An extension of Equation 14.4-2 to variable density is used [127]: q

2

as 3( ρ∞ /ρ + 1) q χ(f ) = exp −2[erfc−1 (2f )]2 4π 2 ρ∞ /ρ + 1

(14.4-7)

The last term in Equation 14.4-6 is an optically thin model for radiative energy loss from the flamelet. Here, σ is the Stefan-Boltzmann constant, p is the pressure, Xi is the ith species mole fraction, ai are polynomial coefficients for the Planck mean absorption coefficients (taken from [93]), and Tb is the far-field (background) temperature. Including the radiation term offers the capability of slightly increased accuracy, but may cause flamelets to be extinguished at low strain rates. Hence, the radiation term should be enabled with caution.

! The default setting in FLUENT is Lei = 1, although prePDF offers the capability to include differential diffusion effects. When activated, the Lewis numbers are automatically calculated from Equation 13.1-4. However, the mixture fraction space equations contain considerable simplification, and most often, better results are obtained with the default Lei = 1 setting. This default is recommended, especially for highly diffusive species such as H2 . The differential diffusion option should be used only to “tweak” a Lei = 1 solution. You can adjust the number of grid points used to discretize the mixture fraction space. Since the species mass fractions and temperature are solved coupled and implicit in f

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space, the memory and time requirements can increase drastically with the number of f grid points, and moderate values are recommended. prePDF also provides parameters to control the stability of the solution of Equations 14.4-5 and 14.4-6. You can adjust two multiplication factors for the solution’s time steps if the solution diverges.

Non-Adiabatic Laminar Flamelets For non-adiabatic flamelets, prePDF follows the approach of [22, 178] and assumes that flamelet species profiles are unaffected by heat loss/gain from the flamelet. This implementation treats the heat losses accurately and consistently. Furthermore, no special non-adiabatic flamelet profiles need to be generated, avoiding a very cumbersome preprocessing step. In addition, the compatibility of prePDF and FLUENT with external flamelet generation packages (e.g., OPPDIF, RIF, RUN-1DL) is retained. The disadvantage to this model is that the effect of the heat losses on the species mass fraction is not taken into account. Also, the effect of the heat loss on the extinction limits is not taken into account. In the equilibrium non-premixed model, the temperature limits are constant values Tmin and Tmax . For the non-adiabatic flamelet model, these temperature limits are surfaces or functions of mixture fraction and scalar dissipation to more closely bound the enthalpy domain. The bottom temperature surface, Tmin (f, χ), is calculated as the minimum of the temperature from the flamelet calculation at point (f ,χ) and Tad (f ) − ∆T − , but cannot be lower than the globally lowest temperature in the flamelet calculation, TMIN : Tmin (f, χ) = max(TMIN , min[(Tad (f ) − ∆T − ), Tfl (f, χ)])

(14.4-8)

The top temperature curve, Tmax (f, χ), is calculated as the maximum of the maximum environment temperature defined by you, TMAX , the temperature from the flamelet calculation at point f , and Tad (f ) + ∆T + : Tmax (f, χ) = max(TMAX , Tad (f ) + ∆T + , Tfl (f, χ))

(14.4-9)

where f χ TMIN TMAX ∆T − ∆T + Tfl Tad (f )

= = = = = = = =


mixture fraction scalar dissipation globally lowest temperature maximum boundary (e.g., hot wall or inlet) temperature in domain maximum temperature drop expected because of heat losses maximum temperature rise over the adiabatic temperature curve temperature in flamelet profile adiabatic (equilibrium) flame temperature

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After flamelet generation, the flamelet profiles are convoluted with the assumed-shape PDFs as in Equation 14.4-3, and then tabulated for look-up in FLUENT. You can set the resolution of the look-up table. The assumption is made that both the enthalpy loss/gain and the scalar dissipation do not fluctuate. The PDF tables have the following dimensions: Tmean (fmean , fvar , H ∗ , χ) Yi,mean (fmean , fvar , H ∗ ) for χ = 0 (i.e., equilibrium solution) Yi,mean (fmean , fvar , χ) for χ 6= 0 ρmean (fmean , fvar , H ∗ , χ) During the FLUENT solution, the equations for the mean mixture fraction, mixture fraction variance, and mean enthalpy are solved. The scalar dissipation field is calculated from the turbulence field and the mixture fraction variance. The mean values of cell temperature, density, and species mass fraction are obtained from the PDF look-up table

14.4.5

Flamelet Import

prePDF can import one or more flamelet files, convolute these flamelets with the assumedshape PDFs (see Equation 14.4-3), and construct look-up tables for use in FLUENT. The flamelet files can be generated in prePDF, or with separate, stand-alone computer codes. Two types of flamelet files can be imported into prePDF: binary files generated by the OPPDIF code [160], and standard format files described in Section 14.4.6 and in Peters and Rogg [196]. When flamelets are generated in physical space (such as with OPPDIF), the species and temperature vary in one spatial dimension. The species and temperature must then be mapped from physical space to mixture fraction space. If the diffusion coefficients of all species are equal, a unique definition of the mixture fraction exists. However, with differential diffusion, the mixture fraction can be defined in a number of ways. prePDF provides four methods of computing the mixture fraction profile along the laminar flamelet: • Average of C and H: Following Drake and Blint [60], the mixture fraction is calculated as the mean value of fC and fH , where fC and f H are the mixture fraction values based on the carbon and hydrogen elements. • Hydrocarbon formula: Following Bilger et al. [21], the mixture fraction is calculated as f=

b − box bfuel − box

(14.4-10)

where

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b=2

YH YO YC + 0.5 − Mw,C Mw,H Mw,O

(14.4-11)

YC , YH , and YO are the mass fractions of carbon, hydrogen, and oxygen atoms, and Mw,C , Mw,H , and Mw,O are the molecular weights. box and bfuel are the values of b at the oxidizer and fuel inlets. • Nitrogen method: The mixture fraction is computed in terms of the mass fraction of the nitrogen species: f=

YN − YN,ox YN,fuel − YN,ox

(14.4-12)

where YN is the elemental mass fraction of nitrogen along the flamelet, YN,ox is the mass fraction of nitrogen at the oxidizer inlet, and YN,fuel is the mass fraction of nitrogen at the fuel inlet. • Read from a file (standard format files only): This option is for flamelets solved in mixture fraction space. If you choose this method, prePDF will search for the mixture fraction keyword Z, as specified in [196], and retrieve the data. If prePDF does not find mixture fraction data in the flamelet file, it will instead use the hydrocarbon formula method described above. The flamelet profiles in the multiple-flamelet data set should vary only in the strain rate imposed; the species and the boundary conditions should be the same. The formats for multiple flamelets are as follows: • OPPDIF format: The multiple-flamelet OPPDIF files should be produced using the CNTN keyword in the OPPDIF script. Alternatively, you can use prePDF to merge a number of single-flamelet OPPDIF files into a multiple-flamelet file. • Standard format: If you have a set of standard format flamelet files, you should manually merge the files into a multiple-flamelet file. (You can use a text editor or the UNIX cat command to merge the files.) When you import the merged file into prePDF, prePDF will search for and count the occurrences of the HEADER keyword to determine the number of flamelets in the file. For either type of file, prePDF will determine the number of flamelet profiles and sort them in ascending strain-rate order. For flamelets generated in physical space, you can select one of the four methods available for the calculation of mixture fraction. The scalar dissipation will be calculated from the strain rate using Equation 14.4-2.


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14.4.6

User Inputs for the Laminar Flamelet Model

Instructions for using prePDF to create PDF tables from generated and imported flamelets are provided here, along with information about related files and formats.

Creating a PDF Table from Generated Laminar Flamelets The procedures for the flamelet calculation approach described in Section 14.4.4 are presented in this section. See Section 14.3.1 for instructions about starting prePDF. Step 1: Activate Laminar Flamelet Generation To specify the generation of a laminar flamelet library, you will use the Define Case panel (Figure 14.4.2). Setup −→Case...

Figure 14.4.2: The Define Case Panel In the Define Case panel, select the Multiple Strained Laminar Flamelets option under Chemistry models if you wish to generate a flamelet file with multiple strained flamelets. If you wish to generate a single flamelet, select the Single Laminar Flamelet option. Next, choose Adiabatic or Non-Adiabatic under Heat transfer options. Finally, select Generate under Flamelet options.

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Step 2: Define the Flamelet Once you have enabled the flamelet generation option, you can use the Flamelet Generation panel (Figure 14.4.3) to define the flamelet. Setup −→Flamelet Generation...

Figure 14.4.3: The Flamelet Generation Panel

Step 2a: Import the Chemical System Data The first step in defining the flamelet is to read the species and reaction definitions for the chemical system. The species thermodynamic, transport and reaction data must be in CHEMKIN format [125]. Information about the format of these files is detailed later in this section.


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To read the chemistry file into prePDF, click on the Chemistry Files... button in the Flamelet Generation panel. When you click this button, a Select File dialog box will open, in which you can specify the chemistry file to be read. Up to 100 species can be included in the flamelet calculation. If the number of species used in the flamelet calculation is greater than n, where n is the maximum number of species specified in the Memory Allocation panel (see Section 14.3.1), prePDF will automatically select the n species with the largest concentrations for inclusion in the PDF file. After the chemistry file has been read, the species it contains will appear in the Defined Species list in the Flamelet Generation panel (as shown in Figure 14.4.3). Step 2b: Define the Fuel and Oxidizer Compositions To define the fuel and oxidizer compositions, you will specify the following parameters under Composition in the Flamelet Generation panel: 1. Select Fuel under Stream. 2. Select a species in the Defined Species list. Select either Mole Fractions or Mass Fractions under Species Composition In... and enter the desired value in the Species Fraction field. 3. When you are satisfied with your entry, select the next species and repeat the process until you have set all mole or mass fractions for the fuel stream. 4. Input the mole or mass fractions for the oxidizer stream by selecting Oxidiser under Stream and repeating steps 1–3. You can check the current setting for a species in a particular stream by selecting the stream and choosing the species name in the Defined Species list. Step 2c: Set the Flamelet Parameters In the Flamelet Generation panel, enter values for the following parameters under Laminar Flamelet Options. Under Mixture Fraction, set the following parameter: # Grid Points specifies the number of mixture fraction grid points distributed between the oxidizer (f = 0) and the fuel (f = 1). Increased resolution will provide greater accuracy, but since the flamelet species and temperature are solved coupled and implicit in f space, the solution time and memory requirements increase linearly with the number of f grid points. The default value of 32 is enough to resolve the temperature distribution in most cases.

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Under Scalar Dissipation, set the following parameters: Value is the scalar dissipation value of the flamelet generated when the Single Laminar Flamelet option has been selected in the Define Case panel. # Maximum Grid Points specifies the maximum number of laminar flamelet profiles to be calculated when the Multiple Strained Laminar Flamelets option has been selected in the Define Case panel. When the Multiple Strained Laminar Flamelets model has been selected, prePDF calculates the flamelets at the following pre-defined scalar dissipation values (in s−1 ): 0 (equilibrium), 0.01, and 0.1, followed by the series 1, 2, 5, 10, 20, 50, 100, 200, 500, . . .. The flamelets will be generated until either the number of flamelets defined in # Maximum Grid Points have been calculated or until the extinction limit has been determined. The extinction limit is defined as the maximum scalar dissipation at which reaction can be sustained, and is determined automatically by prePDF if a sufficiently large number of flamelets have been defined in # Maximum Grid Points. The value of the scalar dissipation at the extinction limit depends on the fuel and oxidizer composition, operating pressure, and chemistry model, and thus determining the value may be sensitive to numerical parameters such as mixture fraction grid resolution in the flamelet computation. You can also choose whether or not to use the Differential Diffusion and Include radiation options. See Section 14.4.4 for details. After the flamelet parameters have been defined, click Apply in the Flamelet Generation panel to register the changes. prePDF automatically calculates an approximate value of the stoichiometric mixture fraction, Stoichiometric f. Note that Stoichiometric f is calculated at the mixture fraction location with the maximum equilibrium temperature, and is thus an approximation of the actual stoichiometric mixture fraction. After calculating the laminar flamelet (see Step 5, below), prePDF will automatically write out the flamelet to a standard flamelet file, then import the flamelet and generate a PDF table. If the solution diverges, you can adjust the values of Initial CFL and Multiply factor under Solution Controls to control the solution algorithm. The first time step is calculated as the explicit diffusion stability-limited time step multiplied by the Initial CFL value. If the solution diverges before the first time step is complete, the Initial CFL value should be lowered. Subsequent time steps are continually multiplied by the Multiply Factor. If the solution diverges after the first time step, this factor should be reduced. Step 2d: Define the Operating Conditions for the Flamelet You can specify the flamelet operating pressure and the temperatures of the inlet streams using the Operating Conditions panel. Setup −→Operating Conditions...


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If you are creating a non-adiabatic flamelet, you will need to input the Nonadiabatic Flamelet Temperature Limits, as described below: Min. Temperature is the globally lowest temperature expected, TMIN in Equation 14.4-8. Max. Temperature is the maximum boundary (hot wall or inlet stream) temperature in the domain, TMAX in Equation 14.4-9. Temperature Drop is the maximum expected temperature drop due to heat loss from the domain (∆T − in Equation 14.4-8). Temperature Increase is the maximum expected temperature increase due to heat gain into the domain (∆T + in Equation 14.4-9). The default value of 1500 K for Temperature Drop can be used for most cases involving hydrocarbon combustion. This value can be decreased if the boundary conditions suggest moderate heat losses. In problems involving extreme temperature conditions, it might be necessary to increase both the Temperature Drop and Temperature Increase values. You can check whether the FLUENT solution is within the PDF table temperature bounds using the non-premixed-combustion-parameters text command and setting the Enable checking of PDF table temperature limits? option to yes. define −→ models −→ species −→non-premixed-combustion-parameters

See Section 14.3.1 for more information about setting operating conditions. Step 3: Set the PDF Table Parameters Once you have defined the flamelet, you will next define the PDF table parameters using the Solution Parameters panel. Setup −→Solution Parameters... Under Fuel Mixture Fraction, set the number of Fuel Mixture Fraction Points and Fuel Mixture Fraction Variance Points. The default Automatic Distribution clustering in the mixture fraction coordinate is recommended. See Section 14.3.1 for details about these parameters. For adiabatic multiple-flamelet problems, you may also set a value for the Scalar Dissipation Variance in the Flamelet Parameters panel (Figure 14.4.4) to use the assumed double-delta PDF for the scalar dissipation. Once the importing of the flamelet library has been completed, the Flamelet Model Parameters panel will report the number of laminar flamelets in the PDF file (Laminar Flamelets in File) and the flamelet file name. Setup −→Flamelet Parameters...

! If you set the Scalar Dissipation Variance to 0, you will be effectively ignoring turbulent fluctuations in the scalar dissipation, i.e., the mean and instantaneous scalar dissipation will be equal.

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Figure 14.4.4: The Flamelet Model Parameters Panel

Step 4: Save an Input File Next you can save an input file containing the flamelet definition and other specifications, using the File/Write/Input... menu item. File −→ Write −→Input... This can be important if you want to revisit your laminar flamelet setup because this setup is not stored in the PDF file. Step 5: Calculate the Flamelet To calculate the flamelet data, you will use the Calculate/Flamelet menu item. Calculate −→Flamelet prePDF will immediately prompt you for the name of the flamelet file. The flamelet profiles will be written to this file automatically when the calculation is complete. The flamelet file will be in the standard file format, and can be imported or merged with other flamelet files, as described in later in this section. After you specify the file name, prePDF will begin the flamelet calculation, reporting its progress in the text window. Just before the flamelet calculation, prePDF will write a monitor file called FLAMELET.MON in your working directory. This file contains the thermodynamic and chemistry information, and can be useful for monitoring and troubleshooting flamelet generation calculations. After the flamelet calculation is complete, prePDF will write the flamelet to disk, and then construct the PDF file. If the flamelet calculation does not converge, decrease the Initial CFL (towards zero) and


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the Multiply factor (towards 1) in the Flamelet Generation panel, and then recalculate the flamelet data. Step 6: Save the PDF File When prePDF has completed the PDF calculation, you can save the PDF file as usual, with the File/Write/PDF... menu item. See Section 14.3.1. File −→ Write −→PDF...

! You can read the PDF file back into prePDF at a later time for postprocessing. You cannot, however, modify the solution parameters and recalculate the PDF table unless you also import the original flamelet file. Since the PDF table for multiple flamelets is three-dimensional, there are viewing options for both the instantaneous physical properties and the PDF integrated physical properties. These options are described below. When you are satisfied with the PDF file and you have saved it, you can continue the non-premixed combustion modeling procedure in FLUENT. The procedures for setting up and solving a flamelet-based model in FLUENT are the same as for other non-premixed combustion models. See Section 14.3.3 for details. Step 7a: Postprocessing of Adiabatic Multiple-Flamelet Files Reviewing Instantaneous Values When you are plotting instantaneous values using the Property Curves panel (Figure 14.4.5), you can plot the specified variable for a constant value of Dimensionless Scalar Dissipation. (You can also plot the variable for a constant value of mixture fraction.) Display −→Property Curves...

Figure 14.4.5: The Property Curves Panel

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Plotting the Scalar Dissipation Distribution You can also plot the distribution of scalar dissipation, using the Display/Scalar Dissipation menu item. Display −→Scalar Dissipation A scalar dissipation distribution plot is shown in Figure 14.4.6.

KEY 1.00E+01

8.00E+00 S c a l a r D i s s i p a t i o n

6.00E+00

4.00E+00

( 1 / s )

2.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

Flamelet Number

SCALAR DISSIPATION DISTRIBUTION

prePDF V4.00

Fluent Inc.

Figure 14.4.6: Scalar Dissipation Distribution

Reviewing 3D Flamelet-PDF Tables For multiple-flamelet models, you can view slices of the 3D flamelet-PDF table using the Flamelet-PDF-Table panel (Figure 14.4.7). Display −→Flamelet PDF Table... The look-up tables generated for multiple-flamelet systems contain the mean temperature, density, and species mass fractions as a function of three quantities: mean mixture fraction, mixture fraction variance, and mean dimensionless scalar dissipation. Consequently, when you ask prePDF to display the look-up tables, you will be displaying them slice-by-slice. In the Flamelet-PDF-Table panel, you can select the variable to be plotted in the Plot Variable drop-down list. Next, you must define how the three-dimensional array of data points available in the look-up table is to be sliced; i.e., which discrete independent variable (either f or χst,d ) is to be held constant and whether the constant value is to be selected as a numerical Value or by discretization index (Slice number).


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Figure 14.4.7: The Flamelet-PDF-Table Panel

If you specify Slice as the Plot type, you will select which discretized variable is to be constant (Scalar Dissipation or F-Mean) and then specify the Slice # (discretization index). For example, the panel shown in Figure 14.4.7 requests a look-up table generated at the tenth discrete value of scalar dissipation. To generate the plot (see Figure 14.4.8), click Display. Alternately, you may want to define a slice of the 3D look-up table based on a specific value of one of the independent quantities. When this is the case, select Value as the Plot type. You can then select a slice of the 3D table that corresponds to a constant Scalar Dissipation Value or F-Mean Value, and supply the physical value of the selected quantity in the Value field. Next, you can set the Refinement Factor, which determines the resolution of the plotted curve. A refinement factor of 1.0 (the default) implies that the plot will use the same number of discrete points that you requested in the Solution Parameters panel. Increasing this factor will cause prePDF to compute and display additional data points, yielding a smoother plot but requiring some time to compute. Finally, click the Lookup button to access the data to be plotted and then click Display to display the plot.

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1.8E+03


1.2E+03

2.50E-01 2.00E-01


K

1.00E-01

5.9E+02 5.00E-02

3.0E+02

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

SCALAR DISSIPATION SLICE NUMBER 10 MEAN FLAME TEMPERATURE FROM FLAMELET-PDF-TABLE

prePDF V4.00

Fluent Inc.

Figure 14.4.8: Display of a Single Slice of a 3D Flamelet-PDF Table

Step 7b: Postprocessing of Non-Adiabatic Multiple Flamelet Files Reviewing Non-Adiabatic Flamelet PDF Tables For non-adiabatic flamelets, you can view slices of the four-dimensional non-adiabatic flamelet tables using the Nonadiabatic-Table panel (Figure 14.4.9). Display −→Nonadiabatic Table... The Nonadiabatic-Table panel is also used for viewing the non-adiabatic PDF tables for equilibrium chemistry models. See Section 14.3.1 for more information about using this panel. In the case of non-adiabatic flamelets, there is the additional parameter of scalar dissipation. In addition to varying the mean enthalpy and mean mixture fraction, you can vary the display of the PDF table by changing the value of Slice # under Scalar dissipation, which gives the table a fourth “dimension”. For the non-adiabatic multiple-flamelet PDF tables, you can plot the scalar dissipation distribution using the Display/Scalar Dissipation menu item in the same way as for the adiabatic multiple-flamelet PDF tables. Display −→Scalar Dissipation


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Figure 14.4.9: The Nonadiabatic-Table Panel for Flamelets

Creating a PDF Table from Imported Laminar Flamelets The procedure for importing flamelets is very similar to the flamelet generation procedure described above, except that the flamelet generation step is skipped. Step 1: Activate Flamelet Import In the Define Case panel (Figure 14.4.2), select the Multiple Strained Laminar Flamelets option under Chemistry models if you wish to import a flamelet file with multiple strained flamelets. If you wish to import a single flamelet, select the Single Laminar Flamelet option. Next, choose Adiabatic or Non-Adiabatic under Heat transfer options. Finally, select Import under Flamelet Options. Setup −→Case... Once you have enabled flamelet import, you will next define the flamelet model parameters and solution parameters.

! The parameters for the flamelet model and the solution process must be defined before you import the flamelet file, because prePDF performs the mixture-fraction calculations and generates the PDF look-up table automatically after it reads the data from the flamelet file. Step 2: Set the PDF Table Parameters Step 2a: Non-Adiabatic Table Parameters If you are modeling a non-adiabatic combustor, you will need to set the Nonadiabatic Flamelet Temperature Limits in the Operating Conditions panel, as described in Step 2d on page 14-103.

14-110



Setup −→Operating Conditions... Step 2b: Mixture Fraction Table Parameters You will next set the resolution of the mixture fraction mean and variance in the Solution Parameters panel, as described in Step 3 on page 14-104. Setup −→Solution Parameters... Step 2c: Scalar Dissipation and Flamelet Conversion Parameters If you are importing flamelets generated in physical space, such as with OPPDIF [160], prePDF will need to construct a mixture fraction profile from the species field (see Section 14.4.5). You can access the parameters for this conversion in the Flamelet Model Parameters panel (Figure 14.4.10). Setup −→Flamelet Parameters...

Figure 14.4.10: The Flamelet Model Parameters Panel The parameters for the flamelet import are as follows: Pressure Conversion Factor specifies a factor for converting pressure data to SI units. If you are reading OPPDIF data, this parameter should be set to 1, since OPPDIF files report the pressure in Pa. If you are importing standard flamelet files, which are formatted files, you should check for the units of pressure reported in the file and input the appropriate conversion factor for the pressure to be in Pa. Mixture Fraction Calculation specifies which of the methods described in Section 14.4.5 should be used to compute the mixture fraction. Read From File is the default and


14-111


recommended option. If the flamelet file does not contain mixture fraction data, prePDF will report this and use the Hydrocarbon Formula option instead. Finally, set the scalar dissipation parameters as described in Step 3 on page 14-104. Step 3: Import the Flamelet File After setting the parameters, you can import the flamelet file. For OPPDIF flamelet files, use the File/Import/Oppdif Flamelets... menu item: File −→ Import −→Oppdif Flamelets... For standard format flamelet files, use the File/Import/Standard Flamelets... menu item: File −→ Import −→Standard Flamelets... After you specify the name of a standard format file to be imported, prePDF will ask you if the file was written for mixture fraction values in ascending (starting from the oxidizer inlet), or descending (starting from the fuel inlet) order. By default, it will assume descending order.

After reading the flamelet file, prePDF will report the species data and then integrate with the β PDF to generate the PDF look-up table. If the number of species in the flamelet file is larger than the species limit in prePDF, the species with the lowest mass fractions are filtered out. The temperature curves are then constructed and the enthalpy domain is discretized. After this, the PDF integrations are performed. Note that this process may take some time, as four-dimensional tables are being generated. Step 4: Save and Postprocess the PDF File When prePDF has completed the PDF calculation, you can save the PDF file as usual, with the File/Write/PDF... menu item. See Section 14.3.1 for details. File −→ Write −→PDF...

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! You can read the PDF file back into prePDF at a later time for postprocessing. You cannot, however, modify the solution parameters and recalculate the PDF table unless you also import the original flamelet file. Postprocessing for the PDF look-up table data is the same as for the PDF table data resulting from flamelet generation (see Step 6 on page 14-106 ).

Merging Single Flamelet Files into a Multiple Flamelet Library If you have a number of single-flamelet files, you can use prePDF to merge them and write out a single file containing the multiple flamelets. You can then read this file back into prePDF. To perform the merging, you will use the MERGE-FLAMELETS text command. FLAMELET-MODEL −→MERGE-FLAMELETS First, you will specify a name for the merged file and the number of single flamelet files. Then you will specify the name of each of the single flamelet files. After all names are entered, prePDF will merge the flamelet data and write out the merged file.

! If your flamelet files have lowercase names, be sure to enclose the file names in quotation marks. If you have a number of single-flamelet files in the standard format, you will need to merge them outside of prePDF, using your text editor or the UNIX cat command.

Files for Flamelet Modeling In this section, information is provided about the standard flamelet files used for the flamelet generation and import, and also the CHEMKIN [125] chemistry files used in the flamelet generation. The flamelet files generated by OPPDIF software [160] or in OPPDIF format are binary, so formatting information is not relevant for them. The Thermodynamic and Transport Databases prePDF uses a thermodynamic database and must be able to access the database file, THERMO.DB. This file must be present in the directory where you run prePDF, or it must be accessed through an environment variable, THERMODB, which points to the location of this file. When the flamelet generation approach is used, prePDF also uses a transport database (for differential diffusion) and must be able to access the database file, TRANSPORT.DB. This file must be present in the directory where you run prePDF or it must be accessed through an environment variable, TRANSPORTDB, which points to the location of this file. In most installations, you will be running prePDF using procedures supplied by Fluent Inc. and these procedures will set the environment variables for you.


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Standard Flamelet Files The data structure for the standard flamelet file format is based on keywords that precede each data section. If any of the keywords in your flamelet data file do not match the supported keywords, you will have to manually edit the file and change the keywords to one of the supported types. (The prePDF flamelet filter is case-insensitive, so you need not worry about capitalization within the keywords.) The following keywords are supported by the prePDF filter: • Header section: HEADER • Main body section: BODY • Number of species: NUMOFSPECIES • Number of grid points: GRIDPOINTS • Pressure: PRESSURE • Strain rate: STRAINRATE • Scalar dissipation: CHI • Temperature: TEMPERATURE and TEMP • Mass fraction: MASSFRACTION• Mixture fraction: Z Sample File A sample flamelet file in the standard format is provided below. Note that not all species are listed in this file. HEADER STRAINRATE 100. NUMOFSPECIES 12 GRIDPOINTS 39 PRESSURE 1. BODY Z 0.0000E+00 4.3000E-07 2.1876E-04 5.9030E-04 2.1967E-03 2.6424E-03 8.9401E-03 1.2800E-02 2.8522E-02 3.0647E-02

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2.1780E-06 9.4701E-04 3.1435E-03 1.7114E-02 3.2680E-02

1.2651E-05 1.4700E-03 4.3038E-03 2.1698E-02 3.4655E-02

7.8456E-05 1.8061E-03 5.6637E-03 2.6304E-02 4.2784E-02



5.2655E-02 6.5420E-02 1.9518E-01 2.8473E-01 9.5897E-01 9.9025E-01 TEMPERATURE 3.0000E+02 3.0013E+02 3.5644E+02 4.3055E+02 6.9655E+02 7.6268E+02 1.4702E+03 1.7516E+03 2.2766E+03 2.2962E+03 2.0671E+03 1.8792E+03 9.6530E+02 7.5025E+02 3.2730E+02 3.0939E+02 MASSFRACTION-H2 3.2354E-07 7.4290E-07 1.2219E-05 1.7873E-05 3.0888E-05 3.3684E-05 1.0484E-04 2.6807E-04 3.1422E-03 4.1281E-03 2.4296E-02 3.7472E-02 1.7135E-01 2.6359E-01 9.5775E-01 9.8996E-01 MASSFRACTION-CH4 . . . . . . . . MASSFRACTION-O 6.8919E-10 2.8720E-09 5.5281E-07 1.7418E-06 2.2484E-05 3.8312E-05 1.4284E-03 2.7564E-03 3.0916E-03 2.3917E-03 5.2235E-05 1.1469E-05 2.7470E-09 8.7551E-11 7.2143E-14 0.0000E+00

8.2531E-02 4.4175E-01 9.9819E-01

1.0637E-01 6.6643E-01 1.0000E+00

1.4122E-01 8.6222E-01

3.0085E+02 4.9469E+02 8.3393E+02 1.9767E+03 2.3044E+03 1.6655E+03 5.7496E+02 3.0248E+02

3.0475E+02 5.8260E+02 9.8775E+02 2.1403E+03 2.3027E+03 1.4355E+03 4.4805E+02 3.0000E+02

3.2382E+02 6.3634E+02 1.1493E+03 2.2444E+03 2.2164E+03 1.1986E+03 3.6847E+02

1.6979E-06 2.1556E-05 3.6720E-05 6.1906E-04 5.3302E-03 5.5159E-02 4.2527E-01 9.9814E-01

3.8179E-06 2.5872E-05 4.3768E-05 1.2615E-03 6.7434E-03 7.9788E-02 6.5658E-01 1.0000E+00

8.3038E-06 2.8290E-05 5.4359E-05 2.3555E-03 1.4244E-02 1.1573E-01 8.5814E-01

. . . . 1.1905E-08 3.6996E-06 6.6385E-05 3.9063E-03 1.7345E-03 2.3011E-06 2.9341E-12 0.0000E+00

. . . . 4.8669E-08 8.3107E-06 1.8269E-04 4.3237E-03 1.2016E-03 3.7414E-07 7.0471E-13 0.0000E+00

. . . . 2.0370E-07 1.3525E-05 4.4320E-04 3.7141E-03 2.4323E-04 4.2445E-08 0.0000E+00

Missing Species prePDF will check whether all species in the flamelet data file exist in the thermodynamic properties databases THERMO.DB and thermodb.scm. If any of the species in the flamelet file do not exist, prePDF will issue an error message and halt the calculation. If this occurs, you can either add the missing species to the databases (as described in Section 14.5), or remove the species from the flamelet file. You should not remove a species from the flamelet data file unless its species concentration is very small (10−3 or less) throughout the flamelet profile. If you remove a low-


14-115


concentration species, you will not have the species concentrations available for viewing in the FLUENT calculation, but the accuracy of the FLUENT calculation will otherwise be unaffected.

! If you choose to remove any species, be sure to also update the number of species (keyword NUMOFSPECIES) in the flamelet data file, to reflect the loss of any species you have removed from the file. If a species with relatively large concentration is missing from the prePDF thermodynamic databases, you will have to add it (as described in Section 14.5). Removing a highconcentration species from the flamelet file is not recommended. Ordering of the Flamelet Data The flamelet files are written in either ascending (starting from the oxidizer inlet, where f = 0), or descending (starting from the fuel inlet, where f = 1) mixture fraction values. When you import the file, prePDF will ask you to specify the order in which the file has been written. Chemistry Files Several chemistry files accompany prePDF, to be used as a basis to perform the singleflamelet calculations. The chemistry files are written in the standard CHEMKIN format, and are provided on the distribution CD in the following directory: ⇓

path/Fluent.Inc/prepdf4.x/db/ where path is the directory where you have installed your Fluent Inc. software and the variable x corresponds to your release version, e.g., 1 for prePDF 4.1. Up to 100 species can be included in the flamelet calculation. If the number of species used in the flamelet calculation is greater than n, where n is the maximum number of species specified in the Memory Allocation panel (see Section 14.3.1), prePDF will automatically select the n species with the largest concentration for inclusion in the PDF file. Description of Chemistry Files Short descriptions of and references for the available chemistry files are presented below. The files are named by the main fuel or mechanism name and the number of reactions, and end with the extension .che. skeletal25.che: Skeletal mechanism for methane oxidation. 17 species and 25 reversible reactions (35 reactions if the forward and backward steps are counted separately). From Table B.1 on p. 262 in [191].

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kee58.che: Kee mechanism for methane oxidation. 18 species and 58 reversible reactions. From Table B.2 on p. 263 in [191]. glarborg152.che: Glarborg mechanism for hydrocarbon oxidation up to C2 . 33 species and 152 reversible reactions. From Table B.4 on p. 270 in [191]. methanol40.che: Mechanism for methanol combustion. The mechanism consists of H2 O2 chain reactions, HO2 formation and consumption, H2 O2 formation and consumption, recombination reactions, CO-CO2 mechanism, CHO consumption, CH2 O consumption, CH2 OH consumption, and CH3 OH consumption. 16 species and 40 reactions. From Chapter 16 and Table 1.1 in [196]. reduced25.che: Skeletal mechanism for methane oxidation. 17 species and 25 reversible reactions (35 reactions if the forward and backward steps are counted separately). From the Table on p. 161 in [245]. drake67.che: Mechanism for the CO-H2 -N2 system. NOx chemistry is also included. 22 species and 67 reversible reactions. From Table 1 on p. 154 in [59]. smooke46.che: Methane combustion. 17 species and 46 reversible reactions. From Table 7 on p. 1787 in [246]. heptane42.che: A chemical kinetic mechanism for the oxidation of heptane. 20 species and 42 reversible reactions. From Table 1 on p. 296 in [32]. hydrogen18.che: Mechanism for H2 combustion. 9 species and 18 reactions. From Chapter 10 and Table 1.1 in [196]. hydrogen37.che: Mechanism for H2 combustion. NOx chemistry is also included. 13 species and 37 reactions. From Table 11.1 on p. 179 in [196].


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14.5

Adding New Species to the prePDF Database

prePDF uses the CHEMKIN database [125], THERMO.DB, for species thermodynamic properties (see [125] for information on the parameters and the format required for the THERMO.DB file). If you wish to add a new species, you will need to add the thermodynamic data to the THERMO.DB file, as well as to the corresponding FLUENT database file, named thermodb.scm. You can use prePDF to generate the required thermodb.scm file: 1. Calculate the PDF look-up table in prePDF with the new species and the new THERMO.DB database file. 2. Generate a FLUENT property file with a default name prepdf.scm. File −→ Write −→Thermodb... 3. You now have two choices: • Rename prepdf.scm to thermodb.scm, and run FLUENT from the local directory where thermodb.scm is. • If you would like to store the new species permanently, edit the file thermodb.scm in the path/Fluent.Inc/fluent6.x/cortex/lib/ installation directory (where path is the directory in which you have installed FLUENT and the variable x corresponds to your release version, e.g., 1 for fluent6.1) and add in the new species from prepdf.scm. Be careful to keep the Scheme lists, enclosed within round parentheses, intact, and also ensure that your editor does not insert carriage-returns to break up the inserted Scheme lists. It is recommended that you save a backup copy of thermodb.scm before making any changes.

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Modeling Premixed

FLUENT has a premixed turbulent combustion model based on the reaction-progress variable approach. Information about this model is provided in the following sections: • Section 15.1: Overview and Limitations • Section 15.2: Premixed Combustion Theory • Section 15.3: Using the Premixed Combustion Model

15.1 15.1.1

Overview and Limitations Overview

In premixed combustion, fuel and oxidizer are mixed at the molecular level prior to ignition. Combustion occurs as a flame front propagating into the unburnt reactants. Examples of premixed combustion include aspirated internal combustion engines, leanpremixed gas turbine combustors, and gas-leak explosions. Premixed combustion is much more difficult to model than non-premixed combustion. The reason for this is that (subsonic) premixed combustion usually occurs as a thin flame that is stretched and contorted by turbulence. The overall rate of propagation of the flame is determined by both the laminar flame speed and the turbulent eddies. The laminar flame speed is determined by the rate that species and heat diffuse upstream into the reactants and burn. To capture the laminar flame speed, the internal flame structure would need to be resolved, as well as the detailed chemical kinetics and molecular diffusion processes. Since practical laminar flame thicknesses are of the order of millimeters or smaller, resolution requirements are usually unaffordable. The effect of turbulence is to wrinkle and stretch the propagating laminar flame sheet, increasing the sheet area and, in turn, the effective flame speed. The large turbulent eddies tend to wrinkle and corrugate the flame sheet, while the small turbulent eddies, if they are smaller than the laminar flame thickness, may penetrate the flame sheet and modify the laminar flame structure. Non-premixed combustion, in comparison, can be greatly simplified to a mixing problem (for example, the mixture fraction approach in Section 14.1). The essence of premixed


15-1

Modeling Premixed Combustion

combustion modeling lies in capturing the turbulent flame speed, which is influenced by both the laminar flame speed and the turbulence. In premixed flames, the fuel and oxidizer are intimately mixed before they enter the combustion device. Reaction then takes place in a combustion zone that separates unburnt reactants and burnt combustion products. Partially premixed flames exhibit the properties of both premixed and diffusion flames. They occur when an additional oxidizer or fuel stream enters a premixed system, or when a diffusion flame becomes lifted off the burner so that some premixing takes place prior to combustion. Premixed and partially premixed flames can be modeled using FLUENT’s finite-rate formulation (see Chapter 13). See also Chapter 16 for information about FLUENT’s partially premixed combustion model. If the flame is perfectly premixed, so only one stream at one equivalence ratio enters the combustor, it is possible to use the premixed combustion model.

15.1.2

Limitations

The following limitations apply to the premixed combustion model: • You must use the segregated solver. The premixed combustion model is not available with either of the coupled solvers. • The premixed combustion model is valid only for turbulent, subsonic flows. These types of flames are called deflagrations. Explosions, also called detonations, where the combustible mixture is ignited by the heat behind a shock wave, can be modeled with the finite-rate model using either the segregated solver or the coupled solver. See Chapter 13 for information about the finite-rate model. • The premixed combustion model cannot be used in conjunction with the pollutant (i.e., soot and NOx ) models. However, a perfectly premixed system can be modeled with the partially premixed model (see Chapter 16). • You cannot use the premixed combustion model to simulate reacting discrete-phase particles, since these would result in a partially premixed system. Only inert particles can be used with the premixed combustion model.

15-2


15.2 Premixed Combustion Theory

15.2

Premixed Combustion Theory

The turbulent premixed combustion model, based on work by Zimont et al. [302, 303, 305], involves the solution of a transport equation for the reaction progress variable. The closure of this equation is based on the definition of the turbulent flame speed.

15.2.1

Propagation of the Flame Front

In many industrial premixed systems, combustion takes place in a thin flame sheet. As the flame front moves, combustion of unburnt reactants occurs, converting unburnt premixed reactants to burnt products. The premixed combustion model thus considers the reacting flow field to be divided into regions of burnt and unburnt species, separated by the flame sheet. The progression of the reaction is therefore the same as the progression of the flame front. The flame front propagation is modeled by solving a transport equation for the scalar quantity c, the (Favre averaged) reaction progress variable: ∂ µt (ρc) + ∇ · (ρ~v c) = ∇ · ∇c + ρSc ∂t Sct

(15.2-1)

where c Sct Sc

= = =

reaction progress variable turbulent Schmidt number for the gradient turbulent flux reaction progress source term (s−1 )

The progress variable is defined as n X

c=

Yi

i=1 n X

(15.2-2)

Yi,ad

i=1

where n Yi Yi,ad

= number of products = mass fraction of species i = mass fraction of species i after complete adiabatic combustion

Based on this definition, c = 0 where the mixture is unburnt and c = 1 where the mixture is burnt: • c = 0: unburnt mixture • c = 1: burnt mixture


15-3


The value of c is defined as a boundary condition at all flow inlets. It is usually specified as either 0 (unburnt) or 1 (burnt). The mean reaction rate in Equation 15.2-1 is modeled as [303] ρSc = ρu Ut |∇c|

(15.2-3)

where ρu Ut

= density of unburnt mixture = turbulent flame speed

Other mean reaction rate models exist [29], and can be specified using user-defined functions. See the separate UDF Manual for details about user-defined functions.

15.2.2

Turbulent Flame Speed

The key to the premixed combustion model is the prediction of Ut , the turbulent flame speed normal to the surface of the flame. The turbulent flame speed is influenced by the following: • laminar flame speed, which is, in turn, determined by the fuel concentration, temperature, and molecular diffusion properties, as well as the detailed chemical kinetics • flame front wrinkling and stretching by large eddies, and flame thickening by small eddies In FLUENT, the turbulent flame speed is computed using a model for wrinkled and thickened flame fronts [303]:

1/2

1/4

Ut = A(u0 )3/4 Ul α−1/4 `t 1/4 τt 0 = Au τc

(15.2-4) (15.2-5)

where A u0 Ul α = k/ρcp `t τt = `t /u0 τc = α/Ul2

15-4

= model constant = RMS (root-mean-square) velocity (m/s) = laminar flame speed (m/s) = molecular heat transfer coefficient of unburnt mixture (thermal diffusivity) (m2 /s) = turbulence length scale (m) = turbulence time scale (s) = chemical time scale (s)



The turbulence length scale, `t , is computed from `t = CD

(u0 )3

(15.2-6)

where is the turbulence dissipation rate. The model is based on the assumption of equilibrium small-scale turbulence inside the flamelet, resulting in a turbulent flame speed expression that is purely in terms of the large-scale turbulent parameters. The default value of 0.52 for A is recommended by [303], and is suitable for most premixed flames. The default value of 0.37 for CD should also be suitable for most premixed flames. The model is strictly applicable when the smallest turbulent eddies in the flow (the Kolmogorov scales) are smaller than the flame thickness, and penetrate into the flame zone. This is called the thin reaction zone combustion region, and can be quantified by Karlovitz numbers, Ka, greater than unity. Ka is defined as

Ka =

v2 tl = η2 tη Ul

(15.2-7)

where tl tη vη = (ν)1/4 ν

= characteristic flame time scale = smallest (Kolmogorov) turbulence time scale = Kolmogorov velocity = kinematic viscosity

Lastly, the model is valid for premixed systems where the flame brush width increases in time, as occurs in most industrial combustors. Flames that propagate for a long period of time equilibrate to a constant flame width, which cannot be captured in this model.

Turbulent Flame Speed for LES For simulations that use the LES turbulence model, the Reynolds-averaged quantities in the turbulent flame speed expression (Equation 15.2-4) are replaced by their equivalent sub-grid quantities. In particular, the large eddy length scale `t is modeled as `t = Cs ∆

(15.2-8)

where Cs is the Smagorinsky constant and ∆ is the cell characteristic length. The RMS velocity in Equation 15.2-4 is replaced by the sub-grid velocity fluctuation, calculated as −1 u0 = `t τsgs


(15.2-9)

15-5


where τsgs is the sub-grid scale mixing rate (time scale), given in Equation 13.1-27.

Flame Stretch Effect Since industrial low-emission combustors often operate near lean blow-off, flame stretching will have a significant effect on the mean turbulent heat release intensity. To take this flame stretching into account, the source term for the progress variable (ρSc in Equation 15.2-1) is multiplied by a stretch factor, G [305]. This stretch factor represents the probability that the stretching will not quench the flame; if there is no stretching (G = 1), the probability that the flame will be unquenched is 100%. The stretch factor, G, is obtained by integrating the log-normal distribution of the turbulence dissipation rate, :  s



 1 1 cr σ  ln + G = erfc −  2 2σ 2 

(15.2-10)

where erfc is the complementary error function, and σ and cr are defined below. σ is the standard deviation of the distribution of : L σ = µstr ln η

!

(15.2-11)

where µstr is the stretch factor coefficient for dissipation pulsation, L is the turbulent integral length scale, and η is the Kolmogorov micro-scale. The default value of 0.26 for µstr (measured in turbulent non-reacting flows) is recommended by [303], and is suitable for most premixed flames. cr is the turbulence dissipation rate at the critical rate of strain [303]: 2 cr = 15νgcr

(15.2-12)

By default, gcr is set to a very high value (1 × 108 ) so no flame stretching occurs. To include flame stretching effects, the critical rate of strain gcr should be adjusted based on experimental data for the burner. Numerical models can suggest a range of physically plausible values [303], or an appropriate value can be determined from experimental data. A reasonable model for the critical rate of strain gcr is gcr =

15-6

BUl2 α

(15.2-13)



where B is a constant (typically 0.5) and α is the thermal diffusivity. Equation 15.2-13 can be implemented in FLUENTusing a property user-defined function. See the separate UDF Manual for details about user-defined functions.

Preferential Diffusion Preferential diffusion accounts for the effect of variations in fuel molecular diffusion coefficients on heat release intensity in premixed turbulent combustion. Inclusion of this effect is important for simulation of combustion with light fuels (e.g., hydrogen) or heavy fuels (e.g., evaporated oil). The model for preferential diffusion is based on the concept of leading points, formulated in [133]. The authors of [133] derived formulas for the changes in mixture composition within the combustion zone due to the difference in the molecular diffusivities of fuel, Dfuel , and oxidizer, Dox . These formulas are rewritten in [305] as

λlp =

      

λ0 (1+Cst )d+d−1 d+Cst

λlp ≥ 1 (15.2-14)

λ0 (Cst +d) 1+λ0 Cst +Cst (1−λ0 d)

λlp < 1

where Cst λ0 λlp

= mass stoichiometric coefficient = stoichiometric ratio of unburnt mixture composition = stoichiometric ratio of leading-point composition

and

d=

s

Dox Dfuel

(15.2-15)

The concept of leading points is applied to the FLUENT model by using λlp instead of λ0 for the formulation of the laminar flame speed, Ul , or the molecular heat transfer coefficient, α. This simple approach results in reasonable agreement with the measurements of mass combustion rates in stirred bombs [305], without the need for additional empirical parameters.

Gradient Diffusion Volume expansion at the flame front can cause counter-gradient diffusion. This effect becomes more pronounced when the ratio of the reactant density to the product density is large, and the turbulence intensity is small. It can be quantified by the ratio (ρu /ρb )(Ul /I), where ρu , ρb , Ul , and I are the unburnt and burnt densities, laminar flame speed, and turbulence intensity, respectively. Values of this ratio greater than one indicate a tendency for counter-gradient diffusion, and the premixed combustion model may be inappropriate. Recent arguments for the validity of the turbulent-flame-speed model in such regimes can be found in Zimont et al. [304].


15-7


15.2.3

Premixed Combustion Model Formulation in FLUENT

FLUENT will solve the transport equation for the reaction progress variable c (Equation 15.2-1), computing the source term, ρSc , based on the theory outlined above: 1/4

ρSc = AGρu I 3/4 [Ul (λlp )]1/2 [α(λlp )]−1/4 `t |∇c| = AGρu I

15.2.4

"

τt τc (λlp )

#1/4

|∇c|

(15.2-16) (15.2-17)

Calculation of Temperature

The calculation method for temperature will depend on whether the model is adiabatic or non-adiabatic.

Adiabatic Temperature Calculation For the adiabatic premixed combustion model, the temperature is assumed to vary linearly between the temperature of the unburnt mixture, Tu , and the temperature of the burnt products under adiabatic conditions, Tad : T = (1 − c)Tu + cTad

(15.2-18)

Non-Adiabatic Temperature Calculation For the non-adiabatic premixed combustion model, FLUENT solves an energy transport equation in order to account for any heat losses or gains within the system. These losses/gains may include heat sources due to chemical reaction or, for example, heat losses due to radiation. The energy equation in terms of sensible enthalpy, h, for the fully premixed fuel (see Equation 11.2-3) is as follows: !

∂ k + kt (ρh) + ∇ · (ρ~v h) = ∇ · ∇h + Sh,chem + Sh,rad ∂t cp

(15.2-19)

Sh,rad represents the heat losses due to radiation and Sh,chem represents the heat gains due to chemical reaction: Sh,chem = ρSc Hcomb Yfuel

(15.2-20)

where Sc Hcomb Yfuel

15-8

= normalized average rate of product formation (s−1 ) = heat of combustion for burning 1 kg of fuel (J/kg) = fuel mass fraction of unburnt mixture



15.2.5

Calculation of Density

When the premixed combustion model is used, FLUENT calculates density using the ideal gas law. For the adiabatic model, pressure variations are neglected and the mean molecular weight is assumed to be constant. The burnt gas density is then calculated from the following relation: ρb Tb = ρu Tu

(15.2-21)

where the subscript u refers to the unburnt cold mixture, and the subscript b refers to the burnt hot mixture. The required inputs are the unburnt density (ρu ), the unburnt temperature (Tu ), and the burnt adiabatic flame temperature (Tb ). For the non-adiabatic model, you can choose to either include or exclude pressure variations in the ideal gas equation of state. If you choose to ignore pressure fluctuations, FLUENT calculates the density from ρT = ρu Tu

(15.2-22)

where T is computed from the energy transport equation, Equation 15.2-19. The required inputs are the unburnt density (ρu ) and the unburnt temperature (Tu ). Note that, from the incompressible ideal gas equation, the expression ρu RTu /pop may be considered to be the effective molecular weight of the gas, where R is the gas constant and pop is the operating pressure. If you want to include pressure fluctuations for a compressible gas, you will need to input the effective molecular weight of the gas. The density will be calculated from the ideal gas equation of state.


15-9


15.3

Using the Premixed Combustion Model

The procedure for setting up and solving a premixed combustion model is outlined below, and then described in detail. Remember that only the steps that are pertinent to premixed combustion modeling are shown here. For information about inputs related to other models that you are using in conjunction with the premixed combustion model, see the appropriate sections for those models. 1. Enable the premixed turbulent combustion model and set the related parameters. Define −→ Models −→Species... 2. Define the physical properties for the unburnt material in the domain. Define −→Materials... 3. Set the value of the progress variable c at flow inlets and exits. Define −→Boundary Conditions... 4. Initialize the value of the progress variable. Solve −→ Initialize −→Patch... 5. Solve the problem and perform postprocessing.

! If you are interested in computing the concentrations of individual species in the domain, you can use the partially premixed model described in Chapter 16. Alternatively, compositions of the unburnt and burnt mixtures can be obtained from external analyses using equilibrium or kinetic calculations.

! See Section 15.3.8 for important information about using a premixed combustion case file from FLUENT 5.

15.3.1

Enabling the Premixed Combustion Model

To enable the premixed combustion model, select Premixed Combustion under Model in the Species Model panel (Figure 15.3.1). Define −→ Models −→Species... When you turn on Premixed Combustion, the panel will expand to show the relevant inputs.

15-10


15.3 Using the Premixed Combustion Model

Figure 15.3.1: The Species Model Panel for Premixed Combustion

15.3.2

Choosing an Adiabatic or Non-Adiabatic Model

Under Premixed Combustion Model in the Species Model panel, choose either Adiabatic (the default) or Non-Adiabatic. This choice will affect only the calculation method used to determine the temperature (either Equation 15.2-18 or Equation 15.2-19).

15.3.3

Modifying the Constants for the Premixed Combustion Model

In general, you will not need to modify the constants used in the equations presented in Section 15.2. The default values are suitable for a wide range of premixed flames. If, however, you want to make some changes to the model constants, you will find them under Model Constants in the Species Model panel. You can set the Turbulence Length Scale Constant (CD in Equation 15.2-6), the Turbulent Flame Speed Constant (A in Equation 15.2-4), the Stretch Factor Coefficient (µstr in Equation 15.2-11) and the Turbulent Schmidt Number (Sct in Equation 15.2-1).


15-11


For a non-adiabatic premixed combustion model, note that the value you specify for the Turbulent Schmidt Number will also be used as the Prandtl number for energy. (The Energy Prandtl Number will therefore not appear in the Viscous Model panel for nonadiabatic premixed combustion models.) These parameters control the level of diffusion for the progress variable and for energy. Since the progress variable is closely related to energy (because the flame progress results in heat release), it is important that the transport equations use the same level of diffusion.

15.3.4

Defining Physical Properties for the Unburnt Mixture

The fluid material in your domain should be assigned the properties of the unburnt mixture, including the molecular heat transfer coefficient (α in Equation 15.2-4), which is also referred to as the thermal diffusivity. α is defined as k/ρcp , and values at standard conditions can be found in combustion handbooks (e.g., [132]). For both adiabatic and non-adiabatic combustion models, you will need to specify the Laminar Flame Speed (Ul in Equation 15.2-4) as a material property. If you want to include the flame stretch effect in your model, you will also need to specify the Critical Rate of Strain (gcr in Equation 15.2-12). As discussed in Section 15.2.2, gcr is set to a very high value (1 × 108 ) by default, so no flame stretching occurs. To include flame stretching effects, you will need to adjust the Critical Rate of Strain based on experimental data for the burner. Since the flame stretching and flame extinction can influence the turbulent flame speed (as discussed in Section 15.2.2), a realistic value for the Critical Rate of Strain is required for accurate predictions. Typical values for CH4 lean premixed combustion range from 3000 to 8000 s−1 [303]. Note that you can specify constant values or user-defined functions to define the Laminar Flame Speed and Critical Rate of Strain. See the separate UDF Manual for details about user-defined functions.

! See Section 15.3.8 for important information about using a premixed combustion case file from FLUENT 5. For adiabatic models, you will also specify the Adiabatic Temperature of Burnt Products (Tad in Equation 15.2-18), which is the temperature of the burnt products under adiabatic conditions. This temperature will be used to determine the linear variation of temperature in an adiabatic premixed combustion calculation. You can specify a constant value or use a user-defined function. For non-adiabatic models, you will instead specify the Heat of Combustion per unit mass of fuel and the Unburnt Fuel Mass Fraction (Hcomb and Yfuel in Equation 15.2-20). FLUENT will use these values to compute the heat losses or gains due to combustion, and include these losses/gains in the energy equation that it uses to calculate temperature. The Heat of Combustion can be specified only as a constant value, but you can specify a constant value or use a user-defined function for the Unburnt Fuel Mass Fraction. To specify the density for a premixed combustion model, choose premixed-combustion in the Density drop-down list and set the Density of Unburnt Reactants and Temperature of

15-12



Unburnt Reactants (Tu and ρu in Equation 15.2-21). For adiabatic premixed models, your input for Temperature of Unburnt Reactants (Tu ) will also be used in Equation 15.2-18 to calculate the temperature. The other properties specified for the unburnt mixture are viscosity, specific heat, thermal conductivity, and any other properties related to other models that are being used in conjunction with the premixed combustion model.

15.3.5

Setting Boundary Conditions for the Progress Variable

For premixed combustion models, you will need to set an additional boundary condition at flow inlets and exits: the progress variable, c. Valid inputs for the Progress Variable are as follows: • c = 0: unburnt mixture • c = 1: burnt mixture

15.3.6

Initializing the Progress Variable

Often, it is sufficient to initialize the progress variable c to 1 (burnt) everywhere and allow the unburnt (c = 0) mixture entering the domain from the inlets to blow the flame back to the stabilizer. A better initialization is to patch an initial value of 0 (unburnt) upstream of the flame holder and a value of 1 (burnt) in the downstream region (after initializing the flow field in the Solution Initialization panel). Solve −→ Initialize −→Patch... See Section 24.13.2 for details about patching values of solution variables.

15.3.7

Postprocessing for Premixed Combustion Calculations

FLUENT provides several additional reporting options for premixed combustion calculations. You can generate graphical plots or alphanumeric reports of the following items: • Progress Variable • Damkohler Number • Stretch Factor • Turbulent Flame Speed • Static Temperature • Product Formation Rate


15-13


• Laminar Flame Speed • Critical Strain Rate • Unburnt Fuel Mass Fraction • Adiabatic Flame Temperature These variables are contained in the Premixed Combustion... category of the variable selection drop-down list that appears in postprocessing panels. See Chapter 29 for a complete list of flow variables, field functions, and their definitions. Chapters 27 and 28 explain how to generate graphics displays and reports of data. Note that Static Temperature and Adiabatic Flame Temperature will appear in the Premixed Combustion... category only for adiabatic premixed combustion calculations; for nonadiabatic calculations, Static Temperature will appear in the Temperature... category. Unburnt Fuel Mass Fraction will appear only for non-adiabatic models.

Computing Species Concentrations If you know the composition of the unburnt and burnt mixtures in your model (i.e., if you have performed external analyses using single-step kinetic calculations or a third-party 1D combustion program), you can compute the species concentrations in the domain using custom field functions: • To determine the concentration of a species in the unburnt mixture, define the custom function Yu (1 − c), where Yu is the mass fraction for the species in the unburnt mixture (specified by you) and c is the value of the progress variable (computed by FLUENT). • To determine the concentration of a species in the burnt mixture, define the custom function Yb c, where Yb is the mass fraction for the species in the burnt mixture (specified by you) and c is the value of the progress variable (computed by FLUENT). See Section 29.5 for details about defining and using custom field functions.

15-14



15.3.8

Starting from a FLUENT 5 Premixed Combustion Case File

If you are using a premixed combustion case file that was created in FLUENT 5, you will need to re-enter values for several parameters that have been moved into the Properties list in the Materials panel: • Adiabatic models – Density of Unburnt Reactants (formerly Density of Unburnt Mixture in the Unburnt Mixture Density panel) – Temperature of Unburnt Reactants (formerly Temperature of Unburnt Mixture in the Unburnt Mixture Density panel ) – Adiabatic Temperature of Burnt Products (formerly Adiabatic Products Temperature in the Species Model panel) – Laminar Flame Speed (formerly Laminar Flame Velocity in the Species Model panel) – Critical Rate of Strain (formerly in the Species Model panel) • Non-adiabatic models – Density of Unburnt Reactants – Temperature of Unburnt Reactants – Heat of Combustion (formerly in the Species Model panel) – Unburnt Fuel Mass Fraction (formerly Fuel Mass Fraction in the Species Model panel) – Laminar Flame Speed – Critical Rate of Strain


15-15


15-16



Modeling Partially Premixed

FLUENT provides a partially premixed combustion model that is based on the nonpremixed combustion model described in Chapter 14 and the premixed combustion model described in Chapter 15. Information about the partially premixed combustion model is presented in the following sections: • Section 16.1: Overview and Limitations • Section 16.2: Theory • Section 16.3: Using the Partially Premixed Combustion Model

16.1 16.1.1

Overview and Limitations Overview

Partially premixed combustion systems are premixed flames with non-uniform fuel-oxidizer mixtures (equivalence ratios). Such flames include premixed jets discharging into a quiescent atmosphere, lean premixed combustors with diffusion pilot flames and/or cooling air jets, and imperfectly mixed inlets. The partially premixed model in FLUENT is a simple combination of the non-premixed model (Chapter 14) and the premixed model (Chapter 15). The premixed reactionprogress variable, c, determines the position of the flame front. Behind the flame front (c = 1), the mixture is burnt and the equilibrium or laminar flamelet mixture fraction solution is used. Ahead of the flame front (c = 0), the species mass fractions, temperature, and density are calculated from the mixed but unburnt mixture fraction. Within the flame (0 < c < 1), a linear combination of the unburnt and burnt mixtures is used.

16.1.2

Limitations

The underlying theory, assumptions, and limitations of the non-premixed and premixed models apply directly to the partially premixed model. In particular, the single-mixturefraction approach is limited to two inlet streams, which may be pure fuel, pure oxidizer, or a mixture of fuel and oxidizer. The two-mixture-fraction model extends the number of inlet streams to three, but incurs a major computational overhead. See Sections 14.1.1 and 15.1.2 for additional limitations.


16-1

Modeling Partially Premixed Combustion

16.2

Theory

The partially premixed model solves a transport equation for the mean reaction progress variable, c (to determine the position of the flame front), as well as the mixture fraction equations, f and f 0 2 . Ahead of the flame (c = 0), the fuel and oxidizer are mixed but unburnt, and behind the flame (c = 1), the mixture is burnt.

16.2.1

Calculation of Scalar Quantities

Mean scalars (such as species mass fraction, temperature, and density), denoted by φ, are calculated from the probability density function (PDF) of f and c as φ=

Z

0

1

Z

1

φ(f, c)p(f, c) df dc

(16.2-1)

0

Under the assumption of thin flames, so that only unburnt reactants and burnt products exist, the mean scalars are determined from φ=c

Z

0

1

φb (f )p(f ) df + (1 − c)

Z

0

1

φu (f )p(f ) df

(16.2-2)

where the subscripts b and u denote burnt and unburnt, respectively. The burnt scalars, φb , are functions of the mixture fraction and are calculated by mixing a mass f of fuel with a mass (1 − f ) of oxidizer and allowing the mixture to equilibrate. When non-adiabatic mixtures and/or laminar flamelets are considered, φb is also a function of enthalpy and/or strain, but this does not alter the basic formulation. The unburnt scalars, φu , are calculated similarly by mixing a mass f of fuel with a mass (1 − f ) of oxidizer, but the mixture is not reacted. Just as in the non-premixed model, the chemistry calculations and PDF integrations for the burnt mixture are performed in prePDF, and look-up tables are constructed for use by FLUENT. Turbulent fluctuation (PDF) and non-adiabatic effects are neglected for the unburnt mixture, so the mean unburnt scalars, φu , are functions of f only. These assumptions are valid for most partially premixed flows, and are made to reduce memory requirements. The unburnt density, temperature, species mass fractions, specific heat, and thermal diffusivity (denoted by φ) are fitted in prePDF to third-order polynomials of f using linear least squares:

φu =

3 X

cn f

n

(16.2-3)

n=0

16-2


16.2 Theory

Since the unburnt scalars are smooth and slowly-varying functions of f , these polynomial fits are generally accurate. Access to polynomials is provided in prePDF, in case you want to modify them.

16.2.2

Laminar Flame Speed

The reaction progress model requires the laminar flame speed (see Equation 15.2-4), which depends strongly on the composition, temperature, and pressure of the unburnt mixture. For perfectly premixed systems as in Chapter 15, the reactant stream has one composition, and the laminar flame speed is approximately constant throughout the domain. However, in partially premixed systems, the laminar flame speed will change as the reactant composition (equivalence ratio) changes, and this must be taken into account. Accurate laminar flame speeds are difficult to determine analytically, and are usually measured from experiments or computed from 1D simulations. prePDF uses fitted curves obtained from Gottgens [89] to calculate the laminar flame speed. These curves were determined for hydrogen (H2 ), methane (CH4 ), acetylene (C2 H2 ), ethylene (C2 H4 ), ethane (C2 H6 ), and propane (C3 H8 ) flames. They are valid for inlet compositions ranging from the lean limit through unity equivalence ratio (stoichiometric), for unburnt temperatures from 298 K to 800 K, and for pressures from 1 bar to 40 bars. prePDF fits these curves to piecewise-linear polynomials. The rich-limit and lean-limit equivalence ratios are also determined and converted to mixture fractions. Mixtures leaner than the lean limit or richer than the rich limit will not burn, and have zero flame speed. The required inputs are values for the mean mixture fraction f at 10 laminar flame speeds. The minimum and maximum f limits for the laminar flame speed are the first and last values of f that are input.

! These flame speed fits are accurate for air mixtures with pure fuels of H2 , CH4 , C2 H2 , C2 H4 , C2 H6 , and C3 H8 . If an oxidizer other than air or a different fuel is used, if the mixture is rich, or if the unburnt temperature or pressure is outside the range of validity, then the curve fits will be incorrect. Although prePDF defaults to a methane-air mixture, the laminar flame speed polynomial and the rich and lean limits are most likely incorrect. The laminar flame speed polynomial should be determined from other sources, such as measurements from the relevant literature or detailed 1D simulations, and input into prePDF.


16-3


16.3

Using the Partially Premixed Combustion Model

The procedure for setting up and solving a partially premixed combustion problem combines parts of the non-premixed combustion setup and the premixed combustion setup. An outline of the procedure is provided in Section 16.3.1, along with information about where to look in the non-premixed and premixed combustion chapters for details. Inputs that are specific to the partially premixed combustion model are provided in Sections 16.3.1 and 16.3.2.

16.3.1

Setup and Solution Procedure

1. Generate a PDF look-up table using prePDF. You can follow the procedure for non-premixed combustion described in Section 14.3.1 or 14.4.6 with one additional step. In the Define Case panel, turn on the Partially Premixed Model option. Setup −→Case...

!

If prePDF warns you, during the look-up calculation, that any parameters are out of the range for which the functions for laminar flame speed and unburnt density, temperature, specific heat and thermal diffusivity are valid, you will need to modify the polynomial coefficients or piecewise-linear points before saving the PDF file. Display −→Partially Premixed Properties... See Section 16.3.2 for details. 2. Read your mesh file into FLUENT and set up any other models you plan to use in conjunction with the partially premixed combustion model (turbulence, radiation, etc.). 3. Enable the partially premixed combustion model. (a) Turn on the Partially Premixed Combustion model in the Species Model panel. Define −→ Models −→Species... (b) If necessary, modify the Model Constants in the Species Model panel. These are the same at the constants for the premixed combustion model and, in most cases, you will not need to change them from their default values. See Section 15.3.3 for details. (c) After you click OK in the Species Model panel, specify (in the Select File dialog box that appears) the name of the PDF file containing the look-up tables you created in prePDF, and read it into FLUENT. 4. Define the physical properties for the unburnt material in the domain. Define −→Materials... FLUENT will automatically select the prepdf-polynomial function for Laminar Flame Speed, indicating that the piecewise-linear polynomial function from the PDF lookup table will be used to compute the laminar flame speed. You may also choose to

16-4


16.3 Using the Partially Premixed Combustion Model

use a user-defined function instead of a piecewise-linear polynomial function. See Section 15.3.4 for information about setting the other properties for the unburnt material. 5. Set the values for the progress variable (c) and the mean mixture fraction (f ) and its variance (f 0 2 ) at flow inlets and exits. (For problems that include a secondary stream, you will define boundary conditions for the mean secondary partial fraction and its variance as well.) Define −→Boundary Conditions... See Section 14.3.3 for guidelines on setting mixture fraction and variance conditions, as well as thermal and velocity conditions at inlets.

!

If you defined the fuel composition in prePDF to be the premixed inlet species, then you should set f = 1 and c = 0. If, however, you set the fuel composition in prePDF to pure fuel, you will need to set the correct equivalence ratio (0 < f < 1) and c = 0 at your inlet. 6. Initialize the value of the progress variable. Solve −→ Initialize −→Patch... See Section 15.3.6 for details. 7. Solve the problem and perform postprocessing. See Section 14.3.3 for guidelines about setting solution parameters. (These guidelines are for non-premixed combustion calculations, but they are relevant for partially premixed as well.)

16.3.2

Modifying the Unburnt Mixture Property Polynomials in prePDF

For the unburnt mixture, prePDF calculates the temperature, density, heat capacity, and thermal diffusivity as polynomial functions of the mean mixture fraction, f (see Equation 16.2-3), and the laminar flame speed as a piecewise-linear polynomial function of f . The unburnt temperature, density, heat capacity, and thermal diffusivity are calculated from the thermodynamic and transport properties in the CHEMKIN database [125]. Since these are generally smooth and slowly varying functions of f , the polynomial fits are usually accurate. However, as outlined in Section 16.2, the laminar flame speed depends on details of the chemical kinetics and molecular transport properties, and is not calculated directly in prePDF. Instead, curve fits are made to flame speeds determined by detailed simulations [89]. These fits are limited to a range of fuels (H2 , CH4 , C2 H2 , C2 H4 , C2 H6 , and


16-5


C3 H8 ), air as the oxidizer, equivalence ratios of the lean limit through 1, unburnt temperatures from 298 K to 800 K, and pressures from 1 bar to 40 bars. If your parameters fall outside this range, prePDF will warn you when it computes the look-up table. In this case, you will need to modify the piecewise-linear points in the Partially Premixed Model Properties panel (Figure 16.3.1) before you save the PDF file. Display −→Partially Premixed Properties...

Figure 16.3.1: The Partially Premixed Model Properties Panel in prePDF For each polynomial function of f (density, temperature, Cp, and thermal diffusivity, you can specify values for c0, c1, c2, and c3 (the polynomial coefficients in Equation 16.2-3). You can also specify the piecewise-linear mixture fraction (f) and its corresponding laminar flame speed (sl) for 10 different points. The first set of values is the lower limit and the last set of values is the upper limit. Outside of either limit, the laminar flame speed is constant and equal to that limit. Note also that you may choose to use a user-defined function for the laminar flame speed, in which case the piecewise-linear fit becomes irrelevant.

16-6


Chapter 17. The Composition PDF Transport Model FLUENT provides a composition PDF transport model for including finite-rate chemistry in turbulent flames. Information about this model is presented in the following sections: • Section 17.1: Overview and Limitations • Section 17.2: Composition PDF Transport Theory • Section 17.3: Using the Composition PDF Transport Model

17.1


17.1.1

Overview

The composition PDF transport model, like the EDC model (see Section 13.1.1), should be used when you are interested in simulating finite-rate chemical kinetic effects in turbulent reacting flows. With an appropriate chemical mechanism, kinetically-controlled species such as CO and NOx , as well as flame extinction and ignition, can be predicted. PDF transport simulations are computationally expensive, and it is recommended that you start your modeling with small grids, and preferably in 2D.

17.1.2

Limitations

The following limitations apply to the composition PDF transport model: • You must use the segregated solver. The composition PDF transport model is not available with either of the coupled solvers. • The composition PDF transport model cannot be used to model conjugate heat transfer. • ISAT tables (see Section 17.2.5) cannot be written or read in parallel.


17-1

The Composition PDF Transport Model

17.2

Composition PDF Transport Theory

Turbulent combustion is governed by the reacting Navier-Stokes equations. While this equation set is accurate, its direct solution (where all turbulent scales are resolved) is far too expensive for practical turbulent flows. In Chapter 13, the species equations are Reynolds-averaged, which leads to unknown terms for the turbulent scalar flux and the mean reaction rate. The turbulent scalar flux is modeled by gradient diffusion, treating turbulent convection as enhanced diffusion. The mean reaction rate is modeled by the finite-rate, eddy-dissipation, or EDC models. Since the reaction rate is invariably highly non-linear, modeling the mean reaction rate in a turbulent flow is difficult and prone to error. An alternative to Reynolds-averaging the species and energy equations is to derive a transport equation for their single-point, joint probability density function (PDF). This PDF, denoted by P , can be considered to be proportional to the fraction of the time that the fluid spends at each species, temperature, and pressure state. P has N + 2 dimensions for the N species, temperature, and pressure spaces. From the PDF, any thermochemical moment (e.g., mean or RMS temperature, mean reaction rate) can be calculated. The composition PDF transport equation is derived from the Navier-Stokes equations as [200]:

+ # " * i ∂ ∂ ∂ ∂ h 00 ∂ 1 ∂Ji,k (ρP ) + (ρui P ) + (ρSk P ) = − ρhui |ψiP + ρ ψ P ∂t ∂xi ∂ψk ∂xi ∂ψk ρ ∂xi (17.2-1)

where P ρ ui Sk ψ 00 ui Ji,k

= Favre joint PDF of composition = mean fluid density = Favre mean fluid velocity vector = reaction rate for species k = composition space vector = fluid velocity fluctuation vector = molecular diffusion flux vector

The notation of h. . .i denotes expectations, and hA|Bi is the conditional probability of event A, given the event B occurs. In Equation 17.2-1, the terms on the left-hand side are closed, while those on the righthand side are not and require modeling. The first term on the left-hand side is the unsteady rate of change of the PDF, the second term is convection by the mean velocity field, and the third term is the reaction rate. The principal strength of the PDF transport approach is that the highly-non-linear reaction term is completely closed and requires no modeling. The two terms on the right-hand side represent scalar convection by turbulence (turbulent scalar flux), and molecular mixing/diffusion, respectively.

17-2


17.2 Composition PDF Transport Theory

The turbulent scalar flux term is unclosed, and is modeled in FLUENT by the gradientdiffusion assumption i ∂ ∂ h 00 ρhui |ψiP = − ∂xi ∂xi

µt ∂P ρSct ∂xi

!

(17.2-2)

where µt is the turbulent viscosity and Sct is the turbulent Schmidt number. A turbulence model, as described in Chapter 10, is required for composition PDF transport simulations, and this determines µt . Since single-point PDFs are described, information about neighboring points is missing and all gradient terms, such as molecular mixing, are unclosed and must be modeled. The mixing model is critical because combustion occurs at the smallest molecular scales when reactants and heat diffuse together. Modeling mixing in PDF methods is not straightforward, and is the weakest link in the PDF transport approach. See Section 17.2.3 for a description of the mixing models.

17.2.1

Solution of the PDF Transport Equation

The PDF has N + 2 dimensions and the solution of its transport equation by conventional finite-difference or finite-volume schemes is not tractable. Instead, a Monte Carlo method is used, which is ideal for high-dimensional equations since the computational cost increases just linearly with the number of dimensions. The disadvantage is that statistical errors are introduced, and these must be carefully controlled. To solve the modeled PDF transport equation, an analogy is made with a stochastic differential equation (SDE) which has identical solutions. The Monte Carlo algorithm involves notional particles which move randomly through physical space due to particle convection, and also through composition space due to molecular mixing and reaction. The particles have mass and, on average, the sum of the particle masses in a cell equals the cell mass (cell density times cell volume). Since practical grids have large changes in cell volumes, the particle masses are adjusted so that the number of particles in a cell is controlled to be approximately constant and uniform. The processes of convection, diffusion, and reaction are treated in fractional steps as described below.

17.2.2

Particle Convection

A spatially second-order-accurate Lagrangian method is used in FLUENT, consisting of two steps. At the first convection step, particles are advanced to a new position 1/2

xi


1 = x0i + u0i ∆t 2

(17.2-3)

17-3


where xi = ui = ∆t =

particle position vector Favre mean fluid-velocity vector at the particle position particle time step

For unsteady flows, the particle time step is the physical time step. For steady-state flows, local time steps are calculated for each cell as ∆t = min(∆tconv , ∆tdiff , ∆tmix )

(17.2-4)

where ∆tconv ∆tdiff ∆tmix ∆x

= = = =

convection number × ∆x / (cell fluid velocity) diffusion number × (∆x)2 / (cell turbulent diffusivity) mixing number × turbulent time scale characteristic cell length = volume1/D where D is the problem dimension

After the first convection step, all other sub-processes, including diffusion and reaction are treated. Finally, the second convection step is calculated as x1i

=

1/2 xi

+ ∆t

1/2 ui

s

1 1 ∂µt 2µt − u0i + + ξi 2 ρSct ∂xi ρ∆tSct

!

(17.2-5)

where ρ ui µt Sct ξi

17.2.3

= = = = =

mean cell fluid density mean fluid-velocity vector at the particle position turbulent viscosity turbulent Schmidt number standardized normal random vector

Particle Mixing

Molecular mixing of species and heat must be modeled and is usually the source of the largest modeling error in the PDF transport approach. FLUENT provides two models for molecular diffusion: the Modified Curl model [114, 182] and the IEM model (which is sometimes called the LSME model) [58].

The Modified Curl Model For the modified Curl model, a few particle pairs are selected at random from all the particles in a cell, and their individual compositions are moved toward their mean composition. For the special case of equal particle mass, the number of particle pairs selected is calculated as

17-4



Npair =

1.5Cφ N ∆t τt

(17.2-6)

where N Cφ τt

= total number of particles in the cell = mixing constant (default = 2) = turbulent time scale (for the k- model this is k/)

The algorithm in [182] is used for the general case of variable particle mass. For each particle pair, a uniform random number ξ is selected and each particle’s composition φ is moved toward the pair’s mean composition by a factor proportional to ξ:

(φ0i mi + φ0j mj ) (mi + mj ) 0 (φi mi + φ0j mj ) 1 0 φj = (1 − ξ)φj + ξ (mi + mj ) φ1i = (1 − ξ)φ0i + ξ

(17.2-7)

where φi and φj are the composition vectors of particles i and j, and mi and mj are the masses of particles i and j.

The IEM Model For the IEM (Interaction by Exchange with the Mean) model, the composition of all particles in a cell are moved a small distance toward the mean composition:

φ1 = φ0 − 1 − e−0.5Cφ /τt

φ0 − φ˜

(17.2-8)

where φ˜ is the Favre mean-composition vector at the particle’s location. Considering that, physically, molecular mixing occurs between neighboring points in space, it is apparent that both the modified Curl and IEM models, which take no account of this, are approximate. However, these models work remarkably well in a wide-range of turbulent reacting flows.

17.2.4

Particle Reaction

The particle composition vector is represented as φ = (Y1 , Y2 , . . . , YN , T, p)


(17.2-9)

17-5


where Yk is the kth species mass fraction, T is the temperature and p the pressure. For the reaction fractional step, the reaction source term is integrated as 1

0

φ =φ +

Z

∆t

Sdt

(17.2-10)

0

where S is the chemical source term. Most realistic chemical mechanisms consist of tens of species and hundreds of reactions. Typically, reaction does not occur until an ignition temperature is reached, but then proceeds very quickly until reactants are consumed. Hence, some reactions have very fast time scales, on the order of 10−10 s, while others have much slower time scales, on the order of 1 s. This time-scale disparity, called numerical stiffness, means that extensive computational work is required to integrate the chemical source term in Equation 17.2-10. In FLUENT, the reaction step (i.e., the calculation of φ1 ) can be performed either by Direct Integration or by In-Situ Adaptive Tabulation (ISAT), as described in the following paragraphs. A typical steady-state PDF transport simulation in FLUENT may have 50000 cells, with 20 particles per cell, and require 1000 iterations to converge. Hence, at least 109 stiff ODE integrations are required. Since each integration typically takes tens or hundreds of milliseconds, on average, the direct integration of the chemistry is extremely CPUdemanding. Equation 17.2-10 may be considered as a mapping. With an initial composition vector φ0 , the final state φ1 depends only on φ0 and the mapping time ∆t. In theory, if a table could be built before the simulation, covering all realizable φ0 states and time steps, the integrations could be avoided by table look-ups. In practice, this a priori tabulation is not feasible since a full table in N + 3 dimensions (N species, temperature, pressure and time-step) is required. To illustrate this, consider a structured table with M points in each dimension. The required table size is M N +3 , and for a conservative estimate of M = 10 discretization points and N = 7 species, the table would contain 1010 entries. On closer examination, the full storage of the entire realizable space is very wasteful because most regions are never accessed. For example, it would be unrealistic to find a composition of YOH = 1, T = 300K in a real combustor. In fact, for steady-state, 3D laminar simulations, the chemistry can be parameterized by the spatial position vector. Thus, mappings must lie on a three dimensional manifold within the N + 3 dimensional composition space. It is, hence, sufficient to tabulate only this accessed region of the composition space. The accessed region, however, depends on the particular chemical mechanism, molecular transport properties, flow geometry, and boundary conditions. For this reason, the accessed region is not known before the simulation and the table cannot be preprocessed. Instead, the table must be built during the simulation, and this is referred to as in-situ tabulation.

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FLUENT employs ISAT [201] to dynamically tabulate the chemistry mappings and accelerate the time to solution. ISAT (In-Situ Adaptive Tabulation) is a method to tabulate the accessed composition space region on-the-fly (in-situ) with error control (adaptive tabulation). When ISAT is used correctly, accelerations of two to three orders of magnitude are typical. However, it is important to understand how ISAT works to use it optimally.

17.2.5

The ISAT Algorithm

ISAT is a powerful tool that enables realistic chemistry to be incorporated in multidimensional flow simulations by accelerating the chemistry calculations. Typical speedups of 100 to 1000 fold are common. This power is apparent if one considers that with a conservative speed-up of 100, a simulation that would take three months without ISAT can be run in one day. At the start of a FLUENT simulation using ISAT, the ISAT table is empty. For the first particle reaction step, Equation 17.2-10 is integrated with a stiff ODE solver. This is called Direct Integration (DI). The first table entry is created and consists of: • The initial composition φ0 • The mapping φ1 • The mapping gradient matrix A = ∂φ1 /∂φ0 • A hyper-ellipsoid of accuracy The next particle’s reaction mapping is calculated as follows: The initial composition vector for this particle is denoted φ0q , where the subscript q denotes a query. The existing table (consisting of one entry at this stage) is queried by interpolating the new mapping as φ1q = φ0q + A(φ0q − φ0 ) (17.2-11) The mapping gradient is hence used to linearly interpolate the table when queried. The ellipsoid of accuracy (EOA) is the elliptical space around the table point φ0 where the linear approximation to the mapping is accurate to the specified tolerance, tol . If the query point φ1q is within the EOA, then the linear interpolation by Equation 17.2-11 is sufficiently accurate, and the mapping is retrieved. Otherwise, a direct integration (DI) is performed and the mapping error = |B(φ1DI − φ1q )| is calculated (here, B is a scaling matrix). If this error is smaller than the specified error tolerance ( < tol ), then the original interpolation φ1q is accurate and the EOA is grown so as to include φ0q . If not, a new table entry is added. Table entries are stored as leaves in a binary tree. When a new table entry is added, the original leaf becomes a node with two leaves—the original leaf and the new entry.


17-7


A cutting hyper-plane is created at the new node, so that the two leaves are on either side of this cutting plane. A composition vector φ0q will hence lie on either side of this hyper-plane. The ISAT algorithm is summarized as follows: 1. The ISAT table is queried for every composition vector during the reaction step. 2. For each query φ0q the table is traversed to identify a leaf whose composition φ0 is close to φ0q . 3. If the query composition φ0q lies within the ellipsoid of accuracy of the leaf, then the mapping φ1q is retrieved using interpolation by Equation 17.2-11. 4. Otherwise, Direct Integration (DI) is performed and the error between the DI and the linear interpolation is measured. 5. If the error is less than the tolerance, then the ellipsoid of accuracy is grown and the DI result is returned. 6. Otherwise, a new table entry is added. At the start of the simulation, most operations are adds and grows. Later, as more of the composition space is tabulated, retrieves become frequent. Since adds and grows are very slow whereas retrieves are relatively quick, initial FLUENT iterations are slow but accelerate as the table is built.

17-8


17.3 Using the Composition PDF Transport Model

17.3

Using the Composition PDF Transport Model

The procedure for setting up and solving a composition PDF transport problem is outlined below, and then described in detail. Remember that only steps that are pertinent to composition PDF transport modeling are shown here. For information about inputs related to other models that you are using in conjunction with the composition PDF transport model, see the appropriate sections for those models. 1. Read a CHEMKIN-formatted gas-phase mechanism file and the associated thermodynamic data file in the CHEMKIN Mechanism panel (see Section 13.1.9). File −→ Import −→CHEMKIN Mechanism...

!

If your chemical mechanism is not in CHEMKIN format, you will have to enter the mechanism into FLUENT as described in Section 13.1.2. 2. Enable a turbulence model. Define −→ Models −→Viscous... 3. Enable the PDF transport model and set the related parameters. Define −→ Models −→Species... 4. Check the material properties in the Materials panel and the reaction parameters in the Reactions panel. The default settings should be sufficient, although you may consider enabling pressure-dependent reactions (see Sections 13.1.1 and 13.1.4 for details). Define −→Materials... 5. Set the operating conditions and boundary conditions. Define −→Operating Conditions... Define −→Boundary Conditions... 6. Check the solver settings. Solve −→ Controls −→Solution... The default settings should be sufficient, although it is recommended to change the discretization to second-order once the solution has converged. 7. Initialize the solution. You may need to patch a high-temperature region to ignite the flame. Solve −→ Initialize −→Initialize... Solve −→ Initialize −→Patch... 8. Set up solution monitors. Solve −→Iterate...


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9. Solve the problem and perform postprocessing.

! A good initial condition can reduce the solution time substantially. It is recommended to start from an existing solution calculated using the EDC model, non-premixed combustion model, or partially premixed combustion model. See Chapters 13, 14, and 16 for further information on such simulations. This procedure is demonstrated in the PDF transport tutorial, which is available at the Fluent User Services Center (www.fluentusers.com).

17.3.1

Enabling the Composition PDF Transport Model

To enable the composition PDF transport model, select Composition PDF Transport in the Species Model panel (Figure 17.3.1). Define −→ Models −→Species...

Figure 17.3.1: The Species Model Panel for Composition PDF Transport When you turn on Composition PDF Transport, the panel will expand to show the relevant inputs.

17.3.2

Setting Integration Parameters

Under Reactions in the Species Model panel, enable Volumetric. Click on the Integration Parameters button to open the Integration Parameters panel (Figure 17.3.2). The stiff ODE integrator has two error tolerances—the Absolute Error Tolerance and the Relative Error Tolerance under ODE parameters—that are set to 10−6 and 10−9 respectively.

17-10



Figure 17.3.2: The Integration Parameters Panel

These should be sufficient for most applications, although these tolerances may need to be decreased for some cases such as ignition. For problems in which the accuracy of the chemistry integrations is crucial, it may be useful to test the accuracy of the error tolerances in simple zero-dimensional and one-dimensional test simulations with parameters comparable to those in the full simulation.

ISAT Parameters If you have selected ISAT under Integration Options, you will then be able to set additional ISAT parameters. The numerical error in ISAT linear interpolation is controlled by the ISAT Error Tolerance under ISAT parameters. It may help to increase this during the initial transient solution. A larger error tolerance implies larger EOAs, greater error, but smaller tables and quicker run times. The default ISAT Error Tolerance of 0.001 should be sufficiently accurate for most flames. For the Max. Storage, it is recommended that you set this parameter to a large fraction of the available memory on your computer. The default value is 100 MB.


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The ISAT table is normalized by a Reference Time Step. The default value of 1ms should be sufficient for most turbulent reacting flames. However, if the largest chemical time scale is much different from 1 ms, the Reference Time Step should be set to this characteristic chemical time scale. You can also specify the Number of Trees and the Verbosity. The Number of Trees is the number of sub-tables within the ISAT table. For larger problems, ISAT efficiency may be increased by increasing the number of trees from the default value of 4. The value of Verbosity allows you to monitor ISAT performance in different levels of detail. See Section 17.3.6 for details about this parameter. To purge the ISAT table, click on Clear ISAT Table. See Section 17.3.7 for more details about using ISAT efficiently.

17.3.3

Selecting the Particle Mixing Model

In the Species Model panel, select Modified Curl or IEM under Mixing Model and specify the value of Cphi (Cφ in Equation 17.2-6). For more information about particle diffusion, see Section 17.2.3.

17.3.4

Defining the Solution Parameters

After you have defined the rest of the problem, you will need to specify solution parameters that are specific to the composition PDF transport model in the Solution Controls panel (Figure 17.3.3). Solve −→ Controls −→Solution... Under PDF Transport Parameters, you can specify the following: Particles per cell sets the number of PDF particles per cell. Higher values of this parameter will reduce statistical error. Local Time Stepping toggles the calculation of local time steps. If this option is disabled, then you will need to specify the Time Step directly. If this option is enabled, then you can specify the following parameters: Convection # specifies the stable convection number (see ∆tconv in Equation 17.2-4). Diffusion # specifies the stable diffusion number (see ∆tdiff in Equation 17.2-4). Mixing # specifies the stable mixing number (see ∆tmix in Equation 17.2-4).

17.3.5

Monitoring the Solution

At low speeds, combustion couples to the fluid flow through density. The Monte Carlo PDF transport algorithm has random fluctuations in the density field, which in turn

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Figure 17.3.3: The Solution Controls Panel for Composition PDF Transport

causes fluctuations in the flow field. For steady-state flows, statistical fluctuations are decreased by averaging over a number of previous iterations in the Iterate panel (Figure 17.3.4). Averaging reduces statistical fluctuations and stabilizes the solution. However, FLUENT often indicates convergence of the flow field before the composition fields (temperatures and species) are converged. You should lower the default convergence criteria in the Residual Monitors panel, and always check that the Total Heat Transfer Rate in the Flux Reports panel is balanced. It is also recommended that you monitor temperature/species on outlet boundaries and ensure that these are steady. By default FLUENT performs one finite-volume iteration and then one PDF transport particle step. This should be optimal for most cases; however, control is provided to perform multiple finite-volume iterations (Number of FV Sub-Iterations) and multiple PDF transport particle steps (Number of PDF Sub-Iterations). By increasing the Iterations in Time Average, fluctuations are smoothed out and residuals level off at smaller values. However, the composition PDF method requires a larger number of iterations to reach steady-state. It is recommended that you use the default of 50 Iterations in Time Average until the steady-state solution is obtained. Then, to gradually decrease the residuals, increase the Iterations in Time Average by setting a Time


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Figure 17.3.4: The Iterate Panel for Composition PDF Transport

Average Increment to a value from 0 to 1 (the value 0.2 is recommended). Subsequent iterations will increase the Iterations in Time Average by the Time Average Increment.

17.3.6

Monitoring ISAT

You can monitor ISAT performance by setting the Verbosity in the ISAT Parameters panel. For a Verbosity of 1, FLUENT writes the following information periodically to a file named isat stats.dat: • Total number of queries • Total number of queries resulting in retrieves • Total number of queries resulting in grows • Total number of queries resulting in adds • Total number of queries resulting in replaces because the table is full The ISAT Verbosity option of 2 is for expert users who are familiar with ISATAB v3.0 [202]. FLUENT writes out the following files for Verbosity = 2: • isat stats.out, as described above • isat log.out lists the ISATAB v3.0 input parameters

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• ODE accuracy.out reports the accuracy of the ODE integrations. For every new ISAT table entry, if the maximum absolute error in temperature or species is greater than any previous error, a line is written to this file. This line consists of the total number of ODE integrations performed up to this time, the maximum absolute species error, the absolute temperature error, the initial temperature and the time step. • ODE diagnostic.out prints diagnostics from the ODE solver • ODE warning.out prints warnings from the ODE solver In parallel, each processor builds its own ISAT table. If Verbosity is enabled in parallel, each compute node writes out the Verbosity file(s) with the node ID number added on to the file name.

17.3.7

Efficient Use of ISAT

Efficient use of ISAT requires thoughtful control. What follows are some detailed recommendations concerning the achievement of this goal. During the initial iterations, before a steady-state solution is attained, transient composition states occur that are not present in the steady-state solution. For example, you might patch a high temperature region in a cold fuel-air mixing zone to ignite the flame, whereas the converged solution never has hot reactants without products. Since all states that are realized in the simulation are tabulated in ISAT, these initial mappings are wasteful of memory, and can degrade ISAT performance substantially. If the table fills the allocated memory and contains entries from an initial transient, it may be beneficial to purge the ISAT table. This is achieved by either clearing it in the Integration Parameters panel, or saving your case and data files, exiting FLUENT, then restarting FLUENT and reading in the case and data. The optimum ISAT table is achieved when a new table is started from the converged FLUENT solution. If you are simulating a range of parametric cases where the flame changes gradually, it is likely beneficial to create such an optimum table for the first case, and then save it. File −→ Write −→ISAT Table... Subsequent runs can start from this table by reading it into memory. File −→ Read −→ISAT Table... Once the ISAT table is full, all queries which cannot be retrieved are directly integrated. Since retrieves are much quicker than direct integrations, larger ISAT tables are faster. Hence, you should set the ISAT Max. Storage to a large fraction of the available memory on your computer.


17-15


ISAT efficiency may be increased by employing multiple tables (also called trees). Increasing the number of trees has the effect of decreasing the table size and hence the time needed to build the table, but increasing the retrieve time. Hence, for long simulations with simple chemistry, a small number of tables (i.e. setting Number of Trees in the ISAT Parameters panel to 1) may be optimal. On the other hand, for short simulations with complex chemistry, computers with limited memory, or simulations with a small ISAT error tolerance, a large number of trees (e.g., 64) is likely optimal since most of the CPU time is spent building the table. The numerical error in the ISAT linear interpolation is controlled by the ISAT Error Tolerance, which has a default value of 0.001. Faster convergence times may be obtained by starting a simulation with a larger error tolerance. Once this coarse table solution has converged, clear the table, lower the ISAT Error Tolerance, and re-converge. It is recommended to always decrease the ISAT Error Tolerance at convergence and ensure that the thermochemical quantities in which you are interested in are unchanged. Note that you will have to clear the table or restart your FLUENT simulation before you can reset this error tolerance. The smaller the error tolerance, the larger the resulting table and hence the more CPU time required to build it. There is a substantial performance penalty in specifying an error tolerance smaller than is needed to achieve acceptable accuracy, and the error tolerance should be decreased gradually and judiciously. From experience, ISAT performs very well on premixed turbulent flames, where the range of composition states are smaller than in non-premixed flames. ISAT performance degrades in flames with large time-scales, where more work is required in the ODE integrator.

17.3.8

Unsteady Composition PDF Transport Simulations

For unsteady composition PDF transport simulations, a fractional step scheme is employed where the PDF particles are advanced over the time step, and then the flow is advanced over the time step. Unlike steady-state simulations, composition statistics are not averaged over iterations, and to reduce statistical error you should increase the number of particles per cell in the Solution Monitors panel. For low speed flows, the thermochemistry couples to the flow through density. Statistical errors in the calculation of density may cause convergence difficulties between time step iterations. If you experience this, increase the number of PDF particles per cell, or decrease the density under-relaxation.

17.3.9

Compressible Composition PDF Transport Simulations

Compressibility is included when ideal-gas is selected as the density method in the Materials panel. For such flows, particle internal energy is increased by p∆v over the time step ∆t, where p is the cell pressure and ∆v is the change in the particle specific volume over the time step.

17-16



17.3.10

Postprocessing for Composition PDF Transport Calculations

Reporting Options FLUENT provides several reporting options for composition PDF transport calculations. You can generate graphical plots or alphanumeric reports of the following items: • Static Temperature • Mean Static Temperature • RMS Static Temperature • Mass fraction of species-n • Mean species-n Mass Fraction • RMS species-n Mass Fraction The instantaneous temperature in a cell is calculated as PNc

Tp mp i=1 mp

Tinstant = Pi=1 Nc

(17.3-1)

where Tinstant Nc Tp mp

= = = =

instantaneous cell temperature at the present iteration number of particles in the cell particle temperature particle mass

Mean and root-mean-square (RMS) temperatures are calculated in FLUENT by averaging instantaneous temperatures over a user-specified number of previous iterations (see Section 17.3.5). Note that for steady-state simulations, instantaneous temperatures and species represent a Monte Carlo realization and are as such unphysical. Mean and RMS quantities are much more useful.

Particle Tracking Options When you have enabled the composition PDF transport model, you can display the trajectories of the PDF particles using the Particle Tracks panel (Figure 17.3.5). Display −→Particle Tracks...


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Figure 17.3.5: The Particle Tracks Panel for Tracking PDF Particles

Select the Track PDF Transport Particles option to enable PDF particle tracking. To speed up the plotting process, you can specify a value n for Skip, which will plot only every nth particle. For details about setting other parameters in the Particle Tracks panel, see Section 21.13.1. When you have finished setting parameters, click Display to display the particle trajectories in the graphics window.

17-18


Chapter 18.

Modeling Pollutant Formation

This chapter discusses the models available in FLUENT for modeling pollutant formation. Information is presented in the following sections: • Section 18.1: NOx Formation • Section 18.2: Soot Formation

18.1

NOx Formation

The following sections present the theoretical background of NOx prediction and information about the usage of the NOx models employed by the solver. • Section 18.1.1: Overview and Limitations • Section 18.1.2: Governing Equations for NOx Transport • Section 18.1.3: Thermal NOx Formation • Section 18.1.4: Prompt NOx Formation • Section 18.1.5: Fuel NOx Formation • Section 18.1.6: NOx Formation by Reburning • Section 18.1.7: NOx Formation in Turbulent Flows • Section 18.1.8: Using the NOx Model

18.1.1


NOx emission consists of mostly nitric oxide (NO). Less significant are nitrogen oxide (NO2 ) and nitrous oxide (N2 O). NOx is a precursor for photochemical smog, contributes to acid rain, and causes ozone depletion. Thus, NOx is a pollutant. The FLUENT NOx model provides a tool to understand the sources of NOx production and to aid in the design of NOx control measures.


18-1


NOx Modeling in FLUENT The FLUENT NOx model provides the capability to model thermal, prompt, and fuel NOx formation as well as NOx consumption due to reburning in combustion systems. It uses rate models developed at the Department of Fuel and Energy, The University of Leeds, England as well as from the open literature. To predict NOx emission, FLUENT solves a transport equation for nitric oxide (NO) concentration. With fuel NOx sources, FLUENT solves an additional transport equation for an intermediate species (HCN or NH3 ). The NOx transport equations are solved based on a given flow field and combustion solution. In other words, NOx is postprocessed from a combustion simulation. It is thus evident that an accurate combustion solution becomes a prerequisite of NOx prediction. For example, thermal NOx production doubles for every 90 K temperature increase when the flame temperature is about 2200 K. Great care must be exercised to provide accurate thermophysical data and boundary condition inputs for the combustion model. Appropriate turbulence, chemistry, radiation and other submodels must be applied. To be realistic, one can only expect results to be as accurate as the input data and the selected physical models. Under most circumstances, NOx variation trends can be accurately predicted but the NOx quantity itself cannot be pinpointed. Accurate prediction of NOx parametric trends can cut down on the number of laboratory tests, allow more design variations to be studied, shorten the design cycle, and reduce product development cost. That is truly the power of the FLUENT NOx model and, in fact, the power of CFD in general.

The Formation of NOx in Flames In laminar flames, and at the molecular level within turbulent flames, the formation of NOx can be attributed to four distinct chemical kinetic processes: thermal NOx formation, prompt NOx formation, fuel NOx formation, and reburning. Thermal NOx is formed by the oxidation of atmospheric nitrogen present in the combustion air. Prompt NOx is produced by high-speed reactions at the flame front, and fuel NOx is produced by oxidation of nitrogen contained in the fuel. The reburning mechanism reduces the total NOx formation by accounting for the reaction of NO with hydrocarbons. The FLUENT NOx model is able to simulate all four of these processes.

Restrictions on NOx Modeling • You must use the segregated solver. The NOx models are not available with either of the coupled solvers. • The NOx models cannot be used in conjunction with the premixed combustion model.

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18.1 NOx Formation

18.1.2

Governing Equations for NOx Transport

FLUENT solves the mass transport equation for the NO species, taking into account convection, diffusion, production and consumption of NO and related species. This approach is completely general, being derived from the fundamental principle of mass conservation. The effect of residence time in NOx mechanisms, a Lagrangian reference frame concept, is included through the convection terms in the governing equations written in the Eulerian reference frame. For thermal and prompt NOx mechanisms, only the NO species transport equation is needed: ∂ (ρYNO ) + ∇ · (ρ~v YNO ) = ∇ · (ρD∇YNO ) + SNO ∂t

(18.1-1)

As discussed in Section 18.1.5, the fuel NOx mechanisms are more involved. The tracking of nitrogen-containing intermediate species is important. FLUENT solves a transport equation for the HCN or NH3 species in addition to the NO species: ∂ (ρYHCN ) + ∇ · (ρ~v YHCN ) = ∇ · (ρDYHCN ) + SHCN ∂t

(18.1-2)

∂ (ρYNH3 ) + ∇ · (ρ~v YNH3 ) = ∇ · (ρDYNH3 ) + SNH3 ∂t

(18.1-3)

where YHCN , YNH3 , and YNO are mass fractions of HCN, NH3 , and NO in the gas phase. The source terms SHCN , SNH3 , and SNO are to be determined next for different NOx mechanisms.

18.1.3

Thermal NOx Formation

The formation of thermal NOx is determined by a set of highly temperature-dependent chemical reactions known as the extended Zeldovich mechanism. The principal reactions governing the formation of thermal NOx from molecular nitrogen are as follows:

k+1

O + N2 * ) N + NO k+2

N + O2 * ) O + NO

(18.1-4) (18.1-5)

A third reaction has been shown to contribute, particularly at near-stoichiometric conditions and in fuel-rich mixtures: k+3

N + OH * ) H + NO


(18.1-6)

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Thermal NOx Reaction Rates The rate constants for these reactions have been measured in numerous experimental studies [23, 79, 175], and the data obtained from these studies have been critically evaluated by Baulch et al. [12] and Hanson and Salimian [99]. The expressions for the rate coefficients for Reactions 18.1-4–18.1-6 used in the NOx model are given below. These were selected based on the evaluation of Hanson and Salimian [99].

k1 = k−1 = k2 = k−2 = k3 = k−3 =

1.8 × 108 e−38370/T 3.8 × 107 e−425/T 1.8 × 104 T e−4680/T 3.8 × 103 T e−20820/T 7.1 × 107 e−450/T 1.7 × 108 e−24560/T

(18.1-7) (18.1-8) (18.1-9) (18.1-10) (18.1-11) (18.1-12)

In the above expressions, k1 , k2 , and k3 are the rate constants for the forward reactions 18.1-4–18.1-6, respectively, and k−1 , k−2 , and k−3 are the corresponding reverse rates. All of these rates have units of m3 /gmol-s. The net rate of formation of NO via Reactions 18.1-4–18.1-6 is given by

d[NO] = k1 [O][N2 ] + k2 [N][O2 ] + k3 [N][OH] − k−1 [NO][N] − k−2 [NO][O] − k−3 [NO][H] dt (18.1-13) where all concentrations have units of gmol/m3 . To calculate the formation rates of NO and N, the concentrations of O, H, and OH are required.

The Quasi-Steady Assumption for [N] The rate of formation of NOx is significant only at high temperatures (greater than 1800 K) because fixation of nitrogen requires the breaking of the strong N2 triple bond (dissociation energy of 941 kJ/gmol). This effect is represented by the high activation energy of Reaction 18.1-4, which makes it the rate-limiting step of the extended Zeldovich mechanism. However, the activation energy for oxidation of N atoms is small. When there is sufficient oxygen, as in a fuel-lean flame, the rate of consumption of free nitrogen atoms becomes equal to the rate of its formation and therefore a quasi-steady state can be established. This assumption is valid for most combustion cases except in extremely fuel-rich combustion conditions. Hence the NO formation rate becomes

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18.1 NOx Formation

1− d[NO] = 2k1 [O][N2 ] dt 1+

k−1 k−2 [NO]2 k1 [N2 ]k2 [O2 ] k−1 [NO] k2 [O2 ]+k3 [OH]

(gmol/m3 -s)

(18.1-14)

Sensitivity of Thermal NOx to Temperature From Equation 18.1-14 it is clear that the rate of formation of NO will increase with increasing oxygen concentration. It also appears that thermal NO formation should be highly dependent on temperature but independent of fuel type. In fact, based on the limiting rate described in Equation 18.1-8, thermal NOx production rate doubles for every 90 K temperature increase beyond 2200 K.

Decoupling NOx and Flame Calculations To solve Equation 18.1-14, concentration of O atoms and the free radical OH will be required in addition to concentration of stable species (i.e., O2 , N2 ). Following the suggestion by Zeldovich, the thermal NOx formation mechanism can be decoupled from the main combustion process, by assuming equilibrium values of temperature, stable species, O atoms, and OH radicals. However, radical concentrations, O atoms in particular, are observed to be more abundant than their equilibrium levels. The effect of partial equilibrium O atoms on NOx formation rate has been investigated [172] during laminar methane-air combustion. The results of these investigations indicate that the level of NOx emission can be underpredicted by as much as 28% in the flame zone, when assuming equilibrium O-atom concentrations.

Determining O Radical Concentration There has been little detailed study of radical concentration in industrial turbulent flames, but work [62] has demonstrated the existence of this phenomenon in turbulent diffusion flames. Presently, there is no definitive conclusion as to the effect of partial equilibrium on NOx formation rates in turbulent flames. Peters and Donnerhack [195] suggest that partial equilibrium radicals can account for no more than a 25% increase in thermal NOx and that fluid dynamics has the dominant effect on NOx formation rate. Bilger et al. [20] suggest that in turbulent diffusion flames, the effect of O atom overshoot on NOx formation rate is very important. To overcome this possible inaccuracy, one approach would be to couple the extended Zeldovich mechanism with a detailed hydrocarbon combustion mechanism involving many reactions, species, and steps. This approach has been used previously for research purposes [169]. However, long computer processing time has made the method economically unattractive and its extension to turbulent flows difficult. To determine the O radical concentration, FLUENT uses one of three approaches—the equilibrium approach, the partial equilibrium approach, and the predicted concentration


18-5


approach—in recognition of the ongoing controversy discussed above. Method 1: Equilibrium Approach The kinetics of the thermal NOx formation rate is much slower than the main hydrocarbon oxidation rate, and so most of the thermal NOx is formed after completion of combustion. Therefore, the thermal NOx formation process can often be decoupled from the main combustion reaction mechanism and the NOx formation rate can be calculated by assuming equilibration of the combustion reactions. Using this approach, the calculation of the thermal NOx formation rate is considerably simplified. The assumption of equilibrium can be justified by a reduction in the importance of radical overshoots at higher flame temperature [61]. According to Westenberg [292], the equilibrium O-atom concentration can be obtained from the expression [O] = kp [O2 ]1/2

(18.1-15)

With kp included, this expression becomes [O] = 3.97 × 105 T −1/2 [O2 ]1/2 e−31090/T

gmol/m3

(18.1-16)

where T is in Kelvin. Method 2: Partial Equilibrium Approach An improvement to method 1 can be made by accounting for third-body reactions in the O2 dissociation-recombination process: O2 + M * )O+O+M

(18.1-17)

Equation 18.1-16 is then replaced by the following expression [282]: [O] = 36.64T 1/2 [O2 ]1/2 e−27123/T

gmol/m3

(18.1-18)

which generally leads to a higher partial O-atom concentration. Method 3: Predicted O Approach When the O-atom concentration is well-predicted using an advanced chemistry model (such as the flamelet submodel of the non-premixed model), [O] can be taken simply from the local O-species mass fraction.

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18.1 NOx Formation

Determining OH Radical Concentration FLUENT uses one of three approaches to determine the OH radical concentration: the exclusion of OH from the thermal NOx calculation approach, the partial equilibrium approach, and the use of the predicted OH concentration approach. Method 1: Exclusion of OH Approach In this approach, the third reaction in the extended Zeldovich mechanism (Equation 18.1-6) is assumed to be negligible through the following observation: k2 [O2 ]eq k3 [OH]eq This assumption is justified for lean fuel conditions and is a reasonable assumption for most cases. Method 2: Partial Equilibrium Approach In this approach, the concentration of OH in the third reaction in the extended Zeldovich mechanism (Equation 18.1-6) is given by [13, 291] [OH] = 2.129 × 102 T −0.57 e−4595/T [O]1/2 [H2 O]1/2 gmol/m3

(18.1-19)

Method 3: Predicted OH Approach As in the predicted O approach, when the OH radical concentration is well-predicted using an advanced chemistry model such as the flamelet model, [OH] can be taken directly from the local OH species mass fraction.

Summary To summarize, thermal NOx formation rate is predicted by Equation 18.1-14. The Oatom concentration needed in Equation 18.1-14 is computed using Equation 18.1-16 for the equilibrium assumption, using Equation 18.1-18 for a partial equilibrium assumption, or using the local O-species mass fraction. You will make the choice during problem setup. In terms of the transport equation for NO (Equation 18.1-1), the NO source term due to thermal NOx mechanisms is Sthermal,NO = Mw,NO

d[NO] dt

(18.1-20)

where Mw,NO is the molecular weight of NO, and d[NO]/dt is computed from Equation 18.1-14.


18-7


18.1.4

Prompt NOx Formation

It is known that during combustion of hydrocarbon fuels, the NOx formation rate can exceed that produced from direct oxidation of nitrogen molecules (i.e., thermal NOx ).

Where and When Prompt NOx Occurs The presence of a second mechanism leading to NOx formation was first identified by Fenimore [71] and was termed “prompt NOx ”. There is good evidence that prompt NOx can be formed in a significant quantity in some combustion environments, such as in lowtemperature, fuel-rich conditions and where residence times are short. Surface burners, staged combustion systems, and gas turbines can create such conditions [7]. At present the prompt NOx contribution to total NOx from stationary combustors is small. However, as NOx emissions are reduced to very low levels by employing new strategies (burner design or furnace geometry modification), the relative importance of the prompt NOx can be expected to increase.

Prompt NOx Mechanism Prompt NOx is most prevalent in rich flames. The actual formation involves a complex series of reactions and many possible intermediate species. The route now accepted is as follows:

CH + N2 N + O2 HCN + OH CN + O2

* ) * ) * ) * )

HCN + N NO + O CN + H2 O NO + CO

(18.1-21) (18.1-22) (18.1-23) (18.1-24)

A number of species resulting from fuel fragmentation have been suggested as the source of prompt NOx in hydrocarbon flames (e.g., CH, CH2 , C, C2 H), but the major contribution is from CH (Equation 18.1-21) and CH2 , via CH2 + N2 * ) HCN + NH

(18.1-25)

The products of these reactions could lead to formation of amines and cyano compounds that subsequently react to form NO by reactions similar to those occurring in oxidation of fuel nitrogen, for example: HCN + N * ) N2 + .....

18-8

(18.1-26)


18.1 NOx Formation

Factors of Prompt NOx Formation Prompt NOx formation is proportional to the number of carbon atoms present per unit volume and is independent of the parent hydrocarbon identity. The quantity of HCN formed increases with the concentration of hydrocarbon radicals, which in turn increases with equivalence ratio. As the equivalence ratio increases, prompt NOx production increases at first, then passes a peak, and finally decreases due to a deficiency in oxygen.

Primary Reaction Reaction 18.1-21 is of primary importance. In recent studies [224], comparison of probability density distributions for the location of the peak NOx with those obtained for the peak CH have shown close correspondence, indicating that the majority of the NOx at the flame base is prompt NOx formed by the CH reaction. Assuming that Reaction 18.1-21 controls the prompt NOx formation rate, d[NO] = k0 [CH][N2 ] dt

(18.1-27)

Modeling Strategy There are, however, uncertainties about the rate data for the above reaction. From Reactions 18.1-21–18.1-25, it can be concluded that the prediction of prompt NOx formation within the flame requires coupling of the NOx kinetics to an actual hydrocarbon combustion mechanism. Hydrocarbon combustion mechanisms involve many steps and, as mentioned previously, are extremely complex and costly to compute. In the present NOx model, a global kinetic parameter derived by De Soete [248] is used. De Soete compared the experimental values of total NOx formation rate with the rate of formation calculated by numerical integration of the empirical overall reaction rates of NOx and N2 formation. He showed that overall prompt formation rate can be predicted from the expression

d[NO] = (overall prompt NOx formation rate) − (overall prompt N2 formation rate) dt (18.1-28) In the early stages of the flame, where prompt NOx is formed under fuel-rich conditions, the O concentration is high and the N radical almost exclusively forms NOx rather than nitrogen. Therefore, the prompt NOx formation rate will be approximately equal to the overall prompt NOx formation rate: d[NO] = kpr [O2 ]a [N2 ][FUEL]e−Ea /RT dt

(18.1-29)

For C2 H4 (ethylene)-air flames,


18-9


kpr Ea

= =

1.2 × 107 (RT /p)a+1 60 kcal/gmol

where a is the oxygen reaction order, R is the universal gas constant, and p is pressure (all in SI units). The rate of prompt NOx formation is found to be of the first order with respect to nitrogen and fuel concentration, but the oxygen reaction order, a, depends on experimental conditions.

Rate for Most Hydrocarbon Fuels Equation 18.1-29 was tested against the experimental data obtained by Backmier et al. [5] for different mixture strengths and fuel types. The predicted results indicated that the model performance declined significantly under fuel-rich conditions and for higher hydrocarbon fuels. To reduce this error and predict the prompt NOx adequately in all conditions, the De Soete model was modified using the available experimental data. A correction factor, f , was developed, which incorporates the effect of fuel type, i.e., number of carbon atoms, and air-to-fuel ratio for gaseous aliphatic hydrocarbons. Equation 18.1-29 now becomes d[NO] 0 0 = f kpr [O2 ]a [N2 ][FUEL]e−Ea /RT dt

(18.1-30)

so that the source term due to prompt NOx mechanism is Sprompt,NO = Mw,NO

d[NO] dt

(18.1-31)

In the above equations, f = 4.75 + 0.0819 n − 23.2φ + 32φ2 − 12.2φ3

(18.1-32)

n is the number of carbon atoms per molecule for the hydrocarbon fuel, and φ is the equivalence ratio. The correction factor is a curve fit for experimental data, valid for aliphatic alkane hydrocarbon fuels (Cn H2n+2 ) and for equivalence ratios between 0.6 and 0 1.6. For values outside the range, the appropriate limit should be used. Values of kpr 0 and Ea are selected in accordance with reference [64]. Here the concept of equivalence ratio refers to an overall equivalence ratio for the flame, rather than any spatially varying quantity in the flow domain. In complex geometries with multiple burners this may lead to some uncertainty in the specification of φ. However, since the contribution of prompt NOx to the total NOx emission is often very small, results are not likely to be biased significantly.

18-10


18.1 NOx Formation

Oxygen Reaction Order Oxygen reaction order depends on flame conditions. According to De Soete [248], oxygen reaction order is uniquely related to oxygen mole fraction in the flame:

a=

   

18.1.5

XO2 ≤ 4.1 × 10−3 −3.95 − 0.9 ln XO2 , 4.1 × 10−3 ≤ XO2 ≤ 1.11 × 10−2 −0.35 − 0.1 ln XO2 , 1.11 × 10−2 < XO2 < 0.03 0, XO2 ≥ 0.03

 1.0,    

(18.1-33)

Fuel NOx Formation

Fuel-Bound N2 It is well known that nitrogen-containing organic compounds present in liquid or solid fossil fuel can contribute to the total NOx formed during the combustion process. This fuel nitrogen is a particularly important source of nitrogen oxide emissions for residual fuel oil and coal, which typically contain 0.3–2% nitrogen by weight. Studies have shown that most of the nitrogen in heavy fuel oils is in the form of heterocycles and it is thought that the nitrogen components of coal are similar [120]. It is believed that pyridine, quinoline, and amine type heterocyclic ring structures are of importance.

Reaction Pathways The extent of conversion of fuel nitrogen to NOx is dependent on the local combustion characteristics and the initial concentration of nitrogen-bound compounds. Fuel-bound nitrogen-containing compounds are released into the gas phase when the fuel droplets or particles are heated during the devolatilization stage. From the thermal decomposition of these compounds, (aniline, pyridine, pyrroles, etc.) in the reaction zone, radicals such as HCN, NH3 , N, CN, and NH can be formed and converted to NOx . The above free radicals (i.e., secondary intermediate nitrogen compounds) are subject to a double competitive reaction path. This chemical mechanism has been subject to several detailed investigations [170]. Although the route leading to fuel NOx formation and destruction is still not completely understood, different investigators seem to agree on a simplified model:

NO O

2 ion dat oxi

Fuel Nitrogen

Nitrogen Intermediates red

uct ion

NO

N2


18-11


Recent investigations [106] have shown that hydrogen cyanide appears to be the principal product if fuel nitrogen is present in aromatic or cyclic form. However, when fuel nitrogen is present in the form of aliphatic amines, ammonia becomes the principal product of fuel nitrogen conversion. In the FLUENT NOx model, sources of NOx emission for gaseous, liquid and coal fuels are considered separately. The nitrogen-containing intermediates are grouped to be HCN or NH3 only. Two transport equations (18.1-1 and 18.1-2 or 18.1-3) are solved. The source terms SHCN , SNH3 , and SNO are to be determined next for different fuel types. Discussions to follow refer only to fuel NOx sources for SNO . Contributions from thermal and prompt mechanisms have been discussed in previous sections.

Fuel NOx from Gaseous and Liquid Fuels The fuel NOx mechanisms for gaseous and liquid fuels are based on different physics but the same chemical reaction pathways. Fuel NOx from Intermediate Hydrogen Cyanide (HCN) When HCN is used as the intermediate species: 2

1: O

NO

ion

dat

oxi

Fuel Nitrogen

HCN

red

uct

ion

2: N O

N2

The source terms in the transport equations can be written as follows:

SHCN = Spl,HCN + SHCN−1 + SHCN−2 SNO = SNO−1 + SNO−2

(18.1-34) (18.1-35)

HCN Production in a Gaseous Fuel The rate of HCN production is equivalent to the rate of combustion of the fuel: Spl,HCN =

18-12

Rcf YN,fuel Mw,HCN Mw,N

(18.1-36)


18.1 NOx Formation where

Spl,HCN Rcf YN,fuel

= source of HCN (kg/m3 -s) = mean limiting reaction rate of fuel (kg/m3 -s) = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, Rcf , is calculated from the Magnussen combustion model, so the gaseous fuel NOx option is available only when the generalized finite-rate model is used. HCN Production in a Liquid Fuel The rate of HCN production is equivalent to the rate of fuel release into the gas phase through droplet evaporation: Spl,HCN = where

Spl,HCN Sfuel YN,fuel V

= = = =

Sfuel YN,fuel Mw,HCN Mw,N V

(18.1-37)

source of HCN (kg/m3 -s) rate of fuel release from the liquid droplets to the gas (kg/s) mass fraction of nitrogen in the fuel cell volume (m3 )

HCN Consumption The HCN depletion rates from reactions (1) and (2) in the above mechanism are the same for both gaseous and liquid fuels, and are given by De Soete [248] as

R1 = A1 XHCN XOa 2 e−E1 /RT

(18.1-38)

−E2 /RT

(18.1-39)

R2 = A2 XHCN XNO e where

R1 , R2 T X A1 A2 E1 E2

= = = = = = =

conversion rates of HCN (s−1 ) instantaneous temperature (K) mole fractions 1.0 ×1010 s−1 3.0 ×1012 s−1 67 kcal/gmol 60 kcal/gmol

The oxygen reaction order, a, is calculated from Equation 18.1-33. Since mole fraction is related to mass fraction through molecular weights of the species (Mw,i ) and the mixture (Mw,m ), Mw,m Yi Xi = Yi = Mw,i Mw,i


ρRT p

!

(18.1-40)

18-13


HCN Sources in the Transport Equation The mass consumption rates of HCN which appear in Equation 18.1-34 are calculated as

where

SHCN−1 SHCN−2 p T R

SHCN−1 = −R1

Mw,HCN p RT

(18.1-41)

SHCN−2 = −R2

Mw,HCN p RT

(18.1-42)

=

consumption rates of HCN in reactions 1 and 2 respectively (kg/m3 -s) = pressure (Pa) = mean temperature (K) = universal gas constant

NOx Sources in the Transport Equation NOx is produced in reaction 1 but destroyed in reaction 2. The sources for Equation 18.1-35 are the same for a gaseous as for a liquid fuel, and are evaluated as follows: Mw,NO Mw,NO p = R1 Mw,HCN RT

(18.1-43)

Mw,NO Mw,NO p = −R2 Mw,HCN RT

(18.1-44)

SNO−1 = −SHCN−1

SNO−2 = SHCN−2

Fuel NOx from Intermediate Ammonia (NH3 ) When NH3 is used as the intermediate species: 2

1: O

NO

ion

dat

oxi

Fuel Nitrogen

NH 3

red

uct

ion

2: N O

N2

The source terms in the transport equations can be written as follows:

SNH3 = Spl,NH3 + SNH3 −1 + SNH3 −2 SNO = SNO−1 + SNO−2

18-14

(18.1-45) (18.1-46)


18.1 NOx Formation

NH3 Production in a Gaseous Fuel The rate of NH3 production is equivalent to the rate of combustion of the fuel: Spl,NH3 = where

Spl,NH3 Rcf YN,fuel

Rcf YN,fuel Mw,NH3 Mw,N

(18.1-47)

= source of NH3 (kg/m3 -s) = mean limiting reaction rate of fuel (kg/m3 -s) = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, Rcf , is calculated from the Magnussen combustion model, so the gaseous fuel NOx option is available only when the generalized finite-rate model is used. NH3 Production in a Liquid Fuel The rate of NH3 production is equivalent to the rate of fuel release into the gas phase through droplet evaporation: Spl,NH3 = where

Spl,NH3 Sfuel YN,fuel V

Sfuel YN,fuel Mw,NH3 Mw,N V

(18.1-48)

= source of NH3 (kg/m3 -s) = rate of fuel release from the liquid droplets to the gas (kg/s) = mass fraction of nitrogen in the fuel = cell volume (m3 )

NH3 Consumption The NH3 depletion rates from reactions (1) and (2) in the above mechanism are the same for both gaseous and liquid fuels, and are given by De Soete [248] as

R1 = A1 XNH3 XOa 2 e−E1 /RT

(18.1-49)

−E2 /RT

(18.1-50)

R2 = A2 XNH3 XNO e where

R1 , R2 T X A1 A2 E1 E2

= = = = = = =


conversion rates of NH3 (s−1 ) instantaneous temperature (K) mole fractions 4.0 ×106 s−1 1.8 ×108 s−1 32 kcal/gmol 27 kcal/gmol

18-15


The oxygen reaction order, a, is calculated from Equation 18.1-33. Since mole fraction is related to mass fraction through molecular weights of the species (Mi ) and the mixture (Mm ), Yi Mw,m Xi = Yi = Mw,i Mw,i

ρRT p

!

(18.1-51)

NH3 Sources in the Transport Equation The mass consumption rates of NH3 which appear in Equation 18.1-45 are calculated as

where

SNH3 −1 SNH3 −2 p T R

SNH3 −1 = −R1

Mw,NH3 p RT

(18.1-52)

SNH3 −2 = −R2

Mw,NH3 p RT

(18.1-53)

=

consumption rates of NH3 in reactions 1 and 2 respectively (kg/m3 -s) = pressure (Pa) = mean temperature (K) = universal gas constant

NOx Sources in the Transport Equation NOx is produced in reaction 1 but destroyed in reaction 2. The sources for Equation 18.1-46 are the same for a gaseous as for a liquid fuel, and are evaluated as follows: Mw,NO Mw,NO p = R1 Mw,NH3 RT

(18.1-54)

Mw,NO Mw,NO p = −R2 Mw,NH3 RT

(18.1-55)

SNO−1 = −SNH3 −1

SNO−2 = SNH3 −2

Fuel NOx from Coal Nitrogen in Char and in Volatiles For the coal it is assumed that fuel nitrogen is distributed between the volatiles and the char. Since there is no reason to assume that N is equally distributed between the volatiles and the char, we have allowed the fraction of N in the volatiles and the char to be specified separately.

18-16


18.1 NOx Formation

When HCN is used as the intermediate species, two variations of fuel NOx mechanisms for coal are included. When NH3 is used as the intermediate species, two variations of fuel NOx mechanisms for coal are included, much like in the calculation of NOx production from the coal via HCN. It is assumed that fuel nitrogen is distributed between the volatiles and the char. Coal Fuel NOx Scheme A [247] The first HCN mechanism assumes that all char N converts to HCN which is then converted partially to NO [247]. The reaction pathway is described as follows:

Char N

Volatile N

1: O 2 HCN

3: Char NO

N2

2: NO N2 With the first scheme, all char-bound nitrogen converts to HCN. Thus,

Sc YN,char Mw,HCN Mw,N V = 0

Schar,HCN = Schar,NO where

Sc YN,char V

= = =

(18.1-56) (18.1-57)

char burnout rate (kg/s) mass fraction of nitrogen in char cell volume (m3 )

Coal Fuel NOx Scheme B [157] The second HCN mechanism assumes that all char N converts to NO directly [157]. The reaction pathway is described as follows:


18-17


Char N

Volatile N

1: O 2 HCN

3: Char NO

N2

2: NO N2 According to Lockwood [157], the char nitrogen is released to the gas phase as NO directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach is followed, then

Schar,HCN = 0 Sc YN,char Mw,NO Schar,NO = Mw,N V

(18.1-58) (18.1-59)

Which HCN Scheme to Use? The second HCN mechanism tends to produce more NOx emission than the first. In general, however, it is difficult to say which one outperforms the other. The source terms for the transport equations are

SHCN = Spvc,HCN + SHCN−1 + SHCN−2 SNO = Schar,NO + SNO−1 + SNO−2 + SNO−3

(18.1-60) (18.1-61)

Source contributions SHCN−1 , SHCN−2 , SNO−1 , and SNO−2 are described previously. Therefore, only the heterogeneous reaction source, SNO−3 , the char NOx source, Schar,NO , and the HCN production source, Spvc,HCN , need to be considered. NOx Reduction on Char Surface The heterogeneous reaction of NO reduction on the char surface has been modeled according to reference [146]: R3 = A3 e−E3 /RT pNO

18-18

(18.1-62)


18.1 NOx Formation where

R3 pNO E3 A3 T

= = = = =

rate of NO reduction (gmol/m2BET -s) mean NO partial pressure (atm) 34 kcal/gmol 230 gmol/m2BET -s-atm mean temperature (K)

The partial pressure pN O is calculated using Dalton’s law: pNO = XNO p The rate of NO consumption due to reaction 3 will then be SNO−3 = where

ABET cs SNO−3

= = =

cs ABET Mw,NO R3 1000

BET surface area (m2 /kg) concentration of particles (kg/m3 ) NO consumption (kg/m3 -s)

BET Surface Area The heterogeneous reaction involving char is mainly an adsorption process whose rate is directly proportional to the pore surface area. The pore surface area is also known as the BET surface area due to the researchers who pioneered the adsorption theory (Brunauer, Emmett and Teller [31]). For commercial adsorbents, the pore (BET) surface areas range from 100,000 to 2 million square meters per kilogram, depending on the microscopic structure. For coal, the BET area is typically 25,000 m2 /kg which is used as the default in FLUENT. The overall source of HCN (Spvc,HCN ) is a combination of volatile contribution (Svol,HCN ) and char contribution (Schar,HCN ): Spvc,HCN = Svol,HCN + Schar,HCN HCN from Volatiles The source of HCN from the volatiles is related to the rate of volatile release: Svol,HCN = where

Svol YN,vol V

Svol YN,vol Mw,HCN Mw,N V

= source of volatiles originating from the coal particles into the gas phase (kg/s) = mass fraction of nitrogen in the volatiles = cell volume (m3 )


18-19


Calculation of sources related to char-bound nitrogen depends on the fuel NOx scheme selection. Coal Fuel NOx Scheme C [247] The first NH3 mechanism assumes that all char N converts to NH3 which is then converted partially to NO [247]. The reaction pathway is described as follows:

Char N

Volatile N

1: O 2 NH 3

3: Char NO

N2

2: NO N2 In this scheme, all char-bound nitrogen converts to NH3 . Thus, Sc YN,char Mw,NH3 Mw,N V = 0

(18.1-63)

Schar,NH3 = Schar,NO where

Sc YN,char V

= = =

(18.1-64)

char burnout rate (kg/s) mass fraction of nitrogen in char cell volume (m3 )

Coal Fuel NOx Scheme D [157] The second NH3 mechanism assumes that all char N converts to NO directly [157]. The reaction pathway is described as follows:

Char N

Volatile N

1: O 2 NH 3

3: Char NO

N2

2: NO N2

18-20


18.1 NOx Formation

According to Lockwood [157], the char nitrogen is released to the gas phase as NO directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach is followed, then

Schar,NH3 = 0 Sc YN,char Mw,NO Schar,NO = Mw,N V

(18.1-65) (18.1-66)

Which NH3 Scheme to Use? The second NH3 mechanism tends to produce more NOx emission than the first. In general, however, it is difficult to say which one outperforms the other. The source terms for the transport equations are

SNH3 = Spvc,NH3 + SNH3 −1 + SNH3 −2 SNO = Schar,NO + SNO−1 + SNO−2 + SNO−3

(18.1-67) (18.1-68)

Source contributions SNH3 −1 , SNH3 −2 , SNO−1 , SNO−2 , SNO−3 , Schar,NO are described previously. Therefore, only the NH3 production source, Spvc,NH3 , needs to be considered. The overall production source of NH3 is a combination of volatile contribution (Svol,NH3 ), and char contribution (Schar,NH3 ): Spvc,NH3 = Svol,NH3 + Schar,NH3

(18.1-69)

NH3 from Volatiles The source of NH3 from the volatiles is related to the rate of volatile release: Svol,NH3 = where

Svol YN,vol V

Svol YN,vol Mw,NH3 Mw,N V

= source of volatiles originating from the coal particles into the gas phase (kg/s) = mass fraction of nitrogen in the volatiles = cell volume (m3 )

Calculation of sources related to char-bound nitrogen depends on the fuel NOx scheme selection.


18-21


18.1.6

NOx Formation From Reburning

The reburning NO mechanism is a pathway whereby NO reacts with hydrocarbons and is subsequently reduced. In general: CHi + NO → HCN + products

(18.1-70)

Three reburn reactions are modeled by FLUENT for 1600 ≤ T ≤ 2100:

CH + NO →1 HCN + O

k

(18.1-71)

k

(18.1-72)

k

(18.1-73)

CH2 + NO →2 HCN + OH CH3 + NO →3 HCN + H2 O If the temperature is outside of this range, NO reburn will not be computed. The rate constants for these reactions are taken from [25]:

k1 = 1 × 108 k2 = 1.4 × 106 e−550/T k3 = 2 × 105

m3 /gmol-s m3 /gmol-s m3 /gmol-s

(18.1-74) (18.1-75) (18.1-76)

The NO depletion rate due to reburn is expressed as d[NO] = −k1 [CH][NO] − k2 [CH2 ][NO] − k3 [CH3 ][NO] dt

(18.1-77)

and the source term for the reburning mechanism in the NO transport equation can be calculated as Sreburning,NO = −Mw,NO

d[NO] dt

(18.1-78)

! To calculate the NO depletion rate due to reburning, FLUENT will obtain the concentrations of CH, CH2 , and CH3 from the species mass fraction results of the combustion calculation. For this reason, you should include these species in the problem definition (either in prePDF—for non-premixed combustion calculations—or in FLUENT).

18-22


18.1 NOx Formation

18.1.7

NOx Formation in Turbulent Flows

The kinetic mechanisms of NOx formation and destruction described in the preceding sections have all been obtained from laboratory experiments using either a laminar premixed flame or shock-tube studies where molecular diffusion conditions are well defined. In any practical combustion system, however, the flow is highly turbulent. The turbulent mixing process results in temporal fluctuations in temperature and species concentration which will influence the characteristics of the flame. The relationships among NOx formation rate, temperature, and species concentration are highly nonlinear. Hence, if time-averaged composition and temperature are employed in any model to predict the mean NOx formation rate, significant errors will result. Temperature and composition fluctuations must be taken into account by considering the probability density functions which describe the time variation.

The Turbulence-Chemistry Interaction Model In turbulent combustion calculations, FLUENT solves the density-weighted time-averaged Navier-Stokes equations for temperature, velocity, and species concentrations or mean mixture fraction and variance. To calculate NO concentration, a time-averaged NO formation rate must be computed at each point in the domain using the averaged flowfield information. Methods of modeling the mean turbulent reaction rate can be based on either moment methods [295] or probability density function (PDF) techniques [115]. FLUENT uses the PDF approach.

! The PDF method described here applies to the NOx transport equations only. The preceding combustion simulation can use either the generalized finite rate chemistry model by Magnussen and Hjertager or the non-premixed combustion model. For details on these combustion models, please see Chapters 13 and 14.

The PDF Approach The PDF method has proven very useful in the theoretical description of turbulent flow [116]. In the FLUENT NOx model, a single- or joint-variable PDF in terms of a normalized temperature, species mass fraction, or the combination of both is used to predict the NOx emission. If the non-premixed combustion model is used to model combustion, then a one- or two-variable PDF in terms of mixture fraction(s) is also available. The mean values of the independent variables needed for the PDF construction are obtained from the solution of the transport equations.


18-23


General Expression for Mean Reaction Rate The mean turbulent reaction rate w can be described in terms of the instantaneous rate w and a single or joint PDF of various variables. In general, w=

Z

···

Z

w(V1 , V2 , . . .)P (V1 , V2 , . . .)dV1 dV2 . . .

(18.1-79)

where V1 , V2 ,... are temperature and/or the various species concentrations present. P is the probability density function (PDF).

Mean Reaction Rate Used in FLUENT The PDF is used for weighting against the instantaneous rates of production of NO (e.g., Equation 18.1-20) and subsequent integration over suitable ranges to obtain the mean turbulent reaction rate. Hence we have S NO =

Z

SNO (V1 )P1 (V1 )dV1

(18.1-80)

or, for two variables S NO =

Z Z

SNO (V1 , V2 , )P (V1 , V2 )dV1 dV2

(18.1-81)

where S NO is the mean turbulent rate of production of NO, SNO is the instantaneous rate of production given by, for example, Equation 18.1-20, and P1 (V1 ) and P (V1 , V2 ) are the PDFs of the variables V1 and, if relevant, V2 . The same treatment applies for the HCN or NH3 source terms. Equation 18.1-80 or 18.1-81 must be integrated at every node and at every iteration. For a PDF in temperature, the limits of integration are determined from the minimum and maximum values of temperature in the combustion solution. For a PDF in mixture fraction, the limits of the integrations in Equation 18.1-80 or 18.1-81 are determined from the values stored in the look-up tables.

Statistical Independence In the case of the two-variable PDF, it is further assumed that the variables V1 and V2 are statistically independent so that P (V1 , V2 ) can be expressed as P (V1 , V2 ) = P1 (V1 )P2 (V2 )

18-24

(18.1-82)


18.1 NOx Formation

Beta PDF Assumed P is assumed to be a two-moment beta function as appropriate for combustion calculations [98, 171]. The equation for the beta function is

P (V ) =

Γ(α + β) α−1 V α−1 (1 − V )β−1 V (1 − V )β−1 = Z 1 Γ(α)Γ(β) V α−1 (1 − V )β−1 dV

(18.1-83)

0

where Γ( ) is the Gamma function, α and β depend on m, the mean value of the quantity in question, and its variance, σ 2 : !

m(1 − m) α=m −1 σ2

(18.1-84) !

m(1 − m) β = (1 − m) −1 σ2

(18.1-85)

The beta function requires that the independent variable V assume values between 0 and 1. Thus, field variables such as temperature must be normalized.

Calculation Method for σ 2 The variance, σ 2 , can be computed by solving a transport equation during the combustion calculation stage. This approach is compute-intensive and is not applicable for a postprocessing treatment of NOx prediction. Instead, calculation of σ 2 is based on an approximate form of the variance transport equation. A transport equation for the variance σ 2 can be derived: µt ∂ 2 ρσ + ∇ · (ρ~v σ 2 ) = ∇ ∇σ 2 + Cg µt (∇m)2 − Cd ρ σ 2 ∂t σt k

(18.1-86)

where the constants σt , Cg and Cd take the values 0.85, 2.86, and 2.0, respectively. Assuming equal production and dissipation of variance, one gets 

µt k Cg µt k Cg  ∂m (∇m)2 = σ2 = ρ Cd ρ Cd ∂x

!2

∂m + ∂y

!2

∂m + ∂z

!2  

(18.1-87)

The term in the brackets is the dissipation rate of the independent variable. For a PDF in mixture fraction, the mixture fraction variance has already been solved as part of the basic combustion calculation, so no additional calculation for σ 2 is required.


18-25


18.1.8

Using the NOx Model

Decoupled Analysis: Overview NOx concentrations generated in combustion systems are generally low. As a result, NOx chemistry has negligible influence on the predicted flow field, temperature, and major combustion product concentrations. It follows that the most efficient way to use the NOx model is as a postprocessor to the main combustion calculation. The recommended procedure is as follows: 1. Calculate your combustion problem using FLUENT as usual. 2. Activate the desired NOx models (thermal, fuel, and/or prompt NOx , with or without reburn) and set the appropriate parameters, as described in this section. Define −→ Models −→ Pollutants −→NOx... 3. In the Solution Controls panel, turn off solution of all variables except species NO and, if the fuel NOx submodel is activated, HCN or NH3 . Solve −→ Controls −→Solution... 4. Also in the Solution Controls panel, set a suitable value for the NO (and HCN or NH3 , if appropriate) under-relaxation. A value of 0.8 to 1.0 is suggested, although lower values may be required for certain problems. That is, if convergence cannot be obtained, try a lower under-relaxation value. 5. In the Residual Monitors panel, decrease the convergence criterion for NO (and HCN or NH3 , if appropriate) to 10−6 . Solve −→ Monitors −→Residual... 6. Perform calculations until convergence (i.e., until the NO (and HCN or NH3 , if solved) species residuals are below 10−6 ) to ensure that the NO and HCN or NH3 concentration fields are no longer evolving. 7. Review the mass fractions of NO (and HCN or NH3 ) with alphanumerics and/or graphics tools in the usual way. 8. Save a new set of case and data files, if desired. Inputs specific to the calculation of NOx formation are explained in the remainder of this section.

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18.1 NOx Formation

Activating the NOx Models To activate the NOx models and set related parameters, you will use the NOx Model panel (Figure 18.1.1). Define −→ Models −→ Pollutants −→NOx...

Figure 18.1.1: The NOx Model Panel Under Models, select the NOx models to be used in the calculation of the NO and HCN concentrations: • To enable thermal NOx , turn on the Thermal NO option. • To enable prompt NOx , turn on the Prompt NO option.


18-27


• To enable fuel NOx , turn on the Fuel NO option. • To enable NO reburn, turn on the Reburn option. (Note that the Reburn option will not appear until you have activated one of the other NO models listed above.) Your selection(s) for Models will activate the calculation of thermal, prompt, and/or fuel NO, with or without reburn, in accordance with the chemical kinetic models described in Sections 18.1.3–18.1.6. Mean NO formation rates will be computed directly from mean concentrations and temperature in the flow field.

Setting Thermal NOx Parameters The NOx routines employ three methods for calculation of thermal NOx (as described in Section 18.1.3). You will specify the method to be used in the NOx Model panel, under Thermal NO Parameters: • To choose the equilibrium method, select Equilibrium in the [O] Model drop-down list. • To choose the partial equilibrium method, select Partial-equilibrium in the [O] Model or [OH] Model drop-down list. • To use the predicted O and/or OH concentration, select Instantaneous in the [O] Model or [OH] Model drop-down list.

Setting Prompt NOx Parameters Prompt NO formation is predicted using Equations 18.1-30 and 18.1-32. The parameters are entered under Prompt NO Parameters in the NOx Model panel: • Specify which of the defined species is the fuel by choosing it in the Fuel Species drop-down list. • Set the Fuel Carbon Number (number of carbon atoms per fuel molecule) • Set the Equivalence Ratio: Equivalence Ratio =

18-28

actual fuel-to-air ratio stoichiometric fuel-to-air ratio


18.1 NOx Formation

Setting Fuel NOx Parameters For fuel NOx models, you will first need to specify the fuel type under Fuel NO Parameters: • For gaseous fuel NOx , select Gas under Fuel Type. • For liquid fuel NOx , select Liquid under Fuel Type. • For solid fuel NOx , select Solid under Fuel Type. Note that you can use only one of the fuel models at a time. Setting Gaseous and Liquid Fuel NOx Parameters If you have selected Gas or Liquid as the Fuel Type under Fuel NO Parameters, you will also need to specify the following: • Select the intermediate species (HCN or NH3) in the N Intermediate drop-down list. • Set the correct mass fraction of nitrogen in the fuel (kg nitrogen per kg fuel) in the Fuel N Mass Fraction field FLUENT will use Equations 18.1-34 and 18.1-35 (for HCN) or Equations 18.1-45 and 18.1-46 (for NH3 ) to predict NO formation for a gaseous or liquid fuel. Setting Solid (Coal) Fuel NOx Parameters For solid fuel, FLUENT will use Equations 18.1-60 and 18.1-61 (for HCN) or Equations 18.1-67 and 18.1-68 (for NH3 ) to predict NO formation. Several inputs (under Fuel NO Parameters) are required for the coal fuel NOx model: • Select the intermediate species (HCN or NH3) in the N Intermediate drop-down list. • Specify the mass fraction of nitrogen in the volatiles and in the char in the Volatile N Mass Fraction and Char N Mass Fraction fields, respectively. • Define the BET internal pore surface area (see Section 18.1.5 for details) of the particles in the BET Surface Area field. • Select the char N conversion path from the Char N Conversion drop-down list as NO, HCN, or NH3. Note that HCN or NH3 can be selected only if the same species has been selected as the intermediate species in the N Intermediate drop-down list.


18-29


Setting Parameters for NOx Reburn There are no special parameters to specify for the NOx reburn model. When you use this model, however, you must be sure to include the species CH, CH2 , and CH3 in your problem definition, as warned in the Reburn Parameters section of the NOx Model panel. See Section 18.1.6 for details.

Setting Turbulence Parameters If you want to take into account turbulent fluctuations (as described in Section 18.1.7) when you compute the specified NO formation (thermal, prompt, and/or fuel, with or without reburn), select one of the options in the PDF Mode drop-down list under Turbulence Interaction. • Select Temperature to take into account fluctuations of temperature. • Select Temperature/Species to take into account fluctuations of temperature and mass fraction of the species selected in the Species drop-down list (which appears when you select this option). • Select Species 1/Species 2 to take into account the fluctuation of mass fractions of two species selected in the Species 1 and Species 2 drop-down lists (which appear when you select this option). • (non-premixed combustion calculations only) Select Mixture Fraction to take into account fluctuation in the mixture fraction(s). The Mixture Fraction option is available only if you are using the non-premixed combustion model to model the reacting system. If the Mixture Fraction option is used, the instantaneous temperatures, density, and species concentrations are taken from the PDF look-up table (created by prePDF) as a function of mixture fraction. The beta PDF in mixture fraction is calculated from the values of mean mixture fraction and variance at each cell. After the instantaneous NOx rates have been calculated at each cell, they are convoluted with the mixture fraction PDF to yield the mean rates in turbulent flow. Extra Input for Non-Adiabatic Non-Premixed Combustion Calculations Using a PDF in Mixture Fraction If you choose the Mixture Fraction option and you are using the non-adiabatic nonpremixed combustion model, an additional option (Use Top Temperature) will appear under Turbulence Interaction. When this option is off (the default condition) the local cell enthalpy is used to calculate the instantaneous temperature used in the NOx rate calculation. This option should be used in most cases. If you enable Use Top Temperature, then in the part of the domain where the turbulent fluctuations are significant, the instantaneous temperatures are calculated in terms of the lowest heat loss (or highest heat

18-30


18.1 NOx Formation

gain) in that part of the domain. (In the equations in Section 14.1.2, the heat loss/gain is H ∗ .) The result of this calculation will be the maximum possible NOx production that can be calculated through the convolution with the mixture fraction PDF. By comparing the default results with those generated using the top temperature option, you can determine how sensitive the NOx calculation is to the local enthalpy variation when the fluctuations are significant. Number of Beta Points You can, optionally, adjust the number of Beta PDF Points. The default value of 10, indicating that the beta function in Equation 18.1-80 or Equation 18.1-81 will be integrated at 10 points on a histogram basis, will yield an accurate solution with reasonable computation time. Increasing this value may improve accuracy, but will also increase the computation time.

Specifying a User-Defined Function for the NOx Rate You can, optionally, choose to specify a user-defined function for the rate of NOx production. The rate returned from the UDF is added to the rate returned from the standard NOx production options, if any are selected. You can also choose to deselect all of the standard NOx production options and use only the UDF rate. Select the desired function in the NOx Rate drop-down list under User-Defined Functions. See the separate UDF Manual for details about user-defined functions.

Postprocessing When you compute NOx formation, the following additional variables will be available for postprocessing: • Mass fraction of NO • Mass fraction of HCN (appropriate fuel NOx model only) • Mass fraction of NH3 (appropriate fuel NOx model only) • Mole fraction of NO • Mole fraction of HCN (appropriate fuel NOx model only) • Mole fraction of NH3 (appropriate fuel NOx model only) • Concentration of NO • Concentration of HCN (appropriate fuel NOx model only) • Concentration of NH3 (appropriate fuel NOx model only)


18-31


• Variance of Temperature (variance of normalized temperature) These variables are contained in the NOx... category of the variable selection drop-down list that appears in postprocessing panels.

18.2

Soot Formation

Information about soot formation is presented in the following sections: • Section 18.2.1: Overview and Limitations • Section 18.2.2: Theory • Section 18.2.3: Using the Soot Models

18.2.1


FLUENT provides two empirical models for the prediction of soot formation in combustion systems. In addition, the predicted soot concentration can be included in the prediction of radiation absorption coefficients within the combustion system. You can include the effect of soot on radiation absorption when you use the P-1, discrete ordinates, or discrete transfer radiation model with a variable absorption coefficient.

Predicting Soot Formation FLUENT predicts soot concentrations in a combustion system using one of two available models: • the single-step Khan and Greeves model [126], in which FLUENT predicts the rate of soot formation based on a simple empirical rate. • the two-step Tesner model [162, 269], in which FLUENT predicts the formation of nuclei particles, with soot formation on the nuclei. The Khan and Greeves model is the default model used by FLUENT when you include soot formation. In both models, combustion of the soot (and particle nuclei) is assumed to be governed by the Magnussen combustion rate [162]. Note that this limits the use of the soot formation models to turbulent flows. Soot formation cannot be predicted by FLUENT for laminar or inviscid flows. Both soot formation models are empirically-based, approximate models of the soot formation process in combustion systems. The detailed chemistry and physics of soot formation are quite complex and are only approximated in the models used by FLUENT. You should view the results of these models as qualitative indicators of your system performance unless you can undertake experimental validation of the results.

18-32


18.2 Soot Formation

Restrictions on Soot Modeling The following restrictions apply to soot formation models: • You must use the segregated solver. The soot models are not available with either of the coupled solvers. • Soot formation can be modeled only for turbulent flows. • The soot model cannot be used in conjunction with the premixed combustion model.

18.2.2

Theory

The Single-Step Soot Formation Model In the single-step Khan and Greeves model [126], FLUENT solves a single transport equation for the soot mass fraction: ∂ µt (ρYsoot ) + ∇ · (ρ~v Ysoot ) = ∇ · ∇Ysoot + Rsoot ∂t σsoot

(18.2-1)

where Ysoot σsoot Rsoot

= soot mass fraction = turbulent Prandtl number for soot transport = net rate of soot generation (kg/m3 -s)

Rsoot , the net rate of soot generation, is the balance of soot formation, Rsoot,form , and soot combustion, Rsoot,comb : Rsoot = Rsoot,form − Rsoot,comb

(18.2-2)

The rate of soot formation is given by a simple empirical rate expression: Rsoot,form = Cs pfuel φr e−E/RT

(18.2-3)

where Cs pfuel φ r E/R

= = = = =

soot formation constant (kg/N-m-s) fuel partial pressure (Pa) equivalence ratio equivalence ratio exponent activation temperature (K)

The rate of soot combustion is the minimum of two rate expressions [162]:


18-33


Rsoot,comb = min[R1 , R2 ]

(18.2-4)

The two rates are computed as R1 = AρYsoot

k

(18.2-5)

and Yox R2 = Aρ νsoot

Ysoot νsoot Ysoot νsoot + Yfuel νfuel

k

(18.2-6)

where A Yox , Yfuel νsoot , νfuel

= constant in the Magnussen model = mass fractions of oxidizer and fuel = mass stoichiometries for soot and fuel combustion

The default constants for the single-step model are valid for a wide range of hydrocarbon fuels.

The Two-Step Soot Formation Model The two-step Tesner model [269] predicts the generation of radical nuclei and then computes the formation of soot on these nuclei. FLUENT thus solves transport equations for two scalar quantities: the soot mass fraction (Equation 18.2-1) and the normalized radical nuclei concentration: ∂ µt (ρb∗nuc ) + ∇ · (ρ~v b∗nuc ) = ∇ · ∇b∗ + R∗nuc ∂t σnuc nuc

(18.2-7)

where b∗nuc σnuc R∗nuc

= normalized radical nuclei concentration (particles ×10−15 /kg) = turbulent Prandtl number for nuclei transport = normalized net rate of nuclei generation (particles ×10−15 /m3 -s)

In these transport equations, the rates of nuclei and soot generation are the net rates, involving a balance between formation and combustion. Soot Generation Rate The two-step model computes the net rate of soot generation, Rsoot , in the same way as the single-step model, as a balance of soot formation and soot combustion: Rsoot = Rsoot,form − Rsoot,comb

18-34

(18.2-8)


18.2 Soot Formation

In the two-step model, however, the rate of soot formation, Rsoot,form , depends on the concentration of radical nuclei, cnuc : Rsoot,form = mp (α − βNsoot )cnuc

(18.2-9)

where mp Nsoot cnuc α β

= = = = =

mean mass of soot particle (kg/particle) concentration of soot particles (particles/m3 ) radical nuclei concentration = ρbnuc (particles/m3 ) empirical constant (s−1 ) empirical constant (m3 /particle-s)

The rate of soot combustion, Rsoot,comb , is computed in the same way as for the single-step model, using Equations 18.2-4–18.2-6. The default constants for the two-step model are for combustion of acetylene (C2 H2 ). According to [1], these values should be modified for other fuels, since the sooting characteristics of acetylene are known to be different from those of saturated hydrocarbon fuels. Nuclei Generation Rate The net rate of nuclei generation in the two-step model is given by the balance of the nuclei formation rate and the nuclei combustion rate: R∗nuc = R∗nuc,form − R∗nuc,comb

(18.2-10)

where R∗nuc,form R∗nuc,comb

= rate of nuclei formation (particles ×10−15 /m3 -s) = rate of nuclei combustion (particles ×10−15 /m3 -s)

The rate of nuclei formation, R∗nuc,form , depends on a spontaneous formation and branching process, described by


R∗nuc,form = η0 + (f − g)c∗nuc − g0 c∗nuc Nsoot

(18.2-11)

η0 = a∗0 cfuel e−E/RT

(18.2-12)

18-35


where c∗nuc a∗0 a0 cfuel f −g g0

= = = = = =

normalized nuclei concentration (= ρb∗nuc ) a0 /1015 pre-exponential rate constant (particles/kg-s) fuel concentration (kg/m3 ) linear branching − termination coefficient (s−1 ) linear termination on soot particles (m3 /particle-s)

Note that the branching term, (f − g)c∗nuc , in Equation 18.2-11 is included only when the kinetic rate, η0 , is greater than the limiting formation rate (105 particles/m3 -s, by default). The rate of nuclei combustion is assumed to be proportional to the rate of soot combustion: R∗nuc,comb = Rsoot,comb

b∗nuc Ysoot

(18.2-13)

where the soot combustion rate, Rsoot,comb , is given by Equation 18.2-4.

Effect of Soot on the Radiation Absorption Coefficient A description of the modeling of soot-radiation interaction is provided in Section 11.3.8.

18.2.3

Using the Soot Models

To compute the soot formation, you will need to start from a converged fluid-flow solution. The procedure for setting up and solving a soot formation model is outlined below, and described in detail on the pages that follow. Remember that only the steps that are pertinent to soot modeling are shown here. For information about inputs related to other models that you are using in conjunction with the soot formation model, see the appropriate sections for those models. 1. Calculate your turbulent combustion (finite-rate or non-premixed) problem using FLUENT as usual. 2. Enable the desired soot formation model and set the related parameters, as described in this section. Define −→ Models −→ Pollutants −→Soot... 3. In the Solution Controls panel, turn off solution of all variables except soot (and nuclei, if you are using the two-step model). Solve −→ Controls −→Solution...

18-36


18.2 Soot Formation

4. Also in the Solution Controls panel, set a suitable value for the soot (and nuclei, for the two-step model) under-relaxation factor(s). A value of 0.8 is suggested, although a lower value may be required for certain problems. That is, if convergence cannot be obtained, try a lower under-relaxation value. 5. In the Residual Monitors panel, decrease the convergence criterion for soot (and nuclei, for the two-step model) to 10−5 . Solve −→ Monitors −→Residual... 6. Define the boundary conditions for soot (and nuclei, for the two-step model) at flow inlets. Define −→Boundary Conditions... 7. Perform calculations until convergence (i.e., until the soot—and nuclei, for the twostep model—residual is below 10−5 ) to ensure that the soot (and nuclei) field is no longer evolving. 8. Review the mass fraction of soot (and nuclei) with alphanumerics and/or graphics tools in the usual way. 9. Save a new set of case and data files, if desired. 10. If you want to calculate a coupled solution for the soot and the flow field, turn on the other variables again and recompute until convergence. (See the end of this section for some advice on coupled calculations.)

Selecting the Soot Model You can enable the calculation of soot formation by selecting a soot model in the Soot Model panel (Figure 18.2.1). Define −→ Models −→ Pollutants −→Soot... Under Soot Formation Model, select either the One-Step or the Two-Step model. The panel will expand to show the appropriate inputs for the selected model. (If you want to include the effects of soot formation on the radiation absorption coefficient, turn on the Generalized Model option under Soot-Radiation Interaction.)

Setting the Combustion Process Parameters For both soot models, you will next define the Process Parameters, which depend on the combustion process that you are modeling. These inputs include the stoichiometry of the fuel and soot combustion and (for the two-step model only) the average size and density of the soot particles:


18-37


Figure 18.2.1: The Soot Model Panel

Mean Diameter of Soot Particle and Mean Density of Soot Particle are the assumed average diameter and average density of the soot particles in the combustion system, used to compute the soot particle mass, mp , in Equation 18.2-9 for the two-step model. Note that the default values for soot density and diameter are taken from [162]. These parameters will not appear when the one-step model is used. Stoichiometry for Soot Combustion is the mass stoichiometry, νsoot , in Equation 18.2-6, which computes the soot combustion rate in both soot models. The default value supplied by FLUENT (2.6667) assumes that the soot is pure carbon and that the oxidizer is O2 . Stoichiometry for Fuel Combustion is the mass stoichiometry, νfuel , in Equation 18.2-6, which computes the soot combustion rate in both soot models. The default value supplied by FLUENT (3.6363) is for combustion of propane (C3 H8 ) by oxygen (O2 ).

Defining the Fuel and Oxidizing Species In addition to defining the stoichiometry for the fuel and soot combustion, you need to tell FLUENT which chemical species in your model should be used as the fuel and oxidizer. In the Soot Model panel under Species Definition, select the fuel in the Fuel drop-down list and the oxidizer in the Oxidant drop-down list.

18-38


18.2 Soot Formation

If you are using the non-premixed model for the combustion calculation and your fuel stream, as defined in prePDF, consists of a mixture of components, you should choose the most appropriate species as the Fuel species for the soot formation model. Similarly, the most significant oxidizing component (e.g., O2 ) should be selected as the Oxidant.

Setting Model Parameters for the Single-Step Model When you choose the single-step model for soot formation, the modeling parameters to be defined are those used in Equations 18.2-3, 18.2-5, and 18.2-6: Soot Formation Constant is the parameter Cs in Equation 18.2-3. Equivalence Ratio Exponent is the exponent r in Equation 18.2-3. Equivalence Ratio Minimum and Equivalence Ratio Maximum are the minimum and maximum values of the fuel equivalence ratio φ in Equation 18.2-3. Equation 18.2-3 will be solved only if Equivalence Ratio Minimum < φ < Equivalence Ratio Maximum; if φ is outside of this range, there is no soot formation. Activation Temperature of Soot Formation Rate is the term E/R in Equation 18.2-3. Magnussen Constant for Soot Combustion is the constant A used in the rate expressions governing the soot combustion rate (Equations 18.2-5 and 18.2-6). Note that the default values for these parameters are for propane fuel [43, 280], and are considered to be valid for a wide range of hydrocarbon fuels.

Setting Model Parameters for the Two-Step Model When you choose the two-step model for soot formation, the modeling parameters to be defined are those used in Equations 18.2-5, 18.2-6, 18.2-9, 18.2-11, and 18.2-12: Limiting Nuclei Formation Rate is the limiting value of the kinetic nuclei formation rate η0 in Equation 18.2-12. Below this limiting value, the branching and termination term, (f − g) in Equation 18.2-11, is not included. Nuclei Branching-Termination Coefficient is the term (f − g) in Equation 18.2-11. Nuclei Coefficient of Linear Termination on Soot is the term g0 in Equation 18.2-11. Preexponential Constant of Nuclei Formation is the pre-exponential term a0 in the kinetic nuclei formation term, Equation 18.2-12. Activation Temperature of Nuclei Formation Rate is the term E/R in the kinetic nuclei formation term, Equation 18.2-12.


18-39


Constant Alpha for Soot Formation Rate is α, the constant in the soot formation rate equation, Equation 18.2-9. Constant Beta for Soot Formation Rate is β, the constant in the soot formation rate equation, Equation 18.2-9. Magnussen Constant for Soot Combustion is the constant A used in the rate expressions governing the soot combustion rate (Equations 18.2-5 and 18.2-6). The default values for the two-step model are the same as in [162] (for an acetylene flame), except for a0 , which is assumed to have the original value from [269]. If your model involves propane fuel rather that acetylene, it is recommended that you change the value of α to 3.5 × 108 [1]. For best results, you should modify both of these parameters, using empirically determined inputs for your specific combustion system.

Defining Boundary Conditions for the Soot Model At flow inlet boundaries, you will need to specify the Soot Mass Fraction, Ysoot , in Equation 18.2-1, and (for the two-step model only) the Nuclei mass concentration, b∗nuc , in Equation 18.2-7. Define −→Boundary Conditions... You can retain the default inlet values of zero for both quantities or you can input non-zero numbers as appropriate for your combustion system.

Coupled Soot Calculations If you are calculating a coupled solution for the soot and the flow field, you will generally need to increase the convergence criteria for soot (and nuclei, for the two-step model) to 10−4 . You may choose to keep the recommended value of 10−5 used for the uncoupled soot calculation, but be aware that the coupled solution may not be able to converge to this stricter tolerance. For coupled calculations you should also use a lower under-relaxation factor for soot (and nuclei, for the two-step model). A value of 0.2 will be suitable in most cases. If you are calculating a coupled solution and you are modeling radiative heat transfer using a variable absorption coefficient, you should enable the Generalized Model for SootRadiation Interaction in the Soot Model panel. When this option is enabled, FLUENT will include the effect of soot on the variable radiation absorption coefficient, as described in Section 11.3.8.

18-40


18.2 Soot Formation

Reporting Soot Quantities FLUENT provides several additional reporting options when your model includes soot formation. You can generate graphical plots or alphanumeric reports of the following items: • Mass fraction of soot • Mass fraction of nuclei (for the two-step model only) Both of these parameters are contained in the Soot... category of the variable selection drop-down list that appears in postprocessing panels.


18-41


18-42


Chapter 19. Predicting Aerodynamically Generated Noise The discipline of acoustics is intimately related to fluid dynamics. Many sounds that are technologically important in industrial contexts are generated aerodynamically and propagated in fluid flows, either in motion or at rest. The full computational aeroacoustic (CAA) approach based on the solution of compressible Navier-Stokes equations is perhaps the most general and direct approach to predicting aerodynamically generated sounds. In this direct method, both generation and propagation of sound waves are directly resolved at the same time by solving the governing fluid dynamics equations. However, since the energy and magnitude of aerodynamically generated sound waves are usually several orders of magnitude smaller than those of the flow, the direct approach requires highly accurate numerical schemes and a sufficiently fine mesh all the way out to the receiver locations. As a result, reliable far-field noise prediction using the direct CAA approach often incurs a prohibitively high computational cost. For predictions of far-field noise, the methods based on Lighthill’s acoustic analogy [151] offers a viable alternative to the direct approach. Once the near-field aerodynamic fields are known, Lighthill’s acoustic analogy allows one to predict far-field noise without much additional effort. The acoustic analogy essentially decouples the propagation of sound from its generation, allowing one to separate the flow solution process from acoustics analysis. FLUENT offers an acoustics prediction capability based on the Ffowcs Williams and Hawkings (FW-H) equation and its integral solutions [73]. The FW-H formulation adopts the most general form of Lighthill’s acoustic analogy, and is capable of predicting sound generated by equivalent acoustic sources such as monopoles, dipoles, and quadrupoles. The major targeted applications include the noise generated by airframes (e.g., airplanes, automobiles, trains). This chapter provides an overview of the underlying theory, the model setup, and the procedure for computing sound in the FLUENT’s acoustics model. • Section 19.1: Overview and Limitations • Section 19.2: Acoustics Model Theory • Section 19.3: Using the Acoustics Model


19-1

Predicting Aerodynamically Generated Noise

19.1


19.1.1

Overview

FLUENT adopts a time-domain integral formulation wherein time histories of sound pressure, or acoustic signals, at prescribed receiver locations are directly computed using two surface integrals. These integrals represent a full contribution from equivalent acoustics sources of monopoles and dipoles, and a partial contribution from quadrupole sources. Time-accurate solutions of the flow-field variables, such as pressure, velocity components, and density on source (emission) surfaces, are required to evaluate the surface integrals. Time-accurate solutions can be obtained from unsteady Reynolds-averaged Navier-Stokes (URANS) equations, large eddy simulation (LES), or detached eddy simulation (DES) as appropriate for the flow at hand and the features that you want to capture. The source surfaces can be placed not only on walls, but also on interior (permeable) surfaces, which will enable you to partially account for the contributions from quadrupoles within the surface. Both broadband and tonal noise can be predicted depending on the nature of the flow (noise source) being considered, turbulence model, and time scale of the flow resolved in the flow calculation. The acoustics model in FLUENT allows you to select multiple source surfaces and receivers. It also permits you either to save the source data for a future use, or to carry out an acoustics calculation “on-the-fly” simultaneously as the transient flow calculation proceeds, or both. Sound pressure signals thus obtained can be processed using the fast Fourier transform (FFT) and associated post-processing capabilities to compute and plot such acoustic quantities as the overall sound pressure level (SPL) and its power spectrum.

19.1.2

Limitations

The following limitations apply to the acoustics model currently implemented in FLUENT: • The acoustics model is only available with the segregated solver. The acoustics model is not available with either of the coupled solvers. • The acoustics model is applicable for predicting propagation of sound toward unbounded fields or free space. Thus, while the model can be legitimately used to predict the far-field noise due to external aerodynamic flows, such as the flows around cars and aircrafts, it cannot be used for predicting the noise propagation inside ducts or wall-enclosed space. • The acoustics model currently can handle only stationary (relative to receivers) source surfaces.

19-2


19.2 Acoustics Model Theory

19.2

Acoustics Model Theory

The Ffowcs Williams and Hawkings (FW-H) equation is essentially an inhomogeneous wave equation that is derived by manipulating the continuity equation and the NavierStokes equations. The FW-H [73, 30] equation can be written as:

∂2 1 ∂ 2 p0 2 0 − ∇ p = {Tij H(f )} a20 ∂t2 ∂xi ∂xj ∂ {[Pij nj + ρui (un − vn )] δ(f )} − ∂xi ∂ + {[ρ0 vn + ρ (un − vn )] δ(f )} ∂t

(19.2-1)

where ui un vi vn δ(f ) H(f )

= = = = = =

fluid velocity component in the xi direction fluid velocity component normal to the surface f = 0 surface velocity components in the xi direction surface velocity component normal to the surface Dirac delta function Heaviside function

p0 is the sound pressure at the far-field (p0 ≡ p − p0 ). f = 0 denotes a mathematical surface introduced to “embed” the exterior flow problem (f > 0) in an unbounded space, which facilitates the use of generalized function theory and the free-space Green function to obtain the solution. The surface (f = 0) corresponds to the source (emission) surface, and can be made coincident with a body (impermeable) surface or a permeable surface off the body surface. ni is the unit normal vector pointing toward the exterior region (f > 0), a0 is the far-field sound speed, and Tij is the Lighthill stress tensor, defined as Tij = ρui uj + Pij − a20 (ρ − ρ0 ) δij

(19.2-2)

Pij is the compressive stress tensor. For a Stokesian fluid, this is given by "

∂ui ∂uj 2 ∂uk Pij = pδij − µ + − δij ∂xj ∂xi 3 ∂xk

#

(19.2-3)

The freestream quantities are denoted by the subscript 0. The solution to Equation 19.2-1 is obtained using the free-space Green function (δ(g)/4πr). The complete solution consists of two surface integrals and one volume integral. The surface integrals represent the contributions from monopole and dipole acoustics sources and partially from quadrupole sources, whereas the volume integral represents quadrupole


19-3


(volume) sources in the region outside the source surface. The contribution of the volume integral becomes small when the flow is subsonic and the source surface encloses a non-linear source region. For this reason, in FLUENT, the volume integral is dropped. Thus, we have p0 (~x, t) = p0T (~x, t) + p0L (~x, t)

(19.2-4)

where

4πp0T (~x, t) =

Z

+

Z



f =0

 

ρ0 U˙n + Un˙



r (1 − Mr )2

 dS

n

o

ρ0 Un rM˙ r + a0 (Mr − M 2 )



 dS

r2 (1 − Mr )3 " # 1 Z L˙ r 0 4πpL (~x, t) = dS a0 f =0 r (1 − Mr )2 " # Z Lr − LM + 2 dS f =0 r 2 (1 − Mr ) n o  Lr rM˙ r + a0 (Mr − M 2 ) 1 Z   + a0 f =0 r2 (1 − Mr )3 f =0

(19.2-5)

(19.2-6)

where ρ (ui − vi ) ρ0 = Pij n ˆ j + ρui (un − vn )

Ui = v i + Li

When the integration surface coincides with an impenetrable wall, the two terms on the right in Equation 19.2-4, p0T (~x, t) and p0L (~x, t), are often referred to as thickness and loading terms, respectively, in light of their physical meanings. The square brackets denote that the kernels of the integrals are computed at the corresponding retarded times, τ , given the observer time, t, where τ =t−

r a0

(19.2-7)

The various subscripted quantities appearing in Equations 19.2-5 and 19.2-6 are the inner products of a vector and a unit vector implied by the subscript. For instance, ~ · ~ˆr = Li ri and Un = U ~ · ~n = Ui ni , where ~r and ~n denote the unit vectors in the Lr = L

19-4


19.3 Using the Acoustics Model

radiation and normal directions, respectively. The dot over a variable denotes source-time differentiation of that variable. As mentioned earlier, the FW-H formulation in FLUENT makes an additional assumption that source surfaces are stationary or non-moving, which implies that vi = vn = Un˙ = LM = M = Mr = M˙ r = 0 in the above equations. Please note the following remarks regarding the applicability of this integral solution: • It is not required that the surface f = 0 coincide with body surfaces or walls. The formulation permits source surfaces to be permeable, and therefore can be placed in the interior of the flow. • When the source surface is placed at a certain distance off the body surface, the integral solutions given by Equations 19.2-5 and 19.2-6 include the contributions from the quadrupole sources within the region enclosed by the source surface.

19.3

Using the Acoustics Model

The procedure for computing sound using the acoustics model in FLUENT consists largely of two steps. In the first step, a time-accurate flow solution is generated, from which time histories of the relevant variables (e.g., pressure, velocity, and density) on the selected source surfaces are obtained. In the second step, sound pressure signals at the userspecified receiver locations are computed using the source data collected during the first step. In computing sound pressure using the FW-H integral solution, FLUENT uses so-called “forward-time projection” to account for the time-delay between the emission time (the time at which the sound is emitted from the source) and the reception time (the time at which the sound arrives at the receiver location). The forward-time projection approach enables you to compute sound at the same time “on-the-fly” as the transient flow solution progresses, without having to save the source data. In this section, the procedure for setting up and using the acoustics model is outlined first, followed by detailed descriptions of each of the steps involved. Remember that only the steps that are pertinent to acoustics modeling are discussed here. For information about the inputs related to other models that you are using in conjunction with the acoustics model, see the appropriate sections for those models. The general procedure for carrying out an acoustics calculation in FLUENT is as follows: 1. Run the transient solution until you obtain a “statistically steady-state” solution as described below. 2. Enable the acoustics model and set the associated model parameters. Define −→ Models −→ Acoustics −→Models & Parameters...


19-5


3. Specify the source surface(s) and choose the options associated with acquisition and saving of the source data. Define −→ Models −→ Acoustics −→Sources... 4. Specify the receiver location(s). Define −→ Models −→ Acoustics −→Receivers... 5. Continue the transient solution for a sufficiently long period of time and save the source data. Solve −→Iterate... 6. Compute and save the sound pressure signals. Report −→ Acoustics −→Read & Compute Sound... 7. Postprocess the sound pressure signals. Plot −→FFT...

! Before you start the acoustics calculation, a FLUENT transient solution should have been be run to a point where the transient flow-field has become “statistically steady”. In practice, this means that the unsteady flow-field under consideration, including all the major flow variables, has become fully developed in such a way that its statistics do not change with time. Monitoring the major flow variables at selected points in the domain is helpful for that purpose. As discussed earlier, URANS, DES, and LES are all legitimate candidates for transient flow calculations. For stationary source surfaces, the frequency of the aerodynamically generated sound heard at the receivers is largely determined by the time scale or frequency of the underlying flow. Therefore, one way to determine the time-step size for the transient computation is to make it small enough to resolve the smallest characteristic time scale of the flow at hand (e.g., vortex-shedding frequency, time scale of large eddies) that can be reproduced by the mesh and turbulence adopted in your model. Once you have obtained a statistically stationary flow-field solution, you are ready to acquire the source data.

19.3.1

Enabling the Acoustics Model

To enable the acoustics model, select Ffowcs-Williams & Hawkings in the Acoustics Models and Parameters panel (Figure 19.3.1). Define −→ Models −→ Acoustics −→Models & Parameters... When you turn on Ffowcs-Williams & Hawkings, the panel will expand to show the relevant fields for user-inputs.

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Figure 19.3.1: The Acoustics Models and Parameters Panel

19.3.2

Setting Model Parameters

Under Model Parameters in the Acoustics Models and Parameters panel, specify the relevant acoustic parameters and constants used by the model. Far-Field Density (ρ0 in Equation 19.2-1) is the far-field fluid density. Far-Field Sound√Speed (a0 in Equations 19.2-5 and 19.2-6) is the sound speed at the farfield (= γRT ). Reference Acoustic Power is used to non-dimensionalize the acoustic power, giving the sound pressure level in dB (see Section 27.10). This parameter is equal to 4 × 10−10 W for airborne sound and 10−12 W for underwater sound. Reference Acoustic Intensity is defined as p2ref /(ρ0 a0 ), although this quantity is not currently used by FLUENT. Source Correlation Length is required when sound is to be computed using a 2D flow result. The FW-H integrals will be evaluated over this length in the depthwise direction using the identical source data. The default values are appropriate for sound propagating in air at atmospheric pressure and temperature.


19-7


19.3.3

Specifying Source Surfaces

In the Acoustics Models and Parameters panel, click the Sources... button to open the Acoustics Source Specification panel (Figure 19.3.2). Here you will specify the source surface(s) to be used in the acoustics calculation and the inputs associated with saving source data to files. Define −→ Models −→ Acoustics −→Sources...

Figure 19.3.2: The Acoustics Source Specification Panel Under Source Zones, you can select multiple emission (source) surfaces and the surface Type you can select is not limited to wall. You can also choose any interior surfaces as source surfaces.

! The ability to choose multiple source surfaces is useful for investigating the contributions from many individual source surfaces. The results based on the use of multiple source surfaces are valid as long as there are negligible acoustic interactions among the surfaces. Thus, some caution needs to be taken when selecting multiple source surfaces. • In cases where multiple source surfaces are selected, no source surface may enclose any of the other source surfaces. Otherwise, the sound pressure calculated based

19-8



on the source surfaces will not be accurate, as the contribution from the enclosed (inner) source surfaces is, in a sense, counted twice. • Likewise, a source surface should not get in the way of the propagation of sound from another source surface. If you specify any interior surfaces as source surfaces, the interior surface must be generated in advance (e.g., in GAMBIT) in such a way that the two cell zones adjacent to the surface have different cell zone IDs. Furthermore, you must correctly specify which of the two zones is occupied by the quadrupole sources (interior cell zone). This will allow FLUENT to determine the direction in which the sound will propagate. When you first attempt to select a legitimate interior surface (i.e., an interior surface having two different cell zones on both sides) as a source surface, the Interior Cell Zone Selection panel (Figure 19.3.3) will appear. You will then need to select the interior cell zones from the two zones listed under the Interior Cell Zone. Figure 19.3.4 shows an example of an interior source surface.

Figure 19.3.3: The Interior Cell Zone Selection Panel

Computing Sound “On-the-Fly” The acoustics model in FLUENT allows you to perform simultaneous calculation of the sound pressure signals at the prescribed receivers without having to write the source data to files, which can save a significant amount of disk space on your machine. To enable this “on-the-fly” calculation of sound, turn on the Extract Acoustic Signals Simultaneously option in the Acoustics Source Specification panel. When this option is chosen, the FLUENT console window will print a message at the end of each time step indicating that the sound pressure signals have been computed (e.g., Extracting sound signals at x receiver locations ..., where x is the number of receivers you specified). Enabling this option instructs FLUENT to compute sound pressure signals at the end of each time step, which will slightly increase the computation time.


19-9


3.36e+03 2.92e+03 2.48e+03 2.04e+03 1.59e+03 1.15e+03 7.12e+02 2.70e+02 -1.71e+02 -6.13e+02 -1.05e+03 -1.50e+03 -1.94e+03 -2.38e+03 -2.82e+03 -3.26e+03 -3.70e+03 -4.14e+03 -4.59e+03 -5.03e+03 -5.47e+03

outer-fluid interior source surface

inner-fluid

Contours of Static Pressure (pascal) (Time=2.2210e-02)

Jan 14, 2003 FLUENT 6.1 (2d, segregated, LES, unsteady)

Figure 19.3.4: An Interior Source Surface

Writing Source Data Files Although the “on-the-fly” capability is a convenient feature, you will want to save the source data as well, because the acquisition of source data during a transient flow-field calculation is the most time-consuming part of acoustics computation, and you most likely will not want to discard it. By saving the source data, you can always reuse it to compute the sound pressure signals at new or additional receiver locations. To enable saving the source data to files, turn on the Write Source Data Files option in the Acoustics Source Specification panel. Once this option is selected, the relevant source data at all face elements of the selected source surfaces will be written on the files you specify. The source data vary depending on the solver option you have chosen and whether the source surface is a wall or not. Table 19.3.1 shows the flow variables saved as the source data. Table 19.3.1: Source Data Saved in Source Data Files Solver Option incompressible incompressible compressible compressible

19-10

Source Surface walls permeable surfaces walls permeable surfaces

Source data p p, u, v, w p ρ, p, u, v, w



To save the source data, you also have to specify the Source Data Root File Name, Write Frequency (in number of time steps), and No. of Time Steps Per File. The Source Data Root File Name is used to give the names of the source data files (e.g., acoustic example xxxx.asd, where xxxx is the global time-step index of the transient solution) and an index file (e.g., acoustic example.index) that will store the information associated with the source data . The Write Frequency allows you to control how often the source data will be written. This will enable you to save disk space if the time-step size used in the transient flow simulation is smaller than necessary to resolve the sound frequency you are attempting to predict. In most situations, however, you will want to save the source data at every time step, and use the default of 1. Specifying the No. of Time Steps Per File allows you to write the source data to multiple files, each containing the source data for a number of time steps specified by you. Splitting the whole source data into smaller segments provides more safety and flexibility in handling source data files. You will find this feature useful if you want to use a selected number of subsequent data files to compute the sound pressure rather than using all of the source data. For example, you may want to exclude an initial portion of the source data from your acoustics calculation because you may realize later that the flow field has not fully attained a statistically steady state. Since acoustics calculations usually generate thousands of time steps of source data, you may want to split the data into several files. After you click Apply, FLUENT will create the index file (e.g., acoustics example.index), which contains information about the source data.

! If you choose to save source data, keep in mind that the source data can use up a considerable amount of disk space, especially if the mesh being used has a large number of face elements on the source surfaces you selected. The amount of source data (i.e., the number of items) written can be estimated from Ntime × Nfaces × Nvars , where Ntime is the number of time steps, Nfaces is the number of face elements on the source surface, and Nvars is the number of source variables (see Table 19.3.1). At this point, if you have chosen to perform your acoustics calculation in two steps, (i.e., saving the source data first, and computing the sound at a later time), you can go ahead and instruct FLUENT to perform a suitable number of time steps, and the source data will be saved to disk. If, however, you have chosen to perform an “on-the-fly” acoustic calculation, then you will need to specify receiver locations (see Section 19.3.4) before you run the unsteady FLUENT solution any further.

19.3.4

Specifying Acoustics Receivers

In the Acoustics Models and Parameters panel, click the Receivers... button to open the Acoustics Receivers Specification panel (Figure 19.3.5). Define −→ Models −→ Acoustics −→Receivers...


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Figure 19.3.5: The Acoustics Receivers Specification Panel

! Note that you can also open the Acoustics Receivers Specification panel by clicking the Receiver... button in the Acoustics Source Specification panel. Increase the No. of Receivers to the total number of receivers for which you want to compute sound, and enter the coordinates for each receiver in the X-Coord., Y-Coord., and Z-Coord. fields. Note that because FLUENT’s acoustics model is ideally suited for farfield noise prediction, the receiver locations you define should be at a reasonable distance from the sources of sound (i.e., the selected acoustic surface), and can fall outside of the computational domain if needed. For each receiver, you will also need to specify a file name in the Signal File Name field. These files will used to store the sound pressure signals at the corresponding receivers. By default, the files will be named receiver-1.dat, receiver-2.dat, etc. Once the receiver locations have been defined, the setup for your acoustic calculation is complete. You can now proceed to instruct FLUENT to a perform transient calculation for a suitable number of time steps. When the calculation is finished, you will have either the source data saved on files (if you chose to save it to a file or files), or the sound pressure signals (if you chose to perform an acoustic calculation “on-the-fly”), or both (if you chose to save the source data to files and if you chose to perform the acoustic calculation “on-the-fly”). If you chose to save the source data to files, the FLUENT console window will print a message at the end of each time step indicating that source data have been written (or appended to) a file (e.g., acoustic example 240.asd).

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19.3.5

Postprocessing for the Acoustics Model

At this point, you will have either the source data saved to files or the sound pressure signals computed, or both. You can process these data to compute and plot various acoustic quantities using FLUENT’s FFT capabilities.

Computing and Saving Sound Data If you have not chosen to perform the acoustic calculation “on-the-fly”, you can compute the sound pressure signals using the source data saved to files. This can be done in the Acoustic Signal Computation panel (Figure 19.3.6). Report −→ Acoustics −→Read and Compute Sound...

Figure 19.3.6: The Acoustic Signal Computation Panel To compute the sound data, use the following procedure: 1. Click Load Index File, and select the index file for your computation in the Select File dialog box. The file will have the name you entered in the Source Data Root Filename field in the Acoustics Source Specification panel, followed by the .index suffix (e.g., acoustic example.index).

!

Note that you can click the Free Data button at any time to free the memory from the data associated with the index file. 2. In the Source Data Files list, select the source data files that you want to use to compute sound. Source data files will all contain the specified root file name followed by the suffix .asd.


19-13


!

You can use any number of source data files. However, note that you should select only consecutive files. 3. In the Active Source Zones list, select the source zones you want to include to compute sound. 4. In the Receivers list, select the receivers for which you want to compute and save sound. Optionally, you can click the Receiver... button to open the Acoustics Receivers Specification panel, and define additional receivers. 5. Click the Compute button to compute and save the sound pressure data. One file will be saved for each receiver you previously specified in the Acoustic Signal Computation panel (e.g., receiver-1.dat). If you chose to perform the acoustic calculation “on-the-fly”, you will only need to write the sound pressure data to files. To do so, open the Write Sound Signals panel (Figure 19.3.7). Report −→ Acoustics −→Write Sound Pressure...

Figure 19.3.7: The Write Sound Signals Panel Click Write. One file will be saved for each receiver you defined in the Acoustic Receivers Specification panel (e.g., receiver-1.dat).

Using the FFT Capabilities Once the sound pressure signals are computed and saved in files, the sound data is ready for you to analyze using FLUENT’s FFT capabilities. In the Fourier Transform (Spectral Analysis) panel (Figure 27.10.1), click on Load Input File... and select the appropriate .dat file. See Section 27.10 for more information on FLUENT’s FFT capabilities. Plot −→FFT...

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Chapter 20. Introduction to Modeling Multiphase Flows A large number of flows encountered in nature and technology are a mixture of phases. Physical phases of matter are gas, liquid, and solid, but the concept of phase in a multiphase flow system is applied in a broader sense. In multiphase flow, a phase can be defined as an identifiable class of material that has a particular inertial response to and interaction with the flow and the potential field in which it is immersed. For example, different-sized solid particles of the same material can be treated as different phases because each collection of particles with the same size will have a similar dynamical response to the flow field. This chapter provides an overview of multiphase modeling in FLUENT, and Chapters 21 and 22 provide details about the multiphase models mentioned here. Chapter 23 provides information about melting and solidification. Information in this chapter is presented in the following sections: • Section 20.1: Multiphase Flow Regimes • Section 20.2: Examples of Multiphase Systems • Section 20.3: Approaches to Multiphase Modeling • Section 20.4: Choosing a Multiphase Model


20-1

Introduction to Modeling Multiphase Flows

20.1

Multiphase Flow Regimes

Multiphase flow can be classified by the following regimes, grouped into four categories: • gas-liquid or liquid-liquid flows – bubbly flow: discrete gaseous or fluid bubbles in a continuous fluid – droplet flow: discrete fluid droplets in a continuous gas – slug flow: large bubbles in a continuous fluid – stratified/free-surface flow: immiscible fluids separated by a clearly-defined interface • gas-solid flows – particle-laden flow: discrete solid particles in a continuous gas – pneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are dune flow, slug flow, packed beds, and homogeneous flow. – fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. The gas rising through the bed suspends the particles. Depending on the gas flow rate, bubbles appear and rise through the bed, intensifying the mixing within the bed. • liquid-solid flows – slurry flow: transport of particles in liquids. The fundamental behavior of liquid-solid flows varies with the properties of the solid particles relative to those of the liquid. In slurry flows, the Stokes number (see Equation 20.4-4) is normally less than 1. When the Stokes number is larger than 1, the characteristic of the flow is liquid-solid fluidization. – hydrotransport: densely-distributed solid particles in a continuous liquid – sedimentation: a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist. • three-phase flows (combinations of the others listed above) Each of these flow regimes is illustrated in Figure 20.1.1.

20-2


20.1 Multiphase Flow Regimes

slug flow

stratified/free-surface flow

sedimentation

bubbly, droplet, or particle-laden flow

pneumatic transport, hydrotransport, or slurry flow

fluidized bed

Figure 20.1.1: Multiphase Flow Regimes


20-3


20.2

Examples of Multiphase Systems

Specific examples of each regime described in Section 20.1 are listed below: • Bubbly flow examples: absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbers • Droplet flow examples: absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbers • Slug flow examples: large bubble motion in pipes or tanks • Stratified/free-surface flow examples: sloshing in offshore separator devices, boiling and condensation in nuclear reactors • Particle-laden flow examples: cyclone separators, air classifiers, dust collectors, and dust-laden environmental flows • Pneumatic transport examples: transport of cement, grains, and metal powders • Fluidized bed examples: fluidized bed reactors, circulating fluidized beds • Slurry flow examples: slurry transport, mineral processing • Hydrotransport examples: mineral processing, biomedical and physiochemical fluid systems • Sedimentation examples: mineral processing

20.3

Approaches to Multiphase Modeling

Advances in computational fluid mechanics have provided the basis for further insight into the dynamics of multiphase flows. Currently there are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the Euler-Euler approach.

20.3.1

The Euler-Lagrange Approach

The Lagrangian discrete phase model in FLUENT (described in Chapter 21) follows the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the timeaveraged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles, bubbles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase. A fundamental assumption made in this model is that the dispersed second phase occupies a low volume fraction, even though high mass loading (m ˙ particles ≥ m ˙ fluid ) is acceptable. The particle or droplet trajectories are computed individually at specified intervals during

20-4


20.3 Approaches to Multiphase Modeling

the fluid phase calculation. This makes the model appropriate for the modeling of spray dryers, coal and liquid fuel combustion, and some particle-laden flows, but inappropriate for the modeling of liquid-liquid mixtures, fluidized beds, or any application where the volume fraction of the second phase is not negligible.

20.3.2

The Euler-Euler Approach

In the Euler-Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phasic volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. These equations are closed by providing constitutive relations that are obtained from empirical information, or, in the case of granular flows, by application of kinetic theory. In FLUENT, three different Euler-Euler multiphase models are available: the volume of fluid (VOF) model, the mixture model, and the Eulerian model.

The VOF Model The VOF model (described in Section 22.2) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. Applications of the VOF model include stratified flows, free-surface flows, filling, sloshing, the motion of large bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquid-gas interface.

The Mixture Model The mixture model (described in Section 22.3) is designed for two or more phases (fluid or particulate). As in the Eulerian model, the phases are treated as interpenetrating continua. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. Applications of the mixture model include particle-laden flows with low loading, bubbly flows, sedimentation, and cyclone separators. The mixture model can also be used without relative velocities for the dispersed phases to model homogeneous multiphase flow.

The Eulerian Model The Eulerian model (described in Section 22.4) is the most complex of the multiphase models in FLUENT. It solves a set of n momentum and continuity equations for each


20-5


phase. Coupling is achieved through the pressure and interphase exchange coefficients. The manner in which this coupling is handled depends upon the type of phases involved; granular (fluid-solid) flows are handled differently than non-granular (fluid-fluid) flows. For granular flows, the properties are obtained from application of kinetic theory. Momentum exchange between the phases is also dependent upon the type of mixture being modeled. FLUENT’s user-defined functions allow you to customize the calculation of the momentum exchange. Applications of the Eulerian multiphase model include bubble columns, risers, particle suspension, and fluidized beds.

20.4

Choosing a Multiphase Model

The first step in solving any multiphase problem is to determine which of the regimes described in Section 20.1 best represents your flow. Section 20.4.1 provides some broad guidelines for determining appropriate models for each regime, and Section 20.4.2 provides details about how to determine the degree of interphase coupling for flows involving bubbles, droplets, or particles, and the appropriate model for different amounts of coupling.

20.4.1

General Guidelines

In general, once you have determined the flow regime that best represents your multiphase system, you can select the appropriate model based on the following guidelines. Additional details and guidelines for selecting the appropriate model for flows involving bubbles, droplets, or particles can be found in Section 20.4.2. • For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the discrete phase model. See Chapter 21 for more information about the discrete phase model. • For bubbly, droplet, and particle-laden flows in which the phases mix and/or dispersed-phase volume fractions exceed 10%, use either the mixture model (described in Section 22.3) or the Eulerian model (described in Section 22.4). See Sections 20.4.2 and 22.1 for details about how to determine which is more appropriate for your case. • For slug flows, use the VOF model. See Section 22.2 for more information about the VOF model. • For stratified/free-surface flows, use the VOF model. See Section 22.2 for more information about the VOF model. • For pneumatic transport, use the mixture model for homogeneous flow (described in Section 22.3) or the Eulerian model for granular flow (described in Section 22.4). See Sections 20.4.2 and 22.1 for details about how to determine which is more appropriate for your case.

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20.4 Choosing a Multiphase Model

• For fluidized beds, use the Eulerian model for granular flow. See Section 22.4 for more information about the Eulerian model. • For slurry flows and hydrotransport, use the mixture or Eulerian model (described, respectively, in Sections 22.3 and 22.4). See Sections 20.4.2 and 22.1 for details about how to determine which is more appropriate for your case. • For sedimentation, use the Eulerian model. See Section 22.4 for more information about the Eulerian model. • For general, complex multiphase flows that involve multiple flow regimes, select the aspect of the flow that is of most interest, and choose the model that is most appropriate for that aspect of the flow. Note that the accuracy of results will not be as good as for flows that involve just one flow regime, since the model you use will be valid for only part of the flow you are modeling.

20.4.2

Detailed Guidelines

For stratified and slug flows, the choice of the VOF model, as indicated in Section 20.4.1, is straightforward. Choosing a model for the other types of flows is less straightforward. As a general guide, there are some parameters that help to identify the appropriate multiphase model for these other flows: the particulate loading, β, and the Stokes number, St. (Note that the word “particle” is used in this discussion to refer to a particle, droplet, or bubble.)

The Effect of Particulate Loading Particulate loading has a major impact on phase interactions. The particulate loading is defined as the mass density ratio of the dispersed phase (d) to that of the carrier phase (c): β=

αd ρd αc ρc

(20.4-1)

ρd ρc

(20.4-2)

The material density ratio γ=

is greater than 1000 for gas-solid flows, about 1 for liquid-solid flows, and less than 0.001 for gas-liquid flows. Using these parameters it is possible to estimate the average distance between the individual particles of the particulate phase. An estimate of this distance has been given by Crowe et al. [46]:


20-7


L π1+κ = dd 6 κ

1/3

(20.4-3)

where κ = βγ . Information about these parameters is important for determining how the dispersed phase should be treated. For example, for a gas-particle flow with a particulate loading of 1, the interparticle space dLd is about 8; the particle can therefore be treated as isolated (i.e., very low particulate loading). Depending on the particulate loading, the degree of interaction between the phases can be divided into three categories: • For very low loading, the coupling between the phases is one-way; i.e., the fluid carrier influences the particles via drag and turbulence, but the particles have no influence on the fluid carrier. The discrete phase, mixture, and Eulerian models can all handle this type of problem correctly. Since the Eulerian model is the most expensive, the discrete phase or mixture model is recommended. • For intermediate loading, the coupling is two-way; i.e., the fluid carrier influences the particulate phase via drag and turbulence, but the particles in turn influence the carrier fluid via reduction in mean momentum and turbulence. The discrete phase, mixture, and Eulerian models are all applicable in this case, but you need to take into account other factors in order to decide which model is more appropriate. See below for information about using the Stokes number as a guide. • For high loading, there is two-way coupling plus particle pressure and viscous stresses due to particles (four-way coupling). Only the Eulerian model will handle this type of problem correctly.

The Significance of the Stokes Number For systems with intermediate particulate loading, estimating the value of the Stokes number can help you select the most appropriate model. The Stokes number can be defined as the relation between the particle response time and the system response time: St =

τd ts

(20.4-4)

ρ d2

d d where τd = 18µ and ts is based on the characteristic length (Ls ) and the characteristic c velocity (Vs ) of the system under investigation: ts = LVss .

For St 1.0, the particle will follow the flow closely and any of the three models (discrete phase, mixture, or Eulerian) is applicable; you can therefore choose the least expensive (the mixture model, in most cases), or the most appropriate considering other factors. For

20-8


20.4 Choosing a Multiphase Model

St > 1.0, the particles will move independently of the flow and either the discrete phase model or the Eulerian model is applicable. For St ≈ 1.0, again any of the three models is applicable; you can choose the least expensive or the most appropriate considering other factors. Examples For a coal classifier with a characteristic length of 1 m and a characteristic velocity of 10 m/s, the Stokes number is 0.04 for particles with a diameter of 30 microns, but 4.0 for particles with a diameter of 300 microns. Clearly the mixture model will not be applicable to the latter case. For the case of mineral processing, in a system with a characteristic length of 0.2 m and a characteristic velocity of 2 m/s, the Stokes number is 0.005 for particles with a diameter of 300 microns. In this case, you can choose between the mixture and Eulerian models. (The volume fractions are too high for the discrete phase model, as noted below.)

Other Considerations Keep in mind that the use of the discrete phase model is limited to low volume fractions. Also, the discrete phase model is the only multiphase model that allows you to specify the particle distribution or include combustion modeling in your simulation.


20-9


20-10


Chapter 21.

Discrete Phase Models

This chapter describes the Lagrangian discrete phase capabilities available in FLUENT and how to use them. Information is organized into the following sections: • Section 21.1: Overview and Limitations of the Discrete Phase Models • Section 21.2: Trajectory Calculations • Section 21.3: Heat and Mass Transfer Calculations • Section 21.4: Spray Models • Section 21.5: Coupling Between the Discrete and Continuous Phases • Section 21.6: Overview of Using the Discrete Phase Models • Section 21.7: Discrete Phase Model Options • Section 21.8: Particle Tracking • Section 21.9: Setting Initial Conditions for the Discrete Phase • Section 21.10: Setting Boundary Conditions for the Discrete Phase • Section 21.11: Setting Material Properties for the Discrete Phase • Section 21.12: Calculation Procedures for the Discrete Phase • Section 21.13: Postprocessing for the Discrete Phase

21.1 21.1.1

Overview and Limitations of the Discrete Phase Models Introduction

In addition to solving transport equations for the continuous phase, FLUENT allows you to simulate a discrete second phase in a Lagrangian frame of reference. This second phase consists of spherical particles (which may be taken to represent droplets or bubbles) dispersed in the continuous phase. FLUENT computes the trajectories of these discrete phase entities, as well as heat and mass transfer to/from them. The coupling between the phases and its impact on both the discrete phase trajectories and the continuous phase flow can be included.


21-1


FLUENT provides the following discrete phase modeling options: • Calculation of the discrete phase trajectory using a Lagrangian formulation that includes the discrete phase inertia, hydrodynamic drag, and the force of gravity, for both steady and unsteady flows • Prediction of the effects of turbulence on the dispersion of particles due to turbulent eddies present in the continuous phase • Heating/cooling of the discrete phase • Vaporization and boiling of liquid droplets • Combusting particles, including volatile evolution and char combustion to simulate coal combustion • Optional coupling of the continuous phase flow field prediction to the discrete phase calculations • Droplet breakup and coalescence These modeling capabilities allow FLUENT to simulate a wide range of discrete phase problems including particle separation and classification, spray drying, aerosol dispersion, bubble stirring of liquids, liquid fuel combustion, and coal combustion. The physical equations used for these discrete phase calculations are described in Sections 21.2–21.5, and instructions for setup, solution, and postprocessing are provided in Sections 21.6– 21.13.

21.1.2

Particles in Turbulent Flows

The dispersion of particles due to turbulence in the fluid phase can be predicted using the stochastic tracking model or the particle cloud model (see Section 21.2.2). The stochastic tracking (random walk) model includes the effect of instantaneous turbulent velocity fluctuations on the particle trajectories through the use of stochastic methods (see Section 21.2.2). The particle cloud model tracks the statistical evolution of a cloud of particles about a mean trajectory (see Section 21.2.2). The concentration of particles within the cloud is represented by a Gaussian probability density function (PDF) about the mean trajectory. In both models, the particles have no direct impact on the generation or dissipation of turbulence in the continuous phase.

21.1.3

Limitations

Limitation on the Particle Volume Fraction The discrete phase formulation used by FLUENT contains the assumption that the second phase is sufficiently dilute that particle-particle interactions and the effects of the particle

21-2


21.1 Overview and Limitations of the Discrete Phase Models

volume fraction on the gas phase are negligible. In practice, these issues imply that the discrete phase must be present at a fairly low volume fraction, usually less than 10–12%. Note that the mass loading of the discrete phase may greatly exceed 10–12%: you may solve problems in which the mass flow of the discrete phase equals or exceeds that of the continuous phase. See Chapters 20 and 22 for information about when you might want to use one of the general multiphase models instead of the discrete phase model.

Limitation on Modeling Continuous Suspensions of Particles The steady-particle Lagrangian discrete phase model described in this chapter is suited for flows in which particle streams are injected into a continuous phase flow with a welldefined entrance and exit condition. The Lagrangian model does not effectively model flows in which particles are suspended indefinitely in the continuum, as occurs in solid suspensions within closed systems such as stirred tanks, mixing vessels, or fluidized beds. The unsteady-particle discrete phase model, however, is capable of modeling continuous suspensions of particles. See Chapters 20 and 22 for information about when you might want to use one of the general multiphase models instead of the discrete phase models.

Limitations on Using the Discrete Phase Model with Other FLUENT Models The following restrictions exist on the use of other models with the discrete phase model: • Streamwise periodic flow (either specified mass flow rate or specified pressure drop) cannot be modeled when the discrete phase model is used. • Adaptive time stepping cannot be used with the discrete phase model. • Only non-reacting particles can be included when the premixed combustion model is used. • Surface injections will not be moved with the grid when a sliding mesh or a moving or deforming mesh is being used. • When multiple reference frames are used in conjunction with the discrete phase model, the display of particle tracks will not, by default, be meaningful. Similarly, coupled discrete-phase calculations are not meaningful. An alternative approach for particle tracking and coupled discrete-phase calculations with multiple reference frames is to track particles based on absolute velocity instead of relative velocity. To make this change, use the define/models/dpm/ tracking/track-in-absolute-frame text command. Note that the results may strongly depend on the location of walls inside the multiple reference frame. The particle injection velocities (specified in the Set Injection Properties panel) are defined relative to the frame of reference in which the particles are tracked. By


21-3


default, the injection velocities are specified relative to the local reference frame. If you enable the track-in-absolute-frame option, the injection velocities are specified relative to the absolute frame.

21.1.4

Overview of Discrete Phase Modeling Procedures

You can include a discrete phase in your FLUENT model by defining the initial position, velocity, size, and temperature of individual particles. These initial conditions, along with your inputs defining the physical properties of the discrete phase, are used to initiate trajectory and heat/mass transfer calculations. The trajectory and heat/mass transfer calculations are based on the force balance on the particle and on the convective/radiative heat and mass transfer from the particle, using the local continuous phase conditions as the particle moves through the flow. The predicted trajectories and the associated heat and mass transfer can be viewed graphically and/or alphanumerically. You can use FLUENT to predict the discrete phase patterns based on a fixed continuous phase flow field (an uncoupled approach), or you can include the effect of the discrete phase on the continuum (a coupled approach). In the coupled approach, the continuous phase flow pattern is impacted by the discrete phase (and vice versa), and you can alternate calculations of the continuous phase and discrete phase equations until a converged coupled solution is achieved. See Section 21.5 for details.

Outline of Steady-State Problem Setup and Solution Procedure The general procedure for setting up and solving a steady-state discrete-phase problem is outlined below: 1. Solve the continuous-phase flow. 2. Create the discrete-phase injections. 3. Solve the coupled flow, if desired. 4. Track the discrete-phase injections, using plots or reports.

Outline of Unsteady Problem Setup and Solution Procedure The general procedure for setting up and solving an unsteady discrete-phase problem is outlined below: 1. Create the discrete-phase injections. 2. Initialize the flow field.

21-4


21.2 Trajectory Calculations

3. Advance the solution in time by taking the desired number of time steps. Particle positions will be updated as the solution advances in time. If you are solving an uncoupled flow, the particle position will be updated at the end of each time step. For a coupled calculation, the positions are iterated on within each time step.

21.2 21.2.1

Trajectory Calculations Equations of Motion for Particles

Particle Force Balance FLUENT predicts the trajectory of a discrete phase particle (or droplet or bubble) by integrating the force balance on the particle, which is written in a Lagrangian reference frame. This force balance equates the particle inertia with the forces acting on the particle, and can be written (for the x direction in Cartesian coordinates) as dup gx (ρp − ρ) = FD (u − up ) + + Fx dt ρp

(21.2-1)

where FD (u − up ) is the drag force per unit particle mass and FD =

18µ CD Re ρp d2p 24

(21.2-2)

Here, u is the fluid phase velocity, up is the particle velocity, µ is the molecular viscosity of the fluid, ρ is the fluid density, ρp is the density of the particle, and dp is the particle diameter. Re is the relative Reynolds number, which is defined as Re ≡

ρdp |up − u| µ

(21.2-3)

The drag coefficient, CD , can be taken from either CD = a1 +

a3 a2 + 2 Re Re

(21.2-4)

where a1 , a2 , and a3 are constants that apply for smooth spherical particles over several ranges of Re given by Morsi and Alexander [177], or CD =


24 b3 Re 1 + b1 Reb2 + Re b4 + Re

(21.2-5)

21-5


where b1 b2 b3 b4

= = = =

exp(2.3288 − 6.4581φ + 2.4486φ2 ) 0.0964 + 0.5565φ exp(4.905 − 13.8944φ + 18.4222φ2 − 10.2599φ3 ) exp(1.4681 + 12.2584φ − 20.7322φ2 + 15.8855φ3 )

(21.2-6)

which is taken from Haider and Levenspiel [96]. The shape factor, φ, is defined as φ=

s S

(21.2-7)

where s is the surface area of a sphere having the same volume as the particle, and S is the actual surface area of the particle. For sub-micron particles, a form of Stokes’ drag law is available [187]. In this case, FD is defined as FD =

18µ dp 2 ρp Cc

(21.2-8)

The factor Cc is the Cunningham correction to Stokes’ drag law, which you can compute from Cc = 1 +

2λ (1.257 + 0.4e−(1.1dp /2λ) ) dp

(21.2-9)

where λ is the molecular mean free path. A high-Mach-number drag law is also available. This drag law is similar to the spherical law (Equation 21.2-4) with corrections [42] to account for a particle Mach number greater than 0.4 at a particle Reynolds number greater than 20. For unsteady models involving discrete phase droplet breakup, a dynamic drag law option is also available. See Section 21.4.4 for a description of this law. Instructions for selecting the drag law are provided in Section 21.7.7.

Including the Gravity Term While Equation 21.2-1 includes a force of gravity on the particle, it is important to note that in FLUENT the default gravitational acceleration is zero. If you want to include the gravity force, you must remember to define the magnitude and direction of the gravity vector in the Operating Conditions panel.

21-6



Other Forces Equation 21.2-1 incorporates additional forces (Fx ) in the particle force balance that can be important under special circumstances. The first of these is the “virtual mass” force, the force required to accelerate the fluid surrounding the particle. This force can be written as Fx =

1ρ d (u − up ) 2 ρp dt

(21.2-10)

and is important when ρ > ρp . An additional force arises due to the pressure gradient in the fluid:

Fx =

!

ρ ∂u up ρp ∂x

(21.2-11)

Forces in Rotating Reference Frames The additional force term, Fx , in Equation 21.2-1 also includes forces on particles that arise due to rotation of the reference frame. These forces arise when you are modeling flows in rotating frames of reference (see Section 9.2). For rotation defined about the z axis, for example, the forces on the particles in the Cartesian x and y directions can be written as !

ρ ρ Ω2 x + 2Ω uy,p − uy 1− ρp ρp

!

(21.2-12)

where uy,p and uy are the particle and fluid velocities in the Cartesian y direction, and !

ρ ρ 1− Ω2 y − 2Ω ux,p − ux ρp ρp

!

(21.2-13)

where ux,p and ux are the particle and fluid velocities in the Cartesian x direction.

Thermophoretic Force Small particles suspended in a gas that has a temperature gradient experience a force in the direction opposite to that of the gradient. This phenomenon is known as thermophoresis. FLUENT can optionally include a thermophoretic force on particles in the additional force term, Fx , in Equation 21.2-1: Fx = −DT,p


1 ∂T mp T ∂x

(21.2-14)

21-7


where DT,p is the thermophoretic coefficient. You can define the coefficient to be constant, polynomial, or a user-defined function, or you can use the form suggested by Talbot [263]: Fx = − where:

Kn λ K k

= = = =

kp CS Ct Cm mp T µ

= = = = = = =

1 ∂T 6πdp µ2 Cs (K + Ct Kn) ρ(1 + 3Cm Kn)(1 + 2K + 2Ct Kn) mp T ∂x

(21.2-15)

Knudsen number = 2 λ/dp mean free path of the fluid k/kp fluid thermal conductivity based on translational energy only = (15/4) µR particle thermal conductivity 1.17 2.18 1.14 particle mass local fluid temperature fluid viscosity

This expression assumes that the particle is a sphere and that the fluid is an ideal gas.

Brownian Force For sub-micron particles, the effects of Brownian motion can optionally be included in the additional force term. The components of the Brownian force are modeled as a Gaussian white noise process with spectral intensity Sn,ij given by [147] Sn,ij = S0 δij

(21.2-16)

where δij is the Kronecker delta function, and S0 =

216νσT π 2 ρd5p

ρp 2 ρ

(21.2-17) Cc

T is the absolute temperature of the fluid, ν is the kinematic viscosity, and σ is the Stefan-Boltzmann constant. Amplitudes of the Brownian force components are of the form

Fbi = ζi

s

πSo ∆t

(21.2-18)

where ζi are zero-mean, unit-variance-independent Gaussian random numbers. The amplitudes of the Brownian force components are evaluated at each time step. The energy

21-8



equation must be enabled in order for the Brownian force to take effect. Brownian force is intended only for non-turbulent models.

Saffman’s Lift Force The Saffman’s lift force, or lift due to shear, can also be included in the additional force term as an option. The lift force used is from Li and Ahmadi [147] and is a generalization of the expression provided by Saffman [219]: F~ =

2Kν 1/2 ρdij (~v − ~vp ) ρp dp (dlk dkl )1/4

(21.2-19)

where K = 2.594 and dij is the deformation tensor. This form of the lift force is intended for small particle Reynolds numbers. Also, the particle Reynolds number based on the particle-fluid velocity difference must be smaller than the square root of the particle Reynolds number based on the shear field. Since this restriction is valid for submicron particles, it is recommended to use this option only for submicron particles.

Stochastic Particle Tracking in Turbulent Flow When the flow is turbulent, FLUENT will predict the trajectories of particles using the mean fluid phase velocity, u, in the trajectory equations (Equation 21.2-1). Optionally, you can include the instantaneous value of the fluctuating gas flow velocity, u = u + u0

(21.2-20)

to predict the dispersion of the particles due to turbulence. FLUENT uses a stochastic method (random walk model) to determine the instantaneous gas velocity, as detailed in Section 21.2.2.

Particle Cloud Tracking in Turbulent Flow Particle dispersion due to turbulent fluctuations can also be modeled with the particle cloud model [15, 16, 111, 154]. The turbulent dispersion of particles about a mean trajectory is calculated using statistical methods. The concentration of particles about the mean trajectory is represented by a Gaussian probability density function (PDF) whose variance is based on the degree of particle dispersion due to turbulent fluctuations. The mean trajectory is obtained by solving the ensemble-averaged equations of motion for all particles represented by the cloud (see Section 21.2.2).


21-9


Integration of the Trajectory Equations The trajectory equations, and any auxiliary equations describing heat or mass transfer to/from the particle, are solved by stepwise integration over discrete time steps. Integration in time of Equation 21.2-1 yields the velocity of the particle at each point along the trajectory, with the trajectory itself predicted by dx = up dt

(21.2-21)

Equations similar to 21.2-1 and 21.2-21 are solved in each coordinate direction to predict the trajectories of the discrete phase. Assuming that the term containing the body force remains constant over each small time interval, and linearizing any other forces acting on the particle, the trajectory equation can be rewritten in simplified form as dup 1 = (u − up ) dt τp

(21.2-22)

where τp is the particle relaxation time. FLUENT uses a trapezoidal scheme for integrating Equation 21.2-22: un+1 − unp 1 p = (u∗ − un+1 ) + ... p ∆t τ

(21.2-23)

where n represents the iteration number and

1 n (u + un+1 ) 2 = un + ∆tunp · ∇un

u∗ = un+1

(21.2-24) (21.2-25)

Equations 21.2-21 and 21.2-22 are solved simultaneously to determine the velocity and position of the particle at any given time. For rotating reference frames, the integration is carried out in the rotating frame with the extra terms described above (Equations 21.2-12 and 21.2-13) to account for system rotation. In all cases, care must be taken that the time step used for integration is sufficiently small that the trajectory integration is accurate in time. (See Section 21.12.)

Droplet Size Distributions For liquid sprays, a convenient representation of the droplet size distribution is the RosinRammler expression. The complete range of sizes is divided into an adequate number of

21-10



discrete intervals; each represented by a mean diameter for which trajectory calculations are performed. If the size distribution is of the Rosin-Rammler type, the mass fraction of droplets of diameter greater than d is given by ¯n

Yd = e−(d/d)

(21.2-26)

where d¯ is the size constant and n is the size distribution parameter. Use of the RosinRammler size distribution is detailed in Section 21.9.7.

Discrete Phase Boundary Conditions When a particle strikes a boundary face, one of several contingencies may arise: • Reflection via an elastic or inelastic collision. • Escape through the boundary. (The particle is lost from the calculation at the point where it impacts the boundary.) • Trap at the wall. Non-volatile material is lost from the calculation at the point of impact with the boundary; volatile material present in the particle or droplet is released to the vapor phase at this point. • Passing through an internal boundary zone, such as radiator or porous jump. • Slide along the wall depending on particle properties and impact angle. You also have the option of implementing a user-defined function to model the particle behavior when hitting the boundary. See the separate UDF Manual for information about user-defined functions. These boundary condition options are described in detail in Section 21.10.

21.2.2

Turbulent Dispersion of Particles

Turbulent dispersion of particles can be modeled using either a stochastic discrete-particle approach or a “cloud” representation of a group of particles about a mean trajectory. In addition, these approaches can be combined to model a set of “clouds” about a mean trajectory that includes the effects of turbulent fluctuations in the gas phase velocities.

! Turbulent dispersion of particles cannot be included if the Spalart-Allmaras turbulence model is used.


21-11


Stochastic Tracking In the stochastic tracking approach, FLUENT predicts the turbulent dispersion of particles by integrating the trajectory equations for individual particles, using the instantaneous 0 fluid velocity, u + u (t), along the particle path during the integration. By computing the trajectory in this manner for a sufficient number of representative particles (termed the “number of tries”), the random effects of turbulence on the particle dispersion may be accounted for. In FLUENT, the Discrete Random Walk (DRW) model is used. In this model, the fluctuating velocity components are discrete piecewise constant functions of time. Their random value is kept constant over an interval of time given by the characteristic lifetime of the eddies. The DRW model may give non-physical results in strongly inhomogeneous diffusiondominated flows, where small particles should become uniformly distributed. Instead, the DRW will show a tendency for such particles to concentrate in low-turbulence regions of the flow. The Integral Time Prediction of particle dispersion makes use of the concept of the integral time scale, T , which describes the time spent in turbulent motion along the particle path, ds: T =

Z

∞

0

up 0 (t)up 0 (t + s) ds up 0 2

(21.2-27)

The integral time is proportional to the particle dispersion rate, as larger values indicate more turbulent motion in the flow. It can be shown that the particle diffusivity is given by ui 0 uj 0 T . For small “tracer” particles that move with the fluid (zero drift velocity), the integral time becomes the fluid Lagrangian integral time, TL . This time scale can be approximated as TL = CL

k

(21.2-28)

where CL is to be determined and is not well known. By matching the diffusivity of tracer particles, ui 0 uj 0 TL , to the scalar diffusion rate predicted by the turbulence model, νt /σ, one can obtain TL ≈ 0.15

k

(21.2-29)

k

(21.2-30)

for the k- model and its variants, and TL ≈ 0.30

21-12



when the Reynolds stress model (RSM) is used [51]. For the k-ω models, substitute ω = /k into Equation 21.2-28. The LES model uses the equivalent LES time scales. The Discrete Random Walk Model In the Discrete Random Walk (DRW) model, or “eddy lifetime” model, the interaction of a particle with a succession of discrete stylized fluid phase turbulent eddies is simulated. Each eddy is characterized by • a Gaussian distributed random velocity fluctuation, u0 , v 0 , and w0 • a time scale, τe The values of u0 , v 0 , and w0 that prevail during the lifetime of the turbulent eddy are sampled by assuming that they obey a Gaussian probability distribution, so that q

0

u = ζ u0 2

(21.2-31)

where ζ is a normally distributed random number, and the remainder of the right-hand side is the local RMS value of the velocity fluctuations. Since the kinetic energy of turbulence is known at each point in the flow, these values of the RMS fluctuating components can be obtained (assuming isotropy) as q

02

u =

q

02

v =

q

w0 2 =

q

2k/3

(21.2-32)

for the k- model, the k-ω model, and their variants. When the RSM is used, non-isotropy of the stresses is included in the derivation of the velocity fluctuations:

u

0

q

(21.2-33)

q

(21.2-34)

q

(21.2-35)

= ζ u0 2

v0 = ζ v02 w0 = ζ w0 2

when viewed in a reference frame in which the second moment of the turbulence is diagonal [301]. For the LES model, the velocity fluctuations are equivalent in all directions. See Section 10.7.3 for details. The characteristic lifetime of the eddy is defined either as a constant: τe = 2TL


(21.2-36)

21-13


where TL is given by Equation 21.2-28 in general (Equation 21.2-29 by default), or as a random variation about TL : τe = −TL log(r)

(21.2-37)

where r is a uniform random number between 0 and 1 and TL is given by Equation 21.2-29. The option of random calculation of τe yields a more realistic description of the correlation function. The particle eddy crossing time is defined as

tcross

"

Le = −τ ln 1 − τ |u − up |

!#

(21.2-38)

where τ is the particle relaxation time, Le is the eddy length scale, and |u − up | is the magnitude of the relative velocity. The particle is assumed to interact with the fluid phase eddy over the smaller of the eddy lifetime and the eddy crossing time. When this time is reached, a new value of the instantaneous velocity is obtained by applying a new value of ζ in Equation 21.2-31. Using the DRW Model The only inputs required for the DRW model are the value for the integral time-scale constant, CL (see Equations 21.2-28 and 21.2-36) and the choice of the method used for the prediction of the eddy lifetime. You can choose to use either a constant value or a random value by selecting the appropriate option in the Set Injection Properties panel for each injection, as described in Section 21.9.15.

! Turbulent dispersion of particles cannot be included if the Spalart-Allmaras turbulence model is used.

Particle Cloud Tracking The particle cloud model is based on the stochastic transport of particles model developed by Litchford and Jeng [154], Baxter and Smith [16], and Jain [111]. The approach uses statistical methods to trace the turbulent dispersion of particles about a mean trajectory. The mean trajectory is calculated from the ensemble average of the equations of motion for the particles represented by the cloud. The cloud enters the domain either as a point source or with an initial diameter. The cloud expands due to turbulent dispersion as it is transported through the domain until it exits. The distribution of particles in the cloud is defined by a probability density function (PDF) based on the position in the cloud relative to the cloud center. The value of the PDF represents the probability of finding particles represented by that cloud with residence time t at location xi in the flow field.

21-14



The average particle number density can be obtained by weighting the total flow rate of particles represented by that cloud, m, ˙ as hn(xi )i = mP ˙ (xi , t)

(21.2-39)

The PDFs for particle position are assumed to be multivariate Gaussian. These are completely described by their mean, µi , and variance, σi 2 , and are of the form 1

P (xi , t) =

(2π)3/2

3 Y

e−s/2

(21.2-40)

σi

i=1

where

s=

3 X x i − µi 2

(21.2-41)

σi

i=1

The mean of the PDF, or the center of the cloud, at a given time represents the most likely location of the particles in the cloud. The mean location is obtained by integrating a particle velocity as defined by an equation of motion for the cloud of particles: µi (t) ≡ hxi (t)i =

Z

t

0

hVi (t1 )idt1 + hxi (0)i

(21.2-42)

The equations of motion are constructed using an ensemble average. The radius of the particle cloud is based on the variance of the PDF. The variance, σi2 (t), of the PDF can be expressed in terms of two particle turbulence statistical quantities: σi2 (t)

=2

Z

0

t

hu02 p,i (t2 )i

Z

0

t2

Rp,ii (t2 , t1 )dt1 dt2

(21.2-43)

0

2 where hup,i i are the mean square velocity fluctuations, and Rp,ij (t2 , t1 ) is the particle velocity correlation function:

Rp,ij (t2 , t1 ) = h

hu0p,i (t2 )u0p,j (t1 )i i1/2

(21.2-44)

02 hu02 p,i (t2 )up,j (t2 )i

By using the substitution τ = |t2 − t1 |, and the fact that Rp,ij (t2 , t1 ) = Rp,ij (t4 , t3 )


(21.2-45)

21-15


whenever |t2 − t1 | = |t4 − t3 |, we can write σi2 (t)

=2

Z

0

t

hu02 p,i (t2 )i

Z

t2

0

Rp,ii (τ )dτ dt2

(21.2-46)

Note that cross correlations in the definition of the variance (Rp,ij , i 6= j) have been neglected. The form of the particle velocity correlation function used determines the particle dispersion in the cloud model. FLUENT uses a correlation function first proposed by Wang [281], and used by Jain [111]. When the gravity vector is aligned with the z-coordinate direction, Rij takes the form:

Rp,11

St2 B 2 + 1 u02 −(τ /τa ) e StT B − 0.5mT γ T = θ θ ! u02 −(τ B/T ) mT St2T γB τ e −1 + + 0.5mT γ + θ θ T !

Rp,22 = Rp,11 u02 StT B −(τ /τa ) u02 −(τ B/T ) Rp,33 = e − e θ θ where B =

(21.2-47) (21.2-48) (21.2-49)

q

1 + m2T γ 2 and τa is the aerodynamic response time of the particle: ρp d2p τa = 18µ

(21.2-50)

and

T = Tf E = γ = St = StT = θ = m =

21-16

mT TmE m 3/4 3/2 Cµ k ( 23 k)1/2 τa g u0 τa TmE τa T St2T (1 + m2T γ 2 ) − 1 u¯ u0

(21.2-51) (21.2-52) (21.2-53) (21.2-54) (21.2-55) (21.2-56) (21.2-57)


21.2 Trajectory Calculations u¯ 0 "u

TmE = Tf E

(21.2-58)

mT = m 1 −

G(m) (1 + St)0.4(1+0.01St)

2 Z∞ √ G(m) = π 0 1+

#

(21.2-59)

2

e−y dy m2 π

5/2 √ ( π erf(y)y − 1 + e−y2 )

(21.2-60)

Using this correlation function, the variance is integrated over the life of the cloud. At any given time, the cloud radius is set to three standard deviations in the coordinate directions. The cloud radius is limited to three standard deviations since at least 99.2% of the area under a Gaussian PDF is accounted for at this distance. Once the cells within the cloud are established, the fluid properties are ensemble-averaged for the mean trajectory, and the mean path is integrated in time. This is done with a weighting factor defined as Z

W (xi , t) ≡ Z

Vcell

P (xi , t)dV

Vcloud

(21.2-61) P (xi , t)dV

If coupled calculations are performed, sources are distributed to the cells in the cloud based on the same weighting factors. Using the Cloud Model The only inputs required for the cloud model are the values of the minimum and maximum cloud diameters. The cloud model is enabled in the Set Injection Properties panel for each injection, as described in Section 21.9.15.

! The cloud model is not available for unsteady particle tracking. 21.2.3

Particle Erosion and Accretion

Particle erosion and accretion rates can be monitored at wall boundaries. The erosion rate is defined as Nparticles

Rerosion =

X

p=1

m ˙ p C(dp )f (α)v b(v) Aface

(21.2-62)

where C(dp ) is a function of particle diameter, α is the impact angle of the particle path with the wall face, f (α) is a function of impact angle, v is the relative particle velocity, and b(v) is a function of relative particle velocity. Default values are C = 1.8 × 10−9 , f = 1, and b = 0.


21-17


Since C, f , and b are defined as boundary conditions at a wall, rather than properties of a material, the default values are not updated to reflect the material being used. You will need to specify appropriate values at all walls. Values of these functions for sand eroding both carbon steel and aluminum are given by Edwards et al. [68]. The erosion rate as calculated above is displayed in units of removed material/(areatime), i.e., mass flux, and can therefore be changed accordingly to the defined units in FLUENT. The functions C and f have to be specified in consistent units to build a dimensionless group with the relative particle velocity and its exponent. To compute an erosion rate in terms of length/time (mm/year, for example) you can either define a custom field function to divide the erosion rate by the density of the wall material or include this division in the units for C and/or f . Please note that the units given by FLUENT when displaying the erosion rate are no more valid in the latter case. Note that the particle erosion and accretion rates can be displayed only when coupled calculations are enabled. The accretion rate is defined as Nparticles

Raccretion =

X

p=1

21.3

m ˙p Aface

(21.2-63)

Heat and Mass Transfer Calculations

Using FLUENT’s discrete phase modeling capability, reacting particles or droplets can be modeled and their impact on the continuous phase can be examined. Several heat and mass transfer relationships, termed “laws”, are available in FLUENT and the physical models employed in these laws are described in this section.

21.3.1

Particle Types in FLUENT

Which laws are to be active depends upon the particle type that you select. In the Set Injection Properties panel you will specify the Particle Type, and FLUENT will use a given set of heat and mass transfer laws for the chosen type. All particle types have pre-defined sequences of physical laws as shown in the table below: Particle Type Inert Droplet Combusting

21-18

Description inert/heating or cooling heating/evaporation/boiling heating; evolution of volatiles/swelling; heterogeneous surface reaction

Laws Activated 1, 6 1, 2, 3, 6

1, 4, 5, 6


21.3 Heat and Mass Transfer Calculations

In addition to the above laws, you can define your own laws using a user-defined function. See the separate UDF Manual for information about user-defined functions. You can also extend combusting particles to include an evaporating/boiling material by selecting Wet Combustion in the Set Injection Properties panel. FLUENT’s physical laws (Laws 1 through 6), which describe the heat and mass transfer conditions listed in this table, are explained in detail in Sections 21.3.2–21.3.6.

21.3.2

Law 1/Law 6: Inert Heating or Cooling

The inert heating or cooling laws (Laws 1 and 6) are applied while the particle temperature is less than the vaporization temperature that you define, Tvap , and after the volatile fraction, fv,0 , of a particle has been consumed. These conditions may be written as Law 1: Tp < Tvap

(21.3-1)

mp ≤ (1 − fv,0 )mp,0

(21.3-2)

Law 6:

where Tp is the particle temperature, mp,0 is the initial mass of the particle, and mp is its current mass. Law 1 is applied until the temperature of the particle/droplet reaches the vaporization temperature. At this point a non-inert particle/droplet may proceed to obey one of the mass-transfer laws (2, 3, 4, and/or 5), returning to Law 6 when the volatile portion of the particle/droplet has been consumed. (Note that the vaporization temperature, Tvap , is thus an arbitrary modeling constant used to define the onset of the vaporization/boiling/volatilization laws.) When using Law 1 or Law 6, FLUENT uses a simple heat balance to relate the particle temperature, Tp (t), to the convective heat transfer and the absorption/emission of radiation at the particle surface: m p cp

dTp 4 = hAp (T∞ − Tp ) + p Ap σ(θR − Tp4 ) dt

(21.3-3)

where mp cp Ap T∞ h p σ θR

= = = = = = = =

mass of the particle (kg) heat capacity of the particle (J/kg-K) surface area of the particle (m2 ) local temperature of the continuous phase (K) convective heat transfer coefficient (W/m2 -K) particle emissivity (dimensionless) Stefan-Boltzmann constant (5.67 x 10−8 W/m2 -K4 ) G 1/4 radiation temperature, ( 4σ )


21-19


Equation 21.3-3 assumes that there is negligible internal resistance to heat transfer, i.e., the particle is at uniform temperature throughout. G is the incident radiation in W/m2 : G=

Z

(21.3-4)

IdΩ

Ω=4π

where I is the radiation intensity and Ω is the solid angle. Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model panel. Equation 21.3-3 is integrated in time using an approximate, linearized form that assumes that the particle temperature changes slowly from one time value to the next: mp cp

n h i h io dTp 4 = Ap − h + p σTp3 Tp + hT∞ + p σθR dt

(21.3-5)

As the particle trajectory is computed, FLUENT integrates Equation 21.3-5 to obtain the particle temperature at the next time value, yielding Tp (t + ∆t) = αp + [Tp (t) − αp ]e−βp ∆t

(21.3-6)

where ∆t is the integration time step and αp =

4 hT∞ + p σθR h + p σTp3 (t)

(21.3-7)

and Ap (h + p σTp3 (t)) βp = m p cp

(21.3-8)

FLUENT can also solve Equation 21.3-5 in conjunction with the equivalent mass transfer equation using a stiff coupled solver. See Section 21.7.3 for details. The heat transfer coefficient, h, is evaluated using the correlation of Ranz and Marshall [205, 206]: Nu =

hdp 1/2 = 2.0 + 0.6Red Pr1/3 k∞

(21.3-9)

where

21-20



dp k∞ Red Pr

= = =

particle diameter (m) thermal conductivity of the continuous phase (W/m-K) Reynolds number based on the particle diameter and the relative velocity (Equation 21.2-3) = Prandtl number of the continuous phase (cp µ/k∞ )

Finally, the heat lost or gained by the particle as it traverses each computational cell appears as a source or sink of heat in subsequent calculations of the continuous phase energy equation. During Laws 1 and 6, particles/droplets do not exchange mass with the continuous phase and do not participate in any chemical reaction.

21.3.3

Law 2: Droplet Vaporization

Law 2 is applied to predict the vaporization from a discrete phase droplet. Law 2 is initiated when the temperature of the droplet reaches the vaporization temperature, Tvap , and continues until the droplet reaches the boiling point, Tbp , or until the droplet’s volatile fraction is completely consumed: Tp < Tbp

(21.3-10)

mp > (1 − fv,0 )mp,0

(21.3-11)

The onset of the vaporization law is determined by the setting of Tvap , a temperature that has no other physical significance. Note that once vaporization is initiated (by the droplet reaching this threshold temperature), it will continue even if the droplet temperature falls below Tvap . Vaporization will be halted only if the droplet temperature falls below the dew point. In such cases, the droplet will remain in Law 2 but no evaporation will be predicted. When the boiling point is reached, the droplet vaporization is predicted by a boiling rate, Law 3, as described in Section 21.3.4.

Mass Transfer During Law 2 During Law 2, the rate of vaporization is governed by gradient diffusion, with the flux of droplet vapor into the gas phase related to the gradient of the vapor concentration between the droplet surface and the bulk gas: Ni = kc (Ci,s − Ci,∞ )

(21.3-12)

where


21-21


Ni kc Ci,s Ci,∞

= = = =

molar flux of vapor (kgmol/m2 -s) mass transfer coefficient (m/s) vapor concentration at the droplet surface (kgmol/m3 ) vapor concentration in the bulk gas (kgmol/m3 )

Note that FLUENT’s vaporization law assumes that Ni is positive (evaporation). If conditions exist in which Ni is negative (i.e., the droplet temperature falls below the dew point and condensation conditions exist), FLUENT treats the droplet as inert (Ni = 0.0). The concentration of vapor at the droplet surface is evaluated by assuming that the partial pressure of vapor at the interface is equal to the saturated vapor pressure, psat , at the particle droplet temperature, Tp : Ci,s =

psat (Tp ) RTp

(21.3-13)

where R is the universal gas constant. The concentration of vapor in the bulk gas is known from solution of the transport equation for species i or from the PDF look-up table for non-premixed or partially premixed combustion calculations: Ci,∞ = Xi

pop RT∞

(21.3-14)

where Xi is the local bulk mole fraction of species i, pop is the operating pressure, and T∞ is the local bulk temperature in the gas. The mass transfer coefficient in Equation 21.3-12 is calculated from a Nusselt correlation [205, 206]: NuAB = where

Di,m Sc dp

kc dp 1/2 = 2.0 + 0.6Red Sc1/3 Di,m

(21.3-15)

= diffusion coefficient of vapor in the bulk (m2 /s) = the Schmidt number, ρDµi,m = particle (droplet) diameter (m)

The vapor flux given by Equation 21.3-12 becomes a source of species i in the gas phase species transport equation, as specified by you (see Section 21.11) or from the PDF look-up table for non-premixed combustion calculations. The mass of the droplet is reduced according to mp (t + ∆t) = mp (t) − Ni Ap Mw,i ∆t

21-22

(21.3-16)



where

Mw,i mp Ap

= molecular weight of species i (kg/kgmol) = mass of the droplet (kg) = surface area of the droplet (m2 )

FLUENT can also solve Equation 21.3-16 in conjunction with the equivalent heat transfer equation using a stiff coupled solver. See Section 21.7.3 for details.

Defining the Vapor Pressure and Diffusion Coefficient You define the vapor pressure as a polynomial or piecewise linear function of temperature (psat (T )) during the problem definition. Note that the vapor pressure definition is critical, as psat is used to obtain the driving force for the evaporation process (Equations 21.3-12 and 21.3-13). You should provide accurate vapor pressure values for temperatures over the entire range of possible droplet temperatures in your problem. Vapor pressure data can be obtained from a physics or engineering handbook (e.g., [192]). You also input the diffusion coefficient, Di,m , during the setup of the discrete phase material properties. Note that the diffusion coefficient inputs that you supply for the continuous phase are not used in the discrete phase model.

Heat Transfer to the Droplet Finally, the droplet temperature is updated according to a heat balance that relates the sensible heat change in the droplet to the convective and latent heat transfer between the droplet and the continuous phase: mp cp where

cp Tp h T∞

dmp dt

hfg p σ θR

dTp dmp = hAp (T∞ − Tp ) + hfg + Ap p σ(θR 4 − Tp 4 ) dt dt

= = = = = = = = =

(21.3-17)

droplet heat capacity (J/kg-K) droplet temperature (K) convective heat transfer coefficient (W/m2 -K) temperature of continuous phase (K) rate of evaporation (kg/s) latent heat (J/kg) particle emissivity (dimensionless) Stefan-Boltzmann constant (5.67 x 10−8 W/m2 -K4 ) I 1/4 radiation temperature, ( 4σ ) , where I is the radiation intensity

Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model panel. The heat transferred to or from the gas phase becomes a source/sink of energy during subsequent calculations of the continuous phase energy equation.


21-23


21.3.4

Law 3: Droplet Boiling

Law 3 is applied to predict the convective boiling of a discrete phase droplet when the temperature of the droplet has reached the boiling temperature, Tbp , and while the mass of the droplet exceeds the non-volatile fraction, (1 − fv,0 ): Tp ≥ Tbp

(21.3-18)

mp > (1 − fv,0 )mp,0

(21.3-19)

and

When the droplet temperature reaches the boiling point, a boiling rate equation is applied [132]: "

q d(dp ) 4k∞ cp,∞ (T∞ − Tp ) = (1 + 0.23 Red ) ln 1 + dt ρp cp,∞ dp hfg

where

cp,∞ ρp k∞

#

(21.3-20)

= heat capacity of the gas (J/kg-K) = droplet density (kg/m3 ) = thermal conductivity of the gas (W/m-K)

Equation 21.3-20 has been derived assuming steady flow at constant pressure. Note that the model requires T∞ > Tbp in order for boiling to occur and that the droplet remains at fixed temperature (Tbp ) throughout the boiling law. When radiation heat transfer is active, FLUENT uses a slight modification of Equation 21.3-20, derived by starting from Equation 21.3-17 and assuming that the droplet temperature is constant. This yields −

dmp hfg = hAp (T∞ − Tp ) + Ap p σ(θR 4 − Tp 4 ) dt

(21.3-21)

or "

#

d(dp ) 2 k∞ Nu 4 − = (T∞ − Tp ) + p σ(θR − Tp4 ) dt ρp hfg dp

(21.3-22)

Using Equation 21.3-9 for the Nusselt number correlation and replacing the Prandtl number term with an empirical constant, Equation 21.3-22 becomes " # √ d(dp ) 2 2k∞ [1 + 0.23 Red ] 4 − = (T∞ − Tp ) + p σ(θR − Tp4 ) dt ρp hfg dp

21-24

(21.3-23)



In the absence of radiation, this result matches that of Equation 21.3-20 in the limit that the argument of the logarithm is close to unity. FLUENT uses Equation 21.3-23 when radiation is active in your model and Equation 21.3-20 when radiation is not active. Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model panel. The droplet is assumed to stay at constant temperature while the boiling rate is applied. Once the boiling law is entered it is applied for the duration of the particle trajectory. The energy required for vaporization appears as a (negative) source term in the energy equation for the gas phase. The evaporated liquid enters the gas phase as species i, as defined by your input for the destination species (see Section 21.11).

21.3.5

Law 4: Devolatilization

The devolatilization law is applied to a combusting particle when the temperature of the particle reaches the vaporization temperature, Tvap , and remains in effect while the mass of the particle, mp , exceeds the mass of the non-volatiles in the particle: Tp ≥ Tvap and Tp ≥ Tbp

(21.3-24)

mp > (1 − fv,0 )(1 − fw,0 )mp,0

(21.3-25)

and

where fw,0 is the mass fraction of the evaporating /boiling material if Wet Combustion is selected (otherwise, fw,0 = 0). As implied by Equation 21.3-24, the boiling point Tbp and the vaporization temperature Tvap should be set equal to each other when Law 4 is to be used. When wet combustion is active, Tbp and Tvap refer to the boiling and evaporation temperatures for the combusting material only. FLUENT provides a choice of four devolatilization models: • the constant rate model (the default model) • the single kinetic rate model • the two competing rates model (the Kobayashi model) • the chemical percolation devolatilization (CPD) model Each of these models is described, in turn, below.


21-25


Choosing the Devolatilization Model You will choose the devolatilization model when you are setting physical properties for the combusting-particle material in the Materials panel, as described in Section 21.11.2. By default, the constant rate model (Equation 21.3-26) will be used.

The Constant Rate Devolatilization Model The constant rate devolatilization law dictates that volatiles are released at a constant rate [14]: − where

mp fv,0 mp,0 A0

1 dmp = A0 fv,0 (1 − fw,0 )mp,0 dt

(21.3-26)

= particle mass (kg) = fraction of volatiles initially present in the particle = initial particle mass (kg) = rate constant (s−1 )

The rate constant A0 is defined as part of your modeling inputs, with a default value of 12 s−1 derived from the work of Pillai [197] on coal combustion. Proper use of the constant devolatilization rate requires that the vaporization temperature, which controls the onset of devolatilization, be set appropriately. Values in the literature show this temperature to be about 600 K [14]. The volatile fraction of the particle enters the gas phase as the devolatilizing species i, defined by you (see Section 21.11). Once in the gas phase, the volatiles may react according to the inputs governing the gas phase chemistry.

The Single Kinetic Rate Model The single kinetic rate devolatilization model assumes that the rate of devolatilization is first-order dependent on the amount of volatiles remaining in the particle [6]: − where

mp fv,0 fw,0 mp,0 k

21-26

dmp = k[mp − (1 − fv,0 )(1 − fw,0 )mp,0 ] dt

(21.3-27)

= particle mass (kg) = mass fraction of volatiles initially present in the particle = mass fraction of evaporating/boiling material (if wet combustion is modeled) = initial particle mass (kg) = kinetic rate (s−1 )



Note that fv,0 , the fraction of volatiles in the particle, should be defined using a value slightly in excess of that determined by proximate analysis. The kinetic rate, k, is defined by input of an Arrhenius type pre-exponential factor and an activation energy: k = A1 e−(E/RT )

(21.3-28)

FLUENT uses default rate constants, A1 and E, as given in [6]. Equation 21.3-27 has the approximate analytical solution:

mp (t + ∆t) = (1 − fv,0 )(1 − fw,0 )mp,0 + [mp (t) − (1 − fv,0 )(1 − fw,0 )mp,0 ]e−k∆t (21.3-29) which is obtained by assuming that the particle temperature varies only slightly between discrete time integration steps. FLUENT can also solve Equation 21.3-29 in conjunction with the equivalent heat transfer equation using a stiff coupled solver. See Section 21.7.3 for details.

The Two Competing Rates Kobayashi Model FLUENT also provides the kinetic devolatilization rate expressions of the form proposed by Kobayashi [130]: R1 = A1 e−(E1 /RTp )

(21.3-30)

R2 = A2 e−(E2 /RTp )

(21.3-31)

where R1 and R2 are competing rates that may control the devolatilization over different temperature ranges. The two kinetic rates are weighted to yield an expression for the devolatilization as Z t Z t mv (t) = (α1 R1 + α2 R2 ) exp − (R1 + R2 ) dt dt (1 − fw,0 )mp,0 − ma 0 0

where

mv (t) mp,0 α1 , α2 ma

= = = =

(21.3-32)

volatile yield up to time t initial particle mass at injection yield factors ash content in the particle

The Kobayashi model requires input of the kinetic rate parameters, A1 , E1 , A2 , and E2 , and the yields of the two competing reactions, α1 and α2 . FLUENT uses default


21-27


values for the yield factors of 0.3 for the first (slow) reaction and 1.0 for the second (fast) reaction. It is recommended in the literature [130] that α1 be set to the fraction of volatiles determined by proximate analysis, since this rate represents devolatilization at low temperature. The second yield parameter, α2 , should be set close to unity, which is the yield of volatiles at very high temperature. By default, Equation 21.3-32 is integrated in time analytically, assuming the particle temperature to be constant over the discrete time integration step. FLUENT can also solve Equation 21.3-32 in conjunction with the equivalent heat transfer equation using a stiff coupled solver. See Section 21.7.3 for details.

The CPD Model In contrast to the coal devolatilization models presented above, which are based on empirical rate relationships, the chemical percolation devolatilization (CPD) model characterizes the devolatilization behavior of rapidly heated coal based on the physical and chemical transformations of the coal structure [77, 78, 91]. General Description During coal pyrolysis, the labile bonds between the aromatic clusters in the coal structure lattice are cleaved, resulting in two general classes of fragments. One set of fragments has a low molecular weight (and correspondingly high vapor pressure) and escapes from the coal particle as a light gas. The other set of fragments consists of tar gas precursors that have a relatively high molecular weight (and correspondingly low vapor pressure) and tend to remain in the coal for a long period of time during typical devolatilization conditions. During this time, reattachment with the coal lattice (which is referred to as crosslinking) can occur. The high molecular weight compounds plus the residual lattice are referred to as metaplast. The softening behavior of a coal particle is determined by the quantity and nature of the metaplast generated during devolatilization. The portion of the lattice structure that remains after devolatilization is comprised of char and mineral-compound-based ash. The CPD model characterizes the chemical and physical processes by considering the coal structure as a simplified lattice or network of chemical bridges that link the aromatic clusters. Modeling the cleavage of the bridges and the generation of light gas, char, and tar precursors is then considered to be analogous to the chemical reaction scheme shown in Figure 21.3.1. The variable £ represents the original population of labile bridges in the coal lattice. Upon heating, these bridges become the set of reactive bridges, £∗ . For the reactive bridges, two competing paths are available. In one path, the bridges react to form side chains, δ. The side chains may detach from the aromatic clusters to form light gas, g1 . As bridges between neighboring aromatic clusters are cleaved, a certain fraction of the coal becomes detached from the coal lattice. These detached aromatic clusters are the

21-28



Figure 21.3.1: Coal Bridge

heavy-molecular-weight tar precursors that form the metaplast. The metaplast vaporizes to form coal tar. While waiting for vaporization, the metaplast can also reattach to the coal lattice matrix (crosslinking). In the other path, the bridges react and become a char bridge, c, with the release of an associated light gas product, g2 . The total population of bridges in the coal lattice matrix can be represented by the variable p, where p = £ + c. Reaction Rates Given this set of variables that characterizes the coal lattice structure during devolatilization, the following set of reaction rate expressions can be defined for each, starting with the assumption that the reactive bridges are destroyed at the same rate at which they ∗ are created ( ∂£ = 0): ∂t d£ dt dc dt dδ dt dg1 dt dg2 dt

= −kb £ = kb =

"

(21.3-33)

£ ρ+1

2ρkb

(21.3-34) #

£ − kg δ ρ+1

(21.3-35)

= kg δ

(21.3-36)

dc dt

(21.3-37)

= 2

where the rate constants for bridge breaking and gas release steps, kb and kg , are expressed in Arrhenius form with a distributed activation energy: k = Ae−(E±Eσ )/RT


(21.3-38)

21-29


where A, E, and Eσ are, respectively, the pre-exponential factor, the activation energy, and the distributed variation in the activation energy, R is the universal gas constant, and T is the temperature. The ratio of rate constants, ρ = kδ /kc , is set to 0.9 in this model based on experimental data. Mass Conservation The following mass conservation relationships are imposed:

g = g1 + g2 g1 = 2f − σ g2 = 2(c − c0 )

(21.3-39) (21.3-40) (21.3-41)

where f is the fraction of broken bridges (f = 1 − p). The initial conditions for this system are given by the following:

c(0) £(0) δ(0) g(0)

= = = =

c0 £0 = p 0 − c 0 2f0 = 2(1 − c0 − £0 ) g1 (0) = g2 (0) = 0

(21.3-42) (21.3-43) (21.3-44) (21.3-45)

where c0 is the initial fraction of char bridges, p0 is the initial fraction of bridges in the coal lattice, and £0 is the initial fraction of labile bridges in the coal lattice. Fractional Change in the Coal Mass Given the set of reaction equations for the coal structure parameters, it is necessary to relate these quantities to changes in coal mass and the related release of volatile products. To accomplish this, the fractional change in the coal mass as a function of time is divided into three parts: light gas (fgas ), tar precursor fragments (ffrag ), and char (fchar ). This is accomplished by using the following relationships, which are obtained using percolation lattice statistics:

r(g1 + g2 )(σ + 1) 4 + 2r(1 − c0 )(σ + 1) 2 ffrag (t) = [ΦF (p) + rΩK(p)] 2 + r(1 − c0 )(σ + 1) fchar (t) = 1 − fgas (t) − ffrag (t) fgas (t) =

21-30

(21.3-46) (21.3-47) (21.3-48)



The variables Φ, Ω, F (p), and K(p) are the statistical relationships related to the cleaving of bridges based on the percolation lattice statistics, and are given by the following equations: "

£ (σ − 1)δ Φ = 1+r + p 4(1 − p) £ δ Ω = − 2(1 − p) p p0 p

F (p) = K(p) =

(21.3-49) (21.3-50)

! σ+1

σ−1

(21.3-51)

σ+1 0 1− p 2

#

p0 p

! σ+1

σ−1

(21.3-52)

r is the ratio of bridge mass to site mass, mb /ma , where

mb = 2Mw,δ ma = Mw,1 − (σ + 1)Mw,δ

(21.3-53) (21.3-54)

where Mw,δ and Mw,1 are the side chain and cluster molecular weights respectively. σ + 1 is the lattice coordination number, which is determined from solid-state Nuclear Magnetic Resonance (NMR) measurements related to coal structure parameters, and p0 is the root of the following equation in p (the total number of bridges in the coal lattice matrix): p0 (1 − p0 )σ−1 = p(1 − p)σ−1

(21.3-55)

In accounting for mass in the metaplast (tar precursor fragments), the part that vaporizes is treated in a manner similar to flash vaporization, where it is assumed that the finite fragments undergo vapor/liquid phase equilibration on a time scale that is rapid with respect to the bridge reactions. As an estimate of the vapor/liquid that is present at any time, a vapor pressure correlation based on a simple form of Raoult’s Law is used. The vapor pressure treatment is largely responsible for predicting pressure-dependent devolatilization yields. For the part of the metaplast that reattaches to the coal lattice, a cross-linking rate expression given by the following equation is used: dmcross = mfrag Across e−(Ecross /RT ) dt

(21.3-56)

where mcross is the amount of mass reattaching to the matrix, mfrag is the amount of mass in the tar precursor fragments (metaplast), and Across and Ecross are rate expression constants.


21-31


CPD Inputs Given the set of equations and corresponding rate constants introduced for the CPD model, the number of constants that must be defined to use the model is a primary concern. For the relationships defined previously, it can be shown that the following parameters are coal-independent [77]: • Ab , Eb , Eσb , Ag , Eg , and Eσg for the rate constants kb and kg • Across , Ecross , and ρ These constants are included in the submodel formulation and are not input or modified during problem setup. There are an additional five parameters that are coal-specific and must be specified during the problem setup: • initial fraction of bridges in the coal lattice, p0 • initial fraction of char bridges, c0 • lattice coordination number, σ + 1 • cluster molecular weight, Mw,1 • side chain molecular weight, Mw,δ The first four of these are coal structure quantities that are obtained from NMR experimental data. The last quantity, representing the char bridges that either exist in the parent coal or are formed very early in the devolatilization process, is estimated based on the coal rank. These quantities are entered in the Materials panel as described in Section 21.11.2. Values for the coal-dependent parameters for a variety of coals are listed in Table 21.3.1.

Particle Swelling During Devolatilization The particle diameter changes during the devolatilization according to the swelling coefficient, Csw , which is defined by you and applied in the following relationship: dp (1 − fw,0 )mp,0 − mp = 1 + (Csw − 1) dp,0 fv,0 (1 − fw,0 )mp,0 where

21-32

dp,0 dp

= =

(21.3-57)

particle diameter at the start of devolatilization current particle diameter



Table 21.3.1: Chemical Structure Parameters for Coal Type Zap (AR) Wyodak (AR) Utah (AR) Ill6 (AR) Pitt8 (AR) Stockton (AR) Freeport (AR) Pocahontas (AR) Blue (Sandia) Rose (AFR) 1443 (lignite, ACERC) 1488 (subbituminous, ACERC) 1468 (anthracite, ACERC)

σ+1 3.9 5.6 5.1 5.0 4.5 4.8 5.3 4.4 5.0 5.8 4.8 4.7 4.7

13

C NMR for 13 Coals

p0 Mw,1 .63 277 .55 410 .49 359 .63 316 .62 294 .69 275 .67 302 .74 299 .42 410 .57 459 .59 297 .54 310 .89 656

Mw,δ 40 42 36 27 24 20 17 14 47 48 36 37 12

c0 .20 .14 0 0 0 0 0 .20 .15 .10 .20 .15 .25

AR refers to eight types of coal from the Argonne premium sample bank [249, 278]. Sandia refers to the coal examined at Sandia National Laboratories [76]. AFR refers to coal examined at Advanced Fuel Research. ACERC refers to three types of coal examined at the Advanced Combustion Engineering Research Center. w,0 )mp,0 −mp The term (1−f is the ratio of the mass that has been devolatilized to the total fv,0 (1−fw,0 )mp,0 volatile mass of the particle. This quantity approaches a value of 1.0 as the devolatilization law is applied. When the swelling coefficient is equal to 1.0, the particle diameter stays constant. When the swelling coefficient is equal to 2.0, the final particle diameter doubles when all of the volatile component has vaporized, and when the swelling coefficient is equal to 0.5 the final particle diameter is half of its initial diameter.

Heat Transfer to the Particle During Devolatilization Heat transfer to the particle during the devolatilization process includes contributions from convection, radiation (if active), and the heat consumed during devolatilization: mp cp

dTp dmp = hAp (T∞ − Tp ) + hfg + Ap p σ(θR 4 − Tp 4 ) dt dt

(21.3-58)

Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model panel. By default, Equation 21.3-58 is solved analytically, by assuming that the temperature and mass of the particle do not change significantly between time steps:


21-33


Tp (t + ∆t) = αp + [Tp (t) − αp ]e−βp ∆t

(21.3-59)

p hfg + Ap p σθR 4 hAp T∞ + dm dt αp = hAp + p Ap σTp 3

(21.3-60)

Ap (h + p σTp 3 ) βp = m p cp

(21.3-61)

where

and

FLUENT can also solve Equation 21.3-58 in conjunction with the equivalent mass transfer equation using a stiff coupled solver. See Section 21.7.3 for details.

21.3.6

Law 5: Surface Combustion

After the volatile component of the particle is completely evolved, a surface reaction begins, which consumes the combustible fraction, fcomb , of the particle. Law 5 is thus active (for a combusting particle) after the volatiles are evolved: mp < (1 − fv,0 )(1 − fw,0 )mp,0

(21.3-62)

and until the combustible fraction is consumed: mp > (1 − fv,0 − fcomb )(1 − fw,0 )mp,0

(21.3-63)

When the combustible fraction, fcomb , has been consumed in Law 5, the combusting particle may contain residual “ash” that reverts to the inert heating law, Law 6 (see Section 21.3.2). With the exception of the multiple surface reactions model, the surface combustion law consumes the reactive content of the particle as governed by the stoichiometric requirement, Sb , of the surface “burnout” reaction: char(s) + Sb ox(g) −→ products(g)

(21.3-64)

where Sb is defined in terms of mass of oxidant per mass of char, and the oxidant and product species are defined in the Set Injection Properties panel. FLUENT provides a choice of four heterogeneous surface reaction rate models for combusting particles:

21-34



• the diffusion-limited rate model (the default model) • the kinetics/diffusion-limited rate model • the intrinsic model • the multiple surface reactions model Each of these models is described in detail below. You will choose the surface combustion model when you are setting physical properties for the combusting-particle material in the Materials panel, as described in Section 21.11.2. By default, the diffusion-limited rate model will be used.

Diffusion-Limited Surface Reaction Rate Model The diffusion-limited surface reaction rate model, the default model in FLUENT, assumes that the surface reaction proceeds at a rate determined by the diffusion of the gaseous oxidant to the surface of the particle: dmp Yox T∞ ρ = −4πdp Di,m dt Sb (Tp + T∞ ) where

Di,m Yox ρ Sb

(21.3-65)

= diffusion coefficient for oxidant in the bulk (m2 /s) = local mass fraction of oxidant in the gas = gas density (kg/m3 ) = stoichiometry of Equation 21.3-64

Equation 21.3-65 is derived from the model of Baum and Street [14] with the kinetic contribution to the surface reaction rate ignored. The diffusion-limited rate model assumes that the diameter of the particles does not change. Since the mass of the particles is decreasing, the effective density decreases, and the char particles become more porous.

Kinetic/Diffusion Surface Reaction Rate Model The kinetic/diffusion-limited rate model assumes that the surface reaction rate is determined either by kinetics or by a diffusion rate. FLUENT uses the model of Baum and Street [14] and Field [74], in which a diffusion rate coefficient

D0 = C1

[(Tp + T∞ )/2]0.75 dp

(21.3-66)

and a kinetic rate R = C2 e−(E/RTp )


(21.3-67)

21-35


are weighted to yield a char combustion rate of dmp D0 R = −Ap pox dt D0 + R

(21.3-68)

where Ap is the surface area of the droplet (πd2p ), pox is the partial pressure of oxidant species in the gas surrounding the combusting particle, and the kinetic rate, R, incorporates the effects of chemical reaction on the internal surface of the char particle (intrinsic reaction) and pore diffusion. In FLUENT, Equation 21.3-68 is recast in terms of the oxidant mass fraction, Yox , as ρRT∞ Yox D0 R dmp = −Ap dt Mw,ox D0 + R

(21.3-69)

The particle size is assumed to remain constant in this model while the density is allowed to decrease. When this model is enabled, the rate constants used in Equations 21.3-66 and 21.3-67 are entered in the Materials panel, as described in Section 21.11.

Intrinsic Model The intrinsic model in FLUENT is based on Smith’s model [243], assuming the order of reaction is equal to unity. Like the kinetic/diffusion model, the intrinsic model assumes that the surface reaction rate includes the effects of both bulk diffusion and chemical reaction (see Equation 21.3-69). The intrinsic model uses Equation 21.3-66 to compute the diffusion rate coefficient, D0 , but the chemical rate, R, is explicitly expressed in terms of the intrinsic chemical and pore diffusion rates: R=η

dp ρ p Ag k i 6

(21.3-70)

η is the effectiveness factor, or the ratio of the actual combustion rate to the rate attainable if no pore diffusion resistance existed [142]: η=

3 (φ coth φ − 1) φ2

(21.3-71)

where φ is the Thiele modulus: "

dp Sb ρp Ag ki pox φ= 2 De ρox

21-36

#1/2

(21.3-72)



ρox is the density of oxidant in the bulk gas (kg/m3 ) and De is the effective diffusion coefficient in the particle pores. Assuming that the pore size distribution is unimodal and the bulk and Knudsen diffusion proceed in parallel, De is given by θ 1 1 De = 2 + τ DKn D0

−1

(21.3-73)

where D0 is the bulk molecular diffusion coefficient and θ is the porosity of the char particle: θ =1−

ρp ρt

(21.3-74)

ρp and ρt are, respectively, the apparent and true densities of the pyrolysis char. τ (in √ Equation 21.3-73) is the tortuosity of the pores. The default value for τ in FLUENT is 2, which corresponds to an average intersecting angle between the pores and the external surface of 45◦ [142]. DKn is the Knudsen diffusion coefficient: DKn = 97.0rp

s

Tp Mw,ox

(21.3-75)

where Tp is the particle temperature and rp is the mean pore radius of the char particle, which can be measured by mercury porosimetry. Note that macropores (rp > 150 ˚ A) dominate in low-rank chars while micropores (rp < 10 ˚ A) dominate in high-rank chars [142]. Ag (in Equations 21.3-70 and 21.3-72) is the specific internal surface area of the char particle, which is assumed in this model to remain constant during char combustion. Internal surface area data for various pyrolysis chars can be found in [242]. The mean value of the internal surface area during char combustion is higher than that of the pyrolysis char [142]. For example, an estimated mean value for bituminous chars is 300 m2 /g [36]. ki (in Equations 21.3-70 and 21.3-72) is the intrinsic reactivity, which is of Arrhenius form: ki = Ai e−(Ei /RTp )

(21.3-76)

where the pre-exponential factor Ai and the activation energy Ei can be measured for each char. In the absence of such measurements, the default values provided by FLUENT (which are taken from a least squares fit of data of a wide range of porous carbons, including chars [242]) can be used.


21-37


To allow a more adequate description of the char particle size (and hence density) variation during combustion, you can specify the burning mode α, relating the char particle diameter to the fractional degree of burnout U (where U = 1 − mp /mp,0 ) by [241] dp = (1 − U )α dp,0

(21.3-77)

where mp is the char particle mass and the subscript zero refers to initial conditions (i.e., at the start of char combustion). Note that 0 ≤ α ≤ 1/3 where the limiting values 0 and 1/3 correspond, respectively, to a constant size with decreasing density (zone 1) and a decreasing size with constant density (zone 3) during burnout. In zone 2, an intermediate value of α = 0.25, corresponding to a decrease of both size and density, has been found to work well for a variety of chars [241]. When this model is enabled, the rate constants used in Equations 21.3-66, 21.3-70, 21.3-72, 21.3-73, 21.3-75, 21.3-76, and 21.3-77 are entered in the Materials panel, as described in Section 21.11.

The Multiple Surface Reactions Model Modeling multiple particle surface reactions follows a pattern similar to the wall surface reaction models, where the surface species is now a “particle surface species”. For the mixture material defined in the Species Model panel, the particle surface species can be depleted or produced by the stoichiometry of the particle surface reaction (defined in the Reactions panel). The particle surface species constitutes the reactive char mass of the particle, hence, if a particle surface species is depleted, the reactive “char” content of the particle is consumed, and in turn, when a surface species is produced, it is added to the particle “char” mass. Any number of particle surface species and any number of particle surface reactions can be defined for any given combusting particle. Multiple injections can be accommodated, and combusting particles reacting according to the multiple surface reactions model can coexist in the calculation, with combusting particles following other char combustion laws. The model is based on oxidation studies of char particles, but it is also applicable to gas-solid reactions in general, not only to char oxidation reactions. See Section 13.3 for information about particle surface reactions.

21-38



Limitations Note the following limitations of the multiple surface reactions model: • The model is not available together with the unsteady tracking option. • The model is available only with the species transport model for volumetric reactions, and not with the non-premixed, premixed, or partially premixed combustion models.

Heat and Mass Transfer During Char Combustion The surface reaction consumes the oxidant species in the gas phase; i.e., it supplies a (negative) source term during the computation of the transport equation for this species. Similarly, the surface reaction is a source of species in the gas phase: the product of the heterogeneous surface reaction appears in the gas phase as a user-selected chemical species. The surface reaction also consumes or produces energy, in an amount determined by the heat of reaction defined by you. The particle heat balance during surface reaction is mp cp

dTp dmp = hAp (T∞ − Tp ) − fh Hreac + Ap p σ(θR 4 − Tp 4 ) dt dt

(21.3-78)

where Hreac is the heat released by the surface reaction. Note that only a portion (1 − fh ) of the energy produced by the surface reaction appears as a heat source in the gasphase energy equation: the particle absorbs a fraction fh of this heat directly. For coal combustion, it is recommended that fh be set at 1.0 if the char burnout product is CO and 0.3 if the char burnout product is CO2 [26]. Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation model and you have activated radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model panel. By default, Equation 21.3-78 is solved analytically, by assuming that the temperature and mass of the particle do not change significantly between time steps. FLUENT can also solve Equation 21.3-78 in conjunction with the equivalent mass transfer equation using a stiff coupled solver. See Section 21.7.3 for details.


21-39


21.4

Spray Models

In addition to the simple injection types described in Section 21.9.2, FLUENT also provides more complex injection types for sprays. For most types of injections, you will need to provide the initial diameter, position, and velocity of the particles. For sprays, however, there are models available for droplet breakup and collision, as well as a drag coefficient that accounts for variation in droplet shape. These models for realistic spray simulations are described in this section. Information is organized into the following subsections: • Section 21.4.1: Atomizer Models • Section 21.4.2: Droplet Collision Model • Section 21.4.3: Spray Breakup Models • Section 21.4.4: Dynamic Drag Model

21.4.1

Atomizer Models

Five atomizer models are available in FLUENT: • plain-orifice atomizer • pressure-swirl atomizer • flat-fan atomizer • air-blast/air-assisted atomizer • effervescent/flashing atomizer You can choose them as injection types and define the associated parameters in the Set Injection Properties panel, as described in Section 21.9.2. Details about the atomizer models are provided below.

General Information All of the models use physical and numerical atomizer parameters, such as orifice diameter and mass flow rate, to calculate initial droplet size, velocity, and position. For realistic atomizer simulations, the droplets must be randomly distributed, both through a dispersion angle and in their time of release. For the other types of injections in FLUENT (non-atomizer), all of the droplets are released along fixed trajectories

21-40


21.4 Spray Models

and at the beginning of the time step. The atomizer models use stochastic trajectory selection and staggering to attain random distribution. Stochastic trajectory selection is the random dispersion of initial droplet directions. All of the atomizer models provide an initial dispersion angle, and the stochastic trajectory selection picks an initial direction within this angle. This approach improves the accuracy of the results for spray-dominated flows. The droplets will be more evenly spread among the computational cells near the atomizer, which improves the coupling to the gas phase by spreading drag more smoothly over the cells near the injection.

The Plain-Orifice Atomizer Model The plain-orifice is the most common type of atomizer and the most simply made. However there is nothing simple about the physics of the internal nozzle flow and the external atomization. In the plain-orifice atomizer, the liquid is accelerated through a nozzle, forms a liquid jet, and then forms droplets. This apparently simple process is dauntingly complex. The plain orifice may operate in three different regimes: single-phase, cavitating, and flipped [250]. The transition between regimes is abrupt, producing dramatically different sprays. The internal regime determines the velocity at the orifice exit, as well as the initial droplet size and the angle of droplet dispersion. Diagrams of each case are shown in Figures 21.4.1, 21.4.2, and 21.4.3.

r

p

p d

1

liquid jet orifice walls

2

downstream gas

L Figure 21.4.1: Single-Phase Nozzle Flow (Liquid completely fills the orifice.)

Internal Nozzle State The plain-orifice model must identify the correct state for the nozzle flow, because the internal nozzle state has a tremendous effect on the external spray. Unfortunately, there


21-41


vapor

liquid jet vapor

orifice walls

downstream gas

Figure 21.4.2: Cavitating Nozzle Flow (Vapor pockets form just after the inlet corners.)

liquid jet orifice walls

downstream gas

Figure 21.4.3: Flipped Nozzle Flow (Downstream gas surrounds the liquid jet inside the nozzle.)

21-42


21.4 Spray Models

is no established theory for determining the nozzle state. One must rely on empirical models that fix experimental data. A suggested list of the governing parameters for the internal nozzle flow is given in Table 21.4.1. Table 21.4.1: List of Governing Parameters for Internal Nozzle Flow nozzle diameter d nozzle length L radius of curvature of the inlet corner r upstream pressure p1 downstream pressure p2 viscosity µ liquid density ρl vapor pressure pv

These may be combined to form geometric non-dimensional groups such as r/d and L/d, as well as the Reynolds number based on “head” (Reh ) and a cavitation parameter (K). dρl Reh = µ K=

s

2(p1 − p2 ) ρl

p1 − pv p1 − p2

(21.4-1)

(21.4-2)

The liquid flow often contracts in the nozzle, as can be seen in Figures 21.4.2 and 21.4.3. Nurick [183] found it helpful to use a coefficient of contraction (Cc ) that represents the area of the stream of contracting liquid over the total cross-sectional area of the nozzle. FLUENT uses Nurick’s fit for the coefficient of contraction: Cc = q

1 2 Cct

1 −

11.4r d

(21.4-3)

Cct is a theoretical constant equal to 0.611, which comes from potential flow analysis of flipped nozzles. Another important parameter used to describe the performance of nozzles is the coefficient of discharge (Cd ). The coefficient of discharge is a ratio of the mass flow rate through the nozzle, divided by the theoretical maximum mass flow rate: Cd =


m ˙ q

A 2ρl (p1 − p2 )

(21.4-4)

21-43


The cavitation number (K in Equation 21.4-2) is an essential parameter for predicting the inception of cavitation. The inception of cavitation is known to occur at a value of Kincep ≈ 1.9 for short, sharp-edged nozzles. However, to include some of the effects of inlet rounding and viscosity, an empirical relationship is used:

Kincep = 1.9 1 −

r d

2

−

1000 Reh

(21.4-5)

Similarly, a critical value of K where flip occurs is defined as Kcrit : Kcrit = 1 +

1 1+

L 4d

1+

2000 Reh

(21.4-6)

e70r/d

If r/d is greater than 0.05, then flip is deemed impossible and Kcrit is set to 1.0. These variables are then used in a decision tree to identify the nozzle state. The decision tree is shown in Figure 21.4.4. Depending on the state of the nozzle, a unique closure is chosen for the above equations. For a single-phase nozzle [149],

Cdu = 0.827 − 0.0085 Cd =

L d

1 1 Cdu

+ 20 (1+2.25L/d) Reh

(21.4-7) (21.4-8)

Equation 21.4-7 is for the ultimate coefficient of discharge, Cdu . Equation 21.4-8 corrects this ultimate coefficient of discharge for the effects of viscosity. For a cavitating nozzle [183], √ Cd = Cc K

(21.4-9)

Cd = Cct

(21.4-10)

For a flipped nozzle [183],

All of the nozzle flow equations are solved iteratively, along with the appropriate relationship for coefficient of discharge as given by the nozzle state. The nozzle state may change as the upstream or downstream pressures change. Once the nozzle state is determined, the exit velocity is found, and appropriate correlations for spray angle and initial droplet size distribution are determined.

21-44


21.4 Spray Models

K ≤ Kincep

K < Kcrit

flipped

K > K incep

K ≥ K crit

K < Kcrit

K ≥ Kcrit

cavitating

flipped

single phase

Figure 21.4.4: Decision Tree for the State of the Cavitating Nozzle

Exit Velocity The estimate of exit velocity (u) for the single-phase nozzle comes from conservation of mass and the assumption of a uniform exit velocity: u=

m ˙ ρl A

(21.4-11)

For the cavitating nozzle, Schmidt and Corradini [227] have shown that the uniform exit velocity is not accurate. Instead, they derived an expression for a higher velocity over a reduced area: u=

2Cc p1 − p2 + (1 − 2Cc )pv q

Cc 2ρl (p1 − pv )

(21.4-12)

This analytical relation is used for cavitating nozzles in FLUENT. For the case of flip, the exit velocity is found from conservation of mass and the value of the reduced flow area: u=

m ˙ ρl Cct A

(21.4-13)

Spray Angle The correlation for spray angle (θ) comes from the work of Ranz [204]:

"

θ 4π = tan−1 2 CA


s

√ # ρg 3 ρl 6

(21.4-14)

21-45

Discrete Phase Models θ = 0.01 2

(21.4-15)

Equation 21.4-14 describes the spray angle for both single-phase and cavitating nozzles. For flipped nozzles, the spray angle has a constant value (Equation 21.4-15). CA is thought to be a constant for a given nozzle geometry. You must choose the value for CA . The larger the value, the narrower the spray. Reitz [210] suggests the following correlation for CA : CA = 3 +

L 3.6d

(21.4-16)

The spray angle is sensitive to the internal flow regime of the nozzle. Hence, you may wish to choose smaller values of CA for cavitating nozzles than for single-phase nozzles. Typical values are from 4.0 to 6.0. The spray angle for flipped nozzles is a small, arbitrary value that represents the lack of any turbulence or initial disturbance from the nozzle. Droplet Diameter Distribution Finally, there must be a droplet diameter distribution for the injection. The droplet diameter distribution is closely related to the nozzle state. FLUENT’s spray models use the most probable droplet size and a spread parameter to define the Rosin-Rammler distribution. For more information about the Rosin-Rammler size distribution, see Section 21.9.7. For single-phase nozzle flows, the correlation of Wu et al. [297] is used. This correlation relates the initial drop size to the estimated turbulence quantities of the liquid jet: d32 = 133.0λWe−0.74

(21.4-17)

where d32 is the Sauter mean diameter, λ is the length scale, and We is the Weber number, which, in this case, is defined to be We ≡

ρl u 2 λ σ

(21.4-18)

where λ = d/8 and σ is the droplet surface tension. For a more detailed discussion of droplet surface tension and the Weber number, see Section 21.4.3. See Section 21.13.8 for more information about mean particle diameters. For cavitating nozzles, FLUENT uses a slight modification to Equation 21.4-17. The initial jet diameter used in Wu’s correlation is calculated from the effective area of the cavitating orifice exit. For an explanation of effective area of cavitating nozzles, see Schmidt and Corradini [227].

21-46


21.4 Spray Models

The length scale for a cavitating nozzle is λ = deff /8, where

deff =

s

4m ˙ πρl u

(21.4-19)

For the case of the flipped nozzle, the initial droplet diameter is set to the diameter of the liquid jet: q

d0 = d Cct

(21.4-20)

where d0 is defined as the most probable diameter. The values for the spread parameter, s, are chosen from past modeling experience and from a review of experimental observations. Table 21.4.2 lists the values of s for the three kinds of nozzles: Table 21.4.2: Values of Spread Parameter for Different Nozzle States State single phase cavitating flipped

Spread Parameter 3.5 1.5 ∞

The larger the value of the spread parameter, the narrower the droplet size distribution. The function that samples the Rosin-Rammler distribution uses the most probable diameter and the spread parameter. Since the correlations of Wu et al. provide the Sauter mean diameter, d32 , these must be converted to the most probable diameter, d0 . Lefebvre [144] gives the most general relationship between the Sauter mean diameter and most probable diameter for a Rosin-Rammler distribution. The simplified version for s=3.5 is as follows:

d0 = 1.2726d32 1 −

1 s

1/s

(21.4-21)

At this point, the initialization of the droplets is complete.

The Pressure-Swirl Atomizer Model Another important type of atomizer is the pressure-swirl atomizer, sometimes referred to by the gas-turbine community as a simplex atomizer. This type of atomizer accelerates the liquid through nozzles known as swirl ports into a central swirl chamber. The swirling liquid pushes against the walls of the swirl chamber and develops a hollow air core. It


21-47


then emerges from the orifice as a thinning sheet, which is unstable, breaking up into ligaments and droplets. The pressure-swirl atomizer is very widely used for liquid-fuel combustion in gas turbines, oil furnaces, and direct-injection spark-ignited automobile engines. The transition from internal injector flow to fully-developed spray can be divided into three steps: film formation, sheet breakup, and atomization. A sketch of how this process is thought to occur is shown in Figure 21.4.5.

film formation sheet breakup

atomization

Figure 21.4.5: Theoretical Progression from the Internal Atomizer Flow to the External Spray The interaction between the air and the sheet is not well understood. It is generally accepted that an aerodynamic instability causes the sheet to break up. The mathematical analysis below assumes that Kelvin-Helmholtz waves grow on the sheet and eventually break the liquid into ligaments. It is then assumed that the ligaments break up into droplets due to varicose instability. Once the liquid forms droplets, the spray behavior is determined by drag, collision, coalescence, and secondary breakup. The model used in this study is called the Linearized Instability Sheet Atomization (LISA) model of Schmidt et al. [229]. The LISA model is divided into two stages: 1. film formation 2. sheet breakup and atomization Both parts of the model are described below. The implementation is slightly improved from that of Schmidt et al. [229]. Film Formation The centrifugal motion of the liquid within the injector creates an air core surrounded by a liquid film. The thickness of this film, t, is related to the mass flow rate by

21-48


21.4 Spray Models

m ˙ = πρut(dinj − t)

(21.4-22)

where dinj is the injector exit diameter, and m ˙ is the mass flow rate, which must be measured experimentally. The other unknown in Equation 21.4-22 is u, the axial component of velocity at the injector exit. This quantity depends on internal details of the injector and is difficult to calculate from first principles. Instead, the approach of Han et al. [97] is used. The total velocity is assumed to be related to the injector pressure by

U = kv

s

2∆p ρl

(21.4-23)

Lefebvre [144] has noted that kv is a function of the injector design and injection pressure. If the swirl ports are treated as nozzles, Equation 21.4-23 is then an expression for the coefficient of discharge for the swirl ports, assuming that the majority of the pressure drop through the injector occurs at the ports. The coefficient of discharge (Cd ) for singlephase nozzles with sharp inlet corners and an L/d of 4 is typically 0.78 or less [149]. If the nozzles are cavitating, the value of Cd may be as low as 0.61. Hence, 0.78 should be a practical upper bound for kv . Reducing kv by 10% to allow for other momentum losses in the injector gives an estimate of 0.7. Physical limits on kv are such that it must be less than unity by conservation of energy, and it must be large enough to permit sufficient mass flow. To guarantee that the size of the air core is non-negative, the following expression is used for kv : "

4m ˙ kv = max 0.7, 2 πd0 ρl cos θ

s

ρl 2∆p

#

(21.4-24)

Assuming that ∆p is known, Equation 21.4-23 can be used to find U . Once U is determined, u is found from u = U cos θ

(21.4-25)

where θ is the spray angle, which is assumed to be known. The tangential component of velocity is assumed equal to the radial component further downstream. The axial component of velocity is assumed to be a constant value. Sheet Breakup and Atomization The pressure-swirl atomizer includes the effects of the surrounding gas, liquid viscosity, and surface tension on the breakup of the liquid sheet. Details of the theoretical development of the model are given in Senecal et al. [230] and are only briefly presented here. For a more accurate and robust implementation, the gas-phase velocity is neglected in


21-49


calculating the relative liquid-gas velocity. This decision avoids depending on the usually under-resolved gas-phase velocity field around the injector. The model assumes that a two-dimensional, viscous, incompressible liquid sheet of thickness 2h moves with velocity U through a quiescent, inviscid, incompressible gas medium. The liquid and gas have densities of ρl and ρg , respectively, and the viscosity of the liquid is µl . A coordinate system is used that moves with the sheet, and a spectrum of infinitesimal disturbances of the form η = η0 eikx+ωt

(21.4-26)

is imposed on the initially steady, motion-producing fluctuating velocities and pressures for both the liquid and the gas. In Equation 21.4-26 η0 is the initial wave amplitude, k = 2π/λ is the wave number, and ω = ωr + iωi is the complex growth rate. The most unstable disturbance has the largest value of ωr , denoted here by Ω, and is assumed to be responsible for sheet breakup. Thus, it is desired to obtain a dispersion relation ω = ω(k) from which the most unstable disturbance can be deduced. Squire [255] and Hagerty and Shea [95] have shown that two solutions, or modes, exist that satisfy the liquid governing equations subject to the boundary conditions at the upper and lower interfaces. For the first solution, called the sinuous mode, the waves at the upper and lower interfaces are exactly in phase. On the other hand, for the varicose mode, the waves are π radians out of phase. It has been shown by numerous authors (e.g., Senecal et al. [230]) that the sinuous mode dominates the growth of varicose waves for low velocities and low gas-to-liquid density ratios. In addition, it can be shown that the sinuous and varicose modes become indistinguishable for high-velocity flows. As a result, the present discussion focuses on the growth of sinuous waves on the liquid sheet. As derived in Senecal et al. [230], the dispersion relation for the sinuous mode is given by ω 2 [tanh(kh) + Q] + [4νl k 2 tanh(kh) + 2iQkU ]+ 4

4νl k tanh(kh) −

4νl2 k 3 ` tanh(`h)

σk 3 − QU k + =0 ρl 2 2

(21.4-27)

where Q = ρg /ρl and `2 = k 2 + ω/νl . It can be shown that above a critical Weber number of Weg = 27/16 (based on the relative velocity, the gas density, and the sheet half-thickness), the fastest-growing waves are short. Below 27/16, the wavelengths are long compared to the sheet thickness. The speed of modern fuel injection is high enough that the film Weber number is often well above this critical limit. Li and Tankin [148] derived a dispersion relation similar to Equation 21.4-27 for a viscous sheet from a linear analysis with a stationary coordinate system. While Li and Tankin’s

21-50


21.4 Spray Models

dispersion relation is quite general, a simplified relation has been presented in Senecal et al. [230] for use in multi-dimensional simulations of pressure-swirl atomizers. The resulting expression for the growth rate is given by

ωr =

 

1 −2νl k 2 tanh(kh) +  tanh(kh) + Q

v " # u 3  u σk t4ν 2 k 4 tanh2 (kh) − Q2 U 2 k 2 − [tanh(kh) + Q] −QU 2 k 2 + l ρl 

(21.4-28)

Two main assumptions have been made to reduce Equation 21.4-27 to Equation 21.4-28. First, an order-of-magnitude analysis using typical values from the inviscid solutions shows that the terms of second order in viscosity can be neglected in comparison to the other terms in Equation 21.4-28. In addition, the density ratio Q is on the order of 10−3 in typical applications and hence it is assumed that Q 1. The physical mechanism of sheet disintegration proposed by Dombrowski and Johns [57] is adopted only for long waves. For long waves, ligaments are assumed to form from the sheet breakup process once the unstable waves reach a critical amplitude. If the surface disturbance has reached a value of ηb at breakup, a breakup time, τ , can be evaluated: Ωτ

η b = η0 e

ηb 1 ⇒ ln Ω η0

!

(21.4-29)

where Ω, the maximum growth rate, is found by numerically maximizing Equation 21.4-28 as a function of k. The maximum is found using a binary search that checks the sign of the derivative. The sheet breaks up and ligaments will be formed at a length given by U ηb Lb = U τ = ln Ω η0

!

(21.4-30)

where the quantity ln( ηη0b ) is an empirical sheet constant from 3 to 12. You must specify the value for this constant, which has a default value of 12. The diameter of the ligaments formed at the point of breakup can be obtained from a mass balance. If it is assumed that the ligaments are formed from tears in the sheet once per wavelength, the resulting diameter is given by

dL =

s

8h Ks

(21.4-31)

where Ks is the wave number corresponding to the maximum growth rate, Ω. The ligament diameter depends on the sheet thickness, which is a function of the breakup


21-51


length. The film thickness is calculated from the breakup length and the radial distance from the center line to the mid-line of the sheet at the atomizer exit, r0 : hend =

r0 h0 r0 + Lb sin

θ 2

(21.4-32)

This mechanism is not logical for short waves. For short waves, the determination of the ligament diameter is simpler. The value of dL is assumed to be linearly proportional to the wavelength that breaks up the sheet dL =

2πCL Ks

(21.4-33)

where CL , or the ligament constant, is equal to 0.5 by default. The wavelength is calculated from the wave number, Ks . In either the long wave or the short wave case, the breakup from ligaments to droplets is assumed to behave according to Weber’s [284] analysis for capillary instability. The variable Oh is the Ohnesorge number and is a combination of Reynolds number and Weber number (see Section 21.4.3 for more details about Oh): d0 = 1.88dL (1 + 3Oh)1/6

(21.4-34)

This procedure determines the most probable droplet size. The spread parameter is assumed to be 3.5, based on past modeling experience [228]. You will specify the spray cone angle. The dispersion angle of the spray is assumed to be a fixed value of 6◦ .

The Air-Blast/Air-Assist Atomizer Model In order to accelerate the breakup of liquid sheets from an atomizer, an additional air stream is often directed through the atomizer. The liquid is formed into a sheet by a nozzle, and the air is then directed against the sheet to promote atomization. This technique is called air-assisted atomization or air-blast atomization, depending on the quantity of air and its velocity. The addition of the external air stream past the sheet produces smaller droplets than without the air. The exact mechanism for this enhanced performance is not completely understood. It is thought that the assisting air may accelerate the sheet instability. The air may also help disperse the droplets, preventing collisions between them. Air-assisted atomization is used in many of the same fields as pressure-swirl atomization, where especially fine atomization is required. FLUENT’s air-blast atomization model is a variation of the pressure-swirl model. One difference is that you set the sheet thickness directly in the air-blast atomizer model. This input is necessary because of the variety of sheet formation mechanisms used in airblast atomizers. Hence the air-blast atomizer model does not contain the sheet formation

21-52


21.4 Spray Models

equations that were included in the pressure-swirl atomizer model (Equations 21.4-22– 21.4-25). You will also specify the maximum relative velocity that is produced by the sheet and air. Though this quantity could be calculated, specifying a value relieves you from the necessity of finely resolving the atomizer internal flow. This feature is convenient for simulations in large domains, where the atomizer is very small by comparison. Another difference is that the air-blast atomizer model assumes that the sheet breakup is always due to short waves. This assumption is a consequence of the greater sheet thickness commonly found in air-blast atomizers. Hence the ligament diameter is assumed to be linearly proportional to the wavelength of the fastest-growing wave on the sheet. Other inputs are similar to the pressure-swirl model. You must provide the mass flow rate and spray angle. The angle in the case of the air-blast atomizer is the initial trajectory of the film as it leaves the end of the orifice. The value of the angle is negative if the initial film trajectory is inward, towards the centerline. You will also provide the inner and outer diameter of the film at the atomizer exit. The air-blast atomizer model does not include the internal gas flows. You must create the atomizing air streams as a boundary condition within the FLUENT case. These streams are ordinary continuous-phase flows and require no special treatment.

The Flat-Fan Atomizer Model The flat-fan atomizer is very similar to the pressure-swirl atomizer, but it makes a flat sheet and does not use swirl. The liquid emerges from a wide, thin orifice as a flat liquid sheet that breaks up into droplets. The primary atomization process is thought to be similar to the pressure-swirl atomizer. Some researchers believe that flat-fan atomization, because of jet impingement, is very similar to the atomization of a flat sheet. The flat-fan model could serve doubly for this application. The flat-fan atomizer is available only for 3D models. An image of the three-dimensional flat fan is shown in Figure 21.4.6. The model assumes that the fan originates from a virtual origin. You will provide the location of this origin, which is the intersection of the lines that mark the sides of the fan. You will also provide the location of the center point of the arc from which the fan originates. FLUENT will find the vector that points from the origin to the center point in order to determine the direction of the injection. You will also provide the half-angle of the fan arc, the width of the orifice (in the normal direction), and the mass flow rate of the liquid. The breakup of the flat fan is calculated very much like the breakup of the sheet in the pressure-swirl atomizer. The sheet breaks up into ligaments that then form droplets. The only difference is that for short waves, the flat fan sheet is assumed to form ligaments at half-wavelength intervals. Hence the ligament diameter for short waves is given by

dL =


s

16h Ks

(21.4-35)

21-53


center point

virtual origin normal vector

Figure 21.4.6: Flat Fan Viewed From Above and From the Side

The Rosin-Rammler spread parameter is assumed to be 3.5 and the dispersion angle is set to 6◦ . In all other respects, the flat-fan atomizer model is like the sheet breakup portion of the pressure-swirl atomizer.

Effervescent Atomizer Model Effervescent atomization is the injection of liquid infused with a super-heated (with respect to downstream conditions) liquid or propellant. As the volatile liquid exits the nozzle, it rapidly changes phase. This phase change quickly breaks up the stream into small droplets with a wide dispersion angle. The model also applies to cases where a very hot liquid is discharged. Since the physics of effervescence is not well understood, the model must rely on rough empirical fits. The photographs of Reitz [210] provide some basic insights. These photographs show a dense liquid core to the spray, surrounded by a wide shroud of smaller droplets. The initial velocity of the droplets is computed from conservation of mass, assuming the exiting jet has a cross-sectional area that is Cct times the nozzle area, where Cct is a constant that you specify during the problem setup: u=

m ˙ ρl Cct A

(21.4-36)

The maximum droplet diameter is set to the effective diameter of the exiting jet: q

dmax = d Cct

21-54

(21.4-37)


21.4 Spray Models

The droplet size is then sampled from a Rosin-Rammler distribution with a spread parameter of 4.0 (see Section 21.9.7). The most probable droplet size depends on the angle, θ, between the droplet’s stochastic trajectory and the injection direction: d0 = dmax e−(θ/Θs )

2

(21.4-38)

The dispersion angle multiplier, Θs , is computed from the quality, x, and the specified value for the dispersion constant, Ceff : Θs =

x Ceff

(21.4-39)

This technique creates a spray with large droplets in the central core and a shroud of smaller surrounding droplets. The droplet temperature is initialized to the initial temperature fraction, f , times the saturation temperature of the droplets. f should be slightly less than 1.0, because the droplet temperatures should be close to boiling. To complete the model, the flashing vapor must also be included in the calculation. This vapor is part of the continuous phase and not part of the discrete phase model. You must create an inlet at the point of injection when you specify boundary conditions for the continuous phase. When the effervescent atomizer model is selected, you will need to specify the nozzle diameter, mass flow rate, mixture quality, saturation temperature of the volatile substance, temperature fraction, spray half-angle, and dispersion constant.

21.4.2

Droplet Collision Model

Introduction When your simulation includes tracking of droplets, FLUENT provides an option for estimating the number of droplet collisions and their outcomes in a computationally efficient manner. The difficulty in any collision calculation is that for N droplets, each droplet has N − 1 possible collision partners. Thus, the number of possible collision pairs is approximately 21 N 2 . (The factor of 12 appears because droplet A colliding with droplet B is identical to droplet B colliding with droplet A. This symmetry reduces the number of possible collision events by half.) An important consideration is that the collision algorithm must calculate 12 N 2 possible collision events at every time step. Since a spray can consist of several million droplets, the computational cost of a collision calculation from first principles is prohibitive. This motivates the concept of parcels. Parcels are statistical representations of a number of individual droplets. For example, if FLUENT tracks a set of parcels, each of which representing 1000 droplets, the cost of the collision calculation is reduced by a factor of 106 . Because the cost of the collision calculation still scales with the square of N , the


21-55


reduction of cost is significant; however, the effort to calculate the possible intersection of so many parcel trajectories would still be prohibitively expensive. The algorithm of O’Rourke [185] efficiently reduces the computational cost of the spray calculation. Rather than using geometry to see if parcel paths intersect, O’Rourke’s method is a stochastic estimate of collisions. O’Rourke also makes the assumption that two parcels may collide only if they are located in the same continuous-phase cell. These two assumptions are valid only when the continuous-phase cell size is small compared to the size of the spray. For these conditions, the method of O’Rourke is second-order accurate at estimating the chance of collisions. The concept of parcels together with the algorithm of O’Rourke makes the calculation of collision possible for practical spray problems. Once it is decided that two parcels of droplets collide, the algorithm further determines the type of collision. Only coalescence and bouncing outcomes are considered. The probability of each outcome is calculated from the collisional Weber number and a fit to experimental observations. The properties of the two colliding parcels are modified based on the outcome of the collision.

Use and Limitations The collision model assumes that the frequency of collisions is much less than the particle time step. If the particle time step is too large, then the results may be timestep-dependent. You should adjust the particle length scale accordingly. Additionally, the model is most applicable for low-Weber-number collisions where collisions result in bouncing and coalescence. Above a collisional Weber number of about 100, the outcome of collision could be shattering. Sometimes the collision model can cause grid-dependent artifacts to appear in the spray. This is a result of the assumption that droplets can collide only within the same cell. These tend to be visible when the source of injection is at a mesh vertex. The coalescence of droplets tends to cause the spray to pull away from cell boundaries. In two dimensions, a finer mesh and more computational droplets can be used to reduce these effects. In three dimensions, best results are achieved when the spray is modeled using a polar mesh with the spray at the center.

Theory As noted above, O’Rourke’s algorithm assumes that two droplets may collide only if they are in the same continuous-phase cell. This assumption can prevent droplets that are quite close to each other, but not in the same cell, from colliding, although the effect of this error is lessened by allowing some droplets that are farther apart to collide. The overall accuracy of the scheme is second-order in space.

21-56


21.4 Spray Models

Probability of Collision The probability of collision of two droplets is derived from the point of view of the larger droplet, called the collector droplet and identified below with the number 1. The smaller droplet is identified in the following derivation with the number 2. The calculation is in the frame of reference of the larger droplet so that the velocity of the collector droplet is zero. Only the relative distance between the collector and the smaller droplet is important in this derivation. If the smaller droplet is on a collision course with the collector, the centers will pass within a distance of r1 + r2 . More precisely, if the smaller droplet center passes within a flat circle centered around the collector of area π(r1 + r2 )2 perpendicular to the trajectory of the smaller droplet, a collision will take place. This disk can be used to define the collision volume, which is the area of the aforementioned disk multiplied by the distance traveled by the smaller droplet in one time step, namely π(r1 + r2 )2 vrel ∆t. The algorithm of O’Rourke uses the concept of a collision volume to calculate the probability of collision. Rather than calculate if the position of the smaller droplet center is within the collision volume, the algorithm calculates the probability of the smaller droplet being within the collision volume. It is known that the smaller droplet is somewhere within the continuous-phase cell of volume V . If there is a uniform probability of the droplet being anywhere within the cell, then the chance of the droplet being within the collision volume is the ratio of the two volumes. Thus, the probability of the collector colliding with the smaller droplet is P1 =

π(r1 + r2 )2 vrel ∆t V

(21.4-40)

Equation 21.4-40 can be generalized for parcels, where there are n1 and n2 droplets in the collector and smaller droplet parcels, respectively. The collector undergoes a mean expected number of collisions given by n2 π(r1 + r2 )2 vrel ∆t n ¯= V

(21.4-41)

The actual number of collisions that the collector experiences is not generally the mean expected number of collisions. The probability distribution of the number of collisions follows a Poisson distribution, according to O’Rourke, which is given by P (n) = e−¯n

n ¯n n!

(21.4-42)

where n is the number of collisions between a collector and other droplets.


21-57


Collision Outcomes Once it is determined that two parcels collide, the outcome of the collision must be determined. In general, the outcome tends to be coalescence if the droplets collide headon, and bouncing if the collision is more oblique. The critical offset is a function of the collisional Weber number and the relative radii of the collector and the smaller droplet. The critical offset is calculated by O’Rourke using the expression

bcrit

v ! u u 2.4f t = (r1 + r2 ) min 1.0,

(21.4-43)

We

where f is a function of r1 /r2 , defined as

r1 r2

=

r1 r2

3

− 2.4

r1 r2

2

r1 (21.4-44) r2 √ The value of the actual collision parameter, b, is (r1 + r2 ) Y , where Y is a uniform deviate. The calculated value of b is compared to bcrit , and if b < bcrit , the result of the collision is coalescence. Equation 21.4-42 gives the number of smaller droplets that coalesce with the collector. The properties of the coalesced droplets are found from the basic conservation laws. f

+ 2.7

In the case of a grazing collision, the new velocities are calculated based on conservation of momentum and kinetic energy. It is assumed that some fraction of the kinetic energy of the droplets is lost to viscous dissipation and angular momentum generation. This fraction is related to b, the collision offset parameter. Using assumed forms for the energy loss, O’Rourke derived the following expression for the new velocity: m1 v1 + m2 v2 + m2 (v1 − v2 ) v10 = m1 + m2

b − bcrit r1 + r2 − bcrit

!

(21.4-45)

This relation is used for each of the components of velocity. No other droplet properties are altered in grazing collisions.

21.4.3

Spray Breakup Models

FLUENT offers two spray breakup models: the Taylor Analogy Breakup (TAB) model and the wave model. The TAB model is recommended for low-Weber-number injections and is well suited for low-speed sprays into a standard atmosphere. For Weber numbers greater than 100, the wave model is more applicable. The wave model is popular for use in high-speed fuel-injection applications. Details for each model are provided below.

21-58


21.4 Spray Models

Taylor Analogy Breakup (TAB) Model Introduction The Taylor Analogy Breakup (TAB) model is a classic method for calculating droplet breakup, which is applicable to many engineering sprays. This method is based upon Taylor’s analogy [265] between an oscillating and distorting droplet and a spring mass system. Table 21.4.3 illustrates the analogous components. Table 21.4.3: Comparison of a Spring-Mass System to a Distorting Droplet Spring-Mass System restoring force of spring external force damping force

Distorting and Oscillating Droplet surface tension forces droplet drag force droplet viscosity forces

The resulting TAB model equation set, which governs the oscillating and distorting droplet, can be solved to determine the droplet oscillation and distortion at any given time. As described in detail below, when the droplet oscillations grow to a critical value the “parent” droplet will break up into a number of smaller “child” droplets. As a droplet is distorted from a spherical shape, the drag coefficient changes. A drag model that incorporates the distorting droplet effects is available in FLUENT. See Section 21.4.4 for details. Use and Limitations The TAB model is best for low-Weber-number sprays. Extremely high-Weber-number sprays result in shattering of droplets, which is not described well by the spring-mass analogy. Droplet Distortion The equation governing a damped, forced oscillator is [186] F − kx − d

dx d2 x =m 2 dt dt

(21.4-46)

where x is the displacement of the droplet equator from its spherical (undisturbed) position. The coefficients of this equation are taken from Taylor’s analogy:

ρg u 2 F = CF m ρl r


(21.4-47)

21-59

Discrete Phase Models k σ = Ck 3 m ρl r d µl = Cd 2 m ρl r

(21.4-48) (21.4-49)

where ρl and ρg are the discrete phase and continuous phase densities, u is the relative velocity of the droplet, r is the undisturbed droplet radius, σ is the droplet surface tension, and µl is the droplet viscosity. The dimensionless constants CF , Ck , and Cd will be defined later. The droplet is assumed to break up if the distortion grows to a critical ratio of the droplet radius. This breakup requirement is given as x > Cb r

(21.4-50)

where Cb is a constant equal to 0.5 if breakup is assumed to occur when the distortion is equal to the droplet radius, i.e., the north and south poles of the droplet meet at the droplet center. This implicitly assumes that the droplet is undergoing only one (fundamental) oscillation mode. Equation 21.4-46 is non-dimensionalized by setting y = x/(Cb r) and substituting the relationships in Equations 21.4-47–21.4-49: d2 y CF ρg u2 Ck σ Cd µl dy = − y− 2 2 3 dt Cb ρl r ρl r ρl r2 dt

(21.4-51)

where breakup now occurs for y > 1. For under-damped droplets, the equation governing y can easily be determined from Equation 21.4-51 if the relative velocity is assumed to be constant:

−(t/td )

y(t) = Wec + e

"

1 (y0 − Wec ) cos(ωt) + ω

!

#

dy0 y0 − Wec + sin(ωt) dt td

(21.4-52)

where

We = Wec = y0 = dy0 = dt 1 = td

21-60

ρg u 2 r σ CF We Ck Cb y(0) dy (0) dt Cd µl 2 ρl r 2

(21.4-53) (21.4-54) (21.4-55) (21.4-56) (21.4-57)


21.4 Spray Models

ω 2 = Ck

σ 1 − 2 3 ρl r td

(21.4-58)

In Equation 21.4-52, u is the relative velocity between the droplet and the gas phase and We is the droplet Weber number, a dimensionless parameter defined as the ratio of aerodynamic forces to surface tension forces. The droplet oscillation frequency is represented by ω. The constants have been chosen to match experiments and theory [134]:

Ck = 8 Cd = 5 1 CF = 3

If Equation 21.4-52 is solved for all droplets, those with y > 1 are assumed to break up. The size and velocity of the new child droplets must be determined. Size of Child Droplets The size of the child droplets is determined by equating the energy of the parent droplet to the combined energy of the child droplets. The energy of the parent droplet is [186]

Eparent



dy π = 4πr2 σ + K ρl r5  5 dt

!2



+ ω2y2

(21.4-59)

where K is the ratio of the total energy in distortion and oscillation to the energy in the ). The child droplets are assumed to be non-distorted fundamental mode, of the order ( 10 3 and non-oscillating. Thus, the energy of the child droplets can be shown to be

Echild

r π dy = 4πr σ + ρl r 5 r32 6 dt 2

!2

(21.4-60)

where r32 is the Sauter mean radius of the droplet size distribution. r32 can be found by equating the energy of the parent and child droplets (i.e., Equations 21.4-59 and 21.4-60), setting y = 1, and ω 2 = 8σ/ρl r3 : r32 =

r 1+

8Ky 2 20

+

ρl r 3 (dy/dt)2 σ

6K−5 120

(21.4-61)

Once the size of the child droplets is determined, the number of child droplets can easily be determined by mass conservation.


21-61


Velocity of Child Droplets The TAB model allows for a velocity component normal to the parent droplet velocity to be imposed upon the child droplets. When breakup occurs, the equator of the parent droplet is traveling at a velocity of dx/dt = Cb r(dy/dt). Therefore, the child droplets will have a velocity normal to the parent droplet velocity given by vnormal = Cv Cb r

dy dt

(21.4-62)

where Cv is a constant of order (1). Although this imposed velocity is assumed to be in a plane normal to the path of the parent droplet, the exact direction in this plane cannot be specified. Therefore, the direction of this imposed velocity is selected randomly, yet is confined in a plane normal to the parent relative velocity vector. Droplet Breakup To model droplet breakup, the TAB model first determines the amplitude for an undamped oscillation (td ≈ ∞) for each droplet at time step n using the following:

A=

v u u t

(y n

− Wec

)2

(dy/dt)n + ω

!2

(21.4-63)

According to Equation 21.4-63, breakup is possible only if the following condition is satisfied: Wec + A > 1

(21.4-64)

This is the limiting case, as damping will only reduce the chance of breakup. If a droplet fails the above criterion, breakup does not occur. The only additional calculations required, then, are to update y using a discretized form of Equation 21.4-52 and its derivative, which are both based on work done by O’Rourke and Amsden [186]:

y

dy dt

n+1

!n+1

−(∆t/td )

= Wec + e

21-62

1 (y − Wec ) cos(ωt) + ω n

"

dy dt

!n

y n − Wec + sin(ωt) td (21.4-65) #

)

Wec − y n+1 = + td

−(∆t/td )

ωe

(

(

1 ω

"

dy dt

!n

y n − Wec cos(ω∆t) − (y n − Wec ) sin(ω∆t) + td #

)

(21.4-66)


21.4 Spray Models

All of the constants in these expressions are assumed to be constant throughout the time step. If the criterion of Equation 21.4-64 is met, then breakup is possible. The breakup time, tbu , must be determined to see if breakup occurs within the time step ∆t. The value of tbu is set to the time required for oscillations to grow sufficiently large that the magnitude of the droplet distortion, y, is equal to unity. The breakup time is determined under the assumption that the droplet oscillation is undamped for its first period. The breakup time is therefore the smallest root greater than tn of an undamped version of Equation 21.4-52: Wec + A cos[ω(t − tn ) + φ] = 1

(21.4-67)

where cos φ =

y n − Wec A

(21.4-68)

(dy/dt)n Aω

(21.4-69)

and sin φ = −

If tbu > tn+1 , then breakup will not occur during the current time step, and y and (dy/dt) are updated by Equations 21.4-65 and 21.4-66. The breakup calculation then continues with the next droplet. Conversely, if tn < tbu < tn+1 , then breakup will occur and the child droplet radii are determined by Equation 21.4-61. The number of child droplets, N , is determined by mass conservation:

N

n+1

=N

n

rn rn+1

3

(21.4-70)

A velocity component normal to the relative velocity vector, with magnitude computed by Equation 21.4-62, is imposed upon the child droplets. It is assumed that the child droplets are neither distorted nor oscillating; i.e., y = (dy/dt) = 0. The breakup process is applied to all of the droplets in the parcel (see Section 21.4.2 for a description of parcels). Hence, there is no need to create another computational droplet after breakup. The TAB model in FLUENT changes the mass, size, and velocity of the current droplet only.


21-63


Wave Breakup Model Introduction An alternative to the TAB model is the wave breakup model of Reitz [209], which considers the breakup of the injected liquid to be induced by the relative velocity between the gas and liquid phases. The model assumes that the time of breakup and the resulting droplet size are related to the fastest-growing Kelvin-Helmholtz instability, derived from the jet stability analysis described below. The wavelength and growth rate of this instability are used to predict details of the newly-formed droplets. Use and Limitations The wave model is appropriate for very-high-speed injection, where the Kelvin-Helmholtz instability is believed to dominate spray breakup (We > 100). Because breakup can increase the number of computational droplets, you may wish to inject a modest number of droplets. You must also specify the model constants, which are thought to depend on the internal flow of the spray nozzle. Jet Stability Analysis The jet stability analysis described in detail by Reitz and Bracco [208] is presented briefly here. The analysis considers the stability of a cylindrical, viscous, liquid jet of radius a issuing from a circular orifice at a velocity v into a stagnant, incompressible, inviscid gas of density ρ2 . The liquid has a density, ρ1 , and viscosity, µ1 , and a cylindrical polar coordinate system is used which moves with the jet. An arbitrary infinitesimal axisymmetric surface displacement of the form η = η0 eikz+ωt

(21.4-71)

is imposed on the initially steady motion and it is thus desired to find the dispersion relation ω = ω(k) which relates the real part of the growth rate, ω, to its wave number, k = 2π/λ. In order to determine the dispersion relation, the linearized hydrodynamic equations for the liquid are solved with wave solutions of the form

φ1 = C1 I0 (kr)eikz+ωt ψ1 = C2 I1 (Lr)eikz+ωt

(21.4-72) (21.4-73)

where φ1 and ψ1 are the velocity potential and stream function, respectively, C1 and C2 are integration constants, I0 and I1 are modified Bessel functions of the first kind, L2 = k 2 + ω/ν1 , and ν1 is the liquid kinematic viscosity [209]. The liquid pressure is

21-64


21.4 Spray Models

obtained from the inviscid part of the liquid equations. In addition, the inviscid gas equations can be solved to obtain the fluctuating gas pressure at r = a: − p21 = −ρ2 (U − iωk)2 kη

K0 (ka) K1 (ka)

(21.4-74)

where K0 and K1 are modified Bessel functions of the second kind and u is the relative velocity between the liquid and the gas. The linearized boundary conditions are

∂η ∂t ∂v1 = − ∂z

v1 = ∂u1 ∂r

(21.4-75) (21.4-76)

and σ ∂2η − p1 + 2µ1 − 2 η + a2 2 a ∂z

!

+ p2 = 0

(21.4-77)

which are mathematical statements of the liquid kinematic free surface condition, continuity of shear stress, and continuity of normal stress, respectively. Note that u1 is the axial perturbation liquid velocity, v1 is the radial perturbation liquid velocity, and σ is the surface tension. Also note that Equation 21.4-76 was obtained under the assumption that v2 = 0. As described by Reitz [209], Equations 21.4-75 and 21.4-76 can be used to eliminate the integration constants C1 and C2 in Equations 21.4-72 and 21.4-73. Thus, when the pressure and velocity solutions are substituted into Equation 21.4-77, the desired dispersion relation is obtained: I 0 (ka) 2kL I1 (ka) I10 (La) ω + 2ν1 k ω 1 − 2 = I0 (ka) k + L2 I0 (ka) I1 (La) 2

σk L 2 − a2 2 2 (1 − k a ) ρ1 a2 L 2 + a2

2

!

"

#

I1 (ka) ρ2 ω + U −i I0 (ka) ρ1 k

2

L 2 − a2 L 2 + a2

!

I1 (ka) K0 (ka) (21.4-78) I0 (ka) K1 (ka)

As shown by Reitz [209], Equation 21.4-78 predicts that a maximum growth rate (or most unstable wave) exists for a given set of flow conditions. Curve fits of numerical solutions to Equation 21.4-78 were generated for the maximum growth rate, Ω, and the corresponding wavelength, Λ, and are given by Reitz [209]:


21-65


Λ (1 + 0.45Oh0.5 )(1 + 0.4Ta0.7 ) = 9.02 0.6 a (1 + 0.87We1.67 2 ) ! ρ 1 a3 (0.34 + 0.38We1.5 2 ) Ω = σ (1 + Oh)(1 + 1.4Ta0.6 )

(21.4-79) (21.4-80)

q √ where Oh = We1 /Re1 is the Ohnesorge number and Ta = Oh We2 is the Taylor number. Furthermore, We1 = ρ1 U 2 a/σ and We2 = ρ2 U 2 a/σ are the liquid and gas Weber numbers, respectively, and Re1 = U a/ν1 is the Reynolds number.

Droplet Breakup In the wave model, the initial parcel diameters of the relatively large injected droplets are modeled using the stability analysis for liquid jets as described above. The breakup of the parcels and resulting droplets of radius a is calculated by assuming that the breakup droplet radius, r, is proportional to the wavelength of the fastest-growing unstable surface wave given by Equation 21.4-79. In other words, r = B0 Λ

(21.4-81)

where B0 is a model constant set equal to 0.61 based on the work of Reitz [209]. Furthermore, the rate of change of droplet radius in a parent parcel is given by da (a − r) =− , r≤a dt τ

(21.4-82)

where the breakup time, τ , is given by τ=

3.726B1 a ΛΩ

(21.4-83)

and Λ and Ω are obtained from Equations 21.4-79 and 21.4-80, respectively. The breakup time constant, B1 , is related to the initial disturbance level on the liquid jet and has been found to vary from one nozzle to another [131].

21.4.4

Dynamic Drag Model

Accurate determination of droplet drag coefficients is crucial for accurate spray modeling. FLUENT provides a method that determines the droplet drag coefficient dynamically, accounting for variations in the droplet shape.

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21.4 Spray Models

Use and Limitations The dynamic drag model is applicable in almost any circumstance. It is compatible with both the TAB and wave models for spray breakup. When the collision model is turned on, collisions reset the distortion and distortion velocities of the colliding droplets.

Theory Many droplet drag models assume the droplet remains spherical throughout the domain. With this assumption, the drag of a spherical object is determined by the following [155]:

Cd,sphere =

      

0.424

Re > 1000 (21.4-84)

24 Re

1+

1 Re2/3 6

Re ≤ 1000

However, as an initially spherical droplet moves through a gas, its shape is distorted significantly when the Weber number is large. In the extreme case, the droplet shape will approach that of a disk. The drag of a disk, however, is significantly higher than that of a sphere. Since the droplet drag coefficient is highly dependent upon the droplet shape, a drag model that assumes the droplet is spherical is unsatisfactory. The dynamic drag model accounts for the effects of droplet distortion, linearly varying the drag between that of a sphere (Equation 21.4-84) and a value of 1.52 corresponding to a disk [155]. The drag coefficient is given by Cd = Cd,sphere (1 + 2.632y)

(21.4-85)

where y is the droplet distortion, as determined by the solution of d2 y CF ρg u2 Ck σ Cd µl dy = − y − dt2 Cb ρl r2 ρl r 3 ρl r2 dt

(21.4-86)

In the limit of no distortion (y = 0), the drag coefficient of a sphere will be obtained, while at maximum distortion (y = 1) the drag coefficient corresponding to a disk will be obtained. Note that Equation 21.4-86 is obtained from the TAB model for spray breakup, described in Section 21.4.3, but the dynamic drag model can be used with either of the breakup models.


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21.5

Coupling Between the Discrete and Continuous Phases

As the trajectory of a particle is computed, FLUENT keeps rack of the heat, mass, and momentum gained or lost by the particle stream that follows that trajectory and these quantities can be incorporated in the subsequent continuous phase calculations. Thus, while the continuous phase always impacts the discrete phase, you can also incorporate the effect of the discrete phase trajectories on the continuum. This two-way coupling is accomplished by alternately solving the discrete and continuous phase equations until the solutions in both phases have stopped changing. This interphase exchange of heat, mass, and momentum from the particle to the continuous phase is depicted qualitatively in Figure 21.5.1.

typical particle trajectory mass-exchange heat-exchange momentum-exchange

typical continuous phase control volume

Figure 21.5.1: Heat, Mass, and Momentum Transfer Between the Discrete and Continuous Phases

Momentum Exchange The momentum transfer from the continuous phase to the discrete phase is computed in FLUENT by examining the change in momentum of a particle as it passes through each control volume in the FLUENT model. This momentum change is computed as

F =

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X

!

18µCD Re (up − u) + Fother m ˙ p ∆t ρp d2p 24

(21.5-1)


21.5 Coupling Between the Discrete and Continuous Phases

where µ ρp dp Re up u CD m ˙p ∆t Fother

= = = = = = = = = =

viscosity of the fluid density of the particle diameter of the particle relative Reynolds number velocity of the particle velocity of the fluid drag coefficient mass flow rate of the particles time step other interaction forces

This momentum exchange appears as a momentum sink in the continuous phase momentum balance in any subsequent calculations of the continuous phase flow field and can be reported by FLUENT as described in Section 21.13.

Heat Exchange The heat transfer from the continuous phase to the discrete phase is computed in FLUENT by examining the change in thermal energy of a particle as it passes through each control volume in the FLUENT model. In the absence of chemical reaction (i.e., for all particle laws except Law 5) this heat exchange is computed as "

Z Tp m ¯p ∆mp Q= cp ∆Tp + −hfg + hpyrol + cp,i dT mp,0 mp,0 Tref

!#

m ˙ p,0

(21.5-2)

where m ¯p mp,0 cp ∆Tp ∆mp hfg hpyrol cp,i Tp Tref m ˙ p,0

= = = = = = = = = = =

average mass of the particle in the control volume (kg) initial mass of the particle (kg) heat capacity of the particle (J/kg-K) temperature change of the particle in the control volume (K) change in the mass of the particle in the control volume (kg) latent heat of volatiles evolved (J/kg) heat of pyrolysis as volatiles are evolved (J/kg) heat capacity of the volatiles evolved (J/kg-K) temperature of the particle upon exit of the control volume (K) reference temperature for enthalpy (K) initial mass flow rate of the particle injection tracked (kg/s)

This heat exchange appears as a source or sink of energy in the continuous phase energy balance during any subsequent calculations of the continuous phase flow field and is reported by FLUENT as described in Section 21.13. A similar equation governs heat exchange under Law 5, in which the heat of surface combustion is incorporated.


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Mass Exchange The mass transfer from the discrete phase to the continuous phase is computed in FLUENT by examining the change in mass of a particle as it passes through each control volume in the FLUENT model. The mass change is computed simply as M=

∆mp m ˙ p,0 mp,0

(21.5-3)

This mass exchange appears as a source of mass in the continuous phase continuity equation and as a source of a chemical species defined by you. The mass sources are included in any subsequent calculations of the continuous phase flow field and are reported by FLUENT as described in Section 21.13.

Under-Relaxation of the Interphase Exchange Terms Note that the interphase exchange of momentum, heat, and mass is under-relaxed during the calculation, so that Fnew = Fold + α(Fcalculated − Fold )

(21.5-4)

Qnew = Qold + α(Qcalculated − Qold )

(21.5-5)

Mnew = Mold + α(Mcalculated − Mold )

(21.5-6)

where α is the under-relaxation factor for particles/droplets that you can set in the Solution Controls panel. The default value for α is 0.5. This value may be reduced to improve the stability of coupled calculations. Note that the value of α does not influence the predictions obtained in the final converged solution.

Interphase Exchange During Stochastic Tracking When stochastic tracking is performed, the interphase exchange terms, computed via Equations 21.5-1 to 21.5-6, are computed for each stochastic trajectory with the particle mass flow rate, m ˙ p0 , divided by the number of stochastic tracks computed. This implies that an equal mass flow of particles follows each stochastic trajectory.

Interphase Exchange During Cloud Tracking When the particle cloud model is used, the interphase exchange terms are computed via Equations 21.5-1 to 21.5-6 based on ensemble-averaged flow properties in the particle

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21.6 Overview of Using the Discrete Phase Models

cloud. The exchange terms are then distributed to all the cells in the cloud based on the weighting factor defined in Equation 21.2-61.

21.6

Overview of Using the Discrete Phase Models

The procedure for setting up and solving a problem involving a discrete phase is outlined below, and described in detail in Sections 21.7–21.13. Only the steps related specifically to discrete phase modeling are shown here. For information about inputs related to other models that you are using in conjunction with the discrete phase models, see the appropriate sections for those models. 1. Enable any of the discrete phase modeling options, if relevant, as described in Section 21.7. 2. If you are using particle tracking, define the unsteady as described in Section 21.8. 3. Specify the initial conditions, as described in Section 21.9. 4. Define the boundary conditions, as described in Section 21.10. 5. Define the material properties, as described in Section 21.11. 6. Set the solution parameters and solve the problem, as described in Section 21.12. 7. Examine the results, as described in Section 21.13.

21.7

Discrete Phase Model Options

This section provides instructions for using the optional discrete phase models available in FLUENT. All of them can be turned on in the Discrete Phase Model panel (Figure 21.7.1). Define −→ Models −→Discrete Phase...

21.7.1

Including Radiation Heat Transfer to the Particles

If you want to include the effect of radiation heat transfer to the particles (Equation 11.3-20), you must turn on the Particle Radiation Interaction option in the Discrete Phase Model panel. You will also need to define additional properties for the particle materials (emissivity and scattering factor), as described in Section 21.11.2. This option is available only when the P-1 or discrete ordinates radiation model is used.

21.7.2

Including the Thermophoretic Force on the Particles

If you want to include the effect of the thermophoretic force on the particle trajectories (Equation 21.2-14), turn on the Thermophoretic Force option in the Discrete Phase Model panel. You will also need to define the thermophoretic coefficient for the particle material, as described in Section 21.11.2.


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Figure 21.7.1: The Discrete Phase Model Panel

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21.7 Discrete Phase Model Options

21.7.3

Including a Coupled Heat-Mass Solution on the Particles

By default, the solution of the particle heat and mass equations are solved in a segregated manner. If you enable the Coupled Heat-Mass Solution option, FLUENT will solve this pair of equations pair using a stiff, coupled ODE solver with error tolerance control. The increased accuracy, however, comes at the expense of increased computational expense.

21.7.4

Including Brownian Motion Effects on the Particles

For sub-micron particles in laminar flow, you may want to include the effects of Brownian motion (described in Section 21.2.1) on the particle trajectories. To do so, turn on the Brownian Motion option in the Discrete Phase Model panel. When Brownian motion effects are included, it is recommended that you also select the Stokes-Cunningham drag law in the Drag Law drop-down list under Drag Parameters, and specify the Cunningham Correction (Cc in Equation 21.2-9).

21.7.5

Including Saffman Lift Force Effects on the Particles

For sub-micron particles, you can also model the lift due to shear (the Saffman lift force, described in Section 21.2.1) in the particle trajectory. To do this, turn on the Saffman Lift Force option in the Discrete Phase Model panel.

21.7.6

Monitoring Erosion/Accretion of Particles at Walls

Particle erosion and accretion rates can be monitored at wall boundaries. These rate calculations can be enabled in the Discrete Phase Model panel when the discrete phase is coupled with the continuous phase (i.e., when Interaction with Continuous Phase is selected). Turning on the Erosion/Accretion option will cause the erosion and accretion rates to be calculated at wall boundary faces when particle tracks are updated. You will also need to set the Impact Angle Function (f (α) in Equation 21.2-62), Diameter Function (C(dp ) in Equation 21.2-62), and Velocity Exponent Function (b(v) in Equation 21.2-62) in the Wall boundary conditions panel for each wall zone (as described in Section 21.10.2).

21.7.7

Alternate Drag Laws

There are five drag laws for the particles that can be selected in the Drag Law drop-down list under Drag Parameters. The spherical, non-spherical, Stokes-Cunningham, and high-Mach-number laws described in Section 21.2.1 are always available, and the dynamic-drag law described in Section 21.4.4 is available only when one of the droplet breakup models is used in conjunction with unsteady tracking. See Section 21.8.2 for information about enabling the droplet breakup models.


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If the spherical law, the high-Mach-number law, or the dynamic-drag law is selected, no further inputs are required. If the nonspherical law is selected, the particle Shape Factor (φ in Equation 21.2-7) must be specified. For the Stokes-Cunningham law, the Cunningham Correction factor (Cc in Equation 21.2-9) must be specified.

21.7.8

User-Defined Functions

User-defined functions can be used to customize the discrete phase model to include additional body forces, modify interphase exchange terms (sources), calculate or integrate scalar values along the particle trajectory, and incorporate non-standard erosion rate definitions. See the separate UDF Manual for information about user-defined functions. In the Discrete Phase Model panel, under User-Defined Functions, there are drop-down lists labeled Body Force, Source, and Scalar Update. If Erosion/Accretion is enabled under Options, there will be an additional drop-down list labeled Erosion/Accretion. These lists will show available user-defined functions that can be selected to customize the discrete phase model.

21.8

Particle Tracking

This section contains information about particle tracking with the discrete phase model. Note that you cannot use adaptive time stepping for an unsteady discrete phase calculation.

21.8.1

Inputs for Particle Tracking

If the discrete phase interacts (i.e., exchanges mass, momentum, and/or energy) with the continuous phase, you should enable the Interaction with the Continuous Phase option. An input for the Number of Continuous Phase Iterations per DPM Iteration will appear, which allows you to control the frequency that the particles are tracked and DPM sources are updated. For steady-state simulations, increasing the Number of Continuous Phase Iterations per DPM Iteration will increase stability but require more iterations to converge. For unsteady simulations (with the implicit solvers), particles are advanced at the end of each time step. If the Number of Continuous Phase Iterations per DPM Iteration is less than the number of iterations required to converge the continuous phase between time steps, then sub-iterations are done. Here, particles are tracked to their new positions during a time step and DPM sources are updated, and then particles are returned to their original state at the beginning of the time step. At the end of the time step, particles are then advanced to their new positions based on the continuous-phase solution.

! In steady-state discrete phase modeling, particles do not interact with each other and are tracked one at a time in the domain. However, for the spray model, discrete phase

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21.8 Particle Tracking

droplets interact with each other in collisions, and hence all droplets are tracked together. For the steady-state spray model, an artificial “time step”, which is determined by the input value for Average Number of Particles per Cell, is required. Here, the artificial time step for the discrete phase is adjusted so that there are approximately the specified number of discrete phase droplets per cell. Increasing the Average Number of Particles per Cell will lower the artificial time step, leading to the need for more discrete-phase iterations by the spray to penetrate the domain.

! When the coupled explicit solver is used with the explicit unsteady formulation, the particles are advanced once per time step and are calculated at the start of the time step (before the flow is updated). Additional inputs are required for each injection in the Set Injection Properties panel. For transient flows, the injection Start Time and Stop Time must be specified under Point Properties. Injections with start and stop times set to zero will be injected only at the start of the calculation (t = 0). Changing injection settings during a transient simulation will not affect particles currently released in the domain. At any point during a simulation, you can clear particles that are currently in the domain by clicking on the Clear Particles button in the Discrete Phase Model panel. If you want to save the particle history during the calculation, you can use the File/Write/ Start Particle History... menu item to specify a particle history filename. File −→ Write −→Start Particle History... During the calculation, FLUENT will write the position, velocity, and other data for each particle at each iteration or time step. To turn the particle history off, select the File/Write/Stop Particle History menu item. File −→ Write −→Stop Particle History

21.8.2

Options for Spray Modeling

When you enable particle tracking, the Discrete Phase Model panel will expand to show options related to spray modeling.

Modeling Spray Breakup To enable the modeling of spray breakup, select the Droplet Breakup option under Spray Model and then select the desired model (TAB or Wave). A detailed description of these models can be found in Section 21.4.3. For the TAB model, you will need to specify a value for y0 (the initial distortion at time equal to zero in Equation 21.4-52) in the y0 field. For the wave model, you will need to specify values for B0 and B1, where B0 is the constant B0 in Equation 21.4-81 and B1 is the constant B1 in Equation 21.4-83. You will


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generally not need to modify the value of B0, as the default value 0.61 is acceptable for nearly all cases. For steady-state simulations, you will also need to specify the Average Number of Particles per Cell, which will control the spray density and be used to calculate the artificial time step of the discrete phase. See Section 21.8.1 for more information. Note that you may want to use the dynamic drag law when you use one of the spray breakup models. See Section 21.7.7 for information about choosing the drag law.

Modeling Droplet Collisions To include the effect of droplet collisions, as described in Section 21.4.2, select the Droplet Collision option under Spray Models. There are no further inputs for this model.

21.9

Setting Initial Conditions for the Discrete Phase

21.9.1

Overview of Initial Conditions

The primary inputs that you must provide for the discrete phase calculations in FLUENT are the initial conditions that define the starting positions, velocities, and other parameters for each particle stream. These initial conditions provide the starting values for all of the dependent discrete phase variables that describe the instantaneous conditions of an individual particle: • Position (x, y, z coordinates) of the particle. • Velocities (u, v, w) of the particle. Velocity magnitudes and spray cone angle can also be used (in 3D) to define the initial velocities (see Section 21.9.8). For moving reference frames, relative velocities should be specified. • Diameter of the particle, dp . • Temperature of the particle, Tp . • Mass flow rate of the particle stream that will follow the trajectory of the individual particle/droplet, m ˙ p (required only for coupled calculations). • Additional parameters if one of the atomizer models described in Section 21.4.1 is used for the injection.

!

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When an atomizer model is selected, you will not input initial diameter, velocity, and position quantities for the particles due to the complexities of sheet and ligament breakup. Instead of initial conditions, the quantities you will input for the atomizer models are global parameters.


21.9 Setting Initial Conditions for the Discrete Phase

These dependent variables are updated according to the equations of motion (Section 21.2) and according to the heat/mass transfer relations applied (Section 21.3) as the particle/droplet moves along its trajectory. You can define any number of different sets of initial conditions for discrete phase particles/droplets provided that your computer has sufficient memory.

21.9.2

Injection Types

You will define the initial conditions for a particle/droplet stream by creating an “injection” and assigning properties to it. FLUENT provides 10 types of injections: • single • group • hollow cone (only in 3D) • solid cone (only in 3D) • surface • plain-orifice atomizer • pressure-swirl atomizer • flat-fan atomizer • air-blast atomizer • effervescent atomizer • read from a file For each non-atomizer injection type, you will specify each of the initial conditions listed in Section 21.9.1, the type of particle that possesses these initial conditions, and any other relevant parameters for the particle type chosen. You should create a single injection when you want to specify a single value for each of the initial conditions (Figure 21.9.1). Create a group injection (Figure 21.9.2) when you want to define a range for one or more of the initial conditions (e.g., a range of diameters or a range of initial positions). To define hollow spray cone injections in 3D problems, create a cone injection (Figure 21.9.3). To release particles from a surface (either a zone surface or a surface you have defined using the items in the Surface menu), you will create a surface injection. (If you create a surface injection, a particle stream will be released from each facet of the surface. You can use the Bounded and Sample Points options in the Plane Surface panel to create injections from a rectangular grid of particles in 3D (see Section 26.6 for details).


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Particle initial conditions (position, velocity, diameter, temperature, and mass flow rate) can also be read from an external file if none of the injection types listed above can be used to describe your injection distribution. The file has the following form: (( x y z u v w diameter temperature mass-flow) name ) with all of the parameters in SI units. All the parentheses are required, but the name is optional. The inputs for setting injections are described in detail in Section 21.9.5.

➞

●

Figure 21.9.1: Particle Injection Defining a Single Particle Stream

➞ ➞ ➞ ➞

● ● ● ●

Figure 21.9.2: Particle Injection Defining an Initial Spatial Distribution of the Particle Streams

▼

▼

▼

●

▼ ▼

Figure 21.9.3: Particle Injection Defining an Initial Spray Distribution of the Particle Velocity

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21.9.3

Particle Types

When you define a set of initial conditions (as described in Section 21.9.5), you will need to specify the type of particle. The particle types available to you depend on the range of physical models that you have defined in the Models family of panels. • An “inert” particle is a discrete phase element (particle, droplet, or bubble) that obeys the force balance (Equation 21.2-1) and is subject to heating or cooling via Law 1 (Section 21.3.2). The inert type is available for all FLUENT models. • A “droplet” particle is a liquid droplet in a continuous-phase gas flow that obeys the force balance (Equation 21.2-1) and that experiences heating/cooling via Law 1 followed by vaporization and boiling via Laws 2 and 3 (Sections 21.3.3 and 21.3.4). The droplet type is available when heat transfer is being modeled and at least two chemical species are active or the non-premixed or partially premixed combustion model is active. You should use the ideal gas law to define the gas-phase density (in the Materials panel, as discussed in Section 7.2.5) when you select the droplet type. • A “combusting” particle is a solid particle that obeys the force balance (Equation 21.2-1) and experiences heating/cooling via Law 1 followed by devolatilization via Law 4 (Section 21.3.5), and a heterogeneous surface reaction via Law 5 (Section 21.3.6). Finally, the non-volatile portion of a combusting particle is subject to inert heating via Law 6. You can also include an evaporating material with the combusting particle by selecting the Wet Combustion option in the Set Injection Properties panel. This allows you to include a material that evaporates and boils via Laws 2 and 3 (Sections 21.3.3 and 21.3.4) before devolatilization of the particle material begins. The combusting type is available when heat transfer is being modeled and at least three chemical species are active or the non-premixed combustion model is active. You should use the ideal gas law to define the gas-phase density (in the Materials panel) when you select the combusting particle type.

21.9.4

Creating, Copying, Deleting, and Listing Injections

You will use the Injections panel (Figure 21.9.4) to create, copy, delete, and list injections. Define −→Injections... (You can also click on the Injections... button in the Discrete Phase Model panel to open the Injections panel.)

Creating Injections To create an injection, click on the Create button. A new injection will appear in the Injections list and the Set Injection Properties panel will open automatically to allow you to set the injection properties (as described in Section 21.9.5).


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Figure 21.9.4: The Injections Panel

Modifying Injections To modify an existing injection, select its name in the Injections list and click on the Set... button. The Set Injection Properties panel will open, and you can modify the properties as needed. If you have two or more injections for which you want to set some of the same properties, select their names in the Injections list and click on the Set... button. The Set Multiple Injection Properties panel will open, which will allow you to set the common properties. For instructions about using this panel, see Section 21.9.17.

Copying Injections To copy an existing injection to a new injection, select the existing injection in the Injections list and click on the Copy button. The Set Injection Properties panel will open with a new injection that has the same properties as the injection you selected. This is useful if you want to set another injection with similar properties.

Deleting Injections You can delete an injection by selecting its name in the Injections list and clicking on the Delete button.

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Listing Injections To list the initial conditions for the particle streams in the selected injection, click on the List button. The list reported by FLUENT in the console window contains, for each particle stream that you have defined, the following (in SI units): • Particle stream number in the column headed NO • Particle type (IN for inert, DR for droplet, or CP for combusting particle) in the column headed TYP • x, y, and z position in the columns headed (X), (Y), and (Z) • x, y, and z velocity in the columns headed (U), (V), and (W) • Temperature in the column headed (T) • Diameter in the column headed (DIAM) • Mass flow rate in the column headed (MFLOW)

Shortcuts for Selecting Injections FLUENT provides a shortcut for selecting injections with names that match a specified pattern. To use this shortcut, enter the pattern under Injection Name Pattern and then click Match to select the injections with names that match the specified pattern. For example, if you specify drop*, all injections that have names beginning with drop (e.g., drop-1, droplet) will be selected automatically. If they are all selected already, they will be deselected. If you specify drop?, all surfaces with names consisting of drop followed by a single character will be selected (or deselected, if they are all selected already).

21.9.5

Defining Injection Properties

Once you have created an injection (using the Injections panel, as described in Section 21.9.4), you will use the Set Injection Properties panel (Figure 21.9.5) to define the injection properties. (Remember that this panel will open when you create a new injection, or when you select an existing injection and click on the Set... button in the Injections panel.) The procedure for defining an injection is as follows: 1. If you want to change the name of the injection from its default name, enter a new one in the Injection Name field. This is recommended if you are defining a large number of injections so you can easily distinguish them. When assigning names to your injections, keep in mind the selection shortcut described in Section 21.9.4.


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Figure 21.9.5: The Set Injection Properties Panel

2. Choose the type of injection in the Injection Type drop-down list. The ten choices (single, group, cone, solid-cone, surface, plain-orifice-atomizer, pressure-swirl-atomizer, air-blast-atomizer, flat-fan-atomizer, effervescent-atomizer, and file) are described in Section 21.9.2. Note that if you select any of the atomizer models, you will also need to set the Viscosity and Droplet Surface Tension in the Materials panel.

!

If you are using sliding or moving/deforming meshes in your simulation, you should not use surface injections because they are not compatible with moving meshes. 3. If you are defining a single injection, go to the next step. For a group, cone, solidcone, or any of the atomizer injections, set the Number of Particle Streams in the group, spray cone, or atomizer. If you are defining a surface injection, choose the surface(s) from which the particles will be released in the Release From Surfaces list. If you are reading the injection from a file, click on the File... button at the bottom of the Set Injection Properties panel and specify the file to be read in the resulting Select File dialog box. The parameters in the injection file must be in SI units.

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4. Select Inert, Droplet, or Combusting as the Particle Type. The available types are described in Section 21.9.3. 5. Choose the material for the particle(s) in the Material drop-down list. If this is the first time you have created a particle of this type, you can choose from all of the materials of this type defined in the database. If you have already created a particle of this type, the only available material will be the material you selected for that particle. You can define additional materials by copying them from the database or creating them from scratch, as discussed in Section 21.11.2 and described in detail in Section 7.1.2. 6. If you are defining a group or surface injection and you want to change from the default linear (for group injections) or uniform (for surface injections) interpolation method used to determine the size of the particles, select rosin-rammler or rosin-rammler-logarithmic in the Diameter Distribution drop-down list. The RosinRammler method for determining the range of diameters for a group injection is described in Section 21.9.7. 7. If you have created a customized particle law using user-defined functions, turn on the Custom option under Laws and specify the appropriate laws as described in Section 21.9.16. 8. If your particle type is Inert, go to the next step. If you are defining Droplet particles, select the gas phase species created by the vaporization and boiling laws (Laws 2 and 3) in the Evaporating Species drop-down list. If you are defining Combusting particles, select the gas phase species created by the devolatilization law (Law 4) in the Devolatilizing Species drop-down list, the gas phase species that participates in the surface char combustion reaction (Law 5) in the Oxidizing Species list, and the gas phase species created by the surface char combustion reaction (Law 5) in the Product Species list. Note that if the Combustion Model for the selected combusting particle material (in the Materials panel) is the multiple-surface-reaction model, then the Oxidizing Species and Product Species lists will be disabled because the reaction stoichiometry has been defined in the mixture material. 9. Click the Point Properties tab (the default), and specify the point properties (position, velocity, diameter, temperature, and—if appropriate—mass flow rate and any atomizer-related parameters) as described for each injection type in Sections 21.9.6– 21.9.14. 10. If the flow is turbulent and you wish to include the effects of turbulence on the particle dispersion, click the Turbulent Dispersion tab, turn on the Stochastic Model and/or the Cloud Model, and set the related parameters as described in Section 21.9.15. 11. If your combusting particle includes an evaporating material, click the Wet Combustion tab, select the Wet Combustion option, and then select the material that


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is evaporating/boiling from the particle before devolatilization begins in the Liquid Material drop-down list. You should also set the volume fraction of the liquid present in the particle by entering the value of the Liquid Fraction. Finally, select the gas phase species created by the evaporating and boiling laws in the Evaporating Species drop-down list in the top part of the panel. 12. If you want to use a user-defined function to initialize the injection properties, click the UDF tab to access the UDF inputs. You can select an Initialization function under User-Defined Functions to modify injection properties at the time the particles are injected into the domain. This allows the position and/or properties of the injection to be set as a function of flow conditions. See the separate UDF Manual for information about user-defined functions.

21.9.6

Point Properties for Single Injections

For a single injection, you will define the following initial conditions for the particle stream under the Point Properties heading (in the Set Injection Properties panel): • Position: Set the x, y, and z positions of the injected stream along the Cartesian axes of the problem geometry in the X-, Y-, and Z-Position fields. (Z-Position will appear only for 3D problems.) • Velocity: Set the x, y, and z components of the stream’s initial velocity in the X-, Y-, and Z-Velocity fields. (Z-Velocity will appear only for 3D problems.) • Diameter: Set the initial diameter of the injected particle stream in the Diameter field. • Temperature: Set the initial (absolute) temperature of the injected particle stream in the Temperature field. • Mass flow rate: For coupled phase calculations (see Section 21.12), set the mass of particles per unit time that follows the trajectory defined by the injection in the Flow Rate field. Note that in axisymmetric problems the mass flow rate is defined per 2π radians and in 2D problems per unit meter depth (regardless of the reference value for length). • Duration of injection: For unsteady particle tracking (see Section 21.8), set the starting and ending time for the injection in the Start Time and Stop Time fields.

21.9.7

Point Properties for Group Injections

For group injections, you will define the properties described in Section 21.9.6 for single injections for the First Point and Last Point in the group. That is, you will define a range of values, φ1 through φN , for each initial condition φ by setting values for φ1 and φN .

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FLUENT assigns a value of φ to the ith injection in the group using a linear variation between the first and last values for φ: φi = φ1 +

φN − φ1 (i − 1) N −1

(21.9-1)

Thus, for example, if your group consists of 5 particle streams and you define a range for the initial x location from 0.2 to 0.6 meters, the initial x location of each stream is as follows: • Stream 1: x = 0.2 meters • Stream 2: x = 0.3 meters • Stream 3: x = 0.4 meters • Stream 4: x = 0.5 meters • Stream 5: x = 0.6 meters

! In general, you should supply a range for only one of the initial conditions in a given group—leaving all other conditions fixed while a single condition varies among the stream numbers of the group. Otherwise you may find, for example, that your simultaneous inputs of a spatial distribution and a size distribution have placed the small droplets at the beginning of the spatial range and the large droplets at the end of the spatial range. Note that you can use a different method for defining the size distribution of the particles, as discussed below.

Using the Rosin-Rammler Diameter Distribution Method By default, you will define the size distribution of particles by inputting a diameter for the first and last points and using the linear equation (21.9-1) to vary the diameter of each particle stream in the group. When you want a different mass flow rate for each particle/droplet size, however, the linear variation may not yield the distribution you need. Your particle size distribution may be defined most easily by fitting the size distribution data to the Rosin-Rammler equation. In this approach, the complete range of particle sizes is divided into a set of discrete size ranges, each to be defined by a single stream that is part of the group. Assume, for example, that the particle size data obeys the following distribution:


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Diameter Range (µm ) 0–70 70–100 100–120 120–150 150–180 180–200

Mass Fraction in Range 0.05 0.10 0.35 0.30 0.15 0.05

The Rosin-Rammler distribution function is based on the assumption that an exponential relationship exists between the droplet diameter, d, and the mass fraction of droplets with diameter greater than d, Yd : Yd = e−(d/d)

n

(21.9-2)

FLUENT refers to the quantity d in Equation 21.9-2 as the Mean Diameter and to n as the Spread Parameter. These parameters are input by you (in the Set Injection Properties panel under the First Point heading) to define the Rosin-Rammler size distribution. To solve for these parameters, you must fit your particle size data to the Rosin-Rammler exponential equation. To determine these inputs, first recast the given droplet size data in terms of the Rosin-Rammler format. For the example data provided above, this yields the following pairs of d and Yd : Mass Fraction with Diameter, d (µm) Diameter Greater than d, Yd 70 0.95 100 0.85 120 0.50 150 0.20 180 0.05 200 (0.00) A plot of Yd vs. d is shown in Figure 21.9.6. Next, derive values of d and n such that the data in Figure 21.9.6 fit Equation 21.9-2. The value for d is obtained by noting that this is the value of d at which Yd = e−1 ≈ 0.368. From Figure 21.9.6, you can estimate that this occurs for d ≈ 131 µm. The numerical value for n is given by n=

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ln(− ln Yd )

ln d/d



1.0 0.9 0.8

Mass Fraction > d, Yd

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50 70 90 110 130 150 170 190 210 230 250

Diameter, d ( µm)

Figure 21.9.6: Example of Cumulative Size Distribution of Particles

By substituting the given data pairs for Yd and d/d into this equation, you can obtain values for n and find an average. Doing so yields an average value of n = 4.52 for the example data above. The resulting Rosin-Rammler curve fit is compared to the example data in Figure 21.9.7. You can input values for Yd and n, as well as the diameter range of the data and the total mass flow rate for the combined individual size ranges, using the Set Injection Properties panel. A second Rosin-Rammler distribution is also available based on the natural logarithm of the particle diameter. If in your case, the smaller-diameter particles in a Rosin-Rammler distribution have higher mass flows in comparison with the larger-diameter particles, you may want better resolution of the smaller-diameter particle streams, or “bins”. You can therefore choose to have the diameter increments in the Rosin-Rammler distribution done uniformly by ln d. In the standard Rosin-Rammler distribution, a particle injection may have a diameter range of 1 to 200 µm. In the logarithmic Rosin-Rammler distribution, the same diameter range would be converted to a range of ln 1 to ln 200, or about 0 to 5.3. In this way, the mass flow in one bin would be less-heavily skewed as compared to the other bins. When a Rosin-Rammler size distribution is being defined for the group of streams, you should define (in addition to the initial velocity, position, and temperature) the following


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1.0 0.9 0.8

Mass Fraction > d, Yd

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50 70 90 110 130 150 170 190 210 230 250

Diameter, d ( µm)

Figure 21.9.7: Rosin-Rammler Curve Fit for the Example Particle Size Data

parameters, which appear under the heading for the First Point: • Total Flow Rate: the total mass flow rate of the N streams in the group. Note that in axisymmetric problems this mass flow rate is defined per 2π radians and in 2D problems per unit meter depth. • Min. Diameter: the smallest diameter to be considered in the size distribution. • Max. Diameter: the largest diameter to be considered in the size distribution. • Mean Diameter: the size parameter, d, in the Rosin-Rammler equation (21.9-2). • Spread Parameter: the exponential parameter, n, in Equation 21.9-2.

21.9.8

Point Properties for Cone Injections

In 3D problems, you can define a hollow or solid cone of particle streams using the cone or solid-cone injection type, respectively. For both types of cone injections, the inputs are as follows:

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• Position: Set the coordinates of the origin of the spray cone in the X-, Y-, and Z-Position fields. • Diameter: Set the diameter of the particles in the stream in the Diameter field. • Temperature: Set the temperature of the streams in the Temperature field. • Axis: Set the x, y, and z components of the vector defining the cone’s axis in the X-Axis, Y-Axis, and Z-Axis fields. • Velocity: Set the velocity magnitude of the particle streams that will be oriented along the specified spray cone angle in the Velocity Mag. field. • Cone angle: Set the included half-angle, θ, of the hollow spray cone in the Cone Angle field, as shown in Figure 21.9.8. • Radius: A non-zero inner radius can be specified to model injectors that do not emanate from a single point. Set the radius r (defined as shown in Figure 21.9.8) in the Radius field. The particles will be distributed about the axis with the specified radius.

θ r origin

axis

Figure 21.9.8: Cone Half Angle and Radius

• Swirl fraction (hollow cone only): Set the fraction of the velocity magnitude to go into the swirling component of the flow in the Swirl Fraction field. The direction of the swirl component is defined using the right-hand rule about the axis (a negative value for the swirl fraction can be used to reverse the swirl direction). • Mass flow rate: For coupled calculations, set the total mass flow rate for the streams in the spray cone in the Total Flow Rate field. Note that you may want to define multiple spray cones emanating from the same initial location in order to include a size distribution of the spray or to include a range of cone angles.


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21.9.9

Point Properties for Surface Injections

For surface injections, you will define all the properties described in Section 21.9.6 for single injections except for the initial position of the particle streams. The initial positions of the particles will be the location of the data points on the specified surface(s). Note that you will set the Total Flow Rate of all particles released from the surface (required for coupled calculations only). If you want, you can scale the individual mass flow rates of the particles by the ratio of the area of the face they are released from to the total area of the surface. To scale the mass flow rates, select the Scale Flow Rate By Face Area option under Point Properties. Note that many surfaces have non-uniform distributions of points. If you want to generate a uniform spatial distribution of particle streams released from a surface in 3D, you can create a bounded plane surface with a uniform distribution using the Plane Surface panel, as described in Section 26.6. In 2D, you can create a rake using the Line/Rake Surface panel, as described in Section 26.5.

! Note also that the surface injections will not be moved with the grid when a sliding mesh or a moving or deforming mesh is being used. A non-uniform size distribution can be used for surface injections, as described below.

Using the Rosin-Rammler Diameter Distribution Method The Rosin-Rammler size distributions described in Section 21.9.7 for group injections is also available for surface injections. If you select one of the Rosin-Rammler distributions, you will need to specify the following parameters under Point Properties, in addition to the initial velocity, temperature, and total flow rate: • Min. Diameter: the smallest diameter to be considered in the size distribution. • Max. Diameter: the largest diameter to be considered in the size distribution. • Mean Diameter: the size parameter, d, in the Rosin-Rammler equation (Equation 21.9-2). • Spread Parameter: the exponential parameter, n, in Equation 21.9-2. • Number of Diameters: the number of diameters in each distribution (i.e., the number of different diameters in the stream injected from each face of the surface). FLUENT will inject streams of particles from each face on the surface, with diameters defined by the Rosin-Rammler distribution function. The total number of injection streams tracked for the surface injection will be equal to the number of diameters in each distribution (Number of Diameters) multiplied by the number of faces on the surface.

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21.9.10

Point Properties for Plain-Orifice Atomizer Injections

For a plain-orifice atomizer injection, you will define the following initial conditions under Point Properties: • Position: Set the x, y, and z positions of the injected stream along the Cartesian axes of the problem geometry in the X-Position, Y-Position, and Z-Position fields. (Z-Position will appear only for 3D problems. • Axis (3D only): Set the x, y, and z components of the vector defining the axis of the orifice in the X-Axis, Y-Axis, and Z-Axis fields. • Temperature: Set the temperature of the streams in the Temperature field. • Mass flow rate: Set the mass flow rate for the streams in the atomizer in the Flow Rate field. • Duration of injection: For unsteady particle tracking (see Section 21.8), set the starting and ending time for the injection in the Start Time and Stop Time fields. • Vapor pressure: Set the vapor pressure governing the flow through the internal orifice (pv in Table 21.4.1) in the Vapor Pressure field. • Diameter: Set the diameter of the orifice in the Injector Inner Diam. field (d in Table 21.4.1). • Orifice length: Set the length of the orifice in the Orifice Length field (L in Table 21.4.1). • Radius of curvature: Set the radius of curvature of the inlet corner in the Corner Radius of Curv. field (r in Table 21.4.1). • Nozzle parameter: Set the constant for the spray angle correlation in the Constant A field (CA in Equation 21.4-16). • Azimuthal angles: For 3D sectors, set the Azimuthal Start Angle and Azimuthal Stop Angle. See Section 21.4.1 for details about how these inputs are used.

21.9.11

Point Properties for Pressure-Swirl Atomizer Injections

For a pressure-swirl atomizer injection, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate, duration of injection (if unsteady), injector inner diameter, and azimuthal angles (if relevant) described in Section 21.9.10, you will need to specify the following parameters under Point Properties:


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• Spray angle: Set the value of the spray angle of the injected stream in the Spray Half Angle field (θ in Equation 21.4-25). • Pressure: Set the pressure upstream of the injection in the Upstream Pressure field (p1 in Table 21.4.1). • Sheet breakup: Set the value of the empirical constant that determines the length of the ligaments that are formed after sheet breakup in the Sheet Constant field (ln( ηη0b ) in Equation 21.4-30). • Ligament diameter: For short waves, set the proportionality constant that linearly relates the ligament diameter, dL , to the wavelength that breaks up the sheet in the Ligament Constant field (see Equations 21.4-31–21.4-34). See Section 21.4.1 for details about how these inputs are used.

21.9.12

Point Properties for Air-Blast/Air-Assist Atomizer Injections

For an air-blast/air-assist atomizer, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate, duration of injection (if unsteady), injector inner diameter, and azimuthal angles (if relevant) described in Section 21.9.10, you will need to specify the following parameters under Point Properties: • Outer diameter: Set the outer diameter of the injector in the Injector Outer Diam. field. This value is used in conjunction with the Injector Inner Diam. to set the thickness of the liquid sheet (t in Equation 21.4-22). • Spray angle: Set the initial trajectory of the film as it leaves the end of the orifice in the Spray Half Angle field (θ in Equation 21.4-25). • Relative velocity: Set the maximum relative velocity that is produced by the sheet and air in the Relative Velocity field. • Sheet breakup: Set the value of the empirical constant that determines the length of the ligaments that are formed after sheet breakup in the Sheet Constant field (ln( ηη0b ) in Equation 21.4-30). • Ligament diameter: For short waves, set the proportionality constant (CL in Equation 21.4-33) that linearly relates the ligament diameter, dL , to the wavelength that breaks up the sheet in the Ligament Constant field. See Section 21.4.1 for details about how these inputs are used.

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21.9.13

Point Properties for Flat-Fan Atomizer Injections

The flat-fan atomizer model is available only for 3D models. For this type of injection, you will define the following initial conditions under Point Properties: • Arc position: Set the coordinates of the center point of the arc from which the fan originates in the X-Center, Y-Center, and Z-Center fields (see Figure 21.4.6). • Virtual position: Set the coordinates of the virtual origin of the fan in the X-Virtual Origin, Y-Virtual Origin, and Z-Virtual Origin fields. This point is the intersection of the lines that mark the sides of the fan (see Figure 21.4.6). • Normal vector: Set the direction that is normal to the fan in the X-Fan Normal Vector, Y-Fan Normal Vector, and Z-Fan Normal Vector fields. • Temperature: Set the temperature of the streams in the Temperature field. • Mass flow rate: Set the mass flow rate for the streams in the atomizer in the Flow Rate field. • Duration of injection: For unsteady particle tracking (see Section 21.8), set the starting and ending time for the injection in the Start Time and Stop Time fields. • Spray half angle: Set the initial half angle of the drops as they leave the end of the orifice in the Spray Half Angle field. • Orifice width: Set the width of the orifice (in the normal direction) in the Orifice Width field. • Sheet breakup: Set the value of the empirical constant that determines the length of the ligaments that are formed after sheet breakup in the Flat Fan Sheet Constant field (see Equation 21.4-30). See Section 21.4.1 for details about how these inputs are used.

21.9.14

Point Properties for Effervescent Atomizer Injections

For an effervescent atomizer injection, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate (including both flashing and non-flashing components), duration of injection (if unsteady), vapor pressure, injector inner diameter, and azimuthal angles (if relevant) described in Section 21.9.10, you will need to specify the following parameters under Point Properties: • Mixture quality: Set the mass fraction of the injected mixture that vaporizes in the Mixture Quality field (x in Equation 21.4-39).


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• Saturation temperature: Set the saturation temperature of the volatile substance in the Saturation Temp. field. • Droplet dispersion: Set the parameter that controls the spatial dispersion of the droplet sizes in the Dispersion Constant field (Ceff in Equation 21.4-39). • Spray angle: Set the initial trajectory of the film as it leaves the end of the orifice in the Maximum Half Angle field. See Section 21.4.1 for details about how these inputs are used.

21.9.15

Modeling Turbulent Dispersion of Particles

As mentioned in Section 21.9.5, you can choose stochastic tracking and/or cloud tracking as the method for modeling turbulent dispersion of particles.

Stochastic Tracking For turbulent flows, if you choose to use the stochastic tracking technique, you must enable it and specify the “number of tries”. Stochastic tracking includes the effect of turbulent velocity fluctuations on the particle trajectories using the DRW model described in Section 21.2.2. 1. Click the Turbulent Dispersion tab in the Set Injection Properties panel. 2. Enable stochastic tracking by turning on the Stochastic Model under Stochastic Tracking. 3. Specify the Number Of Tries: • An input of zero tells FLUENT to compute the particle trajectory based on the mean continuous phase velocity field (Equation 21.2-1), ignoring the effects of turbulence on the particle trajectories. • An input of 1 or greater tells FLUENT to include turbulent velocity fluctuations in the particle force balance as in Equation 21.2-20. The trajectory is computed more than once if your input exceeds 1: two trajectory calculations are performed if you input 2, three trajectory calculations are performed if you input 3, etc. Each trajectory calculation includes a new stochastic representation of the turbulent contributions to the trajectory equation. When a sufficient number of tries is requested, the trajectories computed will include a statistical representation of the spread of the particle stream due to turbulence. Note that for unsteady particle tracking, the Number of Tries is set to 1 if Stochastic Tracking is enabled.

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If you want the characteristic lifetime of the eddy to be random (Equation 21.2-37), enable the Random Eddy Lifetime option. You will generally not need to change the Time Scale Constant (CL in Equation 21.2-28) from its default value of 0.15, unless you are using the Reynolds Stress turbulence model (RSM), in which case a value of 0.3 is recommended. Figure 21.9.9 illustrates a discrete phase trajectory calculation computed via the “mean” tracking (number of tries = 0) and Figure 21.9.10 illustrates the “stochastic” tracking (number of tries > 1) option. When multiple stochastic trajectory calculations are performed, the momentum and mass defined for the injection are divided evenly among the multiple particle/droplet tracks, and are thus spread out in terms of the interphase momentum, heat, and mass transfer calculations. Including turbulent dispersion in your model can thus have a significant impact on the effect of the particles on the continuous phase when coupled calculations are performed.

3.04e-02 2.84e-02 2.63e-02 2.43e-02 2.23e-02 2.03e-02 1.82e-02 1.62e-02 1.42e-02 1.22e-02 1.01e-02 8.10e-03 6.08e-03 4.05e-03 2.03e-03 0.00e+00

Particle Traces Colored by Particle Time (s)

Figure 21.9.9: Mean Trajectory in a Turbulent Flow

Cloud Tracking For turbulent flows, you can also include the effects of turbulent dispersion on the injection. When cloud tracking is used, the trajectory will be tracked as a cloud of particles about a mean trajectory, as described in Section 21.2.2. 1. Click the Turbulent Dispersion tab in the Set Injection Properties panel.


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3.00e-02 2.80e-02 2.60e-02 2.40e-02 2.20e-02 2.00e-02 1.80e-02 1.60e-02 1.40e-02 1.20e-02 1.00e-02 8.00e-03 6.00e-03 4.00e-03 2.00e-03 0.00e+00

Particle Traces Colored by Particle Time (s)

Figure 21.9.10: Stochastic Trajectories in a Turbulent Flow

2. Enable cloud tracking by turning on the Cloud Model under Cloud Tracking. 3. Specify the minimum and maximum cloud diameters. Particles enter the domain with an initial cloud diameter equal to the Min. Cloud Diameter. The particle cloud’s maximum allowed diameter is specified by the Max. Cloud Diameter. You may want to restrict the Max. Cloud Diameter to a relevant length scale for the problem to improve computational efficiency in complex domains where the mean trajectory may become stuck in recirculation regions.

21.9.16

Custom Particle Laws

If the standard FLUENT laws, Laws 1 through 6, do not adequately describe the physics of your discrete phase model, you can modify them by creating custom laws with userdefined functions. See the separate UDF Manual for information about user-defined functions. You can also create custom laws by using a subset of the existing FLUENT laws (e.g., Laws 1, 2, and 4), or a combination of existing laws and user-defined functions. Once you have defined and loaded your user-defined function(s), you can create a custom law by enabling the Custom option under Laws in the Set Injection Properties panel. This will open the Custom Laws panel. In the drop-down list to the left of each of the six particle laws, you can select the appropriate particle law for your custom law. Each list contains the available options that can be chosen (the standard laws plus any user-defined functions you have loaded).

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Figure 21.9.11: The Custom Laws Panel

There is a seventh drop-down list in the Custom Laws panel labeled Switching. You may wish to have FLUENT vary the laws used depending on conditions in the model. You can customize the way FLUENT switches between laws by selecting a user-defined function from this drop-down list. An example of when you might want to use a custom law might be to replace the standard devolatilization law with a specialized devolatilization law that more accurately describes some unique aspects of your model. After creating and loading a user-defined function that details the physics of your devolatilization law, you would visit the Custom Laws panel and replace the standard devolatilization law (Law 2) with your user-defined function.

21.9.17

Defining Properties Common to More Than One Injection

If you have a number of injections for which you want to set the same properties, FLUENT provides a shortcut so that you do not need to visit the Set Injection Properties panel for each injection to make the same changes. As described in Section 21.9.5, if you select more than one injection in the Injections panel, clicking the Set... button will open the Set Multiple Injection Properties panel (Figure 21.9.12) instead of the Set Injection Properties panel. Depending on the type of injections you have selected (single, group, atomizers, etc.), there will be different categories of properties listed under Injections Setup. The names of these categories correspond to the headings within the Set Injection Properties panel


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Figure 21.9.12: The Set Multiple Injection Properties Panel

(e.g., Particle Type and Stochastic Tracking). Only those categories that are appropriate for all of your selected injections (which are shown in the Injections list) will be listed. If all of these injections are of the same type, more categories of properties will be available for you to modify. If the injections are of different types, you will have fewer categories to select from.

Modifying Properties To modify a property, follow these steps: 1. Select the appropriate category in the Injections Setup list. For example, if you want to set the same flow rate for all of the selected injections, select Point Properties. The panel will expand to show the properties that appear under that heading in the Set Injection Properties panel. 2. Set the property (or properties) to be modified, as described below. 3. Click Apply. FLUENT will report the change in the console window.

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!

You must click Apply to save the property settings within each category. If, for example, you want to modify the flow rate and the stochastic tracking parameters, you will need to select Point Properties in the Injections Setup list, specify the flow rate, and click Apply. You would then repeat the process for the stochastic tracking parameters, clicking Apply again when you are done. There are two types of properties that can be modified using the Set Multiple Injection Properties panel. The first type involves one of the following actions: • selecting a value from a drop-down list • choosing an option using a radio button The second type involves one of the following actions: • entering a value in a field • turning an option on or off Setting the first type of property works the same way as in the Set Injection Properties panel. For example, if you select Particle Type in the Injections Setup list, the panel will expand to show the portion of the Set Injection Properties panel where you choose the particle type. You can simply choose the desired type and click Apply. Setting the second type of property requires an additional step. If you select a category in the Injections Setup list that contains this type of property, the expanded portion of the panel will look like the corresponding part of the Set Injection Properties panel, with the addition of Modify check buttons (see Figure 21.9.12). To change one of the properties, first turn on the Modify check button to its left, and then specify the desired status or value. For example, if you would like to enable stochastic tracking, first turn on the Modify check button to the left of Stochastic Model. This will make the property active so you can modify its status. Then, under Property, turn on the Stochastic Model check button. (Be sure to click Apply when you are done setting stochastic tracking parameters.) If you would like to change the value of Number of Tries, select the Modify check button to its left to make it active, and then enter the new value in the field. Make sure you click Apply when you have finished modifying the stochastic tracking properties.

! The setting for a property that has not been activated with the Modify check button is not relevant, because it will not be applied to the selected injections when you click Apply. After you turn on Modify for a particular property, clicking Apply will modify that


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property for all of the selected injections, so make sure that you have the settings the way that you want them before you do this. If you make a mistake, you will have to return to the Set Injection Properties panel for each injection to fix the incorrect setting, if it is not possible to do so in the Set Multiple Injection Properties panel.

Modifying Properties Common to a Subset of Selected Injections Note that it is possible to change a property that is relevant for only a subset of the selected injections. For example, if some of the selected injections are using stochastic tracking and some are not, enabling the Random Eddy Lifetime option and clicking Apply will turn this option on only for those injections that are using stochastic tracking. The other injections will be unaffected.

21.10

Setting Boundary Conditions for the Discrete Phase

When a particle reaches a physical boundary (e.g., a wall or inlet boundary) in your model, FLUENT applies a discrete phase boundary condition to determine the fate of the trajectory at that boundary. The boundary condition, or trajectory fate, can be defined separately for each zone in your FLUENT model.

21.10.1

Discrete Phase Boundary Condition Types

The available boundary conditions, as noted in Section 21.2, include the following: • “reflect” rebounds the particle off the boundary in question with a change in its momentum as defined by the coefficient of restitution. (See Figure 21.10.1.) V2,n coefficient of = V restitution 1,n

θ1

θ 2

Figure 21.10.1: “Reflect” Boundary Condition for the Discrete Phase

The normal coefficient of restitution defines the amount of momentum in the direction normal to the wall that is retained by the particle after the collision with the boundary [262]:

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21.10 Setting Boundary Conditions for the Discrete Phase

en =

v2,n v1,n

(21.10-1)

where vn is the particle velocity normal to the wall and the subscripts 1 and 2 refer to before and after collision, respectively. Similarly, the tangential coefficient of restitution, et , defines the amount of momentum in the direction tangential to the wall that is retained by the particle. A normal or tangential coefficient of restitution equal to 1.0 implies that the particle retains all of its normal or tangential momentum after the rebound (an elastic collision). A normal or tangential coefficient of restitution equal to 0.0 implies that the particle retains none of its normal or tangential momentum after the rebound. Non-constant coefficients of restitution can be specified for wall zones with the “reflect” type boundary condition. The coefficients are set as a function of the impact angle, θ1 , in Figure 21.10.1. Note that the default setting for both coefficients of restitution is a constant value of 1.0 (all normal and tangential momentum retained). • “trap” terminates the trajectory calculations and records the fate of the particle as “trapped”. In the case of evaporating droplets, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary. See Figure 21.10.2. In the case of combusting particles, the remaining volatile mass is passed into the vapor phase.

volatile fraction flashes to vapor θ1

Figure 21.10.2: “Trap” Boundary Condition for the Discrete Phase

• “escape” reports the particle as having “escaped” when it encounters the boundary in question. Trajectory calculations are terminated. See Figure 21.10.3. • “wall-jet” means that the direction and velocity of the droplet particles are given by the resulting momentum flux, which is a function of the impingement angle, φ, and Weber number. See Figure 21.10.4. The wall-jet boundary condition assumes an analogy with an inviscid jet impacting a solid wall. Equation 21.10-2 shows the analytical solution for an axisymmetric


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particle vanishes

Figure 21.10.3: “Escape” Boundary Condition for the Discrete Phase

z y φ

H(Ψ) Ψ

x x side view

top view

Figure 21.10.4: “Wall Jet” Boundary Condition for the Discrete Phase

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21.10 Setting Boundary Conditions for the Discrete Phase

impingement assuming an empirical function for the sheet height (H) as a function of the angle that the drop leaves the impingement (Ψ). Ψ

H(Ψ) = Hπ eβ(1− π )

(21.10-2)

where Hπ is the sheet height at Ψ = π and β is a constant determined from conservation of mass and momentum. The probability that a drop leaves the impingement point at an angle between Ψ and Ψ + δΨ is given by integrating the expression for H(Ψ) π Ψ = − ln[1 − P (1 − e−β )] β

(21.10-3)

where P is a random number between 0 and 1. The expression for β is given in Naber and Reitz [180] as sin(φ) =

eβ + 1 (eβ − 1)(1 + ( βπ )2 )

(21.10-4)

The wall-jet boundary condition is appropriate for high-temperature walls where no significant liquid film is formed, and in high-Weber-number impacts where the spray acts as a jet. The model is not appropriate for regimes where film is important (e.g., port fuel injection in SI engines, rainwater runoff, etc.). • “interior” means that the particles will pass through the internal boundary. This option is available only for internal boundary zones, such as a radiator or a porous jump. It is also possible to use a user-defined function to compute the behavior of the particles at a physical boundary. See the separate UDF Manual for information about user-defined functions. Because you can stipulate any of these conditions at flow boundaries, it is possible to incorporate mixed discrete phase boundary conditions in your FLUENT model.

Default Discrete Phase Boundary Conditions FLUENT assumes the following boundary conditions: • “reflect” at wall, symmetry, and axis boundaries, with both coefficients of restitution equal to 1.0 • “escape” at all flow boundaries (pressure and velocity inlets, pressure outlets, etc.) • “interior” at all internal boundaries (radiator, porous jump, etc.) The coefficient of restitution can be modified only for wall boundaries.


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21.10.2

Inputs for Discrete Phase Boundary Conditions

Discrete phase boundary conditions can be set for boundaries in the panels opened from the Boundary Conditions panel. When one or more injections have been defined, inputs for the discrete phase will appear in the panels (e.g., Figure 21.10.5).

Figure 21.10.5: Discrete Phase Boundary Conditions in the Wall Panel

Select reflect, trap, escape, wall-jet, or user-defined in the Boundary Cond. Type drop-down list under Discrete Phase Model Conditions. (In the Walls panel, you will need to click on the DPM tab to access the Discrete Phase Model Conditions.) These conditions are described in Section 21.10.1. If you select user-defined, you can select a user-defined function in the Boundary Cond. Function drop-down list. For internal boundary zones, such as a radiator or a porous jump, you can also choose an interior boundary condition. The interior condition means that the particles will pass through the internal boundary. If you select the reflect type at a wall (only), you can define a constant, polynomial, piecewise-linear, or piecewise-polynomial function for the Normal and Tangent coefficients of restitution under Discrete Phase Reflection Coefficients. See Section 21.10.1 for details about the boundary condition types and the coefficients of restitution. The panels for defining the polynomial, piecewise-linear, and piecewise-polynomial functions are the

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21.11 Setting Material Properties for the Discrete Phase

same as those used for defining temperature-dependent properties. See Section 7.1.3 for details. If the Erosion/Accretion option is selected in the Discrete Phase Model panel, the erosion rate expression must be specified at the walls. The erosion rate is defined in Equation 21.2-62 as a product of the mass flux and specified functions for the particle diameter, impact angle, and velocity exponent. Under Erosion Model in the Wall panel, you can define a constant, polynomial, piecewise-linear, or piecewise-polynomial function for the Impact Angle Function, Diameter Function, and Velocity Exponent Function (f (α), C(dp ), and b(v) in Equation 21.2-62). See Sections 21.2.3 and 21.7.6 for a detailed description of these functions and Section 7.1.3 for details about using the panels for defining polynomial, piecewise-linear, and piecewise-polynomial functions.

21.11

Setting Material Properties for the Discrete Phase

In order to apply the physical models described in earlier sections to the prediction of the discrete phase trajectories and heat/mass transfer, FLUENT requires many physical property inputs.

21.11.1

Summary of Property Inputs

Tables 21.11.1–21.11.4 summarize which of these property inputs are used for each particle type and in which of the equations for heat and mass transfer each property input is used. Detailed descriptions of each input are provided in Section 21.11.2. Table 21.11.1: Property Inputs for Inert Particles Property Symbol density ρp in Eq. 21.2-1 specific heat cp in Eq. 21.3-3 particle emissivity p in Eq. 21.3-3 particle scattering factor f in Eq. 11.3-20 thermophoretic coefficient DT,p in Eq. 21.2-14

21.11.2

Setting Discrete-Phase Physical Properties

The Concept of Discrete-Phase Materials When you create a particle injection and define the initial conditions for the discrete phase (as described in Section 21.9), you choose a particular material as the particle’s material. All particle streams of that material will have the same physical properties. Discrete-phase materials are divided into three categories, corresponding to the three types of particles available. These material types are inert-particle, droplet-particle, and


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Table 21.11.2: Property Inputs for Droplet Particles Properties Symbol density ρp in Eq. 21.2-1 specific heat cp in Eq. 21.3-17 thermal conductivity kp in Eq. 21.2-15 viscosity µ in Eq. 21.4-49 latent heat hfg in Eq. 21.3-17 vaporization temperature Tvap in Eq. 21.3-10 boiling point Tbp in Eq. 21.3-10, 21.3-18 volatile component fraction fv0 in Eq. 21.3-11, 21.3-19 binary diffusivity Di,m in Eq. 21.3-15 saturation vapor pressure psat (T ) in Eq. 21.3-13 heat of pyrolysis hpyrol in Eq. 21.5-2 droplet surface tension σ in Eq. 21.4-18, 21.4-48 particle emissivity p in Eq. 21.3-17, 21.3-23 particle scattering factor f in Eq. 11.3-20 thermophoretic coefficient DT,p in Eq. 21.2-14

combusting-particle. Each material type will be added to the Material Type list in the Materials panel when an injection of that type of particle is defined (in the Set Injection Properties or Set Multiple Injection Properties panel, as described in Section 21.9). The first time you create an injection of each particle type, you will be able to choose a material from the database, and this will become the default material for that type of particle. That is, if you create another injection of the same type of particle, your selected material will be used for that injection as well. You may choose to modify the predefined properties for your selected particle material, if you want (as described in Section 7.1.2). If you need only one set of properties for each type of particle, you need not define any new materials; you can simply use the same material for all particles.

! If you do not find the material you want in the database, you can select a material that is close to the one you wish to use, and then modify the properties and give the material a new name, as described in Section 7.1.2.

! Note that a discrete-phase material type will not appear in the Material Type list in the Materials panel until you have defined an injection of that type of particles. This means, for example, that you cannot define or modify any combusting-particle materials until you have defined a combusting particle injection (as described in Section 21.9). Defining Additional Discrete-Phase Materials In many cases, a single set of physical properties (density, heat capacity, etc.) is appropriate for each type of discrete phase particle considered in a given model. Sometimes, however, a single model may contain two different types of inert, droplet, or combusting

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Table 21.11.3: Property Inputs for Combusting Particles (Laws 1–4) Properties Symbol density ρp in Eq. 21.2-1 specific heat cp in Eq. 21.3-3 latent heat hfg in Eq. 21.5-2 vaporization temperature Tvap = Tbp in Eq. 21.3-24 volatile component fraction fv0 in Eq. 21.3-25 swelling coefficient Csw in Eq. 21.3-57 burnout stoichiometric ratio Sb in Eq. 21.3-64 combustible fraction fcomb in Eq. 21.3-63 heat of reaction for burnout Hreac in Eq. 21.3-64 21.3-78 fraction of reaction heat given to solid fh in Eq. 21.3-78 particle emissivity p in Eq. 21.3-58, 21.3-78 particle scattering factor f in Eq. 11.3-20 thermophoretic coefficient DT,p in Eq. 21.2-14 devolatilization model –law 4, constant rate constant A0 in Eq. 21.3-26 –law 4, single rate pre-exponential factor A1 in Eq. 21.3-27 activation energy E in Eq. 21.3-27 –law 4, two rates pre-exponential factors A1 , A2 in Eq. 21.3-30, 21.3-31 activation energies E1 , E2 in Eq. 21.3-30, 21.3-31 weighting factors α1 , α2 in Eq. 21.3-32 –law 4, CPD initial fraction of bridges in coal lattice p0 in Eq. 21.3-43 initial fraction of char bridges c0 in Eq. 21.3-42 lattice coordination number σ + 1 in Eq. 21.3-54 cluster molecular weight Mw,1 in Eq. 21.3-54 side chain molecular weight Mw,δ in Eq. 21.3-53


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Table 21.11.4: Property Inputs for Combusting Particles (Law 5) Properties Symbol combustion model –law 5, diffusion rate binary diffusivity Di,m in Eq. 21.3-65 –law 5, diffusion/kinetic rate mass diffusion limited rate constant C1 in Eq. 21.3-66 kinetics limited rate pre-exp. factor C2 in Eq. 21.3-67 kinetics limited rate activ. energy E in Eq. 21.3-67 –law 5, intrinsic rate mass diffusion limited rate constant C1 in Eq. 21.3-66 kinetics limited rate pre-exp. factor Ai in Eq. 21.3-76 kinetics limited rate activ. energy Ei in Eq. 21.3-76 char porosity θ in Eq. 21.3-73 mean pore radius rp in Eq. 21.3-75 specific internal surface area Ag in Eq. 21.3-70, 21.3-72 tortuosity τ in Eq. 21.3-73 burning mode α in Eq. 21.3-77 –law 5, multiple surface reaction binary diffusivity Di,m in Eq. 21.3-65

particles (e.g., heavy particles and gaseous bubbles or two different types of evaporating liquid droplets). In such cases, it is necessary to assign a different set of properties to the two (or more) different types of particles. This is easily accomplished by defining two or more inert, droplet, or combusting particle materials and using the appropriate one for each particle injection. You can define additional discrete-phase materials either by copying them from the database or by creating them from scratch. See Section 7.1.2 for instructions on using the Materials panel to perform these actions.

! Recall that you must define at least one injection (as described in Section 21.9) containing particles of a certain type before you will be able to define additional materials for that particle type.

Description of Properties The properties that appear in the Materials panel vary depending on the particle type (selected in the Set Injection Properties or Set Multiple Injection Properties panel, as described in Sections 21.9.5 and 21.9.17) and the physical models you are using in conjunction with the discrete-phase model. Below, all properties you may need to define for a discrete-phase material are listed. See

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Tables 21.11.1–21.11.4 to see which properties are defined for each type of particle. Density is the density of the particulate phase in units of mass per unit volume of the discrete phase. This density is the mass density and not the volumetric density. Since certain particles may swell during the trajectory calculations, your input is actually an “initial” density. Cp is the specific heat, cp , of the particle. The specific heat may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Cp. See Section 7.1.3 for details about temperature-dependent properties. Thermal Conductivity is the thermal conductivity of the particle. This input is specified in units of W/m-K in SI units or Btu/ft-h-◦ F in British units and is treated as a constant by FLUENT. Latent Heat is the latent heat of vaporization, hfg , required for phase change from an evaporating liquid droplet (Equation 21.3-17) or for the evolution of volatiles from a combusting particle (Equation 21.3-58). This input is supplied in units of J/kg in SI units or of Btu/lbm in British units and is treated as a constant by FLUENT. Thermophoretic Coefficient is the coefficient DT,p in Equation 21.2-14, and appears when the thermophoretic force (which is described in Section 21.2.1) is included in the trajectory calculation (i.e., when the Thermophoretic Force option is enabled in the Discrete Phase Model panel). The default is the expression developed by Talbot [263] (talbot-diffusion-coeff) and requires no input from you. You can also define the thermophoretic coefficient as a function of temperature by selecting one of the function types from the drop-down list to the right of Thermophoretic Coefficient. See Section 7.1.3 for details about temperature-dependent properties. Vaporization Temperature is the temperature, Tvap , at which the calculation of vaporization from a liquid droplet or devolatilization from a combusting particle is initiated by FLUENT. Until the particle temperature reaches Tvap , the particle is heated via Law 1, Equation 21.3-3. This temperature input represents a modeling decision rather than any physical characteristic of the discrete phase. Boiling Point is the temperature, Tbp , at which the calculation of the boiling rate equation (21.3-20) is initiated by FLUENT. When a droplet particle reaches the boiling point, FLUENT applies Law 3 and assumes that the droplet temperature is constant at Tbp . The boiling point should be defined as the saturated vapor temperature at the system pressure that you defined in the Operating Conditions panel. Volatile Component Fraction (fv0 ) is the fraction of a droplet particle that may vaporize via Laws 2 and/or 3 (Sections 21.3.3 and 21.3.4). For combusting particles, it is the fraction of volatiles that may be evolved via Law 4 (Section 21.3.5).


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Binary Diffusivity is the mass diffusion coefficient, Di,m , used in the vaporization law, Law 2 (Equation 21.3-15). This input is also used to define the mass diffusion of the oxidizing species to the surface of a combusting particle, Di,m , as given in Equation 21.3-65. (Note that the diffusion coefficient inputs that you supply for the continuous phase are not used for the discrete phase.) Saturation Vapor Pressure is the saturated vapor pressure, psat , defined as a function of temperature, which is used in the vaporization law, Law 2 (Equation 21.3-13). The saturated vapor pressure may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of its name. (See Section 7.1.3 for details about temperature-dependent properties.) In the case of unrealistic inputs, FLUENT restricts the range of Psat to between 0.0 and the operating pressure. Correct input of a realistic vapor pressure curve is essential for accurate results from the vaporization model. Heat of Pyrolysis is the heat of the instantaneous pyrolysis reaction, hpyrol , that the evaporating/boiling species may undergo when released to the continuous phase. This input represents the conversion of the evaporating species to lighter components during the evaporation process. The heat of pyrolysis should be input as a positive number for exothermic reaction and as a negative number for endothermic reaction. The default value of zero implies that the heat of pyrolysis is not considered. This input is used in Equation 21.5-2. Swelling Coefficient is the coefficient Csw in Equation 21.3-57, which governs the swelling of the coal particle during the devolatilization law, Law 4 (Section 21.3.5). A swelling coefficient of unity (the default) implies that the coal particle stays at constant diameter during the devolatilization process. Burnout Stoichiometric Ratio is the stoichiometric requirement, Sb , for the burnout reaction, Equation 21.3-64, in terms of mass of oxidant per mass of char in the particle. Combustible Fraction is the mass fraction of char, fcomb , in the coal particle, i.e., the fraction of the initial combusting particle that will react in the surface reaction, Law 5 (Equation 21.3-63). Heat of Reaction for Burnout is the heat released by the surface char combustion reaction, Law 5 (Equation 21.3-64). This parameter is input in terms of heat release (e.g., Joules) per unit mass of char consumed in the surface reaction. React. Heat Fraction Absorbed by Solid is the parameter fh (Equation 21.3-78), which controls the distribution of the heat of reaction between the particle and the continuous phase. The default value of zero implies that the entire heat of reaction is released to the continuous phase.

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Devolatilization Model defines which version of the devolatilization model, Law 4, is being used. If you want to use the default constant rate devolatilization model, Equation 21.3-26, retain the selection of constant in the drop-down list to the right of Devolatilization Model and input the rate constant A0 in the field below the list. You can activate one of the optional devolatilization models (the single kinetic rate, two kinetic rates, or CPD model, as described in Section 21.3.5) by choosing single rate, two-competing-rates, or cpd-model in the drop-down list. When the single kinetic rate model (single-rate) is selected, the Single Rate Devolatilization Model panel will appear and you will enter the Pre-exponential Factor, A1 , and the Activation Energy, E, to be used in Equation 21.3-28 for the computation of the kinetic rate. When the two competing rates model (two-competing-rates) is selected, the Two Competing Rates Model panel will appear and you will enter, for the First Rate and the Second Rate, the Pre-exponential Factor (A1 in Equation 21.3-30 and A2 in Equation 21.3-31), Activation Energy (E1 in Equation 21.3-30 and E2 in Equation 21.3-31), and Weighting Factor (α1 and α2 in Equation 21.3-32). The constants you input are used in Equations 21.3-30 through 21.3-32. When the CPD model (cpd-model) is selected, the CPD Model panel will appear and you will enter the Initial Fraction of Bridges in Coal Lattice (p0 in Equation 21.3-43), Initial Fraction of Char Bridges (c0 in Equation 21.3-42), Lattice Coordination Number (σ + 1 in Equation 21.3-54), Cluster Molecular Weight (Mw,1 in Equation 21.3-54), and Side Chain Molecular Weight (Mw,δ in Equation 21.3-53). Note that the Single Rate Devolatilization Model, Two Competing Rates Model, and CPD Model panels are modal panels, which means that you must tend to them immediately before continuing the property definitions. Combustion Model defines which version of the surface char combustion law (Law 5) is being used. If you want to use the default diffusion-limited rate model, retain the selection of diffusion-limited in the drop-down list to the right of Combustion Model. No additional inputs are necessary, because the binary diffusivity defined above will be used in Equation 21.3-65. To use the kinetics/diffusion-limited rate model for the surface combustion model, select kinetics/diffusion-limited in the drop-down list. The Kinetics/Diffusion Limited Combustion Model panel will appear and you will enter the Mass Diffusion Limited Rate Constant (C1 in Equation 21.3-66), Kinetics Limited Rate Pre-exponential Factor (C2 in Equation 21.3-67), and Kinetics Limited Rate Activation Energy (E in Equation 21.3-67). Note that the Kinetics/Diffusion Limited Combustion Model panel is a modal panel, which means that you must tend to it immediately before continuing the property definitions. To use the intrinsic model for the surface combustion model, select intrinsic-model in the drop-down list. The Intrinsic Combustion Model panel will appear and you will


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enter the Mass Diffusion Limited Rate Constant (C1 in Equation 21.3-66), Kinetics Limited Rate Pre-exponential Factor (Ai in Equation 21.3-76), Kinetics Limited Rate Activation Energy (Ei in Equation 21.3-76), Char Porosity (θ in Equation 21.3-73), Mean Pore Radius (rp in Equation 21.3-75), Specific Internal Surface Area (Ag in Equations 21.3-70 and 21.3-72), Tortuosity (τ in Equation 21.3-73), and Burning Mode, alpha (α in Equation 21.3-77). Note that the Intrinsic Combustion Model panel is a modal panel, which means that you must tend to it immediately before continuing the property definitions. To use the multiple surface reactions model, select multiple-surface-reactions in the drop-down list. FLUENT will display a dialog box informing you that you will need to open the Reactions panel, where you can review or modify the particle surface reactions that you specified as described in Section 13.1.2.

!

If you have not yet defined any particle surface reactions, you must be sure to define them now. See Section 13.3.3 for more information about using the multiple surface reactions model. You will notice that the Burnout Stoichiometric Ratio and Heat of Reaction for Burnout are no longer available in the Materials panel, as these parameters are now computed from the particle surface reactions you defined in the Reactions panel. Note that the multiple surface reactions model is available only if the Particle Surface option for Reactions is enabled in the Species Model panel. See Section 13.3.2 for details. When the effect of particles on radiation is enabled (for the P-1 or discrete ordinates radiation model only) in the Discrete Phase Model panel, you will need to define the following additional parameters: Particle Emissivity is the emissivity of particles in your model, p , used to compute radiation heat transfer to the particles (Equations 21.3-3, 21.3-17, 21.3-23, 21.3-58, and 21.3-78) when the P-1 or discrete ordinates radiation model is active. Note that you must enable radiation to particles, using the Particle Radiation Interaction option in the Discrete Phase Model panel. Recommended values of particle emissivity are 1.0 for coal particles and 0.5 for ash [156]. Particle Scattering Factor is the scattering factor, fp , due to particles in the P-1 or discrete ordinates radiation model (Equation 11.3-20). Note that you must enable particle effects in the radiation model, using the Particle Radiation Interaction option in the Discrete Phase Model panel. The recommended value of fp for coal combustion modeling is 0.9 [156]. Note that if the effect of particles on radiation is enabled, scattering in the continuous phase will be ignored in the radiation model. When an atomizer injection model and/or the spray breakup or collision model is enabled in the Set Injection Properties panel (atomizers) and/or Discrete Phase Model panel (spray breakup/collision), you will need to define the following additional parameters:

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21.12 Calculation Procedures for the Discrete Phase

Viscosity is the droplet viscosity, µl . The viscosity may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Viscosity. See Section 7.1.3 for details about temperature-dependent properties. You also have the option of implementing a user-defined function to model the droplet viscosity. See the separate UDF Manual for information about user-defined functions. Droplet Surface Tension is the droplet surface tension, σ. The surface tension may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Droplet Surface Tension. See Section 7.1.3 for details about temperature-dependent properties. You also have the option of implementing a user-defined function to model the droplet surface tension. See the separate UDF Manual for information about user-defined functions.

21.12

Calculation Procedures for the Discrete Phase

Solution of the discrete phase implies integration in time of the force balance on the particle (Equation 21.2-1) to yield the particle trajectory. As the particle is moved along its trajectory, heat and mass transfer between the particle and the continuous phase are also computed via the heat/mass transfer laws (Section 21.3). The accuracy of the discrete phase calculation thus depends on the time accuracy of the integration and upon the appropriate coupling between the discrete and continuous phases when required. Numerical controls are described in Section 21.12.1. Coupling and performing trajectory calculations are described in Section 21.12.2. Sections 21.12.3 and 21.12.4 provide information about resetting interphase exchange terms and using the parallel solver for a discrete phase calculation.

21.12.1

Parameters Controlling the Numerical Integration

You will use two parameters to control the time integration of the particle trajectory equations: • the length scale/step length factor (unsteady) or number of particles per cell (steadystate)–used to set the time step for integration within each control volume • the maximum number of time steps–used to abort trajectory calculations when the particle never exits the flow domain Each of these parameters is set in the Discrete Phase Model panel (Figure 21.12.1) under Tracking Parameters or Spray Model. Define −→ Models −→Discrete Phase...


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Figure 21.12.1: The Discrete Phase Model Panel

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Max. Number Of Steps is the maximum number of time steps used to compute a single particle trajectory via integration of Equations 21.2-1 and 21.2-21. When the maximum number of steps is exceeded, FLUENT abandons the trajectory calculation for the current particle injection and reports the trajectory fate as “incomplete”. The limit on the number of integration time steps eliminates the possibility of a particle being caught in a recirculating region of the continuous phase flow field and being tracked infinitely. Note that you may easily create problems in which the default value of 500 time steps is insufficient for completion of the trajectory calculation. In this case, when trajectories are reported as incomplete within the domain and the particles are not recirculating indefinitely, you can increase the maximum number of steps (up to a limit of 109 ). Length Scale controls the integration time step size used to integrate the equations of motion for the particle. The integration time step is computed by FLUENT based on a specified length scale L, and the velocity of the particle (up ) and of the continuous phase (uc ): ∆t =

L up + uc

(21.12-1)

where L is the Length Scale that you define. As defined by Equation 21.12-1, L is proportional to the integration time step and is equivalent to the distance that the particle will travel before its motion equations are solved again and its trajectory is updated. A smaller value for the Length Scale increases the accuracy of the trajectory and heat/mass transfer calculations for the discrete phase. (Note that particle positions are always computed when particles enter/leave a cell; even if you specify a very large length scale, the time step used for integration will be such that the cell is traversed in one step.) Length Scale will appear in the Discrete Phase Model panel when the Specify Length Scale option is on. Step Length Factor also controls the time step size used to integrate the equations of motion for the particle. It differs from the Length Scale in that it allows FLUENT to compute the time step in terms of the number of time steps required for a particle to traverse a computational cell. To set this parameter instead of the Length Scale, turn off the Specify Length Scale option. The integration time step is computed by FLUENT based on a characteristic time that is related to an estimate of the time required for the particle to traverse the current continuous phase control volume. If this estimated transit time is defined as ∆t∗ , FLUENT chooses a time step ∆t as ∆t =


∆t∗ λ

(21.12-2)

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where λ is the Step Length Factor. As defined by Equation 21.12-2, λ is inversely proportional to the integration time step and is roughly equivalent to the number of time steps required to traverse the current continuous phase control volume. A larger value for the Step Length Factor decreases the discrete phase integration time step. The default value for the Step Length Factor is 5. Step Length Factor will appear in the Discrete Phase Model panel when the Specify Length Scale option is off (the default setting). Average Number of Particles per Cell controls the artificial “time step” size for steadystate spray cases. See Section 21.8.1 for more information. One simple rule of thumb to follow when setting the parameters above is that if you want the particles to advance through a domain consisting of N grid cells into the main flow direction, the Step Length Factor times N should be approximately equal to the Max. Number Of Steps.

! For the integration of the particle trajectories, a trapezoidal scheme is used by default (see Equations 21.2-23–21.2-25). You can switch to the simpler but less accurate scheme that was used in FLUENT 5 by using the text command define/models/dpm/ velocity-gradient-correction. Cases saved in FLUENT 5 will use this scheme by default.

21.12.2

Performing Trajectory Calculations

The trajectories of your discrete phase injections are computed when you display the trajectories using graphics or when you perform solution iterations. That is, you can display trajectories without impacting the continuous phase, or you can include their effect on the continuum (termed a coupled calculation). In turbulent flows, trajectories can be based on mean (time-averaged) continuous phase velocities or they can be impacted by instantaneous velocity fluctuations in the fluid. This section describes the procedures and commands you use to perform coupled or uncoupled trajectory calculations, with or without stochastic tracking or cloud tracking.

Uncoupled Calculations For the uncoupled calculation, you will perform the following two steps: 1. Solve the continuous phase flow field. 2. Plot (and report) the particle trajectories for discrete phase injections of interest. In the uncoupled approach, this two-step procedure completes the modeling effort, as illustrated in Figure 21.12.2. The particle trajectories are computed as they are displayed,

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continuous phase flow field calculation particle trajectory calculation Figure 21.12.2: Uncoupled Discrete Phase Calculations

based on a fixed continuous-phase flow field. Graphical and reporting options are detailed in Section 21.13. This procedure is adequate when the discrete phase is present at a low mass and momentum loading, in which case the continuous phase is not impacted by the presence of the discrete phase.

Coupled Calculations In a coupled two-phase simulation, FLUENT modifies the two-step procedure above as follows: 1. Solve the continuous phase flow field (prior to introduction of the discrete phase). 2. Introduce the discrete phase by calculating the particle trajectories for each discrete phase injection. 3. Recalculate the continuous phase flow, using the interphase exchange of momentum, heat, and mass determined during the previous particle calculation. 4. Recalculate the discrete phase trajectories in the modified continuous phase flow field. 5. Repeat the previous two steps until a converged solution is achieved in which both the continuous phase flow field and the discrete phase particle trajectories are unchanged with each additional calculation. This coupled calculation procedure is illustrated in Figure 21.12.3. When your FLUENT model includes a high mass and/or momentum loading in the discrete phase, the coupled procedure must be followed in order to include the important impact of the discrete phase on the continuous phase flow field.

! When you perform coupled calculations, all defined discrete phase injections will be computed. You cannot calculate a subset of the injections you have defined.


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continuous phase flow field calculation

particle trajectory calculation

update continuous phase source terms

Figure 21.12.3: Coupled Discrete Phase Calculations

Procedures for a Coupled Two-Phase Flow If your FLUENT model includes prediction of a coupled two-phase flow, you should begin with a partially (or fully) converged continuous-phase flow field. You will then create your injection(s) and set up the coupled calculation. For each discrete-phase iteration, FLUENT computes the particle/droplet trajectories and updates the interphase exchange of momentum, heat, and mass in each control volume. These interphase exchange terms then impact the continuous phase when the continuous phase iteration is performed. During the coupled calculation, FLUENT will perform the discrete phase iteration at specified intervals during the continuous-phase calculation. The coupled calculation continues until the continuous phase flow field no longer changes with further calculations (i.e., all convergence criteria are satisfied). When convergence is reached, the discrete phase trajectories no longer change either, since changes in the discrete phase trajectories would result in changes in the continuous phase flow field. The steps for setting up the coupled calculation are as follows: 1. Solve the continuous phase flow field. 2. In the Discrete Phase Model panel (Figure 21.12.1), enable the Interaction with Continuous Phase option. 3. Set the frequency with which the particle trajectory calculations are introduced in the Number Of Continuous Phase Iterations Per DPM Iteration field. If you set this parameter to 5, for example, a discrete phase iteration will be performed every fifth continuous phase iteration. The optimum number of iterations between trajectory calculations depends upon the physics of your FLUENT model.

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!

Note that if you set this parameter to 0, FLUENT will not perform any discrete phase iterations. During the coupled calculation (which you initiate using the Iterate panel in the usual manner) you will see the following information in the FLUENT console as the continuous and discrete phase iterations are performed: iter continuity x-velocity y-velocity k epsilon energy time/it 314 2.5249e-01 2.8657e-01 1.0533e+00 7.6227e-02 2.9771e-02 9.8181e-03 :00:05 315 2.7955e-01 2.5867e-01 9.2736e-01 6.4516e-02 2.6545e-02 4.2314e-03 :00:03 DPM Iteration .... number tracked= 9, number escaped= 1, Done. 316 1.9206e-01 1.1860e-01 6.9573e-01 317 2.0729e-01 3.2982e-02 8.3036e-01 318 3.2820e-01 5.5508e-02 6.0900e-01

aborted= 0, trapped= 0, evaporated = 8,i 5.2692e-02 2.3997e-02 2.4532e-03 :00:02 4.1649e-02 2.2111e-02 2.5369e-01 :00:01 5.9018e-02 2.6619e-02 4.0394e-02 :00:00

Note that you can perform a discrete phase calculation at any time by using the solve/dpm-update text command. Stochastic Tracking in Coupled Calculations If you include the stochastic prediction of turbulent dispersion in the coupled two-phase flow calculations, the number of stochastic tries applied each time the discrete phase trajectories are introduced during coupled calculations will be equal to the Number of Tries specified in the Set Injection Properties panel. Input of this parameter is described in Section 21.9.15. Note that the number of tries should be set to 0 if you want to perform the coupled calculation based on the mean continuous phase flow field. An input of n ≥ 1 requests n stochastic trajectory calculations for each particle in the injection. Note that when the number of stochastic tracks included is small, you may find that the ensemble average of the trajectories is quite different each time the trajectories are computed. These differences may, in turn, impact the convergence of your coupled solution. For this reason, you should include an adequate number of stochastic tracks in order to avoid convergence troubles in coupled calculations. Under-Relaxation of the Interphase Exchange Terms When you are coupling the discrete and continuous phases for steady-state calculations, using the calculation procedures noted above, FLUENT applies under-relaxation to the momentum, heat, and mass transfer terms. This under-relaxation serves to increase the


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stability of the coupled calculation procedure by letting the impact of the discrete phase change only gradually: Enew = Eold + α(Ecalculated − Eold )

(21.12-3)

where Enew is the exchange term, Eold is the previous value, Ecalculated is the newly computed value, and α is the particle/droplet under-relaxation factor. FLUENT uses a default value of 0.5 for α. You can modify α by changing the value in the Discrete Phase Sources field under Under-Relaxation Factors in the Solution Controls panel. You may need to decrease α in order to improve the stability of coupled discrete phase calculations.

21.12.3

Resetting the Interphase Exchange Terms

If you have performed coupled calculations, resulting in non-zero interphase sources/sinks of momentum, heat, and/or mass that you do not want to include in subsequent calculations, you can reset these sources to zero. Solve −→ Initialize −→Reset DPM Sources When you select the Reset DPM Sources menu item, the sources will immediately be reset to zero without any further confirmation from you.

21.12.4

Parallel Processing for the Discrete Phase Model

FLUENT offers two modes of parallel processing for the discrete phase model: the Shared Memory and the Message Passing options under Parallel in the Discrete Phase Model panel. The Shared Memory option is turned on by default and is suitable for computations where the machine running the FLUENT host process is an adequately-large, shared-memory, multiprocessor machine. The Message Passing option is suitable for generic distributed memory cluster computing. The Shared Memory option is implemented using POSIX Threads (pthreads) based on a shared memory model. You use this option by turning on the Workpile Algorithm and specifying the Number of Threads. By default, the Number of Threads is equal to the number of compute nodes specified for the parallel computation. You can modify this value based on the computational requirements of the particle calculations. If, for example, the particle calculations require more computation than the flow calculation, you can increase the Number of Threads (up to the number of available processors) to improve performance. When using the Shared Memory option, the particle calculations are entirely managed by the FLUENT host process. You must make sure that the machine executing the host process has enough memory to accommodate the entire grid.

! Note that the Shared Memory option is not available for Windows 2000. The Message Passing option enables cluster computing and also works on shared memory machines. With this option, the compute node processes themselves perform the particle

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21.13 Postprocessing for the Discrete Phase

work on their local partitions and particle migration to other compute nodes is implemented using message passing primitives. No special requirements are placed on the host machine. Note that this model is not available if the Cloud Model option is turned on under the Turbulent Dispersion tab of the Set Injection Properties panel. The Message Passing option is irrelevant for the serial FLUENT code while the Shared Memory option remains valid. You may seamlessly switch between the Shared Memory option and the Message Passing option at any time during the FLUENT session.

21.13

Postprocessing for the Discrete Phase

After you have completed your discrete phase inputs and any coupled two-phase calculations of interest, you can display and store the particle trajectory predictions. FLUENT provides both graphical and alphanumeric reporting facilities for the discrete phase, including the following: • Graphical display of the particle trajectories • Summary reports of trajectory fates • Step-by-step reports of the particle position, velocity, temperature, and diameter • Alphanumeric reports and graphical display of the interphase exchange of momentum, heat, and mass • Sampling of trajectories at boundaries and lines/planes • Summary reporting of current particles in the domain • Histograms of trajectory data at sample planes • Display of erosion/accretion rates This section provides detailed descriptions of each of these postprocessing options. (Note that plotting or reporting trajectories does not change the source terms.)

21.13.1

Graphical Display of Trajectories

When you have defined discrete phase particle injections, as described in Section 21.9, you can display the trajectories of these discrete particles using the Particle Tracks panel (Figure 21.13.1). Display −→Particle Tracks... The procedure for drawing trajectories for particle injections is as follows:


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Figure 21.13.1: The Particle Tracks Panel

1. Select the particle injection(s) you wish to track in the Release From Injections list. (You can choose to track a specific particle, instead, as described below.) 2. Set the length scale and the maximum number of steps in the Discrete Phase Model panel, as described in Section 21.12.1. Define −→ Models −→Discrete Phase... If stochastic and/or cloud tracking is desired, set the related parameters in the Set Injection Properties panel, as described in Section 21.9.15. 3. Set any of the display options described below. 4. Click on the Display button to draw the trajectories or click on the Pulse button to animate the particle positions. The Pulse button will become the Stop ! button during the animation, and you must click on Stop ! to stop the pulsing.

!

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For unsteady particle tracking simulations, clicking on Display will show only the current location of the particles. Typically, you should select point in the Style dropdown list when displaying transient particle locations since individual positions will be displayed. The Pulse button option is not available for unsteady tracking.



Specifying Individual Particles for Display It is also possible to display the trajectory for an individual particle stream instead of for all the streams in a given injection. To do so, you will first need to determine which particle is of interest. Use the Injections panel to list the particle streams in the desired injection, as described in Section 21.9.4. Define −→Injections... Note the ID numbers listed in the first column of the listing printed in the FLUENT console. Then perform the following steps after step 1 above: 1. Enable the Track Single Particle Stream option in the Particle Tracks panel. 2. In the Stream ID field, specify the ID number of the particle stream for which you want to plot the trajectory.

Options for Particle Trajectory Plots The options mentioned above include the following: You can include the grid in the trajectory display, control the style of the trajectories (including the twisting of ribbonstyle trajectories), and color them by different scalar fields and control the color scale. You can also choose node or cell values for display. If you are “pulsing” the trajectories, you can control the pulse mode. Finally, you can generate an XY plot of the particle trajectory data (e.g., residence time) as a function of time or path length and save this XY plot data to a file. These options are controlled in exactly the same way that pathline-plotting options are controlled. See Section 27.1.4 for details about setting the trajectory plotting options mentioned above. Note that in addition to coloring the trajectories by continuous phase variables, you can also color them according to the following discrete phase variables: particle time, particle velocity, particle diameter, particle density, particle mass, particle temperature, particle law number, particle time step, and particle Reynolds number. These variables are included in the Particle Variables... category of the Color By list. To display the minimum and maximum values in the domain, click the Update Min/Max button.

Graphical Display in Axisymmetric Geometries For axisymmetric problems in which the particle has a non-zero circumferential velocity component, the trajectory of an individual particle is often a spiral about the centerline of rotation. FLUENT displays the r and x components of the trajectory (but not the θ component) projected in the axisymmetric plane.


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21.13.2

Reporting of Trajectory Fates

When you perform trajectory calculations by displaying the trajectories (as described in Section 21.13.1), FLUENT will provide information about the trajectories as they are completed. By default, the number of trajectories with each possible fate (escaped, aborted, evaporated, etc.) is reported: DPM Iteration .... num. tracked = 7, escaped = 4, aborted = 0, trapped = 0, evaporated = 3, inco Done.

You can also track particles through the domain without displaying the trajectories by clicking on the Track button at the bottom of the panel. This allows the listing of reports without also displaying the tracks.

Trajectory Fates The possible fates for a particle trajectory are as follows: • “Escaped” trajectories are those that terminate at a flow boundary for which the “escape” condition is set. • “Incomplete” trajectories are those that were terminated when the maximum allowed number of time steps—as defined by the Max. Number Of Steps input in the Discrete Phase Model panel (see Section 21.12.1)—was exceeded. • “Trapped” trajectories are those that terminate at a flow boundary where the “trap” condition has been set. • “Evaporated” trajectories include those trajectories along which the particles were evaporated within the domain. • “Aborted” trajectories are those that fail to complete due to roundoff reasons. You may want to retry the calculation with a modified length scale and/or different initial conditions.

Summary Reports You can request additional detail about the trajectory fates as the particles exit the domain, including the mass flow rates through each boundary zone, mass flow rate of evaporated droplets, and composition of the particles. 1. Follow steps 1 and 2 in Section 21.13.1 for displaying trajectories.

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2. Select Summary as the Report Type and click Display or Track. A detailed report similar to the following example will appear in the console window. (You may also choose to write this report to a file by selecting File as the Report to option, clicking on the Write... button (which was originally the Display button), and specifying a file name for the summary report file in the resulting Select File dialog box.)

DPM Iteration .... num. tracked = 10, escaped = 8, aborted = 0, trapped = 0, evaporated = 0, inc Fate

Number

---Incomplete Escaped - Zone 7

-----2 8

Elapsed Time (s) Min Max Avg Std Dev ---------- ---------- ---------- ---------- --1.485e+01 2.410e+01 1.947e+01 4.623e+00 4.940e+00 2.196e+01 1.226e+01 4.871e+00

(*)- Mass Transfer Summary -(*) Fate ---Incomplete Escaped - Zone 7

Mass Flow (kg/s) Initial Final Change ---------- ---------- ---------1.388e-03 1.943e-04 -1.194e-03 1.502e-03 2.481e-04 -1.254e-03 (*)- Energy Transfer Summary -(*)

Fate ---Incomplete Escaped - Zone 7

Heat Content (W) Initial Final Change ---------- ---------- ---------4.051e+02 3.088e+02 -9.630e+01 4.383e+02 3.914e+02 -4.696e+01 (*)- Combusting Particles -(*)

Fate ---Incomplete Escaped - Zone 7

Volatile Content (kg/s) Initial Final %Conv ---------- ---------- ------6.247e-04 0.000e+00 100.00 6.758e-04 0.000e+00 100.00

Char Content (kg/s) Initial Final ---------- ---------- -5.691e-04 0.000e+00 1 6.158e-04 3.782e-05

Done.

The report groups together particles with each possible fate, and reports the number of particles, the time elapsed during trajectories, and the mass and energy transfer. This


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information can be very useful for obtaining information such as where particles are escaping from the domain, where particles are colliding with surfaces, and the extent of heat and mass transfer to/from the particles within the domain. Additional information is reported for combusting particles. Elapsed Time The number of particles with each fate is listed under the Number heading. (Particles that escape through different zones or are trapped at different zones are considered to have different fates, and are therefore listed separately.) The minimum, maximum, and average time elapsed during the trajectories of these particles, as well as the standard deviation about the average time, are listed in the Min, Max, Avg, and Std Dev columns. This information indicates how much time the particle(s) spent in the domain before they escaped, aborted, evaporated, or were trapped. Fate

Number


-----2 8

Elapsed Time (s) Min Max Avg Std Dev ---------- ---------- ---------- ---------- --1.485e+01 2.410e+01 1.947e+01 4.623e+00 4.940e+00 2.196e+01 1.226e+01 4.871e+00

Also, on the right side of the report are listed the injection name and index of the trajectories with the minimum and maximum elapsed times. (You may need to use the scroll bar to view this information.)

Elapsed Time (s) Injection, Index Min Max Avg Std Dev Min Max --- ---------- ---------- ---------- -------------------- -----------------+01 2.410e+01 1.947e+01 4.623e+00 injection-0 1 injection-0 0 +00 2.196e+01 1.226e+01 4.871e+00 injection-0 9 injection-0 2

Mass Transfer Summary For all droplet or combusting particles with each fate, the total initial and final mass flow rates and the change in mass flow rate are reported in the Initial, Final, and Change columns. With this information, you can determine how much mass was transferred to the continuous phase from the particles.

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(*)- Mass Transfer Summary -(*) Fate

Mass Flow (kg/s) Initial Final Change ---------- ---------- ---------1.388e-03 1.943e-04 -1.194e-03 1.502e-03 2.481e-04 -1.254e-03


Energy Transfer Summary For all particles with each fate, the total initial and final heat content and the change in heat content are reported in the Initial, Final, and Change columns. This report tells you how much heat was transferred from the continuous phase to the particles. (*)- Energy Transfer Summary -(*) Fate ---Incomplete Escaped - Zone 7

Heat Content (W) Initial Final Change ---------- ---------- ---------4.051e+02 3.088e+02 -9.630e+01 4.383e+02 3.914e+02 -4.696e+01

Combusting Particles If combusting particles are present, FLUENT will include additional reporting on the volatiles and char converted. These reports are intended to help you identify the composition of the combusting particles as they exit the computational domain. (*)- Combusting Particles -(*) Fate

Volatile Content (kg/s) Initial Final %Conv ------------- ---------- ------Incomplete 6.247e-04 0.000e+00 100.00 Escaped - Zone 7 6.758e-04 0.000e+00 100.00

Char Content (kg/s) Initial Final %Conv ---------- ---------- ------5.691e-04 0.000e+00 100.00 6.158e-04 3.782e-05 93.86

The total volatile content at the start and end of the trajectory is reported in the Initial and Final columns under Volatile Content. The percentage of volatiles that has been devolatilized is reported in the %Conv column. The total reactive portion (char) at the start and end of the trajectory is reported in the Initial and Final columns under Char Content. The percentage of char that reacted is reported in the %Conv column.


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Combusting Particle with the Multiple Surface Reaction Model If the multiple surface reaction model is used with combusting particles, FLUENT will include additional reporting on the mass of the individual solid species that constitute the particle mass. (*)- Multiple Surface Reactions -(*) Fate ---Escaped Escaped Escaped Escaped Escaped

-

Zone Zone Zone Zone Zone

6 6 6 6 6

Species Names ------c s cao caso4 caco3

Species Content (kg/s) Initial Final %Conv ---------- ---------- ------6.080e-02 1.487e-06 100.00 3.200e-03 5.077e-06 99.84 0.000e+00 1.153e-03 0.00 0.000e+00 9.266e-04 0.00 8.000e-03 5.260e-03 34.25

The total mass of each solid species in the particles at the start and end of the trajectory is reported in the Initial and Final columns, respectively. The percentage of each species that is reacted is reported in the %Conv column. Note that for the solid reaction products (e.g., if the mass of a solid species has increased in the particle), the conversion is reported to be 0.

21.13.3

Step-by-Step Reporting of Trajectories

At times, you may want to obtain a detailed, step-by-step report of the particle trajectory/trajectories. Such reports can be obtained in alphanumeric format. This capability allows you to monitor the particle position, velocity, temperature, or diameter as the trajectory proceeds. The procedure for generating files containing step-by-step reports is listed below: 1. Follow steps 1 and 2 in Section 21.13.1 for displaying trajectories. You may want to track only one particle at a time, using the Track Single Particle Stream option. 2. Select Step By Step as the Report Type. 3. Select File as the Report to option. (The Display button will become the Write... button.) 4. In the Significant Figures field, enter the number of significant figures to be used in the step-by-step report.

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5. Click on the Write... button and specify a file name for the step-by-step report file in the resulting Select File dialog box. A detailed report similar to the following example will be saved to the specified file before the trajectories are plotted. (You may also choose to print the report in the console by choosing Console as the Report to option and clicking on Display or Track, but the report is so long that it is unlikely to be of use to you in that form.) The step-by-step report lists the particle position and velocity of the particle at selected time steps along the trajectory: Time 0.000e+00 3.773e-05 5.403e-05 9.181e-05 1.296e-04 1.608e-04 . . .

X-Position 1.411e-03 2.411e-03 2.822e-03 3.822e-03 4.821e-03 5.644e-03 . . .

Y-Position 3.200e-03 3.200e-03 3.192e-03 3.192e-03 3.192e-03 3.192e-03 . . .

Z-Velocity 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 . . .

X-Velocity 2.650e+01 2.648e+01 2.647e+01 2.644e+01 2.642e+01 2.639e+01 . . .

Y-Velocity 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 . . .

Z-Veloc 0.000e 0.000e 0.000e 0.000e 0.000e 0.000e . . .

Also listed are the diameter, temperature, density, and mass of the particle. (You may need to use the scroll bar to view this information.) X-Velocity 650e+01 648e+01 647e+01 644e+01 642e+01 639e+01 . . .

21.13.4



Diameter Temperature 2.000e-04 3.000e+02 2.000e-04 3.006e+02 2.000e-04 3.009e+02 2.000e-04 3.015e+02 2.000e-04 3.022e+02 2.000e-04 3.027e+02 . . . . . .

Density 1.30e+03 1.30e+03 1.30e+03 1.30e+03 1.30e+03 1.30e+03 . . .

Mass 5.445e-09 5.445e-09 5.445e-09 5.445e-09 5.445e-09 5.445e-09 . . .

Reporting Current Positions for Unsteady Tracking

When using unsteady tracking, you may want to obtain a report of the particle trajectory/trajectories showing the current positions of the particles. Selecting Current Positions


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under Report Type in the ParticleTracks panel enables the display of the current positions of the particles. The procedure for generating files containing current position reports is listed below: 1. Follow steps 1 and 2 in Section 21.13.1 for displaying trajectories. You may want to track only one particle stream at a time, using the Track Single Particle Stream option. 2. Select Current Position as the Report Type. 3. Select File as the Report to option. (The Display button will become the Write... button.) 4. In the Significant Figures field, enter the number of significant figures to be used in the step-by-step report. 5. Click on the Write... button and specify a file name for the current position report file in the resulting Select File dialog box. The current position report lists the positions and velocities of all particles that are currently in the domain: Time 0.000e+00 1.672e-05 3.342e-05 5.010e-05 6.675e-05 8.338e-05 . . .

X-Position 1.000e-03 1.168e-03 1.337e-03 1.508e-03 1.680e-03 1.854e-03 . . .

Y-Position 3.120e-02 3.128e-02 3.137e-02 3.145e-02 3.153e-02 3.161e-02 . . .

Z-Position 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 . . .

X-Velocity 1.000e+01 1.010e+01 1.019e+01 1.028e+01 1.038e+01 1.047e+01 . . .


Z-Veloc 0.000e 0.000e 0.000e 0.000e 0.000e 0.000e . . .

Also listed are the diameter, temperature, density, and mass of the particles. (You may need to use the scroll bar to view this information.)

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elocity 000e+01 010e+01 019e+01 028e+01 038e+01 047e+01 . . .

21.13.5



Diameter Temperature 7.000e-05 3.000e+02 7.000e-05 3.009e+02 7.000e-05 3.019e+02 7.000e-05 3.028e+02 7.000e-05 3.037e+02 7.000e-05 3.046e+02 . . . . . .

Density Mass 1.300e+03 2.335e-10 1.300e+03 2.335e-10 1.300e+03 2.335e-10 1.300e+03 2.335e-10 1.300e+03 2.335e-10 1.300e+03 2.335e-10 . . . . . .

Reporting of Interphase Exchange Terms and Discrete Phase Concentration

FLUENT reports the magnitudes of the interphase exchange of momentum, heat, and mass in each control volume in your FLUENT model. It can also report the total concentration of the discrete phase. You can display these variables graphically, by drawing contours, profiles, etc. They are all contained in the Discrete Phase Model... category of the variable selection drop-down list that appears in postprocessing panels: • DPM Concentration • DPM Mass Source • DPM X,Y,Z Momentum Source • DPM Swirl Momentum Source • DPM Sensible Enthalpy Source • DPM Enthalpy Source • DPM Absorption Coefficient • DPM Emission • DPM Scattering • DPM Burnout • DPM Evaporation/Devolatilization • DPM (species) Source • DPM Erosion


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• DPM Accretion • DPM (species) Concentration See Chapter 29 for definitions of these variables. Note that these exchange terms are updated and displayed only when coupled calculations are performed. Displaying and reporting particle trajectories (as described in Sections 21.13.1 and 21.13.2) will not affect the values of these exchange terms.

21.13.6

Trajectory Sampling

Particle states (position, velocity, diameter, temperature, and mass flow rate) can be written to files at various boundaries and planes (lines in 2D) using the Sample Trajectories panel (Figure 21.13.2). Report −→ Discrete Phase −→Sample...

Figure 21.13.2: The Sample Trajectories Panel The procedure for generating files containing the particle samples is listed below: 1. Select the injections to be tracked in the Release From Injections list. 2. Select the surfaces at which samples will be written. These can be boundaries from the Boundaries list or planes from the Planes list (in 3D) or lines from the Lines list (in 2D).

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3. Click on the Compute button. Note that for unsteady particle tracking, the Compute button will become the Start button (to initiate sampling) or a Stop button (to stop sampling). Clicking on the Compute button will cause the particles to be tracked and their status to be written to files when they encounter selected surfaces. The file names will be formed by appending .dpm to the surface name. For unsteady particle tracking, clicking on the Start button will open the files and write the file header sections. If the solution is advanced in time by computing some time steps, the particle trajectories will be updated and the particle states will be written to the files as they cross the selected planes or boundaries. Clicking on the Stop button will close the files and end the sampling. For stochastic tracking, it may be useful to repeat this process multiple times and append the results to the same file, while monitoring the sample statistics at each update. To do this, enable the Append Files option before repeating the calculation (clicking on Compute). Similarly, you can cause erosion and accretion rates to be accumulated for repeated trajectory calculations by turning on the Accumulate Erosion/Accretion Rates option. (See also Section 21.13.9.) The format and the information written for the sample output can also be controlled through a user-defined function, which can be selected in the Output drop-down list. See the separate UDF Manual for information about user-defined functions.

21.13.7

Histogram Reporting of Samples

Histograms can be plotted from sample files created in the Sample Trajectories panel (as described in Section 21.13.6) using the Trajectory Sample Histograms panel (Figure 21.13.3). Report −→ Discrete Phase −→Histogram... The procedure for plotting histograms from data in a sample file is listed below: 1. Select a file to be read by clicking on the Read... button. After you read in the sample file, the boundary name will appear in the Sample list. 2. Select the data sample in the Sample list, and then select the data to be plotted from the Fields list. 3. Click on the Plot button at the bottom of the panel to display the histogram. By default, the percent of particles will be plotted on the y axis. You can plot the actual number of particles by deselecting Percent under Options. The number of “bins” or intervals in the plot can be set in the Divisions field. You can delete samples from the list with the Delete button and update the Min/Max values with the Compute button.


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Figure 21.13.3: The Trajectory Sample Histograms Panel

21.13.8

Summary Reporting of Current Particles

For many mass-transfer and flow processes, it is desirable to know the mean diameter of the particles. A mean diameter, Djk , is calculated from the particle size distribution using the following general expression [132]:

j−k

(Djk )

Z

≡

∞

Z 0∞

Dj f (D)dD (21.13-1) Dk f (D)dD

0

where j and k are integers and f (D) is the distribution function (e.g., Rosin-Rammler). D10 , for example, is the average (arithmetic) particle diameter. The Sauter mean diameter (SMD), D32 , is the diameter of a particle whose ratio of volume to surface area is equal to that of all particles in the computation. A summary of common mean diameters is given in Table 21.13.1. Summary information (number, mass, average diameter) for particles currently in the computational domain can be reported using the Particle Summary panel (Figure 21.13.4). Report −→ Discrete Phase −→Summary... The procedure for reporting a summary for particle injections is as follows: 1. Select the particle injection(s) for which you want to generate a summary in the Injections list. FLUENT provides a shortcut for selecting injections with names that match a specified pattern. To use this shortcut, enter the pattern under Injection Name Pattern

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j 1 2 3 2 3 3 4

Table 21.13.1: Common Mean Diameters and Their Fields of Application Order k j + k Name Field of Application 0 1 Mean diameter, D10 Comparisons, evaporation 0 2 Mean surface diameter, D20 Absorption 0 3 Mean volume diameter, D30 Hydrology 1 3 Overall surface diameter, D21 Adsorption 1 4 Overall volume diameter, D31 Evaporation, molecular diffusion 2 5 Sauter mean diameter, D32 Combustion, mass transfer, and efficiency studies 3 7 De Brouckere diameter, D43 Combustion equilibrium

Figure 21.13.4: The Particle Summary Panel


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and then click Match to select the injections with names that match the specified pattern. For example, if you specify drop*, all injections that have names beginning with drop (e.g., drop-1, droplet) will be selected automatically. If they are all selected already, they will be deselected. If you specify drop?, all surfaces with names consisting of drop followed by a single character will be selected (or deselected, if they are all selected already). 2. Click Summary to display the injection summary in the console window.

(*)- Summary for Injection: injection-0 -(*) Total number of parcels : Total number of particles : Total mass : Maximum RMS distance from injector : Maximum particle diameter : Minimum particle diameter : Overall mean diameter (D_10): Overall mean surface area (D_20): Overall mean volume (D_30): Overall surface diameter (D_21): Overall volume diameter (D_31): Overall Sauter diameter (D_32): Overall De Brouckere diameter (D_43):

21.13.9

29 1.030517e+06 2.172738e-06 7.768444e-02 8.131158e-05 1.929668e-06 1.003256e-05 1.827063e-10 4.601987e-15 1.821133e-05 4.587050e-10 2.518790e-05 3.335674e-05

(kg) (m) (m) (m) (m) (m^2) (m^3) (m) (m^2) (m) (m)

Postprocessing of Erosion/Accretion Rates

You can calculate the erosion and accretion rates in a cumulative manner (over a series of injections) by using the Sample Trajectories panel. First select an injection in the Release From Injections list and compute its trajectory. Then turn on the Accumulate Erosion/Accretion Rates option, select the next injection (after deselecting the first one), and click Compute again. The rates will accumulate at the surfaces each time you click Compute.

! Both the erosion rate and the accretion rate are defined at wall face surfaces only, so they cannot be displayed at node values.

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Chapter 22.

General Multiphase Models

This chapter discusses the general multiphase models that are available in FLUENT. Chapter 20 provides a brief introduction to multiphase modeling, Chapter 21 discusses the Lagrangian dispersed phase model, and Chapter 23 describes FLUENT’s model for solidification and melting. • Section 22.1: Choosing a General Multiphase Model • Section 22.2: Volume of Fluid (VOF) Model • Section 22.3: Mixture Model • Section 22.4: Eulerian Model • Section 22.5: Description of Mass Transfer • Section 22.6: Setting Up a General Multiphase Problem • Section 22.7: Solution Strategies for General Multiphase Problems • Section 22.8: Postprocessing for General Multiphase Problems


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22.1

Choosing a General Multiphase Model

As discussed in Section 20.4, the VOF model is appropriate for stratified or free-surface flows, and the mixture and Eulerian models are appropriate for flows in which the phases mix or separate and/or dispersed-phase volume fractions exceed 10%. (Flows in which the dispersed-phase volume fractions are less than or equal to 10% can be modeled using the discrete phase model described in Chapter 21.) To choose between the mixture model and the Eulerian model, you should consider the following, in addition to the detailed guidelines in Section 20.4: • If there is a wide distribution of the dispersed phases, the mixture model may be preferable (i.e. less computationally expensive). If the dispersed phases are concentrated just in portions of the domain, you should use the Eulerian model instead. • If interphase drag laws that are applicable to your system are available (either within FLUENT or through a user-defined function), the Eulerian model can usually provide more accurate results than the mixture model. Even though you can apply the same drag laws to the mixture model, as you can for a non-granular Eulerian simulation, if the interphase drag laws are unknown or their applicability to your system is questionable, the mixture model may be a better choice. • If you want to solve a simpler problem, which requires less computational effort, the mixture model may be a better option, since it solves a smaller number of equations than the Eulerian model. If accuracy is more important than computational effort, the Eulerian model is a better choice. Keep in mind, however, that the complexity of the Eulerian model can make it less computationally stable than the mixture model. Brief overviews of the three models, including their limitations, are provided in Sections 22.1.1, 22.1.2, and 22.1.3. Detailed descriptions of the models are provided in Sections 22.2, 22.3, and 22.4.

22.1.1

Overview and Limitations of the VOF Model

Overview The VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. Typical applications include the prediction of jet breakup, the motion of large bubbles in a liquid, the motion of liquid after a dam break, and the steady or transient tracking of any liquid-gas interface.

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22.1 Choosing a General Multiphase Model

Limitations The following restrictions apply to the VOF model in FLUENT: • You must use the segregated solver. The VOF model is not available with either of the coupled solvers. • All control volumes must be filled with either a single fluid phase or a combination of phases; the VOF model does not allow for void regions where no fluid of any type is present. • Only one of the phases can be compressible. • Streamwise periodic flow (either specified mass flow rate or specified pressure drop) cannot be modeled when the VOF model is used. • Species mixing and reacting flow cannot be modeled when the VOF model is used. • The LES turbulence model cannot be used with the VOF model. • The second-order implicit time-stepping formulation cannot be used with the VOF model. • The VOF model cannot be used for inviscid flows. • The shell conduction model for walls cannot be used with the VOF model.

Steady-State and Transient VOF Calculations The VOF formulation in FLUENT is generally used to compute a time-dependent solution, but for problems in which you are concerned only with a steady-state solution, it is possible to perform a steady-state calculation. A steady-state VOF calculation is sensible only when your solution is independent of the initial conditions and there are distinct inflow boundaries for the individual phases. For example, since the shape of the free surface inside a rotating cup depends on the initial level of the fluid, such a problem must be solved using the time-dependent formulation. On the other hand, the flow of water in a channel with a region of air on top and a separate air inlet can be solved with the steady-state formulation.

22.1.2

Overview and Limitations of the Mixture Model

Overview The mixture model is a simplified multiphase model that can be used to model multiphase flows where the phases move at different velocities, but assume local equilibrium over short spatial length scales. The coupling between the phases should be strong. It can


22-3


also be used to model homogeneous multiphase flows with very strong coupling and the phases moving at the same velocity. The mixture model can model n phases (fluid or particulate) by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. Typical applications include sedimentation, cyclone separators, particle-laden flows with low loading, and bubbly flows where the gas volume fraction remains low. The mixture model is a good substitute for the full Eulerian multiphase model in several cases. A full multiphase model may not be feasible when there is a wide distribution of the particulate phase or when the interphase laws are unknown or their reliability can be questioned. A simpler model like the mixture model can perform as well as a full multiphase model while solving a smaller number of variables than the full multiphase model.

Limitations The following limitations apply to the mixture model in FLUENT: • You must use the segregated solver. The mixture model is not available with either of the coupled solvers. • Only one of the phases can be compressible. • Streamwise periodic flow with specified mass flow rate cannot be modeled when the mixture model is used (the user is allowed to specify a pressure drop). • Species mixing and reacting flow cannot be modeled when the mixture model is used. • Solidification and melting cannot be modeled in conjunction with the mixture model. • The LES turbulence model cannot be used with the mixture model. • The second-order implicit time-stepping formulation cannot be used with the mixture model. • The mixture model cannot be used for inviscid flows. • The shell conduction model for walls cannot be used with the mixture model.

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22.1 Choosing a General Multiphase Model

22.1.3

Overview and Limitations of the Eulerian Model

Overview The Eulerian multiphase model in FLUENT allows for the modeling of multiple separate, yet interacting phases. The phases can be liquids, gases, or solids in nearly any combination. An Eulerian treatment is used for each phase, in contrast to the EulerianLagrangian treatment that is used for the discrete phase model. With the Eulerian multiphase model, the number of secondary phases is limited only by memory requirements and convergence behavior. Any number of secondary phases can be modeled, provided that sufficient memory is available. For complex multiphase flows, however, you may find that your solution is limited by convergence behavior. See Section 22.7.3 for multiphase modeling strategies. FLUENT’s Eulerian multiphase model differs from the Eulerian model in FLUENT 4 in that there is no global distinction between fluid-fluid and fluid-solid (granular) multiphase flows. A granular flow is simply one that involves at least one phase that has been designated as a granular phase. The FLUENT solution is based on the following: • A single pressure is shared by all phases. • Momentum and continuity equations are solved for each phase. • The following parameters are available for granular phases: – Granular temperature (solids fluctuating energy) can be calculated for each solid phase. This is based on an algebraic relation. – Solid-phase shear and bulk viscosities are obtained from application of kinetic theory to granular flows. Frictional viscosity is also available. • Several interphase drag coefficient functions are available, which are appropriate for various types of multiphase regimes. (You can also modify the interphase drag coefficient through user-defined functions, as described in the separate UDF Manual.) • All of the k- turbulence models are available, and may apply to all phases or to the mixture.

Limitations All other features available in FLUENT can be used in conjunction with the Eulerian multiphase model, except for the following limitations:


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• Only the k- models can be used for turbulence. • Particle tracking (using the Lagrangian dispersed phase model) interacts only with the primary phase. • Streamwise periodic flow with specified mass flow rate cannot be modeled when the Eulerian model is used (the user is allowed to specify a pressure drop). • Compressible flow is not allowed. • Inviscid flow is not allowed. • The second-order implicit time-stepping formulation cannot be used with the Eulerian model. • Melting and solidification are not allowed. • Species transport and reactions are not allowed.

Stability and Convergence The process of solving a multiphase system is inherently difficult, and you may encounter some stability or convergence problems, although the current algorithm is more stable than that used in FLUENT 4. If a time-dependent problem is being solved, and patched fields are used for the initial conditions, it is recommended that you perform a few iterations with a small time step, at least an order of magnitude smaller than the characteristic time of the flow. You can increase the size of the time step after performing a few time steps. For steady solutions it is recommended that you start with a small under-relaxation factor for the volume fraction. Another option is to start with a mixture multiphase calculation, and then switch to the Eulerian multiphase model. Stratified flows of immiscible fluids should be solved with the VOF model (see Section 22.2). Some problems involving small volume fractions can be solved more efficiently with the Lagrangian discrete phase model (see Chapter 21). Many stability and convergence problems can be minimized if care is taken during the setup and solution processes (see Section 22.7.3).

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22.2 Volume of Fluid (VOF) Model

22.2

Volume of Fluid (VOF) Model

The VOF formulation relies on the fact that two or more fluids (or phases) are not interpenetrating. For each additional phase that you add to your model, a variable is introduced: the volume fraction of the phase in the computational cell. In each control volume, the volume fractions of all phases sum to unity. The fields for all variables and properties are shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location. Thus the variables and properties in any given cell are either purely representative of one of the phases, or representative of a mixture of the phases, depending upon the volume fraction values. In other words, if the qth fluid’s volume fraction in the cell is denoted as αq , then the following three conditions are possible: • αq = 0: the cell is empty (of the qth fluid). • αq = 1: the cell is full (of the qth fluid) • 0 < αq < 1: the cell contains the interface between the qth fluid and one or more other fluids. Based on the local value of αq , the appropriate properties and variables will be assigned to each control volume within the domain.

22.2.1

The Volume Fraction Equation

The tracking of the interface(s) between the phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the qth phase, this equation has the following form: Sα ∂αq + ~v · ∇αq = q ∂t ρq

(22.2-1)

By default, the source term on the right-hand side of Equation 22.2-1 is zero, but you can specify a constant or user-defined mass source for each phase. See Section 22.5 for more information on the modeling of mass transfer in FLUENT’s general multiphase models. The volume fraction equation will not be solved for the primary phase; the primary-phase volume fraction will be computed based on the following constraint: n X

αq = 1

(22.2-2)

q=1


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22.2.2

Properties

The properties appearing in the transport equations are determined by the presence of the component phases in each control volume. In a two-phase system, for example, if the phases are represented by the subscripts 1 and 2, and if the volume fraction of the second of these is being tracked, the density in each cell is given by ρ = α2 ρ2 + (1 − α2 )ρ1

(22.2-3)

In general, for an n-phase system, the volume-fraction-averaged density takes on the following form: ρ=

X

αq ρq

(22.2-4)

All other properties (e.g., viscosity) are computed in this manner.

22.2.3

The Momentum Equation

A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the phases. The momentum equation, shown below, is dependent on the volume fractions of all phases through the properties ρ and µ. h i ∂ (ρ~v ) + ∇ · (ρ~v~v ) = −∇p + ∇ · µ ∇~v + ∇~v T + ρ~g + F~ ∂t

(22.2-5)

One limitation of the shared-fields approximation is that in cases where large velocity differences exist between the phases, the accuracy of the velocities computed near the interface can be adversely affected.

22.2.4

The Energy Equation

The energy equation, also shared among the phases, is shown below. ∂ (ρE) + ∇ · (~v (ρE + p)) = ∇ · (keff ∇T ) + Sh ∂t

(22.2-6)

The VOF model treats energy, E, and temperature, T , as mass-averaged variables: n X

E=

αq ρq Eq

q=1 n X

(22.2-7) αq ρq

q=1

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where Eq for each phase is based on the specific heat of that phase and the shared temperature. The properties ρ and keff (effective thermal conductivity) are shared by the phases. The source term, Sh , contains contributions from radiation, as well as any other volumetric heat sources. As with the velocity field, the accuracy of the temperature near the interface is limited in cases where large temperature differences exist between the phases. Such problems also arise in cases where the properties vary by several orders of magnitude. For example, if a model includes liquid metal in combination with air, the conductivities of the materials can differ by as much as four orders of magnitude. Such large discrepancies in properties lead to equation sets with anisotropic coefficients, which in turn can lead to convergence and precision limitations.

22.2.5

Additional Scalar Equations

Depending upon your problem definition, additional scalar equations may be involved in your solution. In the case of turbulence quantities, a single set of transport equations is solved, and the turbulence variables (e.g., k and or the Reynolds stresses) are shared by the phases throughout the field.

22.2.6

Interpolation Near the Interface

FLUENT’s control-volume formulation requires that convection and diffusion fluxes through the control volume faces be computed and balanced with source terms within the control volume itself. There are four schemes in FLUENT for the calculation of face fluxes for the VOF model: geometric reconstruction, donor-acceptor, Euler explicit, and implicit. In the geometric reconstruction and donor-acceptor schemes, FLUENT applies a special interpolation treatment to the cells that lie near the interface between two phases. Figure 22.2.1 shows an actual interface shape along with the interfaces assumed during computation by these two methods. The Euler explicit scheme and the implicit scheme treat these cells with the same interpolation as the cells that are completely filled with one phase or the other (i.e., using the standard upwind, second-order, or QUICK scheme), rather than applying a special treatment.

The Geometric Reconstruction Scheme In the geometric reconstruction approach, the standard interpolation schemes that are used in FLUENT are used to obtain the face fluxes whenever a cell is completely filled with one phase or another. When the cell is near the interface between two phases, the geometric reconstruction scheme is used.


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actual interface shape

interface shape represented by the geometric reconstruction (piecewise-linear) scheme

interface shape represented by the donor-acceptor scheme

Figure 22.2.1: Interface Calculations

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The geometric reconstruction scheme represents the interface between fluids using a piecewise-linear approach. In FLUENT this scheme is the most accurate and is applicable for general unstructured meshes. The geometric reconstruction scheme is generalized for unstructured meshes from the work of Youngs [300]. It assumes that the interface between two fluids has a linear slope within each cell, and uses this linear shape for calculation of the advection of fluid through the cell faces. (See Figure 22.2.1.) The first step in this reconstruction scheme is calculating the position of the linear interface relative to the center of each partially-filled cell, based on information about the volume fraction and its derivatives in the cell. The second step is calculating the advecting amount of fluid through each face using the computed linear interface representation and information about the normal and tangential velocity distribution on the face. The third step is calculating the volume fraction in each cell using the balance of fluxes calculated during the previous step.

! When the geometric reconstruction scheme is used, a time-dependent solution must be computed. Also, if you are using a conformal grid (i.e., if the grid node locations are identical at the boundaries where two subdomains meet), you must ensure that there are no two-sided (zero-thickness) walls within the domain. If there are, you will need to slit them, as described in Section 5.7.8.

The Donor-Acceptor Scheme In the donor-acceptor approach, the standard interpolation schemes that are used in FLUENT are used to obtain the face fluxes whenever a cell is completely filled with one phase or another. When the cell is near the interface between two phases, a “donoracceptor” scheme is used to determine the amount of fluid advected through the face [104]. This scheme identifies one cell as a donor of an amount of fluid from one phase and another (neighbor) cell as the acceptor of that same amount of fluid, and is used to prevent numerical diffusion at the interface. The amount of fluid from one phase that can be convected across a cell boundary is limited by the minimum of two values: the filled volume in the donor cell or the free volume in the acceptor cell. The orientation of the interface is also used in determining the face fluxes. The interface orientation is either horizontal or vertical, depending on the direction of the volume fraction gradient of the qth phase within the cell, and that of the neighbor cell that shares the face in question. Depending on the interface’s orientation as well as its motion, flux values are obtained by pure upwinding, pure downwinding, or some combination of the two.

! When the donor-acceptor scheme is used, a time-dependent solution must be computed. Also, the donor-acceptor scheme can be used only with quadrilateral or hexahedral meshes. In addition, if you are using a conformal grid (i.e., if the grid node locations are identical at the boundaries where two subdomains meet), you must ensure that there are no two-sided (zero-thickness) walls within the domain. If there are, you will need to slit


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them, as described in Section 5.7.8.

The Euler Explicit Scheme In the Euler explicit approach, FLUENT’s standard finite-difference interpolation schemes are applied to the volume fraction values that were computed at the previous time step. X αqn+1 − αqn n V + (Ufn αq,f )=0 ∆t f

where

(22.2-8)

n + 1 = index for new (current) time step n = index for previous time step αq,f = face value of the qth volume fraction, computed from the firstor second-order upwind or QUICK scheme V = volume of cell Uf = volume flux through the face, based on normal velocity

This formulation does not require iterative solution of the transport equation during each time step, as is needed for the implicit scheme.

! When the Euler explicit scheme is used, a time-dependent solution must be computed. The Implicit Scheme In the implicit interpolation method, FLUENT’s standard finite-difference interpolation schemes are used to obtain the face fluxes for all cells, including those near the interface. X αqn+1 − αqn n+1 V + (Ufn+1 αq,f )=0 ∆t f

(22.2-9)

Since this equation requires the volume fraction values at the current time step (rather than at the previous step, as for the Euler explicit scheme), a standard scalar transport equation is solved iteratively for each of the secondary-phase volume fractions at each time step. The implicit scheme can be used for both time-dependent and steady-state calculations. See Section 22.6.4 for details.

22.2.7

Time Dependence

For time-dependent VOF calculations, Equation 22.2-1 is solved using an explicit timemarching scheme. FLUENT automatically refines the time step for the integration of the volume fraction equation, but you can influence this time step calculation by modifying the Courant number. You can choose to update the volume fraction once for each time

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step, or once for each iteration within each time step. These options are discussed in more detail in Section 22.6.14.

22.2.8

Surface Tension and Wall Adhesion

The VOF model can also include the effects of surface tension along the interface between each pair of phases. The model can be augmented by the additional specification of the contact angles between the phases and the walls. You can specify a surface tension coefficient as a constant, as a function of temperature, or through a UDF. The solver will include the additional tangential stress terms (causing what is termed as Marangoni convection) that arise due to the variation in surface tension coefficient. Variable surface tension coefficient effects are usually important only in zero/near-zero gravity conditions.

Surface Tension Surface tension arises as a result of attractive forces between molecules in a fluid. Consider an air bubble in water, for example. Within the bubble, the net force on a molecule due to its neighbors is zero. At the surface, however, the net force is radially inward, and the combined effect of the radial components of force across the entire spherical surface is to make the surface contract, thereby increasing the pressure on the concave side of the surface. The surface tension is a force, acting only at the surface, that is required to maintain equilibrium in such instances. It acts to balance the radially inward intermolecular attractive force with the radially outward pressure gradient force across the surface. In regions where two fluids are separated, but one of them is not in the form of spherical bubbles, the surface tension acts to minimize free energy by decreasing the area of the interface. The surface tension model in FLUENT is the continuum surface force (CSF) model proposed by Brackbill et al. [27]. With this model, the addition of surface tension to the VOF calculation results in a source term in the momentum equation. To understand the origin of the source term, consider the special case where the surface tension is constant along the surface, and where only the forces normal to the interface are considered. It can be shown that the pressure drop across the surface depends upon the surface tension coefficient, σ, and the surface curvature as measured by two radii in orthogonal directions, R1 and R2 : 1 1 p2 − p1 = σ + R1 R2

(22.2-10)

where p1 and p2 are the pressures in the two fluids on either side of the interface. In FLUENT, a formulation of the CSF model is used, where the surface curvature is computed from local gradients in the surface normal at the interface. Let n be the surface normal, defined as the gradient of αq , the volume fraction of the qth phase.


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n = ∇αq

(22.2-11)

The curvature, κ, is defined in terms of the divergence of the unit normal, n ˆ [27]: κ=∇·n ˆ

(22.2-12)

where n ˆ=

n |n|

(22.2-13)

The surface tension can be written in terms of the pressure jump across the surface. The force at the surface can be expressed as a volume force using the divergence theorem. It is this volume force that is the source term which is added to the momentum equation. It has the following form: Fvol =

X

pairs ij, i 1000

(22.3-12)

and the acceleration ~a is of the form ~a = ~g − (~vm · ∇)~vm −

∂~vm ∂t

(22.3-13)

The simplest algebraic slip formulation is the so-called drift flux model, in which the acceleration of the particle is given by gravity and/or a centrifugal force and the particulate relaxation time is modified to take into account the presence of other particles. Note that when you are solving a mixture multiphase calculation with slip velocity, you can directly prescribe formulations for the drag function. Available choices are: • Schiller-Naumann (the default formulation) • Morsi-Alexander

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22.3 Mixture Model

• Symmetric • Constant • User-Defined See Section 22.4.3 for more information on these drag functions and their formulations, and Section 22.6.10 for instructions on how to enable them. Note that, if the slip velocity is not solved, the mixture model is reduced to a homogeneous multiphase model. In addition, the mixture model can be customized (using user-defined functions) to use a formulation other than the algebraic slip method for the slip velocity. See the separate UDF Manual for details.

22.3.5

Volume Fraction Equation for the Secondary Phases

From the continuity equation for secondary phase p, the volume fraction equation for secondary phase p can be obtained: ∂ (αp ρp ) + ∇ · (αp ρp~vm ) = −∇ · (αp ρp~vdr,p ) ∂t


(22.3-14)

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22.4

Eulerian Model

To change from a single-phase model, where a single set of conservation equations for momentum, continuity and (optionally) energy is solved, to a multiphase model, additional sets of conservation equations must be introduced. In the process of introducing additional sets of conservation equations, the original set must also be modified. The modifications involve, among other things, the introduction of the volume fractions α1 , α2 , . . . αn for the multiple phases, as well as mechanisms for the exchange of momentum, heat, and mass between the phases. Details about the Eulerian multiphase model are presented in the following subsections: • Section 22.4.1: Volume Fractions • Section 22.4.2: Conservation Equations • Section 22.4.3: Interphase Exchange Coefficients • Section 22.4.4: Solids Pressure • Section 22.4.5: Solids Shear Stresses • Section 22.4.6: Granular Temperature • Section 22.4.7: Description of Heat Transfer • Section 22.4.8: Turbulence Models • Section 22.4.9: Solution Method in FLUENT

22.4.1

Volume Fractions

The description of multiphase flow as interpenetrating continua incorporates the concept of phasic volume fractions, denoted here by αq . Volume fractions represent the space occupied by each phase, and the laws of conservation of mass and momentum are satisfied by each phase individually. The derivation of the conservation equations can be done by ensemble averaging the local instantaneous balance for each of the phases [3] or by using the mixture theory approach [24]. The volume of phase q, Vq , is defined by Vq =

Z

V

αq dV

(22.4-1)

where

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22.4 Eulerian Model

n X

αq = 1

(22.4-2)

ρˆq = αq ρq

(22.4-3)

q=1

The effective density of phase q is

where ρq is the physical density of phase q.

22.4.2

Conservation Equations

The general conservation equations from which the equations solved by FLUENT are derived are presented in this section, followed by the solved equations themselves.

Equations in General Form Conservation of Mass The continuity equation for phase q is n X ∂ (αq ρq ) + ∇ · (αq ρq~vq ) = m ˙ pq ∂t p=1

(22.4-4)

where ~vq is the velocity of phase q and m ˙ pq characterizes the mass transfer from the pth to q th phase. From the mass conservation one can obtain m ˙ pq = −m ˙ qp

(22.4-5)

m ˙ pp = 0

(22.4-6)

and

By default, the source term on the right-hand side of Equation 22.4-4 is zero, but you can specify a constant or user-defined mass source for each phase. A similar term appears in the momentum and enthalpy equations. See Section 22.5 for more information on the modeling of mass transfer in FLUENT’s general multiphase models.


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Conservation of Momentum The momentum balance for phase q yields ∂ (αq ρq~vq ) + ∇ · (αq ρq~vq~vq ) = −αq ∇p + ∇ · τ q + αq ρq~g + ∂t n X

~ pq + m (R ˙ pq~vpq ) + αq ρq (F~q + F~lift,q + F~vm,q )

(22.4-7)

p=1

where τ q is the q th phase stress-strain tensor 2 τ q = αq µq (∇~vq + ∇~vqT ) + αq (λq − µq )∇ · ~vq I 3

(22.4-8)

Here µq and λq are the shear and bulk viscosity of phase q, F~q is an external body force, ~ pq is an interaction force between F~lift,q is a lift force, F~vm,q is a virtual mass force, R phases, and p is the pressure shared by all phases. ~vpq is the interphase velocity, defined as follows. If m ˙ pq > 0 (i.e., phase p mass is being transferred to phase q), ~vpq = ~vp ; if m ˙ pq < 0 (i.e., phase q mass is being transferred to phase p), ~vpq = ~vq ; and ~vpq = ~vqp . ~ pq . Equation 22.4-7 must be closed with appropriate expressions for the interphase force R This force depends on the friction, pressure, cohesion, and other effects, and is subject ~ pq = −R ~ qp and R ~ qq = 0. to the conditions that R FLUENT uses a simple interaction term of the following form: n X

p=1

~ pq = R

n X

Kpq (~vp − ~vq )

(22.4-9)

p=1

where Kpq (= Kqp ) is the interphase momentum exchange coefficient (described in Section 22.4.3). Lift Forces For multiphase flows, FLUENT can include the effect of lift forces on the secondary phase particles (or droplets or bubbles). These lift forces act on a particle mainly due to velocity gradients in the primary-phase flow field. The lift force will be more significant for larger particles, but the FLUENT model assumes that the particle diameter is much smaller than the interparticle spacing. Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles. The lift force acting on a secondary phase p in a primary phase q is computed from [63]

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22.4 Eulerian Model

F~lift = −0.5ρq αp (~vq − ~vp ) × (∇ × ~vq )

(22.4-10)

The lift force F~lift will be added to the right-hand side of the momentum equation for both phases (F~lift,q = −F~lift,p ). In most cases, the lift force is insignificant compared to the drag force, so there is no reason to include this extra term. If the lift force is significant (e.g., if the phases separate quickly), it may be appropriate to include this term. By default, F~lift is not included. The lift force and lift coefficient can be specified for each pair of phases, if desired. Virtual Mass Force For multiphase flows, FLUENT includes the “virtual mass effect” that occurs when a secondary phase p accelerates relative to the primary phase q. The inertia of the primaryphase mass encountered by the accelerating particles (or droplets or bubbles) exerts a “virtual mass force” on the particles [63]: dq~vq dp~vp F~vm = 0.5αp ρq − dt dt The term

dq dt

!

(22.4-11)

denotes the phase material time derivative of the form dq (φ) ∂(φ) = + (~vq · ∇)φ dt ∂t

(22.4-12)

The virtual mass force F~vm will be added to the right-hand side of the momentum equation for both phases (F~vm,q = −F~vm,p ). The virtual mass effect is significant when the secondary phase density is much smaller than the primary phase density (e.g., for a transient bubble column). By default, F~vm is not included. Conservation of Energy To describe the conservation of energy in Eulerian multiphase applications, a separate enthalpy equation can be written for each phase:

n X ∂ ∂pq ~ pq +m (αq ρq hq )+∇·(αq ρq ~uq hq ) = −αq +τ q : ∇~uq −∇·~qq +Sq + (Q ˙ pq hpq ) (22.4-13) ∂t ∂t p=1

where hq is the specific enthalpy of the q th phase, ~qq is the heat flux, Sq is a source term that includes sources of enthalpy (e.g., due to chemical reaction or radiation), Qpq is


22-23


the intensity of heat exchange between the pth and q th phases, and hpq is the interphase enthalpy (e.g., the enthalpy of the vapor at the temperature of the droplets, in the case of evaporation). The heat exchange between phases must comply with the local balance conditions Qpq = −Qqp and Qqq = 0.

Equations Solved by FLUENT The equations for fluid-fluid and granular multiphase flows, as solved by FLUENT, are presented here for the general case of an n-phase flow. Continuity Equation The volume fraction of each phase is calculated from a continuity equation: 

n X



∂ 1  dq ρq  (αq ) + ∇ · (αq~vq ) = m ˙ pq − αq ∂t ρq p=1 dt

(22.4-14)

The solution of this equation for each secondary phase, along with the condition that the volume fractions sum to one (given by Equation 22.4-2), allows for the calculation of the primary-phase volume fraction. This treatment is common to fluid-fluid and granular flows. Fluid-Fluid Momentum Equations The conservation of momentum for a fluid phase q is ∂ (αq ρq~vq ) + ∇ · (αq ρq~vq~vq ) = −αq ∇p + ∇ · τ q + αq ρq~g + ∂t αq ρq (F~q + F~lift,q + F~vm,q ) +

n X

(Kpq (~vp − ~vq ) + m ˙ pq~vpq )

(22.4-15)

p=1

Here ~g is the acceleration due to gravity and τ q , F~q , F~lift,q , and F~vm,q are as defined for Equation 22.4-7. Fluid-Solid Momentum Equations Following the work of [2, 35, 55, 86, 143, 158, 184, 261], FLUENT uses a multi-fluid granular model to describe the flow behavior of a fluid-solid mixture. The solid-phase stresses are derived by making an analogy between the random particle motion arising from particle-particle collisions and the thermal motion of molecules in a gas, taking into account the inelasticity of the granular phase. As is the case for a gas, the intensity of the particle velocity fluctuations determines the stresses, viscosity, and pressure of the solid phase. The kinetic energy associated with the particle velocity fluctuations is represented

22-24


22.4 Eulerian Model

by a “pseudothermal” or granular temperature which is proportional to the mean square of the random motion of particles. The conservation of momentum for the fluid phases is similar to Equation 22.4-15, and that for the sth solid phase is ∂ (αs ρs~vs ) + ∇ · (αs ρs~vs~vs ) = −αs ∇p − ∇ps + ∇ · τ s + αs ρs~g + ∂t αs ρs (F~s + F~lift,s + F~vm,s ) +

N X

(Kls (~vl − ~vs ) + m ˙ ls~vls )

(22.4-16)

l=1

where ps is the sth solids pressure, Kls = Ksl is the momentum exchange coefficient between fluid or solid phase l and solid phase s, N is the total number of phases, and F~q , F~lift,q , and F~vm,q are as defined for Equation 22.4-7. Conservation of Energy The equation solved by FLUENT for the conservation of energy is Equation 22.4-13.

22.4.3

Interphase Exchange Coefficients

It can be seen in Equations 22.4-15 and 22.4-16 that momentum exchange between the phases is based on the value of the fluid-fluid exchange coefficient Kpq and, for granular flows, the fluid-solid and solid-solid exchange coefficients Kls .

Fluid-Fluid Exchange Coefficient For fluid-fluid flows, each secondary phase is assumed to form droplets or bubbles. This has an impact on how each of the fluids is assigned to a particular phase. For example, in flows where there are unequal amounts of two fluids, the predominant fluid should be modeled as the primary fluid, since the sparser fluid is more likely to form droplets or bubbles. The exchange coefficient for these types of bubbly, liquid-liquid or gas-liquid mixtures can be written in the following general form: Kpq =

αq αp ρp f τp

(22.4-17)

where f , the drag function, is defined differently for the different exchange-coefficient models (as described below) and τp , the “particulate relaxation time”, is defined as ρp d2p τp = 18µq

(22.4-18)

where dp is the diameter of the bubbles or droplets of phase p.


22-25


Nearly all definitions of f include a drag coefficient (CD ) that is based on the relative Reynolds number (Re). It is this drag function that differs among the exchange-coefficient models. For all these situations, Kpq should tend to zero whenever the primary phase is not present within the domain. To enforce this, the drag function f is always multiplied by the volume fraction of the primary phase q, as is reflected in Equation 22.4-17. • For the model of Schiller and Naumann [225] f=

CD Re 24

(22.4-19)

where CD =

(

24(1 + 0.15 Re0.687 )/Re Re ≤ 1000 0.44 Re > 1000

(22.4-20)

and Re is the relative Reynolds number. The relative Reynolds number for the primary phase q and secondary phase p is obtained from Re =

ρq |~vp − ~vq |dp µq

(22.4-21)

The relative Reynolds number for secondary phases p and r is obtained from Re =

ρrp |~vr − ~vp |drp µrp

(22.4-22)

where µrp = αp µp + αr µr is the mixture viscosity of the phases p and r. The Schiller and Naumann model is the default method, and it is acceptable for general use for all fluid-fluid pairs of phases. • For the Morsi and Alexander model [177] f=

CD Re 24

(22.4-23)

where CD = a1 +

a2 a3 + 2 Re Re

(22.4-24)

and Re is defined by Equation 22.4-21 or 22.4-22. The a’s are defined as follows:

22-26


22.4 Eulerian Model

  0, 18, 0     3.690, 22.73, 0.0903      1.222, 29.1667, −3.8889    

a1 , a 2 , a 3 =              

0 < Re < 0.1 0.1 < Re < 1 1 < Re < 10 0.6167, 46.50, −116.67 10 < Re < 100 0.3644, 98.33, −2778 100 < Re < 1000 0.357, 148.62, −47500 1000 < Re < 5000 0.46, −490.546, 578700 5000 < Re < 10000 0.5191, −1662.5, 5416700 Re ≥ 10000

(22.4-25)

The Morsi and Alexander model is the most complete, adjusting the function definition frequently over a large range of Reynolds numbers, but calculations with this model may be less stable than with the other models. • For the symmetric model Kpq =

αp (αp ρp + αq ρq )f τpq

(22.4-26)

where τpq

q 2 (αp ρp + αq ρq )( dp +d ) 2 = 18(αp µp + αq µq )

(22.4-27)

and f=

CD Re 24

(22.4-28)

where CD =

(

24(1 + 0.15 Re0.687 )/Re Re ≤ 1000 0.44 Re > 1000

(22.4-29)

and Re is defined by Equation 22.4-21 or 22.4-22. The symmetric model is recommended for flows in which the secondary (dispersed) phase in one region of the domain becomes the primary (continuous) phase in another. For example, if air is injected into the bottom of a container filled halfway with water, the air is the dispersed phase in the bottom half of the container; in the top half of the container, the air is the continuous phase. This model can also be used for the interaction between secondary phases. You can specify different exchange coefficients for each pair of phases. It is also possible to use user-defined functions to define exchange coefficients for each pair of phases. If the


22-27


exchange coefficient is equal to zero (i.e., if no exchange coefficient is specified), the flow fields for the fluids will be computed independently, with the only “interaction” being their complementary volume fractions within each computational cell.

Fluid-Solid Exchange Coefficient The fluid-solid exchange coefficient Ksl can be written in the following general form: Ksl =

αs ρs f τs

(22.4-30)

where f is defined differently for the different exchange-coefficient models (as described below), and τs , the “particulate relaxation time”, is defined as τs =

ρs d2s 18µl

(22.4-31)

where ds is the diameter of particles of phase s. All definitions of f include a drag function (CD ) that is based on the relative Reynolds number (Res ). It is this drag function that differs among the exchange-coefficient models. • For the Syamlal-O’Brien model [260] f=

CD Res αl 2 24vr,s

(22.4-32)

where the drag function has a form derived by Dalla Valle [50] 

4.8

2

 CD = 0.63 + q Res /vr,s

(22.4-33)

This model is based on measurements of the terminal velocities of particles in fluidized or settling beds, with correlations that are a function of the volume fraction and relative Reynolds number [214]: Res =

ρl ds |~vs − ~vl | µl

(22.4-34)

where the subscript l is for the lth fluid phase, s is for the sth solid phase, and ds is the diameter of the sth solid phase particles. The fluid-solid exchange coefficient has the form

22-28


22.4 Eulerian Model

!

3αs αl ρl Res Ksl = CD |~vs − ~vl | 2 4vr,s ds vr,s

(22.4-35)

where vr,s is the terminal velocity correlation for the solid phase [82]:

vr,s = 0.5 A − 0.06 Res +

q

2

(0.06 Res ) + 0.12 Res (2B − A) +

A2

(22.4-36)

with A = αl4.14

(22.4-37)

B = 0.8αl1.28

(22.4-38)

B = αl2.65

(22.4-39)

and

for αl ≤ 0.85, and

for αl > 0.85. This model is appropriate when the solids shear stresses are defined according to Syamlal et al. [261] (Equation 22.4-53). • For the model of Wen and Yu [289], the fluid-solid exchange coefficient is of the following form: 3 αs αl ρl |~vs − ~vl | −2.65 Ksl = CD αl 4 ds

(22.4-40)

where CD =

i 24 h 1 + 0.15(αl Res )0.687 αl Res

(22.4-41)

and Res is defined by Equation 22.4-34. This model is appropriate for dilute systems. • The Gidaspow model [86] is a combination of the Wen and Yu model [289] and the Ergun equation [70]. When αl > 0.8, the fluid-solid exchange coefficient Ksl is of the following form:


22-29


αs αl ρl |~vs − ~vl | −2.65 3 Ksl = CD αl 4 ds

(22.4-42)

where CD =

i 24 h 1 + 0.15(αl Res )0.687 αl Res

(22.4-43)

αs (1 − αl )µl ρl αs |~vs − ~vl | + 1.75 2 αl ds ds

(22.4-44)

When αl ≤ 0.8, Ksl = 150

This model is recommended for dense fluidized beds.

Solid-Solid Exchange Coefficient The solid-solid exchange coefficient Kls has the following form [259]:

Kls =

3 (1 + els )

π 2

2

+ Cfr,ls π8 αs ρs αl ρl (dl + ds )2 g0,ls 2π (ρl d3l + ρs d3s )

|~vl − ~vs |

(22.4-45)

where els Cfr,ls dl g0,ls

22.4.4

= the coefficient of restitution (described in Section 22.4.4) = the coefficient of friction between the lth and sth solid-phase particles (Cfr,ls = 0) = the diameter of the particles of solid l = the radial distribution coefficient (described in Section 22.4.4)

Solids Pressure

For granular flows in the compressible regime (i.e., where the solids volume fraction is less than its maximum allowed value), a solids pressure is calculated independently and used for the pressure gradient term, ∇ps , in the granular-phase momentum equation. Because a Maxwellian velocity distribution is used for the particles, a granular temperature is introduced into the model, and appears in the expression for the solids pressure and viscosities. The solids pressure is composed of a kinetic term and a second term due to particle collisions: ps = αs ρs Θs + 2ρs (1 + ess )αs2 g0,ss Θs

(22.4-46)

where ess is the coefficient of restitution for particle collisions, g0,ss is the radial distribution function, and Θs is the granular temperature. FLUENT uses a default value of 0.9

22-30


22.4 Eulerian Model

for ess , but the value can be adjusted to suit the particle type. The granular temperature Θs is proportional to the kinetic energy of the fluctuating particle motion, and will be described later in this section. The function g0,ss (described below in more detail) is a distribution function that governs the transition from the “compressible” condition with α < αs,max , where the spacing between the solid particles can continue to decrease, to the “incompressible” condition with α = αs,max , where no further decrease in the spacing can occur. A value of 0.63 is the default for αs,max , but you can modify it during the problem setup.

Radial Distribution Function The radial distribution function, g0 , is a correction factor that modifies the probability of collisions between grains when the solid granular phase becomes dense. This function may also be interpreted as the non-dimensional distance between spheres: g0 =

s + dp s

(22.4-47)

where s is the distance between grains. From Equation 22.4-47 it can be observed that for a dilute solid phase s → ∞, and therefore g0 → 1. In the limit when the solid phase compacts, s → 0 and g0 → ∞. The radial distribution function is closely connected to the factor χ of Chapman and Cowling’s [35] theory of non-uniform gases. χ is equal to one for a rare gas, and increases and tends to infinity when the molecules are so close together that motion is not possible. In the literature there is no unique formulation for the radial distribution function. FLUENT employs that proposed in [184]: 

g0 = 1 −

αs αs,max

! 1 −1 3 

(22.4-48)

When the number of solid phases is greater than 1, Equation 22.4-48 is extended to 

g0,ll = 1 −

αl αl,max

! 1 −1 3 

(22.4-49)

where αl,max is specified by you during the problem setup, and g0,lm =


dm g0,ll + dl g0,mm dm + dl

(22.4-50)

22-31


22.4.5

Solids Shear Stresses

The solids stress tensor contains shear and bulk viscosities arising from particle momentum exchange due to translation and collision. A frictional component of viscosity can also be included to account for the viscous-plastic transition that occurs when particles of a solid phase reach the maximum solid volume fraction. The collisional and kinetic parts, and the optional frictional part, are added to give the solids shear viscosity: µs = µs,col + µs,kin + µs,fr

(22.4-51)

Collisional Viscosity The collisional part of the shear viscosity is modeled as [86, 261] 4 Θs µs,col = αs ρs ds g0,ss (1 + ess ) 5 π

1/2

(22.4-52)

Kinetic Viscosity FLUENT provides two expressions for the kinetic part. The default expression is from Syamlal et al. [261]:

µs,kin

√ αs ds ρs Θs π 2 = 1 + (1 + ess ) (3ess − 1) αs g0,ss 6 (3 − ess ) 5

(22.4-53)

The following optional expression from Gidaspow et al. [86] is also available:

µs,kin

√ 2 10ρs ds Θs π 4 = 1 + g0,ss αs (1 + ess ) 96αs (1 + ess ) g0,ss 5

(22.4-54)

Bulk Viscosity The solids bulk viscosity accounts for the resistance of the granular particles to compression and expansion. It has the following form from Lun et al. [158]: 4 Θs λs = αs ρs ds g0,ss (1 + ess ) 3 π

1/2

(22.4-55)

Note that the bulk viscosity is set to a constant value of zero, by default. It is also possible to select the Lun et al. expression or use a user-defined function.

22-32


22.4 Eulerian Model

Frictional Viscosity In dense flow at low shear, where the secondary volume fraction for a solid phase nears the packing limit, the generation of stress is mainly due to friction between particles. The solids shear viscosity computed by FLUENT does not, by default, account for the friction between particles. If the frictional viscosity is included in the calculation, FLUENT uses Schaeffer’s [223] expression: ps sin φ µs,fr = √ 2 I2D

(22.4-56)

where ps is the solids pressure, φ is the angle of internal friction, and I2D is the second invariant of the deviatoric stress tensor. It is also possible to specify a constant or userdefined frictional viscosity.

22.4.6

Granular Temperature

The granular temperature for the sth solids phase is proportional to the kinetic energy of the random motion of the particles. The transport equation derived from kinetic theory takes the form [55]

"

#

3 ∂ (ρs αs Θs ) + ∇ · (ρs αs~vs Θs ) = (−ps I+τ s ) : ∇~vs +∇·(kΘs ∇Θs )−γΘs +φls (22.4-57) 2 ∂t where (−ps I + τ s ) : ∇~vs kΘs ∇Θs γΘs φls

= = = =

the generation of energy by the solid stress tensor the diffusion of energy (kΘs is the diffusion coefficient) the collisional dissipation of energy the energy exchange between the lth fluid or solid phase and the sth solid phase

Equation 22.4-57 contains the term kΘs ∇Θs describing the diffusive flux of granular energy. When the default Syamlal et al. model [261] is used, the diffusion coefficient for granular energy, kΘs is given by

kΘs

√ 15ds ρs αs Θs π 12 16 = 1 + η 2 (4η − 3)αs g0,ss + (41 − 33η)ηαs g0,ss ) 4(41 − 33η) 5 15π

(22.4-58)

where


22-33


1 η = (1 + ess ) 2 FLUENT uses the following expression if the optional model of Gidaspow et al. [86] is enabled:

kΘs

q

s 2 150ρs ds (Θπ) 6 Θs 2 = 1 + αs g0,ss (1 + es ) + 2ρs αs ds (1 + ess )g0,ss 384(1 + ess )g0,ss 5 π

(22.4-59)

The collisional dissipation of energy, γΘs , represents the rate of energy dissipation within the sth solids phase due to collisions between particles. This term is represented by the expression derived by Lun et al. [158] γΘm =

12(1 − e2ss )g0,ss √ ρs αs2 Θ3/2 s ds π

(22.4-60)

The transfer of the kinetic energy of random fluctuations in particle velocity from the sth solids phase to the lth fluid or solid phase is represented by φls [86]: φls = −3Kls Θs

(22.4-61)

FLUENT currently uses an algebraic relation for the granular temperature. This has been obtained by neglecting convection and diffusion in the transport equation, Equation 22.4-57 [261].

22.4.7

Description of Heat Transfer

The internal energy balance for phase q is written in terms of the phase enthalpy, Equation 22.4-13, defined by Hq = cp,q dTq

(22.4-62)

where cp,q is the specific heat at constant pressure of phase q. The thermal boundary conditions used with multiphase flows are the same as those for a single-phase flow. See Chapter 6 for details.

22-34


22.4 Eulerian Model

The Heat Exchange Coefficient The rate of energy transfer between phases is assumed to be a function of the temperature difference Qpq = hpq (Tp − Tq )

(22.4-63)

where hpq (= hqp ) is the heat transfer coefficient between the pth phase and the q th phase. The heat transfer coefficient is related to the pth phase Nusselt number, Nup , by hpq =

6κq αp αq Nup dp 2

(22.4-64)

Here κq is the thermal conductivity of the q th phase. The Nusselt number is typically determined from one of the many correlations reported in the literature. In the case of fluid-fluid multiphase, FLUENT uses the correlation of Ranz and Marshall [205, 206]: 1/3 Nup = 2.0 + 0.6Re1/2 p Pr

(22.4-65)

where Rep is the relative Reynolds number based on the diameter of the pth phase and the relative velocity |u~p − u~q |, and Pr is the Prandtl number of the q th phase: Pr =

c p q µq κq

(22.4-66)

In the case of granular flows (where p = s), FLUENT uses a Nusselt number correlation by Gunn [94], applicable to a porosity range of 0.35–1.0 and a Reynolds number of up to 105 :

1/3 1/3 (22.4-67) Nus = (7 − 10αf + 5αf2 )(1 + 0.7Re0.2 ) + (1.33 − 2.4αf + 1.2αf2 )Re0.7 s Pr s Pr

The Prandtl number is defined as above with q = f . For all these situations, hpq should tend to zero whenever one of the phases is not present within the domain. To enforce this, hpq is always multiplied by the volume fraction of the primary phase q, as reflected in Equation 22.4-64.

22.4.8

Turbulence Models

To describe the effects of turbulent fluctuations of velocities and scalar quantities in a single phase, FLUENT uses various types of closure models, as described in Chapter 10. In comparison to single-phase flows, the number of terms to be modeled in the momentum


22-35


equations in multiphase flows is large, and this makes the modeling of turbulence in multiphase simulations extremely complex. FLUENT provides three methods for modeling turbulence in multiphase flows within the context of the k- models: • mixture turbulence model (default) • dispersed turbulence model • turbulence model for each phase The choice of model depends on the importance of the secondary-phase turbulence in your application.

! Note that the descriptions of each method below are presented based on the standard k- model. The multiphase modifications to the RNG and realizable k- models are similar, and are therefore not presented explicitly.

Mixture Turbulence Model The mixture turbulence model is the default multiphase turbulence model. It represents the first extension of the single-phase k- model, and it is applicable when phases separate, for stratified (or nearly stratified) multiphase flows, and when the density ratio between phases is close to 1. In these cases, using mixture properties and mixture velocities is sufficient to capture important features of the turbulent flow. The k and equations describing this model are as follows: ∂ µt,m (ρm k) + ∇ · (ρm~vm k) = ∇ · ∇k + Gk,m − ρm ∂t σk

(22.4-68)

∂ µt,m (ρm ) + ∇ · (ρm~vm ) = ∇ · ∇ + (C1 Gk,m − C2 ρm ) ∂t σ k

(22.4-69)

and

where the mixture density and velocity, ρm and ~vm , are computed from

ρm =

N X

αi ρi

(22.4-70)

i=1

and

22-36


22.4 Eulerian Model

N X

~vm =

αi ρi~vi

i=1 N X

(22.4-71) αi ρi

i=1

the turbulent viscosity, µt,m , is computed from µt,m = ρm Cµ

k2

(22.4-72)

and the production of turbulence kinetic energy, Gk,m , is computed from Gk,m = µt,m (∇~vm + (∇~vm )T ) : ∇~vm

(22.4-73)

The constants in these equations are the same as those described in Section 10.4.1 for the single-phase k- model.

Dispersed Turbulence Model The dispersed turbulence model is the appropriate model when the concentrations of the secondary phases are dilute. In this case, interparticle collisions are negligible and the dominant process in the random motion of the secondary phases is the influence of the primary-phase turbulence. Fluctuating quantities of the secondary phases can therefore be given in terms of the mean characteristics of the primary phase and the ratio of the particle relaxation time and eddy-particle interaction time. The model is applicable when there is clearly one primary continuous phase and the rest are dispersed dilute secondary phases. Assumptions The dispersed method for modeling turbulence in FLUENT involves the following assumptions: • A modified k- model for the continuous phase: Turbulent predictions for the continuous phase are obtained using the standard k- model supplemented with extra terms that include the interphase turbulent momentum transfer. • Tchen-theory correlations for the dispersed phases: Predictions for turbulence quantities for the dispersed phases are obtained using the Tchen theory of dispersion of discrete particles by homogeneous turbulence [102].


22-37


• Interphase turbulent momentum transfer: In turbulent multiphase flows, the momentum exchange terms contain the correlation between the instantaneous distribution of the dispersed phases and the turbulent fluid motion. It is possible to take into account the dispersion of the dispersed phases transported by the turbulent fluid motion. • A phase-weighted averaging process: The choice of averaging process has an impact on the modeling of dispersion in turbulent multiphase flows. A two-step averaging process leads to the appearance of fluctuations in the phase volume fractions. When the two-step averaging process is used with a phase-weighted average for the turbulence, however, turbulent fluctuations in the volume fractions do not appear. FLUENT uses phase-weighted averaging, so no volume fraction fluctuations are introduced into the continuity equations. Turbulence in the Continuous Phase The eddy viscosity model is used to calculate averaged fluctuating quantities. The Reynolds stress tensor for continuous phase q takes the following form: 2 ~ q )I + ρq µt,q (∇U ~ q + ∇U ~qT ) τ 00q = − (ρq kq + ρq µt,q ∇ · U 3

(22.4-74)

~ q is the phase-weighted velocity. where U The turbulent viscosity µt,q is written in terms of the turbulent kinetic energy of phase q:

µt,q

kq2 = ρq Cµ q

(22.4-75)

and a characteristic time of the energetic turbulent eddies is defined as 3 kq τt,q = Cµ 2 q

(22.4-76)

where q is the dissipation rate and Cµ = 0.09. The length scale of the turbulent eddies is

Lt,q =

s

3 kq3/2 Cµ 2 q

(22.4-77)

Turbulent predictions are obtained from the modified k- model:

22-38


22.4 Eulerian Model

∂ ~ q kq ) = ∇ · (αq µt,q ∇kq ) + αq Gk,q − αq ρq q + αq ρq Πkq (22.4-78) (αq ρq kq ) + ∇ · (αq ρq U ∂t σk and

∂ ~ q q ) = ∇ · (αq µt,q ∇q ) + αq q (C1 Gk,q − C2 ρq q ) + αq ρq Πq (αq ρq q ) + ∇ · (αq ρq U ∂t σ kq (22.4-79) Here Πkq and Πq represent the influence of the dispersed phases on the continuous phase q, and Gk,q is the production of turbulent kinetic energy, as defined in Section 10.4.4. All other terms have the same meaning as in the single-phase k- model. The term Πkq can be derived from the instantaneous equation of the continuous phase and takes the following form, where M represents the number of secondary phases:

Πk q =

M X Kpq

p=1

αq ρq

~p − U ~ q ) · ~vdr ) (< ~vq00 · ~vp00 > +(U

(22.4-80)

which can be simplified to

Πk q =

M X Kpq

p=1

αq ρq

(kpq − 2kq + ~vpq · ~vdr )

(22.4-81)

where klq is the covariance of the velocities of the continuous phase q and the dispersed phase l (calculated from Equation 22.4-89 below), ~vpq is the relative velocity, and ~vdr is the drift velocity (defined by Equation 22.4-94 below). Πq is modeled according to Elgobashi et al. [69]: Πq = C3

q Πk kq q

(22.4-82)

where C3 = 1.2. Turbulence in the Dispersed Phase Time and length scales that characterize the motion are used to evaluate dispersion coefficients, correlation functions, and the turbulent kinetic energy of each dispersed phase. The characteristic particle relaxation time connected with inertial effects acting on a dispersed phase p is defined as


22-39


τF,pq =

−1 αp ρq Kpq

ρp + CV ρq

!

(22.4-83)

The Lagrangian integral time scale calculated along particle trajectories, mainly affected by the crossing-trajectory effect [47], is defined as τt,q

τt,pq = q

(1 + Cβ ξ 2 )

(22.4-84)

where ξ=

|~vpq |τt,q Lt,q

(22.4-85)

and Cβ = 1.8 − 1.35 cos2 θ

(22.4-86)

where θ is the angle between the mean particle velocity and the mean relative velocity. The ratio between these two characteristic times is written as ηpq =

τt,pq τF,pq

(22.4-87)

Following Simonin [236], FLUENT writes the turbulence quantities for dispersed phase p as follows:

kp = kpq = Dt,pq = Dp = b =

b2 + ηpq kq 1 + ηpq ! b + ηpq 2kq 1 + ηpq 1 kpq τt,pq 3 2 1 Dt,pq + kp − b kpq τF,pq 3 3 !−1 ρp (1 + CV ) + CV ρq !

(22.4-88) (22.4-89) (22.4-90) (22.4-91) (22.4-92)

and CV = 0.5 is the added-mass coefficient.

22-40


22.4 Eulerian Model

Interphase Turbulent Momentum Transfer The turbulent drag term for multiphase flows (Kpq (~vp −~vq ) in Equation 22.4-9) is modeled as follows, for dispersed phase p and continuous phase q: ~p − U ~ q ) − Kpq~vdr Kpq (~vp − ~vq ) = Kpq (U

(22.4-93)

The second term on the right-hand side of Equation 22.4-93 contains the drift velocity: Dq Dp ~vdr = − ∇αp − ∇αq σpq αp σpq αq

!

(22.4-94)

Here Dp and Dq are diffusivities, and σpq is a dispersion Prandtl number. When using Tchen theory in multiphase flows, FLUENT assumes Dp = Dq = Dt,pq and the default value for σpq is 0.75. The drift velocity results from turbulent fluctuations in the volume fraction. When multiplied by the exchange coefficient Kpq , it serves as a correction to the momentum exchange term for turbulent flows. This correction is not included, by default, but you can enable it during the problem setup.

Turbulence Model for Each Phase The most general multiphase turbulence model solves a set of k and transport equations for each phase. This turbulence model is the appropriate choice when the turbulence transfer among the phases plays a dominant role. Note that, since FLUENT is solving two additional transport equations for each secondary phase, the per-phase turbulence model is more computationally intensive than the dispersed turbulence model. Transport Equations The Reynolds stress tensor and turbulent viscosity are computed using Equations 22.4-74 and 22.4-75. Turbulence predictions are obtained from ∂ ~ q kq ) = ∇ · (αq µt,q ∇kq ) + (αq Gk,q − αq ρq q ) + (αq ρq kq ) + ∇ · (αq ρq U ∂t σk N X

Klq (Clq kl − Cql kq ) −

l=1

N X

N X ~l − U ~ q ) · µt,l ∇αl + Klq (U ~l − U ~ q ) · µt,q ∇αq (22.4-95) Klq (U αl σl αq σq l=1 l=1

and


22-41


"

∂ ~ q q ) = ∇ · (αq µt,q ∇q ) + q (αq ρq q ) + ∇ · (αq ρq U ∂t σ kq C3

C1 αq Gk,q − C2 αq ρq q +

N X µt,l ~l − U ~ q ) · µt,q ∇αq ~ ~ Klq (Clq kl − Cql kq ) − Klq (Ul − Uq ) · ∇αl + Klq (U αl σl αq σq l=1 l=1 l=1 (22.4-96)

N X

N X

!#

The terms Clq and Cql can be approximated as ηlq Clq = 2, Cql = 2 1 + ηlq

!

(22.4-97)

where ηlq is defined by Equation 22.4-87. Interphase Turbulent Momentum Transfer The turbulent drag term (Kpq (~vp − ~vq ) in Equation 22.4-9) is modeled as follows, where l is the dispersed phase (replacing p in Equation 22.4-9) and q is the continuous phase: N X l=1

Klq (~vl − ~vq ) =

N X

~l − U ~q) − Klq (U

l=1

N X

Klq~vdr,lq

(22.4-98)

l=1

~ l and U ~ q are phase-weighted velocities, and ~vdr,lq is the drift velocity for phase l Here U (computed using Equation 22.4-94, substituting l for p). Note that FLUENT will compute the diffusivities Dl and Dq directly from the transport equations, rather than using Tchen theory (as it does for the dispersed turbulence model). As noted above, the drift velocity results from turbulent fluctuations in the volume fraction. When multiplied by the exchange coefficient Klq , it serves as a correction to the momentum exchange term for turbulent flows. This correction is not included, by default, but you can enable it during the problem setup. The turbulence model for each phase in FLUENT accounts for the effect of the turbulence field of one phase on the other(s). If you want to modify or enhance the interaction of the multiple turbulence fields and interphase turbulent momentum transfer, you can supply these terms using user-defined functions.

22.4.9

Solution Method in FLUENT

For Eulerian multiphase calculations, FLUENT uses the Phase Coupled SIMPLE (PCSIMPLE) algorithm [271] for the pressure-velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm [189] to multiphase flows. The velocities are solved coupled by phases, but in a segregated fashion. The block algebraic multigrid scheme used by the coupled solver described in [287] is used to solve a vector equation formed by the velocity

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22.4 Eulerian Model

components of all phases simultaneously. Then, a pressure correction equation is built based on total volume continuity rather than mass continuity. Pressure and velocities are then corrected so as to satisfy the continuity constraint.

The Pressure-Correction Equation For incompressible multiphase flow, the pressure-correction equation takes the form n X

k=1

(

n ∂ 1 X αk + ∇ · αk~vk0 + ∇ · αk~vk∗ − m ˙ lk ∂t ρk l=1

)

=0

(22.4-99)

where ~vk0 is the velocity correction for the k th phase and ~vk∗ is the value of ~vk at the current iteration. The velocity corrections are themselves expressed as functions of the pressure corrections.

Volume Fractions The volume fractions are obtained from the phase continuity equations. In discretized form, the equation of the k th volume fraction is ap,k αk =

X

(anb,k αnb,k ) + bk = Rk

(22.4-100)

nb

In order to satisfy the condition that all the volume fractions sum to one, n X

αk = 1

(22.4-101)

k=1


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22.5

Description of Mass Transfer

This section describes the modeling of mass transfer in the framework of FLUENT’s general multiphase models (i.e., Eulerian multiphase, mixture multiphase, VOF multiphase). There are numerous kinds of mass transfer processes that can be modeled in FLUENT. You can use models available in FLUENT (e.g. FLUENT’s cavitation model), or define your own mass transfer model via user-defined functions. See Section 22.5.2 and the separate UDF Manual for more information about the modeling of mass transfer via user-defined functions. Information about mass transfer is presented in the following subsections: • Section 22.5.1: Unidirectional Constant Mass Transfer • Section 22.5.2: UDF-Prescribed Mass Transfer • Section 22.5.3: Mass Transfer through Cavitation

! Note that FLUENT’s current cavitation model can only be used in the framework of the mixture multiphase model. Please contact your support engineer if you want to use FLUENT’s previous cavitation model (the model used in FLUENT 5), in the framework of the mixture multiphase model or the Eulerian multiphase model.

22.5.1

Unidirectional Constant Mass Transfer

The unidirectional mass transfer model defines a positive mass flow rate per unit volume from phase p to phase q: m˙pq = max[0, λpq ] − max[0, −λpq ]

(22.5-1)

λpq = rα ˙ p ρq

(22.5-2)

where

and r˙ is a constant rate of particle shrinking or swelling, such as the rate of burning of a liquid droplet.

22.5.2

UDF-Prescribed Mass Transfer

Because there is no universal model for mass transfer, FLUENT provides a UDF that you can use to input models for different types of mass transfer, e.g. evaporation, condensation, boiling, etc. Note that when using this UDF, FLUENT will automatically add the source contribution to all relevant momentum and scalar equations. This contribution is based on the assumption that the mass “created” or “destroyed” will have the same

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22.5 Description of Mass Transfer

momentum and energy of the phase from which it was created or destroyed. If you would like to input your source terms directly into momentum, energy, or scalar equations, then the appropriate path is to use UDFs for all equations, rather than the UDF for mass transfer. See the separate UDF Manual for more information about UDF-based mass transfer in multiphase.

22.5.3

Mass Transfer through Cavitation

This section provides information about the cavitation model used in FLUENT. You can use FLUENT’s current cavitation model to include cavitation effects in two-phase flows when the mixture model is used.

Overview and Limitations of the Cavitation Model A liquid at constant temperature can be subjected to a decreasing pressure, which may fall below the saturated vapor pressure. The process of rupturing the liquid by a decrease of pressure at constant temperature is called cavitation. The liquid also contains the micro-bubbles of non-condensable (dissolved or ingested) gases, or nuclei, which under decreasing pressure may grow and form cavities. In such processes, very large and steep density variations happen in the low-pressure/cavitating regions. The cavitation model implemented here is based on the so-called “full cavitation model”, developed by Singhal et al. [237]. It accounts for all first-order effects (i.e., phase change, bubble dynamics, turbulent pressure fluctuations, and non-condensable gases). However, unlike the original approach [237] assuming single-phase, variable fluid density flows, the cavitation model in FLUENT is under the framework of multi-phase flows, and it has the capability to account for the effects of the slip velocities between the liquid and gaseous phases. The cavitation model can be used with the mixture multiphase model (with or without slip velocities). The following assumptions are made in the cavitation model: • The system under investigation involves only two phases (a liquid and its vapor), and a certain fraction of separately modeled non-condensable gases. • Both bubble formation (evaporation) and collapse (condensation) are taken into account in the model. • The mass fraction of non-condensable gases is known in advance. The following limitations apply to the cavitation model in FLUENT: • The cavitation model cannot be used with the VOF model, because the surface tracking schemes for the VOF model are incompatible with the interpenetrating continua assumption of the cavitation model.


22-45


• The cavitation model can be used only for multiphase simulations that use the mixture model and involve only two phases. It is always preferable to solve for cavitation using the mixture model without slip velocity; slip velocities can be turned on if the problem suggests that there is significant slip between phases. • With the cavitation model, only the secondary phase can be compressible; the primary phase must be incompressible. • Currently, the parameters used in the mass transfer model for cavitation (saturation pressure, liquid to vapor surface tension) do not account for temperature dependence. • By assuming a constant mass-fraction of non-condensable gases, this model cannot be used to predict cavitating flows with gas injections. It also cannot predict the releasing of the non-condensable gases from the fluid (degassing). Vapor Mass Fraction and Vapor Transport The working fluid is assumed to be a mixture of liquid, vapor and non-condensable gases. Standard governing equations in the mixture model and the mixture turbulence model describe the flow and account for the effects of turbulence. A vapor transport equation governs the vapor mass fraction, f, given by: ∂ (ρf ) + ∇(ρv~v f ) = ∇(γ∇f ) + Re − Rc ∂t

(22.5-3)

where ρ is the mixture density, v~v is the velocity vector of the vapor phase, γ is the effective exchange coefficient, and Re and Rc are the vapor generation and condensation rate terms (or phase change rates). The rate expressions are derived from the RayleighPlesset equations, and limiting bubble size considerations (interface surface area per unit volume of vapor) [237]. These rates are functions of the instantaneous, local static pressure and are given by: when p < psat s

Vch 2(psat − p) ρl ρv (1 − f ) Re = Ce σ 3ρl

(22.5-4)

when p > psat s

Vch 2(p − psat ) Rc = Cc ρl ρl f σ 3ρl

(22.5-5)

where the suffixes l and v denote the liquid and vapor phases, Vch is a characteristic √ velocity, which is approximated by the local turbulence intensity, (i.e. Vch = k), σ is

22-46



the surface tension of the liquid, psat is the liquid saturation vapor pressure at the given temperature, and Ce and Cc are empirical constants. The default values are Ce = 0.02 and Cc = 0.01. Turbulence-Induced Pressure Fluctuations Significant effect of turbulence on cavitating flows has been reported [218]. FLUENT’s cavitation model accounts for the turbulence-induced pressure fluctuations by simply raising the phase-change threshold pressure from psat to 1 pv = (psat + pturb ) 2

(22.5-6)

pturb = 0.39ρk

(22.5-7)

where

where k is the local turbulence kinetic energy. Effects of Non-Condensable Gases The operating liquid usually contains small finite amounts of non-condensable gases (e.g., dissolved gases, aeration). Even a very small amount (e.g., 10 ppm) of non-condensable gases can have significant effects on the cavitating flow field due to gases expansion at low pressures. In the present approach, the working fluid is assumed to be a mixture of the liquid phase and the gaseous phase, with the gaseous phase comprising of the liquid vapor and the non-condensable gas. The density of the mixture, ρ, is calculated as ρ = αv ρv + αg ρg + (1 − αv − αg )ρl

(22.5-8)

where ρl , ρv , and ρg are the densities of the liquid, the vapor, and the non-condensable gases, respectively, and αl , αv , and αg are the respective volume fractions. The relationship between the mass fraction (fi ) in Equation 22.5-4 and Equation 22.5-5 and the volume fraction (αi ) in Equation 22.5-8 is αi = fi

ρ ρi

(22.5-9)

The combined volume fraction of vapor and gas (i.e., αv + αg ) is commonly referred to as the void fraction (α).


22-47


Phase Change Rates After accounting for the effects of turbulence-induced pressure fluctuations and noncondensable gases, the final phase rate expressions are written as: when p < pv √

s

k 2(pv − p) Re = Ce ρl ρv (1 − fv − fg ) σ 3ρl

(22.5-10)

when p > pv √

s

k 2(p − pv ) Rc = Cc ρl ρl fv σ 3ρl

(22.5-11)

Additional Guidelines for the Cavitation Model In practical applications of the cavitation model, several factors greatly influence numerical stability. For instance, high pressure difference between the inlet and exit, large ratio of liquid to vapor density, and near zero saturation pressure all cause unfavorable effects on solution convergence. In addition, poor initial conditions very often lead to an unrealistic pressure field and unexpected cavitating zones, which, once present, are then usually very difficult for the model to correct. To help address these potential numerical problems, some tips for using the cavitation model are listed below: • Relaxation Factors: In general, small relaxation factors are advised for all transport equations, especially for the momentum equations. Typically, these relaxation factors are taken between the values of 0.05 and 0.5. The density and the vaporization mass (source term in the vapor equation) can also be relaxed to improve convergence, in particular at the beginning of the iteration process. Typically, the relaxation factor for density is set between the values of 0.1 and 1.0, while for the vaporization mass values between 0.001 and 1.0 may be appropriate. • Initial Conditions: Though no special initial condition settings are required, it is suggested that the vapor fraction is always set to zero. The pressure is set close to the highest pressure among the inlets and outlets to avoid unexpected low pressure and cavitating spots. Also, in complicated cases, it may be beneficial to obtain a realistic pressure field before substantial cavities are formed. This can be achieved by setting near zero relaxation factors for the vaporization mass and for density, and increasing them to reasonable values after a sufficiently high number of iterations. • Non-Condensable Gases: Non-condensable gases are usually present in liquids. Even a small amount (e.g., 15 ppm) of non-condensable gases can have significant effects on both the physical realism and the convergence characteristics of the

22-48



solution. A value of zero for the mass fraction of non-condensable gases should generally be avoided. In some cases, if the liquid is purified of non-condensable gases, a much smaller value (e.g., 10−8 ) may be used to replace the default value of 1.5×10−5 . In fact, higher mass fractions of the non-condensable gases may, in many cases, enhance numerical stability and lead to more realistic results. In particular, when the saturation pressure of a liquid at a certain temperature is zero or very small, non-condensable gases will play a crucial role both numerically and physically. • Limits for Dependent Variables: In many cases, setting the pressure upper limit to a reasonable value can help convergence greatly at the early stage of the solution. It is advised to always limit the maximum pressure when it is possible. • Parameters of the AMG Solver: Tightening the convergence criteria for the AMG solver also can help stability, in particular for the pressure correction and vapor transport equations. By default, the Termination criteria for both variables are set to 0.1. You may reduce these values to 10−4 ; correspondingly the number for Max Cycles may need to increase up to 100. • Relax the Pressure Correction Equation: For cavitating flows, a special relaxation factor is introduced for the pressure correction equation. By default, this factor is set to 0.7. For complicated cases, you may want to reduce the factor. It is recommended, however, that this value is not reduced to less than 0.4. You can set the value of this relaxation factor by typing (rpsetvar,’pressure-correction/relax value)


22-49


22.6

Setting Up a General Multiphase Problem

This section provides instructions and guidelines for using the VOF, mixture, and Eulerian multiphase models. Information is presented in the following subsections: • Section 22.6.1: Steps for Using the General Multiphase Models • Section 22.6.2: Additional Guidelines for Eulerian Multiphase Simulations • Section 22.6.3: Enabling the Multiphase Model and Specifying the Number of Phases • Section 22.6.4: Selecting the VOF Formulation • Section 22.6.5: Defining a Homogeneous Multiphase Flow • Section 22.6.6: Defining Mass Transfer Effects • Section 22.6.7: Including Cavitation Effects • Section 22.6.8: Overview of Defining the Phases • Section 22.6.9: Defining Phases for the VOF Model • Section 22.6.10: Defining Phases for the Mixture Model • Section 22.6.11: Defining Phases for the Eulerian Model • Section 22.6.12: Defining Heat Transfer for the Eulerian Model • Section 22.6.13: Including Body Forces • Section 22.6.14: Setting Time-Dependent Parameters for the VOF Model • Section 22.6.15: Selecting a Turbulence Model for an Eulerian Multiphase Calculation • Section 22.6.16: Setting Boundary Conditions • Section 22.6.17: Setting Initial Volume Fractions • Section 22.6.18: Inputs for Compressible VOF and Mixture Model Calculations • Section 22.6.19: Inputs for Solidification/Melting VOF Calculations

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22.6 Setting Up a General Multiphase Problem

22.6.1

Steps for Using the General Multiphase Models

The procedure for setting up and solving a general multiphase problem is outlined below, and described in detail in the subsections that follow. Remember that only the steps that are pertinent to general multiphase calculations are shown here. For information about inputs related to other models that you are using in conjunction with the multiphase model, see the appropriate sections for those models. See also Section 22.6.2 for guidelines on simplifying Eulerian multiphase simulations. 1. Enable the multiphase model you want to use (VOF, mixture, or Eulerian) and specify the number of phases. For the VOF model, specify the VOF formulation as well. Define −→ Models −→Multiphase... See Sections 22.6.3 and 22.6.4 for details. 2. Copy the material representing each phase from the materials database. Define −→Materials... If the material you want to use is not in the database, create a new material. See Section 7.1.2 for details about copying from the database and creating new materials. See Section 22.6.18 for additional information about specifying material properties for a compressible phase (VOF and mixture models only).

!

If your model includes a particulate (granular) phase, you will need to create a new material for it in the fluid materials category (not the solid materials category). 3. Define the phases, and specify any interaction between them (e.g., surface tension if you are using the VOF model, slip velocity functions if you are using the mixture model, or drag functions if you are using the Eulerian model). Define −→Phases... See Sections 22.6.8–22.6.11 for details. 4. (Eulerian model only) If the flow is turbulent, define the multiphase turbulence model. Define −→ Models −→Viscous... See Section 22.6.15 for details. 5. If body forces are present, turn on gravity and specify the gravitational acceleration. Define −→Operating Conditions... See Section 22.6.13 for details.


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6. Specify the boundary conditions, including the secondary-phase volume fractions at flow boundaries and (if you are modeling wall adhesion in a VOF simulation) the contact angles at walls. Define −→Boundary Conditions... See Section 22.6.16 for details. 7. Set any model-specific solution parameters. Solve −→ Controls −→Solution... See Sections 22.6.14 and 22.7 for details. 8. Initialize the solution and set the initial volume fractions for the secondary phases. Solve −→ Initialize −→Patch... See Section 22.6.17 for details. 9. Calculate a solution and examine the results. See Sections 22.7 and 22.8 for details.

22.6.2

Additional Guidelines for Eulerian Multiphase Simulations

Once you have determined that the Eulerian multiphase model is appropriate for your problem (as described in Sections 20.4 and 22.1), you should consider the computational effort required to solve your multiphase problem. The required computational effort depends strongly on the number of transport equations being solved and the degree of coupling. For the Eulerian multiphase model, which has a large number of highly coupled transport equations, computational expense will be high. Before setting up your problem, try to reduce the problem statement to the simplest form possible. Instead of trying to solve your multiphase flow in all of its complexity on your first solution attempt, you can start with simple approximations and work your way up to the final form of the problem definition. Some suggestions for simplifying a multiphase flow problem are listed below: • use a hexahedral or quadrilateral mesh (instead of a tetrahedral or triangular mesh) • reduce the number of phases You may find that even a very simple approximation will provide you with useful information about your problem. See Section 22.7.3 for more solution strategies for Eulerian multiphase calculations.

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22.6.3

Enabling the Multiphase Model and Specifying the Number of Phases

To enable the VOF, mixture, or Eulerian multiphase model, select Volume of Fluid, Mixture, or Eulerian as the Model in the Multiphase Model panel (Figure 22.6.1). Define −→ Models −→Multiphase...

Figure 22.6.1: The Multiphase Model Panel The panel will expand to show the relevant inputs for the selected multiphase model. If you selected the VOF model, the inputs are as follows: • number of phases • VOF formulation (see Section 22.6.4) • (optional) implicit body force formulation (see Section 22.6.13) If you selected the mixture model, the inputs are as follows: • number of phases


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• whether or not to compute the slip velocities (see Section 22.6.5) • (optional) implicit body force formulation (see Section 22.6.13) • (optional) cavitation effects (see Section 22.6.7) If you selected the Eulerian model, the inputs are as follows: • number of phases • (optional) cavitation effects (see Section 22.6.7) To specify the number of phases for the multiphase calculation, enter the appropriate value in the Number of Phases field. You can specify up to 20 phases.

22.6.4

Selecting the VOF Formulation

To specify the VOF formulation to be used, select the appropriate VOF Scheme under VOF Parameters in the Multiphase Model panel. The VOF formulations that are available in FLUENT are as follows: • Time-dependent with the geometric reconstruction interpolation scheme: This formulation should be used whenever you are interested in the time-accurate transient behavior of the VOF solution. To use this formulation, select Geo-Reconstruct (the default) as the VOF Scheme. FLUENT will automatically turn on the unsteady formulation with first-order discretization for time in the Solver panel. • Time-dependent with the donor-acceptor interpolation scheme: This formulation should be used instead of the time-dependent formulation with the geometric reconstruction scheme if your mesh contains highly twisted hexahedral cells. For such cases, the donor-acceptor scheme may provide more accurate results. To use this formulation, select Donor-Acceptor as the VOF Scheme. FLUENT will automatically turn on the unsteady formulation with first-order discretization for time in the Solver panel. • Time-dependent with the Euler explicit interpolation scheme: Since the donoracceptor scheme is available only for quadrilateral and hexahedral meshes, it cannot be used for a hybrid mesh containing twisted hexahedral cells. For such cases, you should use the time-dependent Euler explicit scheme. This formulation can also be used for other cases in which the geometric reconstruction scheme does not give satisfactory results, or the flow calculation becomes unstable.

22-54



To use this formulation, select Euler Explicit as the VOF Scheme. FLUENT will automatically turn on the unsteady formulation with first-order discretization for time in the Solver panel. While the Euler explicit time-dependent formulation is less computationally expensive than the geometric reconstruction scheme, the interface between phases will not be as sharp as that predicted with the geometric reconstruction scheme. To reduce this diffusivity, it is recommended that you use the second-order discretization scheme for the volume fraction equations. In addition, you may want to consider turning the geometric reconstruction scheme back on after calculating a solution with the implicit scheme, in order to obtain a sharper interface. • Time-dependent with the implicit interpolation scheme: This formulation can be used if you are looking for a steady-state solution and you are not interested in the intermediate transient flow behavior, but the final steady-state solution is dependent on the initial flow conditions and/or you do not have a distinct inflow boundary for each phase. To use this formulation, select Implicit as the VOF Scheme, and enable an Unsteady calculation in the Solver panel (opened with the Define/Models/Solver... menu item).

!

The issues discussed above for the Euler explicit time-dependent formulation also apply to the implicit time-dependent formulation. You should take the precautions described above to improve the sharpness of the interface. • Steady-state with the implicit interpolation scheme: This formulation can be used if you are looking for a steady-state solution, you are not interested in the intermediate transient flow behavior, and the final steady-state solution is not affected by the initial flow conditions and there is a distinct inflow boundary for each phase. To use this formulation, select Implicit as the VOF Scheme.

!

The issues discussed above for the Euler explicit time-dependent formulation also apply to the implicit steady-state formulation. You should take the precautions described above to improve the sharpness of the interface.

! For the geometric reconstruction and donor-acceptor schemes, if you are using a conformal grid (i.e., if the grid node locations are identical at the boundaries where two subdomains meet), you must ensure that there are no two-sided (zero-thickness) walls within the domain. If there are, you will need to slit them, as described in Section 5.7.8.

Examples To help you determine the best formulation to use for your problem, examples that use different formulations are listed below:


22-55


• jet breakup: time-dependent with the geometric reconstruction scheme (or the donor-acceptor or Euler explicit scheme if problems occur with the geometric reconstruction scheme) • shape of the liquid interface in a centrifuge: time-dependent with the implicit interpolation scheme • flow around a ship’s hull: steady-state with the implicit interpolation scheme

22.6.5

Defining a Homogeneous Multiphase Flow

If you are using the mixture model, you have the option to disable the calculation of slip velocities and solve a homogeneous multiphase flow (i.e., one in which the phases all move at the same velocity). By default, FLUENT will compute the slip velocities for the secondary phases, as described in Section 22.3.4. If you want to solve a homogeneous multiphase flow, turn off Slip Velocity under Mixture Parameters.

22.6.6

Defining Mass Transfer Effects

As discussed in Section 22.5, mass transfer effects in the framework of FLUENT’s general multiphase models (i.e., Eulerian multiphase, mixture multiphase, VOF multiphase) can be modeled in one of three ways: • unidirectional constant mass transfer • UDF-prescribed mass transfer • mass transfer through cavitation Because of the different procedures and limitations involved, defining mass transfer through cavitation is described separately in Section 22.6.7. To define mass transfer in a multiphase simulation, either as unidirectional constant or using a UDF, you will need to use the Phase Interaction panel (e.g., Figure 22.6.2). Define −→Phases... 1. In the Phases panel (Figure 22.6.3), click the Interaction... button to open the Phase Interaction panel. 2. Click the Mass tab in the Phase Interaction panel. 3. Select the desired correlation for the Mass Transfer Function. Available choices are: constant enables a constant, unidirectional mass transfer.

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Figure 22.6.2: The Phase Interaction Panel for Mass Transfer

user-defined allows you to implement a correlation reflecting a model of your choice, through a user-defined function. FLUENT will automatically include the terms needed to model mass transfer in all relevant conservation equations. Another option to model mass transfer between phases is through the use of user-defined scalars (UDSs) and their inclusion in the relevant conservation equations. This approach is a more involved but more powerful, allowing you to split the source terms according to a model of your choice. See the separate UDF Manual for more information on using user-defined scalars (UDSs) in the framework of a multiphase simulation.

22.6.7

Including Cavitation Effects

For mixture model calculations, it is possible to include the effects of cavitation, using FLUENT’s cavitation model described in Section 22.5.3. To enable the cavitation model, turn on Cavitation under Interphase Mass Transfer in the Multiphase Model panel. When you are using FLUENT’s cavitation model, you will specify three parameters to be used in the calculation of mass transfer due to cavitation. Under Cavitation Parameters in the Multiphase Model panel, set the Vaporization Pressure (psat in Equation 22.5-6), the mass fraction of Non Condensable Gas , and the Liquid Surface Tension. The default value of psat is 2540 Pa, the vaporization pressure for water at ambient temperature. Note that psat and the surface tension are properties of the liquid, depending mainly on


22-57


temperature. Non Condensable Gas is the mass fraction of dissolved gases, which depends on the purity of the liquid. See Section 22.5.3 for details about modeling cavitation.

22.6.8

Overview of Defining the Phases

To define the phases (including their material properties) and any interphase interaction (e.g., surface tension and wall adhesion for the VOF model, slip velocity for the mixture model, drag functions for the mixture and the Eulerian models), you will use the Phases panel (Figure 22.6.3). Define −→Phases...

Figure 22.6.3: The Phases Panel Each item in the Phase list in this panel is one of two types, as indicated in the Type list: primary-phase indicates that the selected item is the primary phase, and secondary-phase indicates that the selected item is a secondary phase. To specify any interaction between the phases, click the Interaction... button. Instructions for defining the phases and interaction are provided in Sections 22.6.9, 22.6.10, and 22.6.11 for the VOF, mixture, and Eulerian models, respectively.

22.6.9

Defining Phases for the VOF Model

Instructions for specifying the necessary information for the primary and secondary phases and their interaction in a VOF calculation are provided below.

! In general, you can specify the primary and secondary phases whichever way you prefer. It is a good idea, especially in more complicated problems, to consider how your choice will affect the ease of problem setup. For example, if you are planning to patch an initial volume fraction of 1 for one phase in a portion of the domain, it may be more convenient

22-58



to make that phase a secondary phase. Also, if one of the phases is compressible, it is recommended that you specify it as the primary phase to improve solution stability.

! Recall that only one of the phases can be compressible. Be sure that you do not select a compressible material (i.e., a material that uses the compressible ideal gas law for density) for more than one of the phases. See Section 22.6.18 for details.

Defining the Primary Phase To define the primary phase in a VOF calculation, follow these steps: 1. Select phase-1 in the Phase list. 2. Click Set..., and the Primary Phase panel (Figure 22.6.4) will open.

Figure 22.6.4: The Primary Phase Panel

3. In the Primary Phase panel, enter a Name for the phase. 4. Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list. 5. Define the material properties for the Phase Material. (a) Click Edit..., and the Material panel will open. (b) In the Material panel, check the properties, and modify them if necessary. (See Chapter 7 for general information about setting material properties, Section 22.6.18 for specific information related to compressible VOF calculations, and Section 22.6.19 for specific information related to melting/solidification VOF calculations.)

!

If you make changes to the properties, remember to click Change before closing the Material panel. 6. Click OK in the Primary Phase panel.


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Defining a Secondary Phase To define a secondary phase in a VOF calculation, follow these steps: 1. Select the phase (e.g., phase-2) in the Phase list. 2. Click Set..., and the Secondary Phase panel (Figure 22.6.5) will open.

Figure 22.6.5: The Secondary Phase Panel for the VOF Model

3. In the Secondary Phase panel, enter a Name for the phase. 4. Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list. 5. Define the material properties for the Phase Material, following the procedure outlined above for setting the material properties for the primary phase. 6. Click OK in the Secondary Phase panel.

Including Surface Tension and Wall Adhesion Effects As discussed in Section 22.2.8, the importance of surface tension effects depends on the value of the capillary number, Ca (defined by Equation 22.2-16), or the Weber number, We (defined by Equation 22.2-17). Surface tension effects can be neglected if Ca 1 or We 1.

! Note that the calculation of surface tension effects will be more accurate if you use a quadrilateral or hexahedral mesh in the area(s) of the computational domain where surface tension is significant. If you cannot use a quadrilateral or hexahedral mesh for the entire domain, then you should use a hybrid mesh, with quadrilaterals or hexahedra in the affected areas. If you want to include the effects of surface tension along the interface between one or more pairs of phases, as described in Section 22.2.8, click Interaction... to open the Phase Interaction panel (Figure 22.6.6).

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Figure 22.6.6: The Phase Interaction Panel for the VOF Model (Surface Tension Tab)

Follow the steps below to include surface tension (and, if appropriate, wall adhesion) effects along the interface between one or more pairs of phases: 1. Click the Surface Tension tab. 2. If you want to include wall adhesion, turn on the Wall Adhesion option. When Wall Adhesion is enabled, you will need to specify the contact angle at each wall as a boundary condition (as described in Section 22.6.16). 3. For each pair of phases between which you want to include the effects of surface tension, specify a constant surface tension coefficient. Alternatively you can specify a temperature dependent or a user-defined surface tension coefficient. See Section 22.2.8 for more information on surface tension, and the separate UDF Manual for more information on user-defined functions. All surface tension coefficients are equal to 0 by default, representing no surface tension effects along the interface between the two phases.

! For calculations involving surface tension, it is recommended that you also turn on the Implicit Body Force treatment for the Body Force Formulation in the Multiphase Model panel. This treatment improves solution convergence by accounting for the partial equilibrium of the pressure gradient and surface tension forces in the momentum equations. See Section 24.3.3 for details.


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22.6.10

Defining Phases for the Mixture Model

Instructions for specifying the necessary information for the primary and secondary phases and their interaction for a mixture model calculation are provided below.

! Recall that only one of the phases can be compressible. Be sure that you do not select a compressible material (i.e., a material that uses the compressible ideal gas law for density) for more than one of the phases. See Section 22.6.18 for details.

Defining the Primary Phase The procedure for defining the primary phase in a mixture model calculation is the same as for a VOF calculation. See Section 22.6.9 for details.

Defining a Secondary Phase To define a secondary phase in a mixture model calculation, follow these steps: 1. Select the phase (e.g., phase-2) in the Phase list. 2. Click Set..., and the Secondary Phase panel (Figure 22.6.7) will open.

Figure 22.6.7: The Secondary Phase Panel for the Mixture Model

3. In the Secondary Phase panel, enter a Name for the phase.

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4. Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list. 5. Define the material properties for the Phase Material, following the same procedure you used to set the material properties for the primary phase (see Section 22.6.9). For a particulate phase (which must be placed in the fluid materials category, as mentioned in Section 22.6.1), you need to specify only the density; you can ignore the values for the other properties, since they will not be used. 6. In the Secondary Phase panel, specify the Diameter of the bubbles, droplets, or particles of this phase (dp in Equation 22.3-11). You can specify a constant value, or use a user-defined function. See the separate UDF Manual for details about user-defined functions. Note that when you are using the mixture model without slip velocity, this input is not necessary, and it will not be available to you. 7. Click OK in the Secondary Phase panel.

Defining Drag Between Phases For mixture multiphase flows with slip velocity, you can specify he drag function to be used in the calculation. The functions available here are a subset of those discussed in Section 22.6.11. See Section 22.3.4 for more information. To specify drag laws, click Interaction... to open the Phase Interaction panel (Figure 22.6.8), and then click the Drag tab.

Figure 22.6.8: The Phase Interaction Panel for the Mixture Model (Drag Tab)


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Defining the Slip Velocity If you are solving for slip velocities during the mixture calculation, and you want to modify the slip velocity definition, click Interaction... to open the Phase Interaction panel (Figure 22.6.9), and then click the Slip tab.

Figure 22.6.9: The Phase Interaction Panel for the Mixture Model (Slip Tab)

Under Slip Velocity, you can specify the slip velocity function for each secondary phase with respect to the primary phase by choosing the appropriate item in the adjacent drop-down list. • Select maninnen-et-al (the default) to use the algebraic slip method of Manninen et al. [163], described in Section 22.3.4. • Select none if the secondary phase has the same velocity as the primary phase (i.e., no slip velocity). • Select user-defined to use a user-defined function for the slip velocity. See the separate UDF Manual for details.

22.6.11

Defining Phases for the Eulerian Model

Instructions for specifying the necessary information for the primary and secondary phases and their interaction for an Eulerian multiphase calculation are provided below.

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Defining the Primary Phase The procedure for defining the primary phase in an Eulerian multiphase calculation is the same as for a VOF calculation. See Section 22.6.9 for details.

Defining a Non-Granular Secondary Phase To define a non-granular (i.e., liquid or vapor) secondary phase in an Eulerian multiphase calculation, follow these steps: 1. Select the phase (e.g., phase-2) in the Phase list. 2. Click Set..., and the Secondary Phase panel (Figure 22.6.10) will open.

Figure 22.6.10: The Secondary Phase Panel for a Non-Granular Phase

3. In the Secondary Phase panel, enter a Name for the phase. 4. Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list. 5. Define the material properties for the Phase Material, following the same procedure you used to set the material properties for the primary phase (see Section 22.6.9).


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6. In the Secondary Phase panel, specify the Diameter of the bubbles or droplets of this phase. You can specify a constant value, or use a user-defined function. See the separate UDF Manual for details about user-defined functions. 7. Click OK in the Secondary Phase panel.

Defining a Granular Secondary Phase To define a granular (i.e., particulate) secondary phase in an Eulerian multiphase calculation, follow these steps: 1. Select the phase (e.g., phase-2) in the Phase list. 2. Click Set..., and the Secondary Phase panel (Figure 22.6.11) will open.

Figure 22.6.11: The Secondary Phase Panel for a Granular Phase

3. In the Secondary Phase panel, enter a Name for the phase. 4. Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list.

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5. Define the material properties for the Phase Material, following the same procedure you used to set the material properties for the primary phase (see Section 22.6.9). For a granular phase (which must be placed in the fluid materials category, as mentioned in Section 22.6.1), you need to specify only the density; you can ignore the values for the other properties, since they will not be used. 6. Turn on the Granular option. 7. (optional) Turn on the Packed Bed option if you want to freeze the velocity field for the granular phase. Note that when you select the packed bed option for a phase, you should also use the fixed velocity option with a value of zero for all velocity components for all interior cell zones for that phase. 8. In the Secondary Phase panel, specify the following properties of the particles of this phase: Diameter specifies the diameter of the particles. You can select constant in the drop-down list and specify a constant value, or select user-defined to use a user-defined function. See the separate UDF Manual for details about userdefined functions. Granular Viscosity specifies the kinetic part of the granular viscosity of the particles (µs,kin in Equation 22.4-51). You can select constant (the default) in the drop-down list and specify a constant value, select syamlal-obrien to compute the value using Equation 22.4-53, select gidaspow to compute the value using Equation 22.4-54, or select user-defined to use a user-defined function. Granular Bulk Viscosity specifies the solids bulk viscosity (λq in Equation 22.4-8). You can select constant (the default) in the drop-down list and specify a constant value, select lun-et-al to compute the value using Equation 22.4-55, or select user-defined to use a user-defined function. Frictional Viscosity specifies a shear viscosity based on the viscous-plastic flow (µs,fr in Equation 22.4-51). By default, the frictional viscosity is neglected, as indicated by the default selection of none in the drop-down list. If you want to include the frictional viscosity, you can select constant and specify a constant value, select schaeffer to compute the value using Equation 22.4-56, or select user-defined to use a user-defined function. Angle of Internal Friction specifies a constant value for the angle φ used in Schaeffer’s expression for frictional viscosity (Equation 22.4-56). This parameter is relevant only if you have selected schaeffer or user-defined for the Frictional Viscosity. Granular Conductivity specifies the solids granular conductivity (kΘs in Equation 22.4-57). You can select syamlal-obrien to compute the value using Equation 22.4-58, select gidaspow to compute the value using Equation 22.4-59, or select user-defined to use a user-defined function. Note, however, that FLUENT currently uses an algebraic relation for the granular temperature. This


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has been obtained by neglecting convection and diffusion in the transport equation, Equation 22.4-57 [261]. Packing Limit specifies the maximum volume fraction for the granular phase (αs,max ). For monodispersed spheres, the packing limit is about 0.63, which is the default value in FLUENT. In polydispersed cases, however, smaller spheres can fill the small gaps between larger spheres, so you may need to increase the maximum packing limit. 9. Click OK in the Secondary Phase panel.

Defining the Interaction Between Phases For both granular and non-granular flows, you will need to specify the drag function to be used in the calculation of the momentum exchange coefficients. For granular flows, you will also need to specify the restitution coefficient(s) for particle collisions. It is also possible to include an optional lift force and/or virtual mass force (described below) for both granular and non-granular flows. To specify these parameters, click Interaction... to open the Phase Interaction panel (Figure 22.6.12).

Figure 22.6.12: The Phase Interaction Panel for the Eulerian Model

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Specifying the Drag Function FLUENT allows you to specify a drag function for each pair of phases. Follow the steps below: 1. Click the Drag tab to display the Drag Function inputs. 2. For each pair of phases, select the appropriate drag function from the corresponding drop-down list. • Select schiller-naumann to use the fluid-fluid drag function described by Equation 22.4-20. The Schiller and Naumann model is the default method, and it is acceptable for general use in all fluid-fluid multiphase calculations. • Select morsi-alexander to use the fluid-fluid drag function described by Equation 22.4-24. The Morsi and Alexander model is the most complete, adjusting the function definition frequently over a large range of Reynolds numbers, but calculations with this model may be less stable than with the other models. • Select symmetric to use the fluid-fluid drag function described by Equation 22.4-29. The symmetric model is recommended for flows in which the secondary (dispersed) phase in one region of the domain becomes the primary (continuous) phase in another. For example, if air is injected into the bottom of a container filled halfway with water, the air is the dispersed phase in the bottom half of the container; in the top half of the container, the air is the continuous phase. • Select wen-yu to use the fluid-solid drag function described by Equation 22.4-41. The Wen and Yu model is applicable for dilute phase flows, in which the total secondary phase volume fraction is significantly lower than that of the primary phase. • Select gidaspow to use the fluid-solid drag function described by Equation 22.4-43. The Gidaspow model is recommended for dense fluidized beds. • Select syamlal-obrien to use the fluid-solid drag function described by Equation 22.4-33. The Syamlal-O’Brien model is recommended for use in conjunction with the Syamlal-O’Brien model for granular viscosity. • Select syamlal-obrien-symmetric to use the solid-solid drag function described by Equation 22.4-45. The symmetric Syamlal-O’Brien model is appropriate for a pair of solid phases. • Select constant to specify a constant value for the drag function, and then specify the value in the text field. • Select user-defined to use a user-defined function for the drag function (see the separate UDF Manual for details). • If you want to temporarily ignore the interaction between two phases, select none.


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Specifying the Restitution Coefficients (Granular Flow Only) For granular flows, you need to specify the coefficients of restitution for collisions between particles (els in Equation 22.4-45 and ess in Equation 22.4-46). In addition to specifying the restitution coefficient for collisions between each pair of granular phases, you will also specify the restitution coefficient for collisions between particles of the same phase. Follow the steps below: 1. Click the Collisions tab to display the Restitution Coefficient inputs. 2. For each pair of phases, specify a constant restitution coefficient. All restitution coefficients are equal to 0.9 by default. Including the Lift Force For both granular and non-granular flows, it is possible to include the effect of lift forces (F~lift in Equation 22.4-10) on the secondary phase particles, droplets, or bubbles. These lift forces act on a particle, droplet, or bubble mainly due to velocity gradients in the primary-phase flow field. In most cases, the lift force is insignificant compared to the drag force, so there is no reason to include it. If the lift force is significant (e.g., if the phases separate quickly), you may want to include this effect.

! Note that the lift force will be more significant for larger particles, but the FLUENT model assumes that the particle diameter is much smaller than the interparticle spacing. Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles. To include the effect of lift forces, follow these steps: 1. Click the Lift tab to display the Lift Coefficient inputs. 2. For each pair of phases, select the appropriate specification method from the corresponding drop-down list. Note that, since the lift forces for a particle, droplet, or bubble are due mainly to velocity gradients in the primary-phase flow field, you will not specify lift coefficients for pairs consisting of two secondary phases; lift coefficients are specified only for pairs consisting of a secondary phase and the primary phase. • Select none (the default) to ignore the effect of lift forces. • Select constant to specify a constant lift coefficient, and then specify the value in the text field. • Select user-defined to use a user-defined function for the lift coefficient (see the separate UDF Manual for details).

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Including the Virtual Mass Force For both granular and non-granular flows, it is possible to include the “virtual mass force” (F~vm in Equation 22.4-11) that is present when a secondary phase accelerates relative to the primary phase. The virtual mass effect is significant when the secondary phase density is much smaller than the primary phase density (e.g., for a transient bubble column). To include the effect of the virtual mass force, turn on the Virtual Mass option in the Phase Interaction panel. The virtual mass effect will be included for all secondary phases; it is not possible to enable it just for a particular phase.

22.6.12

Defining Heat Transfer for the Eulerian Model

To define heat transfer in a multiphase Eulerian simulation, you will need to visit the Phase Interaction panel, after you have turned on the energy equation in the Energy panel. Define −→Phases... 1. Click the Interaction... ure 22.6.13).

button to open the Phase Interaction panel (e.g., Fig-

Figure 22.6.13: The Phase Interaction Panel for Heat Transfer

2. Click on the Heat tab in the Phase Interaction panel.


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3. Select the desired correlation for the Heat Transfer Coefficient. Available choices are: gunn is frequently used for Eulerian multiphase simulations involving a granular phase. ranz-marshall is frequently used for Eulerian multiphase simulations not involving a granular phase. none allows you to ignore the effects of heat transfer between the two phases user-defined allows you to implement a correlation reflecting a model of your choice, through a user-defined function. 4. Set the appropriate thermal boundary conditions. You will specify the thermal boundary conditions for each individual phase on most boundaries, and for the mixture on some boundaries. See Chapter 6 for more information on boundary conditions, and Section 22.6.16 for more information on specifying boundary conditions for a Eulerian multiphase calculation. See Section 22.4.7 for more information on heat transfer in the framework of a Eulerian multiphase simulation.

22.6.13

Including Body Forces

In many cases, the motion of the phases is due, in part, to gravitational effects. To include this body force, turn on Gravity in the Operating Conditions panel and specify the Gravitational Acceleration. Define −→Operating Conditions... For VOF calculations, you should also turn on the Specified Operating Density option in the Operating Conditions panel, and set the Operating Density to be the density of the lightest phase. (This excludes the buildup of hydrostatic pressure within the lightest phase, improving the round-off accuracy for the momentum balance.) If any of the phases is compressible, set the Operating Density to zero.

! For VOF and mixture calculations involving body forces, it is recommended that you also turn on the Implicit Body Force treatment for the Body Force Formulation in the Multiphase Model panel. This treatment improves solution convergence by accounting for the partial equilibrium of the pressure gradient and body forces in the momentum equations. See Section 24.3.3 for details.

22.6.14

Setting Time-Dependent Parameters for the VOF Model

If you are using the time-dependent VOF formulation in FLUENT, an explicit solution for the volume fraction is obtained either once each time step or once each iteration,

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depending upon your inputs to the model. You also have control over the time step used for the volume fraction calculation. To compute a time-dependent VOF solution, you will need to enable the Unsteady option in the Solver panel (and choose the appropriate Unsteady Formulation, as discussed in Section 24.15.1). If you choose the Geo-Reconstruct, Donor-Acceptor, or Euler Explicit scheme, FLUENT will turn on the first-order unsteady formulation for you automatically, so you need not visit the Solver panel yourself. Define −→ Models −→Solver... There are two inputs for the time-dependent calculation in the Multiphase Model panel: • By default, FLUENT will solve the volume fraction equation(s) once for each time step. This means that the convective flux coefficients appearing in the other transport equations will not be completely updated each iteration, since the volume fraction fields will not change from iteration to iteration. If you want FLUENT to solve the volume fraction equation(s) at every iteration within a time step, turn on the Solve VOF Every Iteration option under VOF Parameters. When FLUENT solves these equations every iteration, the convective flux coefficients in the other transport equations will be updated based on the updated volume fractions at each iteration. In general, if you anticipate that the location of the interface will change as the other flow variables converge during the time step, you should enable the Solve VOF Every Iteration option. This situation arises when large time steps are being used in hopes of reaching a steady-state solution, for example. If small time steps are being used, however, it is not necessary to perform the additional work of solving for the volume fraction every iteration, so you can leave this option turned off. This choice is the more stable of the two, and requires less computational effort per time step than the first choice.

!

If you are using sliding meshes, or dynamic meshes with layering and/or remeshing, using the Solve VOF Every Iteration option may yield more accurate results, although at a greater computational cost. • When FLUENT performs a time-dependent VOF calculation, the time step used for the volume fraction calculation will not be the same as the time step used for the rest of the transport equations. FLUENT will refine the time step for VOF automatically, based on your input for the maximum Courant Number allowed near the free surface. The Courant number is a dimensionless number that compares the time step in a calculation to the characteristic time of transit of a fluid element across a control volume: ∆t ∆xcell /vfluid


(22.6-1)

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In the region near the fluid interface, FLUENT divides the volume of each cell by the sum of the outgoing fluxes. The resulting time represents the time it would take for the fluid to empty out of the cell. The smallest such time is used as the characteristic time of transit for a fluid element across a control volume, as described above. Based upon this time and your input for the maximum allowed Courant Number, a time step is computed for use in the VOF calculation. For example, if the maximum allowed Courant number is 0.25 (the default), the time step will be chosen to be at most one-fourth the minimum transit time for any cell near the interface. Note that these inputs are not required when the implicit scheme is used.

22.6.15

Selecting a Turbulence Model for an Eulerian Multiphase Calculation

If you are using the Eulerian model to solve a turbulent flow, you will need to choose one of the three turbulence models described in Section 22.4.8 in the Viscous Model panel (Figure 22.6.14).

Figure 22.6.14: The Viscous Model Panel for an Eulerian Multiphase Calculation

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The procedure is as follows: 1. Select k-epsilon under Model. 2. Select the desired k-epsilon Model and any other related parameters, as described for single-phase calculations in Section 10.10. 3. Under k-epsilon Multiphase Model, indicate the desired multiphase turbulence model (see Section 22.4.8 for details about each): • Select Mixture to use the mixture turbulence model. This is the default model. • Select Dispersed to use the dispersed turbulence model. This model is applicable when there is clearly one primary continuous phase and the rest are dispersed dilute secondary phases. • Select Per Phase to use a k- turbulence model for each phase. This model is appropriate when the turbulence transfer among the phases plays a dominant role.

Including Source Terms By default, the interphase momentum, k, and sources are not included in the calculation. If you want to include any of these source terms, you can enable them using the multiphase-options command in the define/models/viscous/multiphase-turbulence/ text menu. Note that the inclusion of these terms can slow down convergence noticeably. If you are looking for additional accuracy, you may want to compute a solution first without these sources, and then continue the calculation with these terms included. In most cases these terms can be neglected.

22.6.16

Setting Boundary Conditions

Multiphase boundary conditions are set in the Boundary Conditions panel (Figure 22.6.15), but the procedure for setting multiphase boundary conditions is slightly different than for single-phase models. You will need to set some conditions separately for individual phases, while other conditions are shared by all phases (i.e., the mixture), as described in detail below. Define −→Boundary Conditions...

Boundary Conditions for the Mixture and the Individual Phases The conditions you need to specify for the mixture and those you need to specify for the individual phases will depend on which of the three multiphase models you are using. Details for each model are provided below.


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Figure 22.6.15: The Boundary Conditions Panel

VOF Model If you are using the VOF model, the conditions you need to specify for each type of zone are listed below and summarized in Table 22.6.1. • For an exhaust fan, inlet vent, intake fan, outlet vent, pressure inlet, pressure outlet, or velocity inlet, there are no conditions to be specified for the primary phase. For each secondary phase, you will need to set the volume fraction as a constant, a profile (see Section 6.26), or a user-defined function (see the separate UDF Manual). All other conditions are specified for the mixture. • For a mass flow inlet, you will need to set the mass flow rate or mass flux for each individual phase. All other conditions are specified for the mixture.

!

Note that if you read a VOF case that was set up in a version of FLUENT prior to 6.1, you will need to redefine the conditions at the mass flow inlets. • For an axis, fan, outflow, periodic, porous jump, radiator, solid, symmetry, or wall zone, all conditions are specified for the mixture; there are no conditions to be set for the individual phases. • For a fluid zone, mass sources are specified for the individual phases, and all other sources are specified for the mixture. If the fluid zone is not porous, all other conditions are specified for the mixture. If the fluid zone is porous, you will enable the Porous Zone option in the Fluid panel for the mixture. The porosity inputs (if relevant) are also specified for the

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mixture. The resistance coefficients and direction vectors, however, are specified separately for each phase. See Section 6.19.6 for details about these inputs. All other conditions are specified for the mixture. See Chapter 6 for details about the relevant conditions for each type of boundary. Note that the pressure far-field boundary is not available with the VOF model.

Table 22.6.1: Phase-Specific and Mixture Conditions for the VOF Model Type Primary Phase exhaust fan nothing inlet vent intake fan outlet vent pressure inlet pressure outlet velocity inlet mass flow inlet mass flow/flux axis nothing fan outflow periodic porous jump radiator solid symmetry wall pressure far-field not available fluid mass source; other porous inputs


Secondary Phase volume fraction

Mixture all others

mass flow/flux nothing

all others all others

not available mass source; other porous inputs

not available porous zone; porosity; all others

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Mixture Model If you are using the mixture model, the conditions you need to specify for each type of zone are listed below and summarized in Table 22.6.2. • For an exhaust fan, outlet vent, or pressure outlet, there are no conditions to be specified for the primary phase. For each secondary phase, you will need to set the volume fraction as a constant, a profile (see Section 6.26), or a user-defined function (see the separate UDF Manual). All other conditions are specified for the mixture. • For an inlet vent, intake fan, or pressure inlet, you will specify for the mixture which direction specification method will be used at this boundary (Normal to Boundary or Direction Vector). If you select the Direction Vector specification method, you will specify the coordinate system (3D only) and flow-direction components for the individual phases. For each secondary phase, you will need to set the volume fraction (as described above). All other conditions are specified for the mixture. • For a mass flow inlet, you will need to set the mass flow rate or mass flux for each individual phase. All other conditions are specified for the mixture.

!

Note that if you read a mixture multiphase case that was set up in a version of FLUENT previous to 6.1, you will need to redefine the conditions at the mass flow inlets. • For a velocity inlet, you will specify the velocity for the individual phases. For each secondary phase, you will need to set the volume fraction (as described above). All other conditions are specified for the mixture. • For an axis, fan, outflow, periodic, porous jump, radiator, solid, symmetry, or wall zone, all conditions are specified for the mixture; there are no conditions to be set for the individual phases. • For a fluid zone, mass sources are specified for the individual phases, and all other sources are specified for the mixture. If the fluid zone is not porous, all other conditions are specified for the mixture. If the fluid zone is porous, you will enable the Porous Zone option in the Fluid panel for the mixture. The porosity inputs (if relevant) are also specified for the mixture. The resistance coefficients and direction vectors, however, are specified separately for each phase. See Section 6.19.6 for details about these inputs. All other conditions are specified for the mixture. See Chapter 6 for details about the relevant conditions for each type of boundary. Note that the pressure far-field boundary is not available with the mixture model.

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Table 22.6.2: Phase-Specific and Mixture Conditions for the Mixture Model Type exhaust fan outlet vent pressure outlet inlet vent intake fan pressure inlet mass flow inlet velocity inlet

Primary Phase nothing

Secondary Phase volume fraction

Mixture all others

coord. system; flow direction

dir. spec. method; all others all others all others

axis fan outflow periodic porous jump radiator solid symmetry wall pressure far-field fluid

nothing

coord. system; flow direction; volume fraction mass flow/flux velocity; volume fraction nothing



not available porous zone; porosity; all others


mass flow/flux velocity

all others

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Eulerian Model If you are using the Eulerian model, the conditions you need to specify for each type of zone are listed below and summarized in Tables 22.6.3, 22.6.4, 22.6.5, and 22.6.6. Note that the specification of turbulence parameters will depend on which of the three multiphase turbulence models you are using, as indicated in Tables 22.6.4–22.6.6. See Sections 22.4.8 and 22.6.15 for more information about multiphase turbulence models. • For an exhaust fan, outlet vent, or pressure outlet, there are no conditions to be specified for the primary phase if you are modeling laminar flow or using the mixture turbulence model (the default multiphase turbulence model), except for backflow total temperature if heat transfer is on. For each secondary phase, you will need to set the volume fraction as a constant, a profile (see Section 6.26), or a user-defined function (see the separate UDF Manual). If the phase is granular, you will also need to set its granular temperature. If heat transfer is on, you will also need to set the backflow total temperature. If you are using the mixture turbulence model, you will need to specify the turbulence boundary conditions for the mixture; if you are using the dispersed turbulence model, you will need to specify them for the primary phase; if you are using the per-phase turbulence model, you will need to specify them for the primary phase and for each secondary phase. All other conditions are specified for the mixture. • For an inlet vent, intake fan, or pressure inlet, you will specify for the mixture which direction specification method will be used at this boundary (Normal to Boundary or Direction Vector). If you select the Direction Vector specification method, you will specify the coordinate system (3D only) and flow-direction components for the individual phases. If heat transfer is on, you will also need to set the total temperature for the individual phases. For each secondary phase, you will need to set the volume fraction (as described above). If the phase is granular, you will also need to set its granular temperature. If you are using the mixture turbulence model, you will need to specify the turbulence boundary conditions for the mixture; if you are using the dispersed turbulence model, you will need to specify them for the primary phase; if you are using the per-phase turbulence model, you will need to specify them for the primary phase and for each secondary phase. All other conditions are specified for the mixture. • For a velocity inlet, you will specify the velocity for the individual phases. If heat transfer is on, you will also need to set the total temperature for the individual phases.

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For each secondary phase, you will need to set the volume fraction (as described above). If the phase is granular, you will also need to set its granular temperature. If you are using the mixture turbulence model, you will need to specify the turbulence boundary conditions for the mixture; if you are using the dispersed turbulence model, you will need to specify them for the primary phase; if you are using the per-phase turbulence model, you will need to specify them for the primary phase and for each secondary phase. All other conditions are specified for the mixture. • For an axis, outflow, periodic, solid, or symmetry zone, all conditions are specified for the mixture; there are no conditions to be set for the individual phases. • For a wall zone, shear conditions are specified for the individual phases; all other conditions are specified for the mixture, including thermal boundary conditions, if heat transfer is on. • For a fluid zone, all source terms and fixed values are specified for the individual phases, unless you are using the mixture turbulence model or the dispersed turbulence model. If you are using the mixture turbulence model, source terms and fixed values for turbulence are specified instead for the mixture; if you are using the dispersed turbulence model, they are specified only for the primary phase. If the fluid zone is not porous, all other conditions are specified for the mixture. If the fluid zone is porous, you will enable the Porous Zone option in the Fluid panel for the mixture. The porosity inputs (if relevant) are also specified for the mixture. The resistance coefficients and direction vectors, however, are specified separately for each phase. See Section 6.19.6 for details about these inputs. All other conditions are specified for the mixture. See Chapter 6 for details about the relevant conditions for each type of boundary. Note that the pressure far-field, fan, porous jump, and radiator boundaries are not available with the Eulerian model.


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Table 22.6.3: Phase-Specific and Mixture Conditions for the Eulerian Model (for Laminar Flow) Type exhaust fan outlet vent pressure outlet inlet vent intake fan pressure inlet

velocity inlet

axis outflow periodic solid symmetry wall pressure far-field fan porous jump radiator mass flow inlet fluid

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Primary Phase Secondary Phase (tot. temperature) volume fraction; gran. temperature (tot. temperature) coord. system; coord. system; flow direction flow direction; (tot. temperature) volume fraction; gran. temperature (tot. temperature) velocity velocity; (tot. temperature) volume fraction; gran. temperature (tot. temperature) nothing nothing

Mixture all others

dir. spec. method; all others

all others

all others

shear condition not available


all others not available

all source terms; all fixed values; other porous inputs

all source terms; all fixed values; other porous inputs

porous zone; porosity; all others



Table 22.6.4: Phase-Specific and Mixture Conditions for the Eulerian Model (with the Mixture Turbulence Model) Type exhaust fan outlet vent pressure outlet inlet vent intake fan pressure inlet

velocity inlet



Primary Phase Secondary Phase (tot. temperature) volume fraction; gran. temperature (tot. temperature) coord. system; coord. system; flow direction flow direction; (tot. temperature) volume fraction; gran. temperature (tot. temperature) velocity velocity; (tot. temperature) volume fraction; gran. temperature (tot. temperature) nothing nothing

Mixture all others


all others

all others




other source terms; other fixed values; other porous inputs

other source terms; other fixed values; other porous inputs

source terms for turbulence; fixed values for turbulence; porous zone; porosity; all others

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Table 22.6.5: Phase-Specific and Mixture Conditions for the Eulerian Model (with the Dispersed Turbulence Model) Type exhaust fan outlet vent pressure outlet inlet vent intake fan pressure inlet

velocity inlet


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Primary Phase Secondary Phase turb. parameters volume fraction; (tot. temperature) gran. temperature (tot. temperature) coord. system; coord. system; flow direction; flow direction; turb. parameters; volume fraction; (tot. temperature) gran. temperature (tot. temperature) velocity; velocity; turb. parameters volume fraction; (tot. temperature) gran. temperature (tot. temperature) nothing nothing

Mixture all others

dir. spec. method all others

all others

all others




momentum, mass, turb. sources; momentum, mass, turb. fixed values; other porous inputs

momentum and mass sources; momentum and mass fixed values; other porous inputs




Table 22.6.6: Phase-Specific and Mixture Conditions for the Eulerian Model (with the PerPhase Turbulence Model) Type exhaust fan outlet vent pressure outlet inlet vent intake fan pressure inlet

velocity inlet



Primary Phase Secondary Phase turb. parameters volume fraction; (tot. temperature) turb. parameters; gran. temperature (tot. temperature) coord. system; coord. system; flow direction; flow direction; turb. parameters volume fraction; (tot. temperature) turb. parameters; gran. temperature (tot. temperature) velocity; velocity; turb. parameters volume fraction; (tot. temperature) turb. parameters; gran. temperature (tot. temperature) nothing nothing

Mixture all others


all others

all others







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Steps for Setting Boundary Conditions The steps you need to perform for each boundary are as follows: 1. Select the boundary in the Zone list in the Boundary Conditions panel. 2. Set the conditions for the mixture at this boundary, if necessary. (See above for information about which conditions need to be set for the mixture.) (a) In the Phase drop-down list, select mixture. (b) If the current Type for this zone is correct, click Set... to open the corresponding panel (e.g., the Pressure Inlet panel); otherwise, choose the correct zone type in the Type list, confirm the change (when prompted), and the corresponding panel will open automatically. (c) In the corresponding panel for the zone type you have selected (e.g., the Pressure Inlet panel, shown in Figure 22.6.16), specify the mixture boundary conditions.

Figure 22.6.16: The Pressure Inlet Panel for a Mixture Note that only those conditions that apply to all phases, as described above, will appear in this panel.

!

For a VOF calculation, if you enabled the Wall Adhesion option in the Phase Interaction panel, you can specify the contact angle at the wall for each pair of phases (as shown in Figure 22.6.17). The contact angle (θw in Figure 22.2.2) is the angle between the wall and the tangent to the interface at the wall, measured inside the first phase of the pair listed in the Wall panel. For example, if you are setting the contact angle between the oil and air phases in the Wall panel shown in Figure 22.6.17, θw is measured inside the oil phase. The default value for all pairs is 90 degrees, which is equivalent to no wall adhesion effects (i.e., the interface is normal to the adjacent wall). A contact

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Figure 22.6.17: The Wall Panel for a Mixture in a VOF Calculation with Wall Adhesion angle of 45◦ , for example, corresponds to water creeping up the side of a container, as is common with water in a glass. (d) Click OK when you are done setting the mixture boundary conditions. 3. Set the conditions for each phase at this boundary, if necessary. (See above for information about which conditions need to be set for the individual phases.) (a) In the Phase drop-down list, select the phase (e.g., water).

!

Note that, when you select one of the individual phases (rather than the mixture), only one type of zone appears in the Type list. It is not possible to assign phase-specific zone types at a given boundary; the zone type is specified for the mixture, and it applies to all of the individual phases. (b) Click Set... to open the panel for this phase’s conditions (e.g., the Pressure Inlet panel, shown in Figure 22.6.18).


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Figure 22.6.18: The Pressure Inlet Panel for a Phase (c) Specify the conditions for the phase. Note that only those conditions that apply to the individual phase, as described above, will appear in this panel. (d) Click OK when you are done setting the phase-specific boundary conditions.

Steps for Copying Boundary Conditions The steps for copying boundary conditions for a multiphase flow are slightly different from those described in Section 6.1.5 for a single-phase flow. The modified steps are listed below: 1. In the Boundary Conditions panel, click the Copy... button. This will open the Copy BCs panel. 2. In the From Zone list, select the zone that has the conditions you want to copy. 3. In the To Zones list, select the zone or zones to which you want to copy the conditions. 4. In the Phase drop-down list, select the phase for which you want to copy the conditions (either mixture or one of the individual phases).

!

Note that copying the boundary conditions for one phase does not automatically result in the boundary conditions for the other phases and the mixture being copied as well. You need to copy the conditions for each phase on each boundary of interest. 5. Click Copy. FLUENT will set all of the selected phase’s (or mixture’s) boundary conditions on the zones selected in the To Zones list to be the same as that phase’s conditions on the zone selected in the From Zone list. (You cannot copy a subset of the conditions, such as only the thermal conditions.) See Section 6.1.5 for additional information about copying boundary conditions, including limitations.

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22.6.17

Setting Initial Volume Fractions

Once you have initialized the flow (as described in Section 24.13), you can define the initial distribution of the phases. For a transient simulation, this distribution will serve as the initial condition at t = 0; for a steady-state simulation, setting an initial distribution can provide added stability in the early stages of the calculation. You can patch an initial volume fraction for each secondary phase using the Patch panel. Solve −→ Initialize −→Patch... If the region in which you want to patch the volume fraction is defined as a separate cell zone, you can simply patch the value there. Otherwise, you can create a cell “register” that contains the appropriate cells and patch the value in the register. See Section 24.13.2 for details.

22.6.18

Inputs for Compressible VOF and Mixture Model Calculations

If you are using the VOF or mixture model for a compressible flow, note the following: • Only one of the phases can be compressible (i.e., you can select the ideal gas law for the density of only one phase’s material). • If you are using the VOF model, for stability reasons it is better (although not required) if the primary phase is compressible. • If you specify the total pressure at a boundary (e.g., for a pressure inlet or intake fan) the specified value for temperature at that boundary will be used as total temperature for the compressible phase, and as static temperature for the other phases (which are incompressible). • For each mass flow inlet, you will need to specify mass flow or mass flux for each individual phase.

!

Note that if you read a case file that was set up in a version of FLUENT previous to 6.1, you will need to redefine the conditions at the mass flow inlets. See Section 22.6.16 for more information on defining conditions for a mass flow inlet in VOF and mixture multiphase calculations. See Section 8.5 for more information about compressible flows.


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22.6.19

Inputs for Solidification/Melting VOF Calculations

If you are including melting or solidification in your VOF calculation, note the following: • It is possible to model melting or solidification in a single phase or in multiple phases. • For phases that are not melting or solidifying, you must set the latent heat (L), liquidus temperature (Tliquidus ), and solidus temperature (Tsolidus ) to zero. See Chapter 23 for more information about melting and solidification.

22.7

Solution Strategies for General Multiphase Problems

Solution strategies for the VOF, mixture, and Eulerian models are provided in Sections 22.7.1, 22.7.2, and 22.7.3, respectively.

22.7.1

Solution Strategies for the VOF Model

Several recommendations for improving the accuracy and convergence of the VOF solution are presented here.

Setting the Reference Pressure Location The site of the reference pressure can be moved to a location that will result in less roundoff in the pressure calculation. By default, the reference pressure location is the center of the cell at or closest to the point (0,0,0). You can move this location by specifying a new Reference Pressure Location in the Operating Conditions panel. Define −→Operating Conditions... The position that you choose should be in a region that will always contain the least dense of the fluids (e.g., the gas phase, if you have a gas phase and one or more liquid phases). This is because variations in the static pressure are larger in a more dense fluid than in a less dense fluid, given the same velocity distribution. If the zero of the relative pressure field is in a region where the pressure variations are small, less round-off will occur than if the variations occur in a field of large non-zero values. Thus in systems containing air and water, for example, it is important that the reference pressure location be in the portion of the domain filled with air rather than that filled with water.

Pressure Interpolation Scheme For all VOF calculations, you should use the body-force-weighted pressure interpolation scheme or the PRESTO! scheme. Solve −→ Controls −→Solution...

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22.7 Solution Strategies for General Multiphase Problems

Discretization Scheme Selection for the Implicit and Euler Explicit Formulations When the implicit or Euler explicit scheme is used you should use the second-order or QUICK discretization scheme for the volume fraction equations in order to improve the sharpness of the interface between phases. Solve −→ Controls −→Solution...

Pressure-Velocity Coupling and Under-Relaxation for the Time-Dependent Formulations Another change that you should make to the solver settings is in the pressure-velocity coupling scheme and under-relaxation factors that you use. The PISO scheme is recommended for transient calculations in general. Using PISO allows for increased values on all under-relaxation factors, without a loss of solution stability. You can generally increase the under-relaxation factors for all variables to 1 and expect stability and a rapid rate of convergence (in the form of few iterations required per time step). For calculations on tetrahedral or triangular meshes, an under-relaxation factor of 0.7–0.8 for pressure is recommended for improved stability with the PISO scheme. Solve −→ Controls −→Solution... As with any FLUENT simulation, the under-relaxation factors will need to be decreased if the solution exhibits unstable, divergent behavior with the under-relaxation factors set to 1. Reducing the time step is another way to improve the stability.

Under-Relaxation for the Steady-State Formulation If you are using the steady-state implicit VOF scheme, the under-relaxation factors for all variables should be set to values between 0.2 and 0.5 for improved stability.

22.7.2

Solution Strategies for the Mixture Model

Setting the Under-Relaxation Factor for the Slip Velocity You should begin the mixture calculation with a low under-relaxation factor for the slip velocity. A value of 0.2 or less is recommended. If the solution shows good convergence behavior, you can increase this value gradually.

Calculating an Initial Solution For some cases (e.g., cyclone separation), you may be able to obtain a solution more quickly if you compute an initial solution without solving the volume fraction and slip


22-91


velocity equations. Once you have set up the mixture model, you can temporarily disable these equations and compute an initial solution. Solve −→ Controls −→Solution... In the Solution Controls panel, deselect Volume Fraction and Slip Velocity in the Equations list. You can then compute the initial flow field. Once a converged flow field is obtained, turn the Volume Fraction and Slip Velocity equations back on again, and compute the mixture solution.

22.7.3

Solution Strategies for the Eulerian Model

Calculating an Initial Solution To improve convergence behavior, you may want to compute an initial solution before solving the complete Eulerian multiphase model. There are two methods you can use to obtain an initial solution for an Eulerian multiphase calculation: • Set up and solve the problem using the mixture model (with slip velocities) instead of the Eulerian model. You can then enable the Eulerian model, complete the setup, and continue the calculation using the mixture-model solution as a starting point. • Set up the Eulerian multiphase calculation as usual, but compute the flow for only the primary phase. To do this, deselect Volume Fraction in the Equations list in the Solution Controls panel. Once you have obtained an initial solution for the primary phase, turn the volume fraction equations back on and continue the calculation for all phases.

! You should not try to use a single-phase solution obtained without the mixture or Eulerian model as a starting point for an Eulerian multiphase calculation. Doing so will not improve convergence, and may make it even more difficult for the flow to converge.

Temporarily Ignoring Lift and Virtual Mass Forces If you are planning to include the effects of lift and/or virtual mass forces in a steady-state Eulerian multiphase simulation, you can often reduce stability problems that sometimes occur in the early stages of the calculation by temporarily ignoring the action of the lift and the virtual mass forces. Once the solution without these forces starts to converge, you can interrupt the calculation, define these forces appropriately, and continue the calculation.

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22.8 Postprocessing for General Multiphase Problems

Using W-Cycle Multigrid For problems involving a packed-bed granular phase with very small particle sizes (on the order of 10 µm), convergence can be obtained by using the W-cycle multigrid for the pressure. Under Fixed Cycle Parameters in the Multigrid Controls panel, you may need to use higher values for Pre Sweeps, Post Sweeps, and Max Cycles. When you are choosing the values for these parameters, you should also increase the Verbosity to 1 in order to monitor the AMG performance; i.e., to make sure that the pressure equation is solved to a desired level of convergence within the AMG solver during each global iteration. See Section 22.6.11 for more information about granular phases, and Sections 24.5.2 and 24.19.3 for details about multigrid cycles.

22.8

Postprocessing for General Multiphase Problems

Each of the three general multiphase models provides a number of additional field functions that you can plot or report. You can also report flow rates for individual phases for all three models, and display velocity vectors for the individual phases in a mixture or Eulerian calculation. Information about these postprocessing topics is provided in the following subsections: • Section 22.8.1: Available Postprocessing Variables • Section 22.8.2: Displaying Velocity Vectors for Individual Phases • Section 22.8.3: Reporting Fluxes for Individual Phases • Section 22.8.4: Reporting Forces on Walls for Individual Phases • Section 22.8.5: Reporting Flow Rates for Individual Phases

22.8.1

Available Postprocessing Variables

When you use one of the general multiphase models, some additional field functions will be available for postprocessing, as listed in this section. Most field functions that are available in single phase calculations will be available for either the mixture or each individual phase, as appropriate for the general multiphase model and specific options that you are using. See Chapter 29 for a complete list of field functions and their definitions. Chapters 27 and 28 explain how to generate graphics displays and reports of data.


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VOF Model For VOF calculations you can generate graphical plots or alphanumeric reports of the following additional item: • Volume fraction (in the Phases... category), available for each phase. The non-phase-specific variables that are available (e.g., variables in the Pressure... and Velocity... categories) represent mixture quantities. Thermal quantities will be available only for calculations that include the energy equation.

Mixture Model For calculations with the mixture model, you can generate graphical plots or alphanumeric reports of the following additional items: • Diameter (in the Properties... category), available only for secondary phases. • Volume fraction (in the Phases... category), available for each phase. The non-phase-specific variables that are available (e.g., variables in the Pressure... category) represent mixture quantities. Thermal quantities will be available only for calculations that include the energy equation.

Eulerian Model For Eulerian multiphase calculations you can generate graphical plots or alphanumeric reports of the following additional items: • Diameter (in the Properties... category), available only for secondary phases. • Granular Conductivity (in the Properties... category), available only for granular phases. • Granular Pressure (in the Granular Pressure... category), available only for granular phases. • Granular Temperature (in the Granular Temperature... category), available only for granular phases. • Volume fraction (in the Phases... category), available for each phase. The availability of turbulence quantities will depend on which multiphase turbulence model you used in the calculation. Thermal quantities will be available (on a per-phase basis) only for calculations that include the energy equation.

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22.8 Postprocessing for General Multiphase Problems

22.8.2

Displaying Velocity Vectors for Individual Phases

For mixture and Eulerian calculations, it is possible to display velocity vectors for the individual phases using the Vectors panel. Display −→Vectors... To display the velocity of a particular phase, select Velocity in the Vectors Of dropdown list, and then select the desired phase in the Phase drop-down list. You can also choose Relative Velocity to display the phase velocity relative to a moving reference frame. To display the mixture velocity ~vm (relevant for mixture model calculations only), select Velocity (or Relative Velocity for the mixture velocity relative to a moving reference frame), and mixture as the Phase. Note that you can color vectors by values of any available variable, for any phase you defined. To do so, make the appropriate selections in the Color By and following Phase drop-down lists.

22.8.3

Reporting Fluxes for Individual Phases

When you use the Flux Reports panel to compute fluxes through boundaries, you will be able to specify whether the report is for the mixture or for an individual phase. Report −→Fluxes... Select mixture in the Phase drop-down list at the bottom of the panel to report fluxes for the mixture, or select the name of a phase to report fluxes just for that phase.

22.8.4

Reporting Forces on Walls for Individual Phases

For Eulerian calculations, when you use the Force Reports panel to compute forces or moments on wall boundaries, you will be able to specify the individual phase for which you want to compute the forces. Report −→Forces... Select the name of the desired phase in the Phase drop-down list on the left side of the panel.

22.8.5

Reporting Flow Rates for Individual Phases

You can obtain a report of mass flow rate for each phase (and the mixture) through each flow boundary using the report/mass-flow text command: report −→mass-flow When you specify the phase of interest (the mixture or an individual phase), FLUENT will list each zone, followed by the mass flow rate through that zone for the specified phase. An example is shown below.


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/report> mf (mixture water air) domain id/name [mixture] air zone 10 (spiral-press-outlet): -1.2330244 zone 3 (pressure-outlet): -9.7560663 zone 11 (spiral-vel-inlet): 0.6150589 zone 8 (spiral-wall): 0 zone 1 (walls): 0 zone 4 (velocity-inlet): 4.9132133 net mass-flow: -5.4608185

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Chapter 23. Melting

Modeling Solidification and

This chapter describes how you can model solidification and melting in FLUENT. Information is organized into the following sections: • Section 23.1: Overview and Limitations of the Solidification/Melting Model • Section 23.2: Theory for the Solidification/Melting Model • Section 23.3: Using the Solidification/Melting Model

23.1

Overview and Limitations of the Solidification/Melting Model

23.1.1

Overview

FLUENT can be used to solve fluid flow problems involving solidification and/or melting taking place at one temperature (e.g., in pure metals) or over a range of temperatures (e.g., in binary alloys). Instead of tracking the liquid-solid front explicitly, FLUENT uses an enthalpy-porosity formulation. The liquid-solid mushy zone is treated as a porous zone with porosity equal to the liquid fraction, and appropriate momentum sink terms are added to the momentum equations to account for the pressure drop caused by the presence of solid material. Sinks are also added to the turbulence equations to account for reduced porosity in the solid regions. FLUENT provides the following capabilities for modeling solidification and melting: • Calculation of liquid-solid solidification/melting in pure metals as well as in binary alloys • Modeling of continuous casting processes (i.e., “pulling” of solid material out of the domain) • Modeling of the thermal contact resistance between solidified material and walls (e.g., due to the presence of an air gap) • Modeling of species transport with solidification/melting


23-1

Modeling Solidification and Melting

• Postprocessing of quantities related to solidification/melting (i.e., liquid fraction and pull velocities) These modeling capabilities allow FLUENT to simulate a wide range of solidification/melting problems, including melting, freezing, crystal growth, and continuous casting. The physical equations used for these calculations are described in Section 23.2, and instructions for setting up and solving a solidification/melting problem are provided in Section 23.3.

23.1.2

Limitations

As mentioned in Section 23.1.1, the formulation in FLUENT can be used to model the solidification/melting of pure materials, as well as alloys. The liquid fraction versus temperature relationship used in FLUENT is the lever rule; i.e., a linear relationship (Equation 23.2-3). Other relationships are possible [258], but are not currently available in FLUENT. The following limitations apply to the solidification/melting model in FLUENT: • The solidification/melting model can be used only with the segregated solver; it is not available with the coupled solvers. • The solidification/melting model cannot be used for compressible flows. • Of the general multiphase models (VOF, mixture, and Eulerian), only the VOF model can be used with the solidification/melting model. • With the exception of species diffusivities, you cannot specify material properties separately for the solid and liquid materials. • When using the solidification/melting model in conjunction with modeling species transport with reactions, there is no mechanism to restrict the reactions to only the liquid region; i.e., the reactions are solved everywhere.

23-2


23.2 Theory for the Solidification/Melting Model

23.2

Theory for the Solidification/Melting Model

An enthalpy-porosity technique [274, 275, 276] is used in FLUENT for modeling the solidification/melting process. In this technique, the melt interface is not tracked explicitly. Instead, a quantity called the liquid fraction, which indicates the fraction of the cell volume that is in liquid form, is associated with each cell in the domain. The liquid fraction is computed at each iteration, based on an enthalpy balance. The mushy zone is a region in which the liquid fraction lies between 0 and 1. The mushy zone is modeled as a “pseudo” porous medium in which the porosity decreases from 1 to 0 as the material solidifies. When the material has fully solidified in a cell, the porosity becomes zero and hence the velocities also drop to zero. In this section, an overview of the solidification/melting theory is given. Please refer to [276] for details on the enthalpy-porosity method.

23.2.1

Energy Equation

The enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, ∆H: H = h + ∆H

(23.2-1)

where h = href + and href Tref cp

Z

T

Tref

cp dT

(23.2-2)

= reference enthalpy = reference temperature = specific heat at constant pressure

The liquid fraction, β, can be defined as

β = 0 if T < Tsolidus β = 1 if T > Tliquidus β=

T − Tsolidus if Tsolidus < T < Tliquidus Tliquidus − Tsolidus

(23.2-3)

Equation 23.2-3 is referred to as the lever rule. The latent heat content can now be written in terms of the latent heat of the material, L:


23-3


∆H = βL

(23.2-4)

The latent heat content can vary between zero (for a solid) and L (for a liquid). In the case of multicomponent solidification with species segregation; i.e., solidification or melting with species transport, the solidus and liquidus temperatures are computed instead of specified (Equations 23.2-5 and 23.2-6).

Tsolidus = Tmelt +

X

Ki m i Y i

(23.2-5)

X

m i Yi

(23.2-6)

solutes

Tliquidus = Tmelt +

solutes

where Ki is the partition coefficient of solute i, which is the ratio of the concentration in solid to that in liquid at the interface, Yi is the mass fraction of solute i, and mi is the slope of the liquidus surface with respect to Yi . It is assumed that the last species material of the mixture is the solvent and that the other species are the solutes. For solidification/melting problems, the energy equation is written as ∂ (ρH) + ∇ · (ρ~v H) = ∇ · (k∇T ) + S ∂t where

H ρ ~v S

(23.2-7)

= enthalpy (see Equation 23.2-1) = density = fluid velocity = source term

The solution for temperature is essentially an iteration between the energy equation (Equation 23.2-7) and the liquid fraction equation (Equation 23.2-3). Directly using Equation 23.2-3 to update the liquid fraction usually results in poor convergence of the energy equation. In FLUENT, the method suggested by Voller and Swaminathan [277] is used to update the liquid fraction. For pure metals, where Tsolidus and Tliquidus are equal, a method based on specific heat, given by [276], is used instead.

23.2.2

Momentum Equations

The enthalpy-porosity technique treats the mushy region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions. The momentum sink due to the reduced porosity in the mushy zone takes the following form:

23-4



S=

(1 − β)2 Amush (~v − ~vp ) (β 3 + )

(23.2-8)

where β is the liquid volume fraction, is a small number (0.001) to prevent division by zero, Amush is the mushy zone constant, and ~vp is the solid velocity due to the pulling of solidified material out of the domain (also referred to as the pull velocity). The mushy zone constant measures the amplitude of the damping; the higher this value, the steeper the transition of the velocity of the material to zero as it solidifies. Very large values may cause the solution to oscillate. The pull velocity is included to account for the movement of the solidified material as it is continuously withdrawn from the domain in continuous casting processes. The presence of this term in Equation 23.2-8 allows newly solidified material to move at the pull velocity. If solidified material is not being pulled from the domain, ~vp = 0. More details about the pull velocity are provided in Section 23.2.5.

23.2.3

Turbulence Equations

Sinks are added to all of the turbulence equations in the mushy and solidified zones to account for the presence of solid matter. The sink term is very similar to the momentum sink term (Equation 23.2-8): S=

(1 − β)2 Amush φ (β 3 + )

(23.2-9)

where φ represents the turbulence quantity being solved (k, , ω, etc.), and the mushy zone constant, Amush , is the same as the one used in Equation 23.2-8.

23.2.4

Species Equations

In the case of solidification/melting with species transport, the following species equation is solved: ∂ (ρYi ) + ∇ · (ρ [β~vliq Yi,liq + (1 − β)~vp Yi,sol ]) = −∇ · J~i + Ri ∂t

(23.2-10)

where J~i is given by J~i = −ρ[βDi,m,liq ∇Yi,liq + (1 − β)Di,m,sol ∇Yi,sol ]

(23.2-11)

Here Yi is the average species mass fraction in a cell:


23-5


Yi = βYi,liq + (1 − β)Yi,sol

(23.2-12)

Yi,liq and Yi,sol are related by the partition coefficient Ki : Yi,sol = Ki Yi,liq

(23.2-13)

~vliq is the velocity of the liquid and ~vp is the solid (pull) velocity. ~vp is set to zero if pull velocities are not included in the solution. The liquid velocity can be found from the average velocity (as determined by the flow equation) as ~vliq =

23.2.5

(~v − ~vp (1 − β)) β

(23.2-14)

Pull Velocity for Continuous Casting

In continuous casting processes, the solidified matter is usually continuously pulled out from the computational domain, as shown in Figure 23.2.1. Consequently, the solid material will have a finite velocity that needs to be accounted for in the enthalpy-porosity technique.

mushy zone

solidified shell

vp

liquid pool

wall

Figure 23.2.1: “Pulling” a Solid in Continuous Casting

As mentioned in Section 23.2.2, the enthalpy-porosity approach treats the solid-liquid mushy zone as a porous medium with porosity equal to the liquid fraction. A suitable sink term is added in the momentum equation to account for the pressure drop due to the porous structure of the mushy zone. For continuous casting applications, the relative velocity between the molten liquid and the solid is used in the momentum sink term (Equation 23.2-8) rather than the absolute velocity of the liquid. The exact computation of the pull velocity for the solid material is dependent on the Young’s modulus and Poisson’s ratio of the solid and the forces acting on it. FLUENT

23-6



uses a Laplacian equation to approximate the pull velocities in the solid region based on the velocities at the boundaries of the solidified region: ∇2~vp = 0

(23.2-15)

FLUENT uses the following boundary conditions when computing the pull velocities: • At a velocity inlet, a stationary wall, or a moving wall, the specified velocity is used. • At all other boundaries (including the liquid-solid interface between the liquid and solidified material), a zero-gradient velocity is used. The pull velocities are computed only in the solid region. Note that FLUENT can also use a specified constant value or custom field function for the pull velocity, instead of computing it. See Section 23.3.2 for details.

23.2.6

Contact Resistance at Walls

FLUENT’s solidification/melting model can account for the presence of an air gap between the walls and the solidified material, using an additional heat transfer resistance between walls and cells with liquid fraction less than 1. This contact resistance is accounted for by modifying the conductivity of the fluid near the wall. Thus, the wall heat flux, as shown in Figure 23.2.2, is written as q=

(T − Tw ) (l/k + Rc (1 − β))

(23.2-16)

where T , Tw , and l are defined in Figure 23.2.2, k is the thermal conductivity of the fluid, β is the liquid volume fraction, and Rc is the contact resistance, which has the same units as the inverse of the heat transfer coefficient.


23-7


wall near-wall cell Tw

●

T

l

T

Tw ●

●

Rc

●

l/k

Figure 23.2.2: Circuit for Contact Resistance

23.3

Using the Solidification/Melting Model

23.3.1

Setup Procedure

The procedure for setting up a solidification/melting problem is described below. (Note that this procedure includes only those steps necessary for the solidification/melting model itself; you will need to set up other models, boundary conditions, etc. as usual.) 1. To activate the solidification/melting model, turn on the Solidification/Melting option in the Solidification and Melting panel (Figure 23.3.1). Define −→ Models −→Solidification & Melting... FLUENT will automatically enable the energy equation, so you do not have to visit the Energy panel before turning on the solidification/melting model. 2. Under Parameters, specify the value of the Mushy Zone Constant (Amush in Equation 23.2-8). Values between 104 and 107 are recommended for most computations. The higher the value of the Mushy Zone Constant, the steeper the damping curve becomes, and the faster the velocity drops to zero as the material solidifies. Very large values may cause the solution to oscillate as control volumes alternately solidify and melt with minor perturbations in liquid volume fraction.

23-8


23.3 Using the Solidification/Melting Model

Figure 23.3.1: The Solidification and Melting Panel

3. If you want to include the pull velocity in your simulation (as described in Sections 23.2.2 and 23.2.5), turn on the Include Pull Velocities option under Parameters. 4. If you are including pull velocities and you want FLUENT to compute them (using Equation 23.2-15) based on the specified velocity boundary conditions, as described in Section 23.2.5, turn on the Compute Pull Velocities option and specify the number of Flow Iterations Per Pull Velocity Iteration.

!

It is not necessary to have FLUENT compute the pull velocities. See Section 23.3.2 for information about other approaches. The default value of 1 for the Flow Iterations Per Pull Velocity Iteration indicates that the pull velocity equations will be solved after each iteration of the solver. If you increase this value, the pull velocity equations will be solved less frequently. You may want to increase the number of Flow Iterations Per Pull Velocity Iteration if the liquid fraction equation is almost converged (i.e., the position of the liquid-solid interface is not changing very much). This will speed up the calculation, although the residuals may jump when the pull velocities are updated. 5. In the Materials panel, specify the Melting Heat (L in Equation 23.2-3), Solidus Temperature (Tsolidus in Equation 23.2-3), and Liquidus Temperature (Tliquidus in Equation 23.2-3) for the material being used in your model. Define −→Materials... If you are solving for species transport, you will also have to specify the Melting Temperature of pure solvent (Tmelt in Equations 23.2-5 and 23.2-6). The solvent is the last species material of the mixture material. For each solute, you will have to specify the slope of the liquidus surface (Slope of Liquidus Line) with respect to the concentration of the solute (mi in Equations 23.2-5 and 23.2-6), the Partition Coefficient (Ki ), and the rate of Diffusion in Solid. It is not necessary to specify mi and Ki for the solvent.


23-9


6. Set the boundary conditions. Define −→Boundary Conditions... In addition to the usual boundary conditions, consider the following: • If you want to account for the presence of an air gap between a wall and an adjacent solidified region (as described in Section 23.2.6), specify a nonzero value, a profile, or a user-defined function for Contact Resistance (Rc in Equation 23.2-16) under Thermal Conditions in the Wall panel. • If you want to specify the gradient of the surface tension with respect to the temperature at a wall boundary, you can use the Marangoni Stress option for the wall Shear Condition. See Section 6.13.1 for details. • If you want FLUENT to compute the pull velocities during the calculation, note how your specified velocity conditions are used in this calculation (see Section 23.2.5). Section 23.3.2 contains additional information about modeling continuous casting. See Sections 23.3.3 and 23.3.4 for information about solving a solidification/melting model and postprocessing the results.

23.3.2

Procedures for Modeling Continuous Casting

As described in Sections 23.2.2 and 23.2.5, you can include the pull velocities in your solidification/melting calculation to model continuous casting. There are three approaches to modeling continuous casting in FLUENT: • Specify constant or variable pull velocities. To use this approach (the default), do not turn on the Compute Pull Velocities option. If you use this approach, you will need to patch constant values or custom field functions for the pull velocities, after you initialize the solution. Solve −→ Initialize −→Patch... See Section 24.13.2 for details about patching values. Note that it is acceptable to patch values for the pull velocities in the entire domain, because the patched values will be used only if the liquid fraction, β, is less than 1. • Have FLUENT compute the pull velocities (using Equation 23.2-15) during the calculation, based on the specified velocity boundary conditions. To use this approach, turn on the Compute Pull Velocities option. This method is computationally expensive, and is recommended only if the pull velocities are strongly dependent on the location of the liquid-solid interface. If you have FLUENT compute the pull velocities, then there are no additional inputs or setup procedures beyond those presented in Section 23.3.1.

23-10


23.3 Using the Solidification/Melting Model

• Have FLUENT compute the pull velocities just once, and then use those values for the remainder of the calculation. To use this approach, perform one iteration with FLUENT computing the pull velocities, and then turn off the Compute Pull Velocities option and continue the calculation. For the remainder of the calculation, FLUENT will use the values computed for the pull velocities at the first iteration.

23.3.3

Solution Procedure

Before solving the coupled fluid flow and heat transfer problem, you may want to patch an initial temperature or solve the steady conduction problem as an initial condition. The coupled problem can then be solved as either steady or unsteady. Because of the nonlinear nature of these problems, however, in most cases an unsteady solution approach is preferred. You can specify the under-relaxation factor applied to the liquid fraction equation in the Solution Controls panel. Solve −→ Controls −→Solution... Specify the desired value in the Liquid Fraction Update field under Under-Relaxation Factors. This sets the value of αβ in the following equation for updating the liquid fraction from one iteration (n) to the next (n + 1): βn+1 = βn + αβ ∆β

(23.3-1)

where ∆β is the predicted change in liquid fraction. In many cases, there is no need to change the default value of αβ . If, however, there are convergence difficulties, reducing the value may improve the solution convergence. Convergence difficulties can be expected in steady-state calculations, continuous casting simulations, simulations involving multicomponent solidification, and simulations where a large value of the mushy zone constant is used.

23.3.4

Postprocessing

For solidification/melting calculations, you can generate graphical plots or alphanumeric reports of the following items, which are all available in the Solidification/Melting... category of the variable selection drop-down list that appears in postprocessing panels: • Liquid Fraction • Contact Resistivity • X, Y, Z or Axial, Radial, Swirl Pull Velocity


23-11


The first two items are available for all solidification/melting simulations, and the others will appear only if you are including pull velocities (either computed or specified) in the simulation. See Chapter 29 for a complete list of field functions and their definitions. Chapters 27 and 28 explain how to generate graphics displays and reports of data. Figure 23.3.2 shows filled contours of liquid fraction for a continuous crystal growth simulation.

1.00e+00 9.00e-01 8.00e-01 7.00e-01 6.00e-01 5.00e-01 4.00e-01 3.00e-01 2.00e-01 1.00e-01 0.00e+00

Contours of Liquid Fraction

Figure 23.3.2: Liquid Fraction Contours for Continuous Crystal Growth

23-12


Chapter 24.

Using the Solver

This chapter describes the FLUENT solver and how to use it. Details about the solver algorithms used by FLUENT are provided in Sections 24.1–24.5. Section 24.6 provides an overview of how to use the solver, and the remaining sections provide detailed instructions. • Section 24.1: Overview of Numerical Schemes • Section 24.2: Discretization • Section 24.3: Segregated Solver • Section 24.4: Coupled Solver • Section 24.5: Multigrid Method • Section 24.6: Overview of How to Use the Solver • Section 24.7: Choosing the Discretization Scheme • Section 24.8: Choosing the Pressure-Velocity Coupling Method • Section 24.9: Setting Under-Relaxation Factors • Section 24.10: Changing the Courant Number • Section 24.11: Turning on FAS Multigrid • Section 24.12: Setting Solution Limits • Section 24.13: Initializing the Solution • Section 24.14: Performing Steady-State Calculations • Section 24.15: Performing Time-Dependent Calculations • Section 24.16: Monitoring Solution Convergence • Section 24.17: Animating the Solution • Section 24.18: Executing Commands During the Calculation • Section 24.19: Convergence and Stability


24-1

Using the Solver

24.1

Overview of Numerical Schemes

FLUENT allows you to choose either of two numerical methods: • segregated solver • coupled solver Using either method, FLUENT will solve the governing integral equations for the conservation of mass and momentum, and (when appropriate) for energy and other scalars such as turbulence and chemical species. In both cases a control-volume-based technique is used that consists of: • Division of the domain into discrete control volumes using a computational grid. • Integration of the governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables (“unknowns”) such as velocities, pressure, temperature, and conserved scalars. • Linearization of the discretized equations and solution of the resultant linear equation system to yield updated values of the dependent variables. The two numerical methods employ a similar discretization process (finite-volume), but the approach used to linearize and solve the discretized equations is different. The general solution methods are described first in Sections 24.1.1 and 24.1.2, followed by a discussion of the linearization methods in Section 24.1.3.

24.1.1

Segregated Solution Method

The segregated solver is the solution algorithm previously used by FLUENT 4. Using this approach, the governing equations are solved sequentially (i.e., segregated from one another). Because the governing equations are non-linear (and coupled), several iterations of the solution loop must be performed before a converged solution is obtained. Each iteration consists of the steps illustrated in Figure 24.1.1 and outlined below: 1. Fluid properties are updated, based on the current solution. (If the calculation has just begun, the fluid properties will be updated based on the initialized solution.) 2. The u, v, and w momentum equations are each solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field.

24-2


24.1 Overview of Numerical Schemes

3. Since the velocities obtained in Step 2 may not satisfy the continuity equation locally, a “Poisson-type” equation for the pressure correction is derived from the continuity equation and the linearized momentum equations. This pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied. 4. Where appropriate, equations for scalars such as turbulence, energy, species, and radiation are solved using the previously updated values of the other variables. 5. When interphase coupling is to be included, the source terms in the appropriate continuous phase equations may be updated with a discrete phase trajectory calculation. 6. A check for convergence of the equation set is made. These steps are continued until the convergence criteria are met.

Update properties.

Solve momentum equations.

Solve pressure-correction (continuity) equation. Update pressure, face mass flow rate.

Solve energy, species, turbulence, and other scalar equations.

Converged?

Stop

Figure 24.1.1: Overview of the Segregated Solution Method


24-3

Using the Solver

24.1.2

Coupled Solution Method

The coupled solver solves the governing equations of continuity, momentum, and (where appropriate) energy and species transport simultaneously (i.e., coupled together). Governing equations for additional scalars will be solved sequentially (i.e., segregated from one another and from the coupled set) using the procedure described for the segregated solver in Section 24.1.1. Because the governing equations are non-linear (and coupled), several iterations of the solution loop must be performed before a converged solution is obtained. Each iteration consists of the steps illustrated in Figure 24.1.2 and outlined below: 1. Fluid properties are updated, based on the current solution. (If the calculation has just begun, the fluid properties will be updated based on the initialized solution.) 2. The continuity, momentum, and (where appropriate) energy and species equations are solved simultaneously. 3. Where appropriate, equations for scalars such as turbulence and radiation are solved using the previously updated values of the other variables. 4. When interphase coupling is to be included, the source terms in the appropriate continuous phase equations may be updated with a discrete phase trajectory calculation. 5. A check for convergence of the equation set is made. These steps are continued until the convergence criteria are met.

24.1.3

Linearization: Implicit vs. Explicit

In both the segregated and coupled solution methods the discrete, non-linear governing equations are linearized to produce a system of equations for the dependent variables in every computational cell. The resultant linear system is then solved to yield an updated flow-field solution. The manner in which the governing equations are linearized may take an “implicit” or “explicit” form with respect to the dependent variable (or set of variables) of interest. By implicit or explicit we mean the following: • implicit: For a given variable, the unknown value in each cell is computed using a relation that includes both existing and unknown values from neighboring cells. Therefore each unknown will appear in more than one equation in the system, and these equations must be solved simultaneously to give the unknown quantities.

24-4


24.1 Overview of Numerical Schemes

Update properties.

Solve continuity, momentum, energy, and species equations simultaneously.

Solve turbulence and other scalar equations.

Converged?

Stop

Figure 24.1.2: Overview of the Coupled Solution Method

• explicit: For a given variable, the unknown value in each cell is computed using a relation that includes only existing values. Therefore each unknown will appear in only one equation in the system and the equations for the unknown value in each cell can be solved one at a time to give the unknown quantities. In the segregated solution method each discrete governing equation is linearized implicitly with respect to that equation’s dependent variable. This will result in a system of linear equations with one equation for each cell in the domain. Because there is only one equation per cell, this is sometimes called a “scalar” system of equations. A point implicit (Gauss-Seidel) linear equation solver is used in conjunction with an algebraic multigrid (AMG) method to solve the resultant scalar system of equations for the dependent variable in each cell. For example, the x-momentum equation is linearized to produce a system of equations in which u velocity is the unknown. Simultaneous solution of this equation system (using the scalar AMG solver) yields an updated u-velocity field. In summary, the segregated approach solves for a single variable field (e.g., p) by considering all cells at the same time. It then solves for the next variable field by again considering all cells at the same time, and so on. There is no explicit option for the segregated solver. In the coupled solution method you have a choice of using either an implicit or explicit linearization of the governing equations. This choice applies only to the coupled set of


24-5

Using the Solver

governing equations. Governing equations for additional scalars that are solved segregated from the coupled set, such as for turbulence, radiation, etc., are linearized and solved implicitly using the same procedures as in the segregated solution method. Regardless of whether you choose the implicit or explicit scheme, the solution procedure shown in Figure 24.1.2 is followed. If you choose the implicit option of the coupled solver, each equation in the coupled set of governing equations is linearized implicitly with respect to all dependent variables in the set. This will result in a system of linear equations with N equations for each cell in the domain, where N is the number of coupled equations in the set. Because there are N equations per cell, this is sometimes called a “block” system of equations. A point implicit (block Gauss-Seidel) linear equation solver is used in conjunction with an algebraic multigrid (AMG) method to solve the resultant block system of equations for all N dependent variables in each cell. For example, linearization of the coupled continuity, x-, y-, z-momentum, and energy equation set will produce a system of equations in which p, u, v, w, and T are the unknowns. Simultaneous solution of this equation system (using the block AMG solver) yields at once updated pressure, u-, v-, w-velocity, and temperature fields. In summary, the coupled implicit approach solves for all variables (p, u, v, w, T ) in all cells at the same time. If you choose the explicit option of the coupled solver, each equation in the coupled set of governing equations is linearized explicitly. As in the implicit option, this too will result in a system of equations with N equations for each cell in the domain. And likewise, all dependent variables in the set will be updated at once. However, this system of equations is explicit in the unknown dependent variables. For example, the x-momentum equation is written such that the updated x velocity is a function of existing values of the field variables. Because of this, a linear equation solver is not needed. Instead, the solution is updated using a multi-stage (Runge-Kutta) solver. Here you have the additional option of employing a full approximation storage (FAS) multigrid scheme to accelerate the multi-stage solver. In summary, the coupled explicit approach solves for all variables (p, u, v, w, T ) one cell at a time. Note that the FAS multigrid is an optional component of the explicit approach, while the AMG is a required element in both the segregated and coupled implicit approaches.

24-6


24.2 Discretization

24.2

Discretization

FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the governing equations about each control volume, yielding discrete equations that conserve each quantity on a control-volume basis. Discretization of the governing equations can be illustrated most easily by considering the steady-state conservation equation for transport of a scalar quantity φ. This is demonstrated by the following equation written in integral form for an arbitrary control volume V as follows: I

~= ρφ ~v · dA

I

~+ Γφ ∇φ · dA

Z

V

Sφ dV

(24.2-1)

where ρ ~v ~ A Γφ ∇φ Sφ

= = = = = =

density velocity vector (= u ˆı + v ˆ in 2D) surface area vector diffusion coefficient for φ gradient of φ (= ∂φ/∂x) ˆı + (∂φ/∂y) ˆ in 2D) source of φ per unit volume

Equation 24.2-1 is applied to each control volume, or cell, in the computational domain. The two-dimensional, triangular cell shown in Figure 24.2.1 is an example of such a control volume. Discretization of Equation 24.2-1 on a given cell yields NX faces f

~f = ρf ~vf φf · A

NX faces

~ f + Sφ V Γφ (∇φ)n · A

(24.2-2)

f

where Nfaces φf ~f ρf ~vf · A ~ Af (∇φ)n V

= = = = = =

number of faces enclosing cell value of φ convected through face f mass flux through the face area of face f , |A| (= |Axˆı + Ay ˆ| in 2D) magnitude of ∇φ normal to face f cell volume

The equations solved by FLUENT take the same general form as the one given above and apply readily to multi-dimensional, unstructured meshes composed of arbitrary polyhedra. By default, FLUENT stores discrete values of the scalar φ at the cell centers (c0 and c1 in Figure 24.2.1). However, face values φf are required for the convection terms in Equa-


24-7

Using the Solver

c1 A c0

Figure 24.2.1: Control Volume Used to Illustrate Discretization of a Scalar Transport Equation

tion 24.2-2 and must be interpolated from the cell center values. This is accomplished using an upwind scheme. Upwinding means that the face value φf is derived from quantities in the cell upstream, or “upwind,” relative to the direction of the normal velocity vn in Equation 24.2-2. FLUENT allows you to choose from several upwind schemes: first-order upwind, second-order upwind, power law, and QUICK. These schemes are described in Sections 24.2.1–24.2.4. The diffusion terms in Equation 24.2-2 are central-differenced and are always secondorder accurate.

24.2.1

First-Order Upwind Scheme

When first-order accuracy is desired, quantities at cell faces are determined by assuming that the cell-center values of any field variable represent a cell-average value and hold throughout the entire cell; the face quantities are identical to the cell quantities. Thus when first-order upwinding is selected, the face value φf is set equal to the cell-center value of φ in the upstream cell

24.2.2

Power-Law Scheme

The power-law discretization scheme interpolates the face value of a variable, φ, using the exact solution to a one-dimensional convection-diffusion equation ∂ ∂ ∂φ (ρuφ) = Γ ∂x ∂x ∂x

(24.2-3)

where Γ and ρu are constant across the interval ∂x. Equation 24.2-3 can be integrated to yield the following solution describing how φ varies with x:

24-8


24.2 Discretization

exp(Pe Lx ) − 1 φ(x) − φ0 = φL − φ0 exp(Pe) − 1

(24.2-4)

where φ0 φL

= φ|x=0 = φ|x=L

and Pe is the Peclet number: Pe =

ρuL Γ

(24.2-5)

The variation of φ(x) between x = 0 and x = L is depicted in Figure 24.2.2 for a range of values of the Peclet number. Figure 24.2.2 shows that for large Pe, the value of φ at x = L/2 is approximately equal to the upstream value. This implies that when the flow is dominated by convection, interpolation can be accomplished by simply letting the face value of a variable be set equal to its “upwind” or upstream value. This is the standard first-order scheme for FLUENT. φL Pe < -1

Pe = -1

φ

Pe= 0

Pe = 1

Pe > 1

φ0

0

L X

Figure 24.2.2: Variation of a Variable φ Between x = 0 and x = L (Equation 24.2-3)

If the power-law scheme is selected, FLUENT uses Equation 24.2-4 in an equivalent “power law” format [189], as its interpolation scheme. As discussed in Section 24.2.1, Figure 24.2.2 shows that for large Pe, the value of φ at x = L/2 is approximately equal to the upstream value. When Pe=0 (no flow, or pure


24-9

Using the Solver

diffusion), Figure 24.2.2 shows that φ may be interpolated using a simple linear average between the values at x = 0 and x = L. When the Peclet number has an intermediate value, the interpolated value for φ at x = L/2 must be derived by applying the “power law” equivalent of Equation 24.2-4.

24.2.3

Second-Order Upwind Scheme

When second-order accuracy is desired, quantities at cell faces are computed using a multidimensional linear reconstruction approach [8]. In this approach, higher-order accuracy is achieved at cell faces through a Taylor series expansion of the cell-centered solution about the cell centroid. Thus when second-order upwinding is selected, the face value φf is computed using the following expression: φf = φ + ∇φ · ∆~s

(24.2-6)

where φ and ∇φ are the cell-centered value and its gradient in the upstream cell, and ∆~s is the displacement vector from the upstream cell centroid to the face centroid. This formulation requires the determination of the gradient ∇φ in each cell. This gradient is computed using the divergence theorem, which in discrete form is written as faces 1 NX ~ ∇φ = φ˜f A V f

(24.2-7)

Here the face values φ˜f are computed by averaging φ from the two cells adjacent to the face. Finally, the gradient ∇φ is limited so that no new maxima or minima are introduced.

24.2.4

QUICK Scheme

For quadrilateral and hexahedral meshes, where unique upstream and downstream faces and cells can be identified, FLUENT also provides the QUICK scheme for computing a higher-order value of the convected variable φ at a face. QUICK-type schemes [145] are based on a weighted average of second-order-upwind and central interpolations of the variable. For the face e in Figure 24.2.3, if the flow is from left to right, such a value can be written as

Sd Sc Su + 2Sc Sc φe = θ φP + φE + (1 − θ) φP − φW S c + Sd S c + Sd Su + S c Su + S c

(24.2-8)

θ = 1 in the above equation results in a central second-order interpolation while θ = 0 yields a second-order upwind value. The traditional QUICK scheme is obtained by setting

24-10


24.2 Discretization

Su

Sc

Sd

W

∆x w P

∆x e E

w

e

Figure 24.2.3: One-Dimensional Control Volume

θ = 1/8. The implementation in FLUENT uses a variable, solution-dependent value of θ, chosen so as to avoid introducing new solution extrema. The QUICK scheme will typically be more accurate on structured grids aligned with the flow direction. Note that FLUENT allows the use of the QUICK scheme for unstructured or hybrid grids as well; in such cases the usual second-order upwind discretization scheme (described in Section 24.2.3) will be used at the faces of non-hexahedral (or nonquadrilateral, in 2D) cells. The second-order upwind scheme will also be used at partition boundaries when the parallel solver is used.

24.2.5

Central-Differencing Scheme

A second-order-accurate central-differencing discretization scheme is available for the momentum equations when you are using the LES turbulence model. This scheme provides improved accuracy for LES calculations. The central-differencing scheme calculates the face value for a variable (φf ) as follows: φf,CD =

1 1 (φ0 + φ1 ) + (∇φr,0 · ~r0 + ∇φr,1 · ~r1 ) 2 2

(24.2-9)

where the indices 0 and 1 refer to the cells that share face f , ∇φr,0 and ∇φr,1 are the reconstructed gradients at cells 0 and 1, respectively, and ~r is the vector directed from the cell centroid toward the face centroid. It is well known that central-differencing schemes can produce unbounded solutions and non-physical wiggles, which can lead to stability problems for the numerical procedure. These stability problems can often be avoided if a deferred approach is used for the central-differencing scheme. In this approach, the face value is calculated as follows:

φf =

φf,UP | {z }

implicit part


+

(φf,CD − φf,UP ) |

{z

explicit part

(24.2-10)

}

24-11

Using the Solver

where UP stands for upwind. As indicated, the upwind part is treated implicitly while the difference between the central-difference and upwind values is treated explicitly. Provided that the numerical solution converges, this approach leads to pure second-order differencing.

24.2.6

Linearized Form of the Discrete Equation

The discretized scalar transport equation (Equation 24.2-2) contains the unknown scalar variable φ at the cell center as well as the unknown values in surrounding neighbor cells. This equation will, in general, be non-linear with respect to these variables. A linearized form of Equation 24.2-2 can be written as aP φ =

X

anb φnb + b

(24.2-11)

nb

where the subscript nb refers to neighbor cells, and aP and anb are the linearized coefficients for φ and φnb . The number of neighbors for each cell depends on the grid topology, but will typically equal the number of faces enclosing the cell (boundary cells being the exception). Similar equations can be written for each cell in the grid. This results in a set of algebraic equations with a sparse coefficient matrix. For scalar equations, FLUENT solves this linear system using a point implicit (Gauss-Seidel) linear equation solver in conjunction with an algebraic multigrid (AMG) method which is described in Section 24.5.3.

24.2.7

Under-Relaxation

Because of the nonlinearity of the equation set being solved by FLUENT, it is necessary to control the change of φ. This is typically achieved by under-relaxation, which reduces the change of φ produced during each iteration. In a simple form, the new value of the variable φ within a cell depends upon the old value, φold , the computed change in φ, ∆φ, and the under-relaxation factor, α, as follows: φ = φold + α∆φ

24.2.8

(24.2-12)

Temporal Discretization

For transient simulations, the governing equations must be discretized in both space and time. The spatial discretization for the time-dependent equations is identical to the steady-state case. Temporal discretization involves the integration of every term in the differential equations over a time step ∆t. The integration of the transient terms is straightforward, as shown below.

24-12


24.2 Discretization

A generic expression for the time evolution of a variable φ is given by ∂φ = F (φ) ∂t

(24.2-13)

where the function F incorporates any spatial discretization. If the time derivative is discretized using backward differences, the first-order accurate temporal discretization is given by φn+1 − φn = F (φ) ∆t

(24.2-14)

and the second-order discretization is given by 3φn+1 − 4φn + φn−1 = F (φ) 2∆t

(24.2-15)

where φ = a scalar quantity n + 1 = value at the next time level, t + ∆t n = value at the current time level, t n − 1 = value at the previous time level, t − ∆t Once the time derivative has been discretized, a choice remains for evaluating F (φ): in particular, which time level values of φ should be used in evaluating F ?

Implicit Time Integration One method is to evaluate F (φ) at the future time level: φn+1 − φn = F (φn+1 ) ∆t

(24.2-16)

This is referred to as “implicit” integration since φn+1 in a given cell is related to φn+1 in neighboring cells through F (φn+1 ): φn+1 = φn + ∆tF (φn+1 )

(24.2-17)

This implicit equation can be solved iteratively by initializing φi to φn and iterating the equation φi = φn + ∆tF (φi )

(24.2-18)

for the first-order implicit formulation, or


24-13

Using the Solver

φi = 4/3φn − 1/3φn−1 + 2/3∆tF (φi )

(24.2-19)

for the second-order implicit formulation, until φi stops changing (i.e., converges). At that point, φn+1 is set to φi . The advantage of the fully implicit scheme is that it is unconditionally stable with respect to time step size.

Explicit Time Integration A second method is available when the coupled explicit solver is used. This method evaluates F (φ) at the current time level: φn+1 − φn = F (φn ) ∆t

(24.2-20)

and is referred to as “explicit” integration since φn+1 can be expressed explicitly in terms of the existing solution values, φn : φn+1 = φn + ∆tF (φn )

(24.2-21)

(This method is also referred to as “global time stepping”.) Here, the time step ∆t is restricted to the stability limit of the underlying solver (i.e., a time step corresponding to a Courant number of approximately 1). In order to be time-accurate, all cells in the domain must use the same time step. For stability, this time step must be the minimum of all the local time steps in the domain. The use of explicit time stepping is fairly restrictive. It is used primarily to capture the transient behavior of moving waves, such as shocks, because it is more accurate and less expensive than the implicit time stepping methods in such cases. You cannot use explicit time stepping in the following cases: • Calculations with the segregated or coupled implicit solver. The explicit time stepping formulation is available only with the coupled explicit solver. • Incompressible flow. Explicit time stepping cannot be used to compute timeaccurate incompressible flows (i.e., gas laws other than ideal gas). Incompressible solutions must be iterated to convergence within each time step. • Convergence acceleration. FAS multigrid and residual smoothing cannot be used with explicit time stepping because they destroy the time accuracy of the underlying solver.

24-14


24.2 Discretization

24.2.9

Evaluation of Derivatives

The derivative ∇φ of a given variable φ is used to discretize the convection and diffusion terms of the equations of motion. The gradient is computed using the Green-Gauss theorem as

(∇φ)c0 =

1X ~f φ A V f f

(24.2-22)

where φf is the value of φ at the cell face centroid, and the summation is over all the faces enclosing the cell. Cell-Based Derivative Evaluation By default, the face value, φf , in Equation 24.2-22 is taken from the arithmetic average of the values at the neighboring cell centers, i.e., φf =

φc0 + φc1 2

(24.2-23)

To use this option, select Cell-Based under Gradient Option in the Solver panel. Node-Based Derivative Evaluation Alternatively, φf can be computed by the arithmetic average of the nodal values on the face.

φf =

Nf 1 X φ Nf n n

(24.2-24)

where Nf is the number of nodes on the face. The nodal values, φn in Equation 24.2-24, are constructed from the weighted average of the cell values surrounding the nodes, following the approach originally proposed by Holmes and Connel[105] and Rauch et al.[207]. This scheme reconstructs exact values of a linear function at a node from surrounding cell-centered values on arbitrary unstructured meshes by solving a constrained minimization problem, preserving a second-order spatial accuracy. The node-based averaging scheme is known to be more accurate than the default cellbased scheme for unstructured meshes, most notably for triangular and tetrahedral meshes. To use this option, select Node-Based under Gradient Option in the Solver panel.


24-15

Using the Solver

24.3

The Segregated Solver

In this section, special practices related to the discretization of the momentum and continuity equations and their solution by means of the segregated solver are addressed. These practices are most easily described by considering the steady-state continuity and momentum equations in integral form:

I

~=− ρ~v ~v · dA

I

~=0 ρ ~v · dA

I

~+ pI · dA

I

~+ τ · dA

(24.3-1) Z

F~ dV

(24.3-2)

V

where I is the identity matrix, τ is the stress tensor, and F~ is the force vector.

24.3.1

Discretization of the Momentum Equation

The discretization scheme described in Section 24.2 for a scalar transport equation is also used to discretize the momentum equations. For example, the x-momentum equation can be obtained by setting φ = u: aP u =

X

anb unb +

nb

X

pf A · ˆı + S

(24.3-3)

If the pressure field and face mass fluxes were known, Equation 24.3-3 could be solved in the manner outlined in Section 24.2, and a velocity field obtained. However, the pressure field and face mass fluxes are not known a priori and must be obtained as a part of the solution. There are important issues with respect to the storage of pressure and the discretization of the pressure gradient term; these are addressed next. FLUENT uses a co-located scheme, whereby pressure and velocity are both stored at cell centers. However, Equation 24.3-3 requires the value of the pressure at the face between cells c0 and c1, shown in Figure 24.2.1. Therefore, an interpolation scheme is required to compute the face values of pressure from the cell values.

Pressure Interpolation Schemes The default scheme in FLUENT interpolates the pressure values at the faces using momentum equation coefficients [213]. This procedure works well as long as the pressure variation between cell centers is smooth. When there are jumps or large gradients in the momentum source terms between control volumes, the pressure profile has a high gradient at the cell face, and cannot be interpolated using this scheme. If this scheme is used, the discrepancy shows up in overshoots/undershoots of cell velocity.

24-16


24.3 The Segregated Solver

Flows for which the standard pressure interpolation scheme will have trouble include flows with large body forces, such as in strongly swirling flows, in high-Rayleigh-number natural convection and the like. In such cases, it is necessary to pack the mesh in regions of high gradient to resolve the pressure variation adequately. Another source of error is that FLUENT assumes that the normal pressure gradient at the wall is zero. This is valid for boundary layers, but not in the presence of body forces or curvature. Again, the failure to correctly account for the wall pressure gradient is manifested in velocity vectors pointing in/out of walls. Several alternate methods are available for cases in which the standard pressure interpolation scheme is not valid: • The linear scheme computes the face pressure as the average of the pressure values in the adjacent cells. • The second-order scheme reconstructs the face pressure in the manner used for second-order accurate convection terms (see Section 24.2.3). This scheme may provide some improvement over the standard and linear schemes, but it may have some trouble if it is used at the start of a calculation and/or with a bad mesh. The second-order scheme is not applicable for flows with discontinuous pressure gradients imposed by the presence of a porous medium in the domain or the use of the VOF or mixture model for multiphase flow. • The body-force-weighted scheme computes the face pressure by assuming that the normal gradient of the difference between pressure and body forces is constant. This works well if the body forces are known a priori in the momentum equations (e.g., buoyancy and axisymmetric swirl calculations). • The PRESTO! (PREssure STaggering Option) scheme uses the discrete continuity balance for a “staggered” control volume about the face to compute the “staggered” (i.e., face) pressure. This procedure is similar in spirit to the staggered-grid schemes used with structured meshes [189]. Note that for triangular and tetrahedral meshes, comparable accuracy is obtained using a similar algorithm. See Section 24.7.3 for recommendations on when to use these alternate schemes.

24.3.2

Discretization of the Continuity Equation

Equation 24.3-1 may be integrated over the control volume in Figure 24.2.1 to yield the following discrete equation NX faces

J f Af = 0

(24.3-4)

f


24-17

Using the Solver

where Jf is the mass flux through face f , ρvn . As described in Section 24.1, the momentum and continuity equations are solved sequentially. In this sequential procedure, the continuity equation is used as an equation for pressure. However, pressure does not appear explicitly in Equation 24.3-4 for incompressible flows, since density is not directly related to pressure. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) family of algorithms [189] is used for introducing pressure into the continuity equation. This procedure is outlined in Section 24.3.3. In order to proceed further, it is necessary to relate the face values of velocity, ~vn , to the stored values of velocity at the cell centers. Linear interpolation of cell-centered velocities to the face results in unphysical checker-boarding of pressure. FLUENT uses a procedure similar to that outlined by Rhie and Chow [213] to prevent checkerboarding. The face value of velocity is not averaged linearly; instead, momentum-weighted averaging, using weighting factors based on the aP coefficient from equation 24.3-3, is performed. Using this procedure, the face flux, Jf , may be written as Jf = Jˆf + df (pc0 − pc1 )

(24.3-5)

where pc0 and pc1 are the pressures within the two cells on either side of the face, and Jˆf contains the influence of velocities in these cells (see Figure 24.2.1). The term df is a function of a ¯P , the average of the momentum equation aP coefficients for the cells on either side of face f .

Density Interpolation Schemes For compressible flow calculations (i.e., calculations that use the ideal gas law for density), FLUENT applies upwind interpolation of density at cell faces. (For incompressible flows, FLUENT uses arithmetic averaging.) Three interpolation schemes are available for the density upwinding at cell faces: first-order upwind (default), second-order-upwind, and QUICK. The first-order upwind scheme (based on [122]) sets the density at the cell face to be the upstream cell-center value. This scheme provides stability for the discretization of the pressure-correction equation, and gives good results for most classes of flows. The first-order scheme is the default scheme for compressible flows. The second-order upwind scheme provides stability for supersonic flows and captures shocks better than the first-order upwind scheme. The QUICK scheme for density is similar to the QUICK scheme used for other variables. See Section 24.2.4 for details.

! The second-order upwind and QUICK schemes for density are not available for compressible multiphase calculations; the first-order upwind scheme is used for the compressible phase, and arithmetic averaging is used for the incompressible phases.

24-18



See Section 24.7.4 for recommendations on choosing an appropriate density interpolation scheme for your compressible flow.

24.3.3

Pressure-Velocity Coupling

Pressure-velocity coupling is achieved by using Equation 24.3-5 to derive an equation for pressure from the discrete continuity equation (Equation 24.3-4) FLUENT provides the option to choose among three pressure-velocity coupling algorithms: SIMPLE, SIMPLEC, and PISO. See Section 24.8 for instructions on how to select these algorithms.

SIMPLE The SIMPLE algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field. If the momentum equation is solved with a guessed pressure field p∗ , the resulting face flux, Jf∗ , computed from Equation 24.3-5 Jf∗ = Jˆf∗ + df (p∗c0 − p∗c1 )

(24.3-6)

does not satisfy the continuity equation. Consequently, a correction Jf0 is added to the face flux Jf∗ so that the corrected face flux, Jf Jf = Jf∗ + Jf0

(24.3-7)

satisfies the continuity equation. The SIMPLE algorithm postulates that Jf0 be written as Jf0 = df (p0c0 − p0c1 )

(24.3-8)

where p0 is the cell pressure correction. The SIMPLE algorithm substitutes the flux correction equations (Equations 24.3-7 and 24.3-8) into the discrete continuity equation (Equation 24.3-4) to obtain a discrete equation for the pressure correction p0 in the cell: aP p 0 =

X

anb p0nb + b

(24.3-9)

nb

where the source term b is the net flow rate into the cell:

b=

NX faces

Jf∗ Af

(24.3-10)

f


24-19

Using the Solver

The pressure-correction equation (Equation 24.3-9) may be solved using the algebraic multigrid (AMG) method described in Section 24.5.3. Once a solution is obtained, the cell pressure and the face flux are corrected using p = p∗ + αp p0

(24.3-11)

Jf = Jf∗ + df (p0c0 − p0c1 )

(24.3-12)

Here αp is the under-relaxation factor for pressure (see Section 24.2.7 for information about under-relaxation). The corrected face flux, Jf , satisfies the discrete continuity equation identically during each iteration.

SIMPLEC A number of variants of the basic SIMPLE algorithm are available in the literature. In addition to SIMPLE, FLUENT offers the SIMPLEC (SIMPLE-Consistent) algorithm [270]. SIMPLE is the default, but many problems will benefit from the use of SIMPLEC, as described in Section 24.8.1. The SIMPLEC procedure is similar to the SIMPLE procedure outlined above. The only difference lies in the expression used for the face flux correction, Jf0 . As in SIMPLE, the correction equation may be written as Jf = Jf∗ + df (p0c0 − p0c1 )

(24.3-13)

However, the coefficient df is redefined as a function of (aP − nb anb ) The use of this modified correction equation has been shown to accelerate convergence in problems where pressure-velocity coupling is the main deterrent to obtaining a solution. P

PISO The Pressure-Implicit with Splitting of Operators (PISO) pressure-velocity coupling scheme, part of the SIMPLE family of algorithms, is based on the higher degree of the approximate relation between the corrections for pressure and velocity. One of the limitations of the SIMPLE and SIMPLEC algorithms is that new velocities and corresponding fluxes do not satisfy the momentum balance after the pressure-correction equation is solved. As a result, the calculation must be repeated until the balance is satisfied. To improve the efficiency of this calculation, the PISO algorithm performs two additional corrections: neighbor correction and skewness correction.

24-20



Neighbor Correction The main idea of the PISO algorithm is to move the repeated calculations required by SIMPLE and SIMPLEC inside the solution stage of the pressure-correction equation [109]. After one or more additional PISO loops, the corrected velocities satisfy the continuity and momentum equations more closely. This iterative process is called a momentum correction or “neighbor correction”. The PISO algorithm takes a little more CPU time per solver iteration, but it can dramatically decrease the number of iterations required for convergence, especially for transient problems. Skewness Correction For meshes with some degree of skewness, the approximate relationship between the correction of mass flux at the cell face and the difference of the pressure corrections at the adjacent cells is very rough. Since the components of the pressure-correction gradient along the cell faces are not known in advance, an iterative process similar to the PISO neighbor correction described above is desirable [72]. After the initial solution of the pressure-correction equation, the pressure-correction gradient is recalculated and used to update the mass flux corrections. This process, which is referred to as “skewness correction”, significantly reduces convergence difficulties associated with highly distorted meshes. The PISO skewness correction allows FLUENT to obtain a solution on a highly skewed mesh in approximately the same number of iterations as required for a more orthogonal mesh. Skewness - Neighbor Coupling For meshes with a high degree of skewness, the simultaneous coupling of the neighbor and skewness corrections at the same pressure correction equation source may cause divergence or a lack of robustness. An alternate, although more expensive, method for handling the neighbor and skewness corrections inside the PISO algorithm is to apply one or more iterations of skewness correction for each separate iteration of neighbor correction. For each individual iteration of the classical PISO algorithm from [109], this technique allows a more accurate adjustment of the face mass flux correction according to the normal pressure correction gradient.

Special Treatment for Strong Body Forces in Multiphase Flows When large body forces (e.g., gravity or surface tension forces) exist in multiphase flows, the body force and pressure gradient terms in the momentum equation are almost in equilibrium, with the contributions of convective and viscous terms small in comparison. Segregated algorithms converge poorly unless partial equilibrium of pressure gradient and body forces is taken into account. FLUENT provides an optional “implicit body force” treatment that can account for this effect, making the solution more robust.


24-21

Using the Solver

The basic procedure involves augmenting the correction equation for the face flow rate, Equation 24.3-12, with an additional term involving corrections to the body force. This results in extra body force correction terms in Equation 24.3-10, and allows the flow to achieve a realistic pressure field very early in the iterative process. This option is available only for multiphase calculations, but it is turned off by default. Section 22.6.13 includes instructions for turning on the implicit body force treatment. In addition, FLUENT allows you to control the change in the body forces through the use of an under-relaxation factor for body forces.

24.3.4

Steady-State and Time-Dependent Calculations

If you are performing a steady-state calculation, the governing equations for the segregated solver do not contain time-dependent terms . For steady-state flows, Section 24.2 describes control-volume-based discretization of the steady-state transport equation (see Equation 24.2-1). For time-dependent flows, the discretized form of the generic transport equations is of the following form: Z

V

I I Z ∂ρφ ~ ~ dV + ρφ ~v · dA = Γφ ∇φ · dA + Sφ dV ∂t V

(24.3-14)

where ∂ρφ ∂t

= conservative form of transient derivative of transported variable φ ρ = density ~v = velocity vector (= u ˆı + v ˆ in 2D) ~ A = surface area vector Γφ = diffusion coefficient for φ ∇φ = gradient of φ (= ∂φ/∂x) ˆı + (∂φ/∂y) ˆ in 2D) Sφ = source of φ per unit volume The temporal discretization of the transient derivative in the Equation 24.3-14 is described in Section 24.2.8, including first and second order schemes in time. The segregated solver in FLUENT uses an implicit discretization of the transport equation (Equation 24.3-14). As a standard default approach, all convective, diffusive, and source terms are evaluated from the fields for time level n+1.

Z

V

24-22

I I Z ∂ρφ ~ = Γφ n+1 ∇φn+1 · dA ~ + Sφ n+1 dV dV + ρn+1 φn+1 ~v n+1 · dA ∂t V

(24.3-15)


24.4 The Coupled Solver

The Frozen Flux Formulation The standard fully-implicit discretization of the convective part of Equation 24.3-15 produces non-linear terms in the resulting equations. In addition, solving these equations generally requires numerous iterations per time step. As an alternative, FLUENT provides an optional way to discretize the convective part of Equation 24.3-14 using the mass flux at the cell faces from the previous time level n. I

~= ρφ ~v · dA

I

~ ρn φn+1 ~v n · dA

(24.3-16)

The solution still has the same order of accuracy but the non-linear character of the discretized transport equation is essentially reduced and the convergence within each time step is improved. To use this feature, turn on the Use Frozen Flux Formulation? option in the Solver panel.

! This option is only available for single-phase transient problems that use the segregated solver and do not use a moving/deforming mesh model.

24.4

The Coupled Solver

The coupled solver in FLUENT solves the governing equations of continuity, momentum, and (where appropriate) energy and species transport simultaneously as a set, or vector, of equations. Governing equations for additional scalars will be solved sequentially (i.e., segregated from one another and from the coupled set).

24.4.1

Governing Equations in Vector Form

The system of governing equations for a single-component fluid, written to describe the mean flow properties, is cast in integral, Cartesian form for an arbitrary control volume V with differential surface area dA as follows: I Z ∂ Z W dV + [F − G] · dA = H dV ∂t V V

(24.4-1)

where the vectors W, F, and G are defined as     ρ           ρu  

  ρv         ˆ   ρvu + p i    

  0      τxi

       

W = ρv  , F = ρvv + pˆj , G = τyi              ˆ ρw  τzi       ρvw + p k            ρE    τ v + q  ij j ρvE + pv and the vector H contains source terms such as body forces and energy sources.


24-23

Using the Solver

Here ρ, v, E, and p are the density, velocity, total energy per unit mass, and pressure of the fluid, respectively. τ is the viscous stress tensor, and q is the heat flux. Total energy E is related to the total enthalpy H by E = H − p/ρ

(24.4-2)

H = h + |v|2 /2

(24.4-3)

where

The Navier-Stokes equations as expressed in Equation 24.4-1 become (numerically) very stiff at low Mach number due to the disparity between the fluid velocity v and the acoustic speed c (speed of sound). This is also true for incompressible flows, regardless of the fluid velocity, because acoustic waves travel infinitely fast in an incompressible fluid (speed of sound is infinite). The numerical stiffness of the equations under these conditions results in poor convergence rates. This difficulty is overcome in FLUENT’s coupled solver by employing a technique called (time-derivative) preconditioning [288].

24.4.2

Preconditioning

Time-derivative preconditioning modifies the time-derivative term in Equation 24.4-1 by pre-multiplying it with a preconditioning matrix. This has the effect of re-scaling the acoustic speed (eigenvalue) of the system of equations being solved in order to alleviate the numerical stiffness encountered in low Mach number and incompressible flow. Derivation of the preconditioning matrix begins by transforming the dependent variable in Equation 24.4-1 from conserved quantities W to primitive variables Q using the chainrule as follows: I Z ∂W ∂ Z Q dV + [F − G] · dA = H dV ∂Q ∂t V V

(24.4-4)

where Q is the vector {p, u, v, w, T }T and the Jacobian ∂W/∂Q is given by   

∂W  =  ∂Q  

ρp ρp u ρp v ρp w ρp H − δ

0 ρ 0 0 ρu

0 0 ρ 0 ρv

0 0 0 ρ ρw

ρT ρT u ρT v ρT w ρT H + ρCp

       

(24.4-5)

where

24-24



∂ρ ∂ρ ρp = , ρT = ∂p T ∂T p and δ = 1 for an ideal gas and δ = 0 for an incompressible fluid. The choice of primitive variables Q as dependent variables is desirable for several reasons. First, it is a natural choice when solving incompressible flows. Second, when we use second-order accuracy we need to reconstruct Q rather than W in order to obtain more accurate velocity and temperature gradients in viscous fluxes, and pressure gradients in inviscid fluxes. And finally, the choice of pressure as a dependent variable allows the propagation of acoustic waves in the system to be singled out [272]. We precondition the system by replacing the Jacobian matrix ∂W/∂Q (Equation 24.4-5) with the preconditioning matrix Γ so that the preconditioned system in conservation form becomes Γ

I Z ∂ Z Q dV + [F − G] · dA = H dV ∂t V V

(24.4-6)

where 

   Γ=   

Θ Θu Θv Θw ΘH − δ

0 ρ 0 0 ρu

0 0 ρ 0 ρv

0 0 0 ρ ρw

ρT ρT u ρT u ρT u ρT H + ρCp

       

(24.4-7)

The parameter Θ is given by

Θ=

1 ρT − 2 Ur ρCp

!

(24.4-8)

The reference velocity Ur appearing in Equation 24.4-8 is chosen locally such that the eigenvalues of the system remain well conditioned with respect to the convective and diffusive time scales [288]. The resultant eigenvalues of the preconditioned system (Equation 24.4-6) are given by u, u, u, u0 + c0 , u0 − c0

(24.4-9)

where


24-25

Using the Solver

u = v·n ˆ 0 u = u (1 − α) c

0

=

α = β =

q

α2 u2 + Ur2

1 − βUr2 /2 ρT ρp + ρCp

!

For an ideal gas, β = (γRT )−1 = 1/c2 . Thus, when Ur = c (at sonic speeds and above), α = 0 and the eigenvalues of the preconditioned system take their traditional form, u ± c. At low speed, however, as Ur → 0, α → 1/2 and all eigenvalues become of the same order as u. For constant-density flows, β = 0 and α = 1/2 regardless of the values of Ur . As long as the reference velocity is of the same order as the local velocity, all eigenvalues remain of the order u. Thus, the eigenvalues of the preconditioned system remain well conditioned at all speeds. Note that the non-preconditioned Navier-Stokes equations are recovered exactly from Equation 24.4-6 by setting 1/Ur2 to ρp , the derivative of density with respect to pressure. In this case Γ reduces exactly to the Jacobian ∂W/∂Q. Although Equation 24.4-6 is conservative in the steady state, it is not, in a strict sense, conservative for time-dependent flows. This is not a problem, however, since the preconditioning has already destroyed the time accuracy of the equations and we will not employ them in this form for unsteady calculations.

Flux-Difference Splitting The inviscid flux vector F appearing in Equation 24.4-6 is evaluated by a standard upwind, flux-difference splitting [216]. This approach acknowledges that the flux vector F contains characteristic information propagating through the domain with speed and direction according to the eigenvalues of the system. By splitting F into parts, where each part contains information traveling in a particular direction (i.e., characteristic information), and upwind differencing the split fluxes in a manner consistent with their corresponding eigenvalues, we obtain the following expression for the discrete flux at each face: F=

1 1 ˆ (FR + FL ) − Γ |A| δQ 2 2

(24.4-10)

Here δQ is the spatial difference QR − QL . The fluxes FR = F (QR ) and FL = F (QL ) are computed using the (reconstructed) solution vectors QR and QL on the “right” and ˆ is defined by “left” side of the face. The matrix |A|

24-26



ˆ = M |Λ| M −1 |A|

(24.4-11)

where Λ is the diagonal matrix of eigenvalues and M is the modal matrix that diagonalizes Γ−1 A, where A is the inviscid flux Jacobian ∂F/∂Q. For the non-preconditioned system (and an ideal gas) Equation 24.4-10 reduces to Roe’s ˆ At flux-difference splitting [216] when Roe-averaged values are used to evaluate Γ |A|. present, arithmetic averaging of states QR and QL is used. In its current form, Equation 24.4-10 can be viewed as a second-order central difference plus an added matrix dissipation. The added matrix dissipation term is not only responsible for producing an upwinding of the convected variables, and of pressure and flux velocity in supersonic flow, but it also provides the pressure-velocity coupling required for stability and efficient convergence of low-speed and incompressible flows.

24.4.3

Time Marching for Steady-State Flows

The coupled set of governing equations (Equation 24.4-6) in FLUENT is discretized in time for both steady and unsteady calculations. In the steady case, it is assumed that time marching proceeds until a steady-state solution is reached. Temporal discretization of the coupled equations is accomplished by either an implicit or an explicit time-marching scheme. These two algorithms are described below.

Explicit Scheme In the explicit scheme a multi-stage, time-stepping algorithm [113] is used to discretize the time derivative in Equation 24.4-6. The solution is advanced from iteration n to iteration n + 1 with an m-stage Runge-Kutta scheme, given by

Q0 = Qn ∆Qi = −αi ∆tΓ−1 Ri−1 Qn+1 = Qm where ∆Qi ≡ Qi − Qn and i = 1, 2, . . . , m is the stage counter for the m-stage scheme. αi is the multi-stage coefficient for the ith stage. The residual Ri is computed from the intermediate solution Qi and, for Equation 24.4-6, is given by i

R =

NX faces

F(Qi ) − G(Qi ) · A − V H

(24.4-12)

The time step ∆t is computed from the CFL (Courant-Friedrichs-Lewy) condition


24-27

Using the Solver

∆t =

CFL∆x λmax

(24.4-13)

where λmax is the maximum of the local eigenvalues defined by Equation 24.4-9. The convergence rate of the explicit scheme can be accelerated through use of the fullapproximation storage (FAS) multigrid method described in Section 24.5.4. Implicit Residual Smoothing The maximum time step can be further increased by increasing the support of the scheme through implicit averaging of the residuals with their neighbors. The residuals are filtered through a Laplacian smoothing operator: ¯ i = Ri + R

X

¯j − R ¯i) (R

(24.4-14)

This equation can be solved with the following Jacobi iteration: P ¯ m−1 Ri + R j m ¯ Ri = P 1+ 1

(24.4-15)

Two Jacobi iterations are usually sufficient to allow doubling the time step with a value of = 0.5.

Implicit Scheme In the implicit scheme, an Euler implicit discretization in time of the governing equations (Equation 24.4-6) is combined with a Newton-type linearization of the fluxes to produce the following linearized system in delta form [286]: 

D +

NX faces j



Sj,k  ∆Qn+1 = −Rn

(24.4-16)

The center and off-diagonal coefficient matrices, D and Sj,k are given by

NX faces V D = Γ+ Sj,i ∆t j

Sj,k =

24-28

∂Fj ∂Gj − ∂Qk ∂Qk

!

(24.4-17) (24.4-18)



and the residual vector Rn and time step ∆t are defined as in Equation 24.4-12 and Equation 24.4-13, respectively. Equation 24.4-16 is solved using a point Gauss-Seidel scheme in conjunction with an algebraic multigrid (AMG) method (see Section 24.5.3) adapted for coupled sets of equations.

24.4.4

Temporal Discretization for Unsteady Flows

For time-accurate calculations, explicit and implicit time-stepping schemes are available. (The implicit approach is also referred to as “dual time stepping”.)

Explicit Time Stepping In the explicit time stepping approach, the explicit scheme described above is employed, using the same time step in each cell of the domain, and with preconditioning disabled.

Dual Time Stepping To provide for efficient, time-accurate solution of the preconditioned equations, we employ a dual time-stepping, multi-stage scheme. Here we introduce a preconditioned pseudotime-derivative term into Equation 24.4-1 as follows: I Z ∂ Z ∂ Z W dV + Γ Q dV + [F − G] · dA = H dV ∂t V ∂τ V V

(24.4-19)

where t denotes physical-time and τ is a pseudo-time used in the time-marching procedure. Note that as τ → ∞, the second term on the LHS of Equation 24.4-19 vanishes and Equation 24.4-1 is recovered. The time-dependent term in Equation 24.4-19 is discretized in an implicit fashion by means of either a first- or second-order accurate, backward difference in time. This is written in semi-discrete form as follows:

"

#

Γ 0 ∂W 1 I k+1 + ∆Q + [F − G] · dA ∆τ ∆t ∂Q V 1 0 Wk − 1 Wn + 2 Wn−1 =H + ∆t

where {0 = 1 = 1/2, 2 = 0} gives first-order time accuracy, and {0 = 3/2, 1 = 2, 2 = 1/2} gives second-order. k is the inner iteration counter and n represents any given physical-time level.


24-29

Using the Solver

The pseudo-time-derivative is driven to zero at each physical time level by a series of inner iterations using either the implicit or explicit time-marching algorithm. Throughout the (inner) iterations in pseudo-time, Wn and Wn−1 are held constant and Wk is computed from Qk . As τ → ∞, the solution at the next physical time level Wn+1 is given by W(Qk ). Note that the physical time step ∆t is limited only by the level of desired temporal accuracy. The pseudo-time-step ∆τ is determined by the CFL condition of the (implicit or explicit) time-marching scheme.

24.5

Multigrid Method

The FLUENT solver contains two forms of multigrid: algebraic (AMG) and full-approximation storage (FAS). As discussed in Section 24.1.3, AMG is an essential component of both the segregated and coupled implicit solvers, while FAS is an important, but optional, component of the coupled explicit solver. (Note that when the coupled explicit solver is used, since the scalar equations (e.g., turbulence) are solved using the segregated approach, AMG will also be used.) This section describes the mathematical basis of the multigrid approach. Common aspects of AMG and FAS are presented first, followed by separate sections that provide details unique to each method. Information about user inputs and controls for the multigrid solver is provided in Sections 24.19.3 and 24.19.4.

24.5.1

Approach

FLUENT uses a multigrid scheme to accelerate the convergence of the solver by computing corrections on a series of coarse grid levels. The use of this multigrid scheme can greatly reduce the number of iterations and the CPU time required to obtain a converged solution, particularly when your model contains a large number of control volumes.

The Need for Multigrid Implicit solution of the linearized equations on unstructured meshes is complicated by the fact that there is no equivalent of the line-iterative methods that are commonly used on structured grids. Since direct matrix inversion is out of the question for realistic problems and “whole-field” solvers that rely on conjugate-gradient (CG) methods have robustness problems associated with them, the methods of choice are point implicit solvers like Gauss-Seidel. Although the Gauss-Seidel scheme rapidly removes local (high-frequency) errors in the solution, global (low-frequency) errors are reduced at a rate inversely related to the grid size. Thus, for a large number of nodes, the solver “stalls” and the residual reduction rate becomes prohibitively low. The multi-stage scheme used in the coupled explicit solver can efficiently remove local (high-frequency) errors as well. That is, the effect of the solution in one cell is communi-

24-30


24.5 Multigrid Method

cated to adjacent cells relatively quickly. However, the scheme is less effective at reducing global (low-frequency) errors—errors which exist over a large number of control volumes. Thus, global corrections to the solution across a large number of control volumes occur slowly, over many iterations. This implies that performance of the multi-stage scheme will deteriorate as the number of control volumes increases. Multigrid techniques allow global error to be addressed by using a sequence of successively coarser meshes. This method is based upon the principle that global (low-frequency) error existing on a fine mesh can be represented on a coarse mesh where it again becomes accessible as local (high-frequency) error: because there are fewer coarse cells overall, the global corrections can be communicated more quickly between adjacent cells. Since computations can be performed at exponentially decaying expense in both CPU time and memory storage on coarser meshes, there is the potential for very efficient elimination of global error. The fine-grid relaxation scheme or “smoother”, in this case either the pointimplicit Gauss-Seidel or the explicit multi-stage scheme, is not required to be particularly effective at reducing global error and can be tuned for efficient reduction of local error.

The Basic Concept in Multigrid Consider the set of discretized linear (or linearized) equations given by A φe + b = 0

(24.5-1)

where φe is the exact solution. Before the solution has converged there will be a defect d associated with the approximate solution φ: Aφ + b = d

(24.5-2)

We seek a correction ψ to φ such that the exact solution is given by φe = φ + ψ

(24.5-3)

Substituting Equation 24.5-3 into Equation 24.5-1 gives

A (φ + ψ) + b = 0 A ψ + (A φ + b) = 0

(24.5-4) (24.5-5)

Now using Equations 24.5-2 and 24.5-5 we obtain Aψ + d = 0


(24.5-6)

24-31

Using the Solver

which is an equation for the correction in terms of the original fine level operator A and the defect d. Assuming the local (high-frequency) errors have been sufficiently damped by the relaxation scheme on the fine level, the correction ψ will be smooth and therefore more effectively solved on the next coarser level.

Restriction and Prolongation Solving for corrections on the coarse level requires transferring the defect down from the fine level (restriction), computing corrections, and then transferring the corrections back up from the coarse level (prolongation). We can write the equations for coarse level corrections ψ H as AH ψ H + R d = 0

(24.5-7)

where AH is the coarse level operator and R the restriction operator responsible for transferring the fine level defect down to the coarse level. Solution of Equation 24.5-7 is followed by an update of the fine level solution given by φnew = φ + P ψ H

(24.5-8)

where P is the prolongation operator used to transfer the coarse level corrections up to the fine level.

Unstructured Multigrid The primary difficulty with using multigrid on unstructured grids is the creation and use of the coarse grid hierarchy. On a structured grid, the coarse grids can be formed simply by removing every other grid line from the fine grids and the prolongation and restriction operators are simple to formulate (e.g., injection and bilinear interpolation). The difficulties of applying multigrid on unstructured grids are overcome in separate fashion by each of the two multigrid methods used in FLUENT. While the basic principles discussed so far and the cycling strategy described in Section 24.5.2 are the same, the techniques for construction of restriction, prolongation, and coarse grid operators are different, as discussed in Section 24.5.3 and Section 24.5.4 for the AMG and FAS methods, respectively.

24.5.2

Multigrid Cycles

A multigrid cycle can be defined as a recursive procedure that is applied at each grid level as it moves through the grid hierarchy. Four types of multigrid cycles are available in FLUENT: the V, W, F, and flexible (“flex”) cycles. The V and W cycles are available in both AMG and FAS, while the F and flexible cycles are restricted to the AMG method

24-32



only. (The W and flex AMG cycles are not available for solving the coupled equation set due to the amount of computation required.)

The V and W Cycles Figures 24.5.1 and 24.5.2 show the V and W multigrid cycles (defined below). In each figure, the multigrid cycle is represented by a square, and then expanded recursively to show the individual steps that are performed within the cycle. The individual steps are represented by a circle, one or more squares, and a triangle, connected by lines: circlesquare-triangle for a V cycle, or circle-square-square-triangle for a W cycle. The squares in this group expand again, into circle-square-triangle or circle-square-square-triangle, and so on. You may want to follow along in the figures as you read the steps below. For the V and W cycles, the traversal of the hierarchy is governed by three parameters, β1 , β2 , and β3 , as follows: 1. First, iterations are performed on the current grid level to reduce the high-frequency components of the error (local error). For AMG, one iteration consists of one forward and one backward Gauss-Seidel sweep. For FAS, one iteration consists of one pass of the multi-stage scheme (described in Section 24.4.3). These iterations are referred to as pre-relaxation sweeps because they are performed before moving to the next coarser grid level. The number of pre-relaxation sweeps is specified by β1 . In Figures 24.5.1 and 24.5.2 this step is represented by a circle and marks the start of a multigrid cycle. The high-wave-number components of error should be reduced until the remaining error is expressible on the next coarser mesh without significant aliasing. If this is the coarsest grid level, then the multigrid cycle on this level is complete. (In Figures 24.5.1 and 24.5.2 there are 3 coarse grid levels, so the square representing the multigrid cycle on level 3 is equivalent to a circle, as shown in the final diagram in each figure.)

!

In the AMG method, the default value of β1 is zero (i.e., no pre-relaxation sweeps are performed). 2. Next, the problem is “restricted” to the next coarser grid level using Equation 24.5-7. In Figures 24.5.1 and 24.5.2, the restriction from a finer grid level to a coarser grid level is designated by a downward-sloping line. 3. The error on the coarse grid is reduced by performing a specified number (β2 ) of multigrid cycles (represented in Figures 24.5.1 and 24.5.2 as squares). Commonly, for fixed multigrid strategies β2 is either 1 or 2, corresponding to V-cycle and Wcycle multigrid, respectively.


24-33

Using the Solver

grid level

multigrid cycle

0

pre-relaxation sweeps

0

post-relaxation sweeps and/or Laplacian smoothings

1 0 1 2

0 1 2 3

0 1 2 3

Figure 24.5.1: V-Cycle Multigrid grid level

multigrid cycle

0

pre-relaxation sweeps

0

post-relaxation sweeps and/or Laplacian smoothings

1 0 1 2

0 1 2 3

0 1 2 3

Figure 24.5.2: W-Cycle Multigrid

24-34



4. Next, the cumulative correction computed on the coarse grid is “interpolated” back to the fine grid using Equation 24.5-8 and added to the fine grid solution. In the FAS method, the corrections are additionally smoothed during this step using the Laplacian smoothing operator discussed in Section 24.4.3. In Figures 24.5.1 and 24.5.2 the prolongation is represented by an upward-sloping line. The high-frequency error now present at the fine grid level is due to the prolongation procedure used to transfer the correction. 5. In the final step, iterations are performed on the fine grid to remove the highfrequency error introduced on the coarse grid by the multigrid cycles. These iterations are referred to as post-relaxation sweeps because they are performed after returning from the next coarser grid level. The number of post-relaxation sweeps is specified by β3 . In Figures 24.5.1 and 24.5.2, this relaxation procedure is represented by a single triangle. For AMG, the default value of β3 is 1.

!

Note, however, that if you are using AMG with V-cycle to solve an energy equation with a solid conduction model presented with anisotropic or very high conductivity coefficient, there is a possibility of divergence with a default post-relaxation sweep of 1. In such cases you should increase the post-relaxation sweep (e.g., to 2) in the AMG section for better convergence. Since the default value for β1 is 0 (i.e., pre-relaxation sweeps are not performed),this procedure is roughly equivalent to using the solution from the coarse level as the initial guess for the solution at the fine level. For FAS, the default value of β3 is zero (i.e., post-relaxation sweeps are not performed); post-relaxation sweeps are never performed at the end of the cycle for the finest grid level, regardless of the value of β3 . This is because for FAS, postrelaxation sweeps at the fine level are equivalent to pre-relaxation sweeps during the next cycle.

24.5.3

Algebraic Multigrid (AMG)

This algorithm is referred to as an “algebraic” multigrid scheme because, as we shall see, the coarse level equations are generated without the use of any geometry or rediscretization on the coarse levels; a feature that makes AMG particularly attractive for use on unstructured meshes. The advantage being that no coarse grids have to be constructed or stored, and no fluxes or source terms need be evaluated on the coarse levels. This approach is in contrast with FAS (sometimes called “geometric”) multigrid in which a hierarchy of meshes is required and the discretized equations are evaluated on every level. In theory, the advantage of FAS over AMG is that the former should perform


24-35

Using the Solver

better for non-linear problems since non-linearities in the system are carried down to the coarse levels through the re-discretization; when using AMG, once the system is linearized, non-linearities are not “felt” by the solver until the fine level operator is next updated.

AMG Restriction and Prolongation Operators The restriction and prolongation operators used here are based on the additive correction (AC) strategy described for structured grids by Hutchinson and Raithby [108]. Inter-level transfer is accomplished by piecewise constant interpolation and prolongation. The defect in any coarse level cell is given by the sum of those from the fine level cells it contains, while fine level corrections are obtained by injection of coarse level values. In this manner the prolongation operator is given by the transpose of the restriction operator P = RT

(24.5-9)

The restriction operator is defined by a coarsening or “grouping” of fine level cells into coarse level ones. In this process each fine level cell is grouped with one or more of its “strongest” neighbors, with a preference given to currently ungrouped neighbors. The algorithm attempts to collect cells into groups of fixed size, typically two or four, but any number can be specified. In the context of grouping, strongest refers to the neighbor j of the current cell i for which the coefficient Aij is largest. For sets of coupled equations Aij is a block matrix and the measure of its magnitude is simply taken to be the magnitude of its first element. In addition, the set of coupled equations for a given cell are treated together and not divided amongst different coarse cells. This results in the same coarsening for each equation in the system.

AMG Coarse Level Operator The coarse level operator AH is constructed using a Galerkin approach. Here we require that the defect associated with the corrected fine level solution must vanish when transferred back to the coarse level. Therefore we may write R dnew = 0

(24.5-10)

Upon substituting Equations 24.5-2 and 24.5-8 for dnew and φnew we have

R [A φnew + b] = 0 h

R A φ + P ψH + b

i

= 0

(24.5-11)

Now rearranging and using Equation 24.5-2 once again gives

24-36



R A P ψ H + R (A φ + b) = 0 R A P ψH + R d = 0

(24.5-12)

Comparison of Equation 24.5-12 with Equation 24.5-7 leads to the following expression for the coarse level operator: AH = R A P

(24.5-13)

The construction of coarse level operators thus reduces to a summation of diagonal and corresponding off-diagonal blocks for all fine level cells within a group to form the diagonal block of that group’s coarse cell.

The F Cycle The multigrid F cycle is essentially a combination of the V and W cycles described in Section 24.5.2. Recall that the multigrid cycle is a recursive procedure. The procedure is expanded to the next coarsest grid level by performing a single multigrid cycle on the current level. Referring to Figures 24.5.1 and 24.5.2, this means replacing the square on the current level (representing a single cycle) with the procedure shown for the 0-1 level cycle (the second diagram in each figure). We see that a V cycle consists of: pre sweep → restrict → V cycle → prolongate → post sweep and a W cycle: pre sweep → restrict → W cycle → W cycle → prolongate → post sweep An F cycle is formed by a W cycle followed by a V cycle: pre sweep → restrict → W cycle → V cycle → prolongate → post sweep As expected, the F cycle requires more computation than the V cycle, but less than the W cycle. However, its convergence properties turn out to be better than the V cycle and roughly equivalent to the W cycle. The F cycle is the default AMG cycle type for the coupled equation set.


24-37

Using the Solver

The Flexible Cycle For the flexible cycle, the calculation and use of coarse grid corrections is controlled in the multigrid procedure by the logic illustrated in Figure 24.5.3. This logic ensures that coarser grid calculations are invoked when the rate of residual reduction on the current grid level is too slow. In addition, the multigrid controls dictate when the iterative solution of the correction on the current coarse grid level is sufficiently converged and should thus be applied to the solution on the next finer grid. These two decisions are controlled by the parameters α and β shown in Figure 24.5.3, as described in detail below. Note that the logic of the multigrid procedure is such that grid levels may be visited repeatedly during a single global iteration on an equation. For a set of 4 multigrid levels, referred to as 0, 1, 2, and 3, the flex-cycle multigrid procedure for solving a given transport equation might consist of visiting grid levels as 0-1-2-3-2-3-2-1-0-1-2-1-0, for example. level

Solve for φ on level 0 (fine) grid

0

R0 relaxation

0

0

R i> β R i-1

1

1

return R 0i< α R 00 or i > i max,fine

R i< α R 0 or i > i max,coarse

Solve for φ′ on level 1 grid 1

1

R i> β R i-1

2

2

R i< α R 0 or i > i max,coarse

Solve for φ′ on level 2 grid 2

2

R i> β R i-1

3

3

R i< α R 0 or i > i max,coarse etc.

Figure 24.5.3: Logic Controlling the Flex Multigrid Cycle

The main difference between the flexible cycle and the V and W cycles is that the satisfaction of the residual reduction tolerance and termination criterion determine when and how often each level is visited in the flexible cycle, whereas in the V and W cycles the traversal pattern is explicitly defined. The Residual Reduction Rate Criteria The multigrid procedure invokes calculations on the next coarser grid level when the error reduction rate on the current level is insufficient, as defined by

24-38



Ri > βRi−1

(24.5-14)

Here Ri is the absolute sum of residuals (defect) computed on the current grid level after the ith relaxation on this level. The above equation states that if the residual present in the iterative solution after i relaxations is greater than some fraction, β (between 0 and 1), of the residual present after the (i − 1)th relaxation, the next coarser grid level should be visited. Thus β is referred to as the residual reduction tolerance, and determines when to “give up” on the iterative solution at the current grid level and move to solving the correction equations on the next coarser grid. The value of β controls the frequency with which coarser grid levels are visited. The default value is 0.7. A larger value will result in less frequent visits, and a smaller value will result in more frequent visits. The Termination Criteria Provided that the residual reduction rate is sufficiently rapid, the correction equations will be converged on the current grid level and the result applied to the solution field on the next finer grid level. The correction equations on the current grid level are considered sufficiently converged when the error in the correction solution is reduced to some fraction, α (between 0 and 1), of the original error on this grid level: Ri < αR0

(24.5-15)

Here, Ri is the residual on the current grid level after the ith iteration on this level, and R0 is the residual that was initially obtained on this grid level at the current global iteration. The parameter α, referred to as the termination criterion, has a default value of 0.1. Note that the above equation is also used to terminate calculations on the lowest (finest) grid level during the multigrid procedure. Thus, relaxations are continued on each grid level (including the finest grid level) until the criterion of this equation is obeyed (or until a maximum number of relaxations has been completed, in the case that the specified criterion is never achieved).

24.5.4

Full-Approximation Storage (FAS) Multigrid

FLUENT’s approach to forming the multigrid grid hierarchy for FAS is simply to coalesce groups of cells on the finer grid to form coarse grid cells. Coarse grid cells are created by agglomerating the cells surrounding a node, as shown in Figure 24.5.4. Depending on the grid topology, this can result in cells with irregular shapes and variable numbers of faces. The grid levels are, however, simple to construct and are embedded, resulting in simple prolongation and relaxation operators. It is interesting to note that although the coarse grid cells look very irregular, the discretization cannot “see” the jaggedness in the cell faces. The discretization uses only the


24-39

Using the Solver

Figure 24.5.4: Node Agglomeration to Form Coarse Grid Cells

area projections of the cell faces and therefore each group of “jagged” cell faces separating two irregularly-shaped cells is equivalent to a single straight line (in 2D) connecting the endpoints of the jagged segment. (In 3D, the area projections form an irregular, but continuous, geometrical shape.) This optimization decreases the memory requirement and the computation time.

FAS Restriction and Prolongation Operators FAS requires restriction of both the fine grid solution φ and its residual (defect) d. The restriction operator R used to transfer the solution to the next coarser grid level is formed using a full-approximation scheme [28]. That is, the solution for a coarse cell is obtained by taking the volume average of the solution values in the embedded fine grid cells. Residuals for the coarse grid cell are obtained by summing the residuals in the embedded fine grid cells. The prolongation operator P used to transfer corrections up to the fine level is constructed to simply set the fine grid correction to the associated coarse grid value. The coarse grid corrections ψ H , which are brought up from the coarse level and applied to the fine level solution, are computed from the difference between the solution calculated on the coarse level φH and the initial solution restricted down to the coarse level Rφ. Thus correction of the fine level solution becomes

φnew = φ + P φH − Rφ

(24.5-16)

FAS Coarse Level Operator The FAS coarse grid operator AH is simply that which results from a re-discretization of the governing equations on the coarse level mesh. Since the discretized equations presented in Sections 24.2 and 24.4 place no restrictions on the number of faces that make up a cell, there is no problem in performing this re-discretization on the coarse grids composed of irregularly shaped cells.

24-40



There is some loss of accuracy when the finite-volume scheme is used on the irregular coarse grid cells, but the accuracy of the multigrid solution is determined solely by the finest grid and is therefore not affected by the coarse grid discretization. In order to preserve accuracy of the fine grid solution, the coarse level equations are modified to include source terms [112] which insure that corrections computed on the coarse grid φH will be zero if the residuals on the fine grid dh are zero as well. Thus, the coarse grid equations are formulated as AH φH + dH = dH (Rφ) − Rdh

(24.5-17)

Here dH is the coarse grid residual computed from the current coarse grid solution φH , and dH (Rφ) is the coarse grid residual computed from the restricted fine level solution Rφ. Initially, these two terms will be the same (because initially we have φH = Rφ) and cancel from the equation, leaving AH φH = −Rdh

(24.5-18)

So there will be no coarse level correction when the fine grid residual dh is zero.


24-41

Using the Solver

24.6

Overview of How to Use the Solver

Once you have defined your model and specified which solver you want to use (see Section 1.6), you are ready to run the solver. The following steps outline a general procedure you can follow: 1. Choose the discretization scheme and, for the segregated solver, the pressure interpolation scheme (see Section 24.7). 2. (segregated solver only) Select the pressure-velocity coupling method (see Section 24.8). 3. (segregated solver only) Select the porous media velocity method (see Section 6.19). 4. Select how you want the derivatives to be evaluated by choosing a gradient option (see Section 24.2.9). 5. Set the under-relaxation factors (see Section 24.9). 6. (coupled explicit solver only) Turn on FAS multigrid (see Section 24.11). 7. Make any additional modifications to the solver settings that are suggested in the chapters or sections that describe the models you are using. 8. Initialize the solution (see Section 24.13). 9. Enable the appropriate solution monitors (see Section 24.16). 10. Start calculating (see Section 24.14 for steady-state calculations, or Section 24.15 for time-dependent calculations). 11. If you have convergence trouble, try one of the methods discussed in Section 24.19. The default settings for the first three items listed above are suitable for most problems and need not be changed. The following sections outline how these and other solution parameters can be changed, and when you may wish to change them.

24-42


24.7 Choosing the Discretization Scheme

24.7

Choosing the Discretization Scheme

FLUENT allows you to choose the discretization scheme for the convection terms of each governing equation. (Second-order accuracy is automatically used for the viscous terms.) When the segregated solver is used, all equations are, by default, solved using the firstorder upwind discretization for convection. When one of the coupled solvers is used, the flow equations are solved using the second-order scheme by default, and the other equations use the first-order scheme by default. See Section 24.2 for a complete description of the discretization schemes available in FLUENT. In addition, when you use the segregated solver, you can specify the pressure interpolation scheme. See Section 24.3.1 for a description of the pressure interpolation schemes available in FLUENT.

24.7.1

First Order vs. Second Order

When the flow is aligned with the grid (e.g., laminar flow in a rectangular duct modeled with a quadrilateral or hexahedral grid) the first-order upwind discretization may be acceptable. When the flow is not aligned with the grid (i.e., when it crosses the grid lines obliquely), however, first-order convective discretization increases the numerical discretization error (numerical diffusion). For triangular and tetrahedral grids, since the flow is never aligned with the grid, you will generally obtain more accurate results by using the second-order discretization. For quad/hex grids, you will also obtain better results using the second-order discretization, especially for complex flows. In summary, while the first-order discretization generally yields better convergence than the second-order scheme, it generally will yield less accurate results, especially on tri/tet grids. See Section 24.19 for information about controlling convergence. For most cases, you will be able to use the second-order scheme from the start of the calculation. In some cases, however, you may need to start with the first-order scheme and then switch to the second-order scheme after a few iterations. For example, if you are running a high-Mach-number flow calculation that has an initial solution much different than the expected final solution, you will usually need to perform a few iterations with the first-order scheme and then turn on the second-order scheme and continue the calculation to convergence. For a simple flow that is aligned with the grid (e.g., laminar flow in a rectangular duct modeled with a quadrilateral or hexahedral grid), the numerical diffusion will be naturally low, so you can generally use the first-order scheme instead of the second-order scheme without any significant loss of accuracy. Finally, if you run into convergence difficulties with the second-order scheme, you should try the first-order scheme instead.


24-43

Using the Solver

24.7.2

Other Discretization Schemes

The QUICK discretization scheme may provide better accuracy than the second-order scheme for rotating or swirling flows solved on quadrilateral or hexahedral meshes. In general, however, the second-order scheme is sufficient and the QUICK scheme will not provide significant improvements in accuracy. A power law scheme is also available, but it will generally yield the same accuracy as the first-order scheme. The central-differencing scheme is available only when you are using the LES turbulence model, and it should be used only when the mesh spacing is fine enough so that the magnitude of the local Peclet number (Equation 24.2-5) is less than 1.

24.7.3

Choosing the Pressure Interpolation Scheme

As discussed in Section 24.3.1, a number of pressure interpolation schemes are available when the segregated solver is used in FLUENT. For most cases the “standard” scheme is acceptable, but some types of models may benefit from one of the other schemes: • For problems involving large body forces, the body-force-weighted scheme is recommended. • For flows with high swirl numbers, high-Rayleigh-number natural convection, highspeed rotating flows, flows involving porous media, and flows in strongly curved domains, use the PRESTO! scheme. • For compressible flows, the second-order scheme is recommended. • Use the second-order scheme for improved accuracy when one of the other schemes is not applicable.

!

The second-order scheme cannot be used with porous media or with the VOF or mixture model for multiphase flow. Note that you will not specify the pressure interpolation scheme if you are using the Eulerian multiphase model. FLUENT will use the solution method described in Section 22.4.9 for Eulerian multiphase calculations.

24.7.4

Choosing the Density Interpolation Scheme

As discussed in Section 24.3.2, three density interpolation schemes are available when the segregated solver is used to solve a single-phase compressible flow. The first-order upwind scheme (the default) provides stability for the discretization of the pressure-correction equation, and gives good results for most classes of flows. If

24-44


24.7 Choosing the Discretization Scheme

you are calculating a compressible flow with shocks, the first-order upwind scheme may tend to smooth the shocks; you should use the second-order-upwind or QUICK scheme for such flows. For compressible flows with shocks, using the QUICK scheme for all variables, including density, is highly recommended for quadrilateral, hexahedral, or hybrid meshes.

! Note that you will not be able to specify the density interpolation scheme for a compressible multiphase calculation; the first-order upwind scheme will be used for the compressible phase.

24.7.5

User Inputs

You can specify the discretization scheme and, for the segregated solver, the pressure interpolation scheme in the Solution Controls panel (Figure 24.7.1). Solve −→ Controls −→Solution...

Figure 24.7.1: The Solution Controls Panel for the Segregated Solver For each scalar equation listed under Discretization (Momentum, Energy, Turbulence Kinetic Energy, etc. for the segregated solver or Turbulence Kinetic Energy, Turbulence Dissipation Rate, etc. for the coupled solvers) you can choose First Order Upwind, Second Order Upwind, Power Law, QUICK, or (if you are using the LES turbulence model) Central Differencing in the adjacent drop-down list. For the coupled solvers, you can choose


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Using the Solver

either First Order Upwind or Second Order Upwind for the Flow equations (which include momentum and energy). Note that the panel shown in Figure 24.7.1 is for the segregated solver. If you are using the segregated solver, select the pressure interpolation scheme under Discretization in the drop-down list next to Pressure. You can choose Standard, Linear, Second Order, Body Force Weighted, or PRESTO!. If you are using the segregated solver and your flow is compressible (i.e., you are using the ideal gas law for density), select the density interpolation scheme under Discretization in the drop-down list next to Density. You can choose First Order Upwind, Second Order Upwind, or QUICK. (Note that Density will not appear for incompressible or multiphase flows.) If you change the settings for Discretization, but you then want to return to FLUENT’s default settings, you can click the Default button. FLUENT will change the settings to the defaults and the Default button will become the Reset button. To get your settings back again, you can click the Reset button.

24.8

Choosing the Pressure-Velocity Coupling Method

FLUENT provides three methods for pressure-velocity coupling in the segregated solver: SIMPLE, SIMPLEC, and PISO. Steady-state calculations will generally use SIMPLE or SIMPLEC, while PISO is recommended for transient calculations. PISO may also be useful for steady-state and transient calculations on highly skewed meshes.

! Pressure-velocity coupling is relevant only for the segregated solver; you will not specify it for the coupled solvers.

24.8.1

SIMPLE vs. SIMPLEC

In FLUENT, both the standard SIMPLE algorithm and the SIMPLEC (SIMPLE-Consistent) algorithm are available. SIMPLE is the default, but many problems will benefit from the use of SIMPLEC, particularly because of the increased under-relaxation that can be applied, as described below. For relatively uncomplicated problems (laminar flows with no additional models activated) in which convergence is limited by the pressure-velocity coupling, you can often obtain a converged solution more quickly using SIMPLEC. With SIMPLEC, the pressurecorrection under-relaxation factor is generally set to 1.0, which aids in convergence speedup. In some problems, however, increasing the pressure-correction under-relaxation to 1.0 can lead to instability. For such cases, you will need to use a more conservative under-relaxation value or use the SIMPLE algorithm. For complicated flows involving turbulence and/or additional physical models, SIMPLEC will improve convergence only if it is being limited by the pressure-velocity coupling. Often it will be one of the additional modeling parameters that limits convergence; in this case, SIMPLE and SIMPLEC will give similar convergence rates.

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24.8 Choosing the Pressure-Velocity Coupling Method

24.8.2

PISO

The PISO algorithm (see Section 24.3.3) with neighbor correction is highly recommended for all transient flow calculations, especially when you want to use a large time step. (For problems that use the LES turbulence model, which usually requires small time steps, using PISO may result in increased computational expense, so SIMPLE or SIMPLEC should be considered instead.) PISO can maintain a stable calculation with a larger time step and an under-relaxation factor of 1.0 for both momentum and pressure. For steady-state problems, PISO with neighbor correction does not provide any noticeable advantage over SIMPLE or SIMPLEC with optimal under-relaxation factors. PISO with skewness correction is recommended for both steady-state and transient calculations on meshes with a high degree of distortion. When you use PISO neighbor correction, under-relaxation factors of 1.0 or near 1.0 are recommended for all equations. If you use just the PISO skewness correction for highlydistorted meshes, set the under-relaxation factors for momentum and pressure so that they sum to 1 (e.g., 0.3 for pressure and 0.7 for momentum). If you use both PISO methods, follow the under-relaxation recommendations for PISO neighbor correction, above. For most problems, it is not necessary to disable the default coupling between neighbor and skewness corrections. For highly distorted meshes, however, disabling the default coupling between neighbor and skewness corrections is recommended.

24.8.3

User Inputs

You can specify the pressure-velocity coupling method in the Solution Controls panel (Figure 24.7.1). Solve −→ Controls −→Solution... Choose SIMPLE, SIMPLEC, or PISO in the Pressure-Velocity Coupling drop-down list under Discretization. If you choose PISO, the panel will expand to show the PISO Parameters. By default, the number of iterations for Skewness Correction and Neighbor Correction are set to 1. If you want to use only Skewness Correction, then set the number of iterations for Neighbor Correction to 0. Likewise, if you want to use only Neighbor Correction, then set the number of iterations for Skewness Correction to 0. For most problems, you do not need to change the default iteration values. By default, the Skewness-Neighbor Coupling option is turned on to allow for a more economical but a less robust variation of the PISO algorithm.


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Using the Solver

24.9

Setting Under-Relaxation Factors

As discussed in Section 24.2.7, the segregated solver uses under-relaxation to control the update of computed variables at each iteration. This means that all equations solved using the segregated solver, including the non-coupled equations solved by the coupled solvers (turbulence and other scalars, as discussed in Section 24.1.2), will have underrelaxation factors associated with them. In FLUENT, the default under-relaxation parameters for all variables are set to values that are near optimal for the largest possible number of cases. These values are suitable for many problems, but for some particularly nonlinear problems (e.g., some turbulent flows or high-Rayleigh-number natural-convection problems) it is prudent to reduce the under-relaxation factors initially. It is good practice to begin a calculation using the default under-relaxation factors. If the residuals continue to increase after the first 4 or 5 iterations, you should reduce the under-relaxation factors. Occasionally, you may make changes in the under-relaxation factors and resume your calculation, only to find that the residuals begin to increase. This often results from increasing the under-relaxation factors too much. A cautious approach is to save a data file before making any changes to the under-relaxation factors, and to give the solution algorithm a few iterations to adjust to the new parameters. Typically, an increase in the under-relaxation factors brings about a slight increase in the residuals, but these increases usually disappear as the solution progresses. If the residuals jump by a few orders of magnitude, you should consider halting the calculation and returning to the last good data file saved. Note that viscosity and density are under-relaxed from iteration to iteration. Also, if the enthalpy equation is solved directly instead of the temperature equation (i.e., for nonpremixed combustion calculations), the update of temperature based on enthalpy will be under-relaxed. To see the default under-relaxation factors, you can click the Default button in the Solution Controls panel. For most flows, the default under-relaxation factors do not usually require modification. If unstable or divergent behavior is observed, however, you need to reduce the underrelaxation factors for pressure, momentum, k, and from their default values to about 0.2, 0.5, 0.5, and 0.5. (It is usually not necessary to reduce the pressure under-relaxation for SIMPLEC.) In problems where density is strongly coupled with temperature, as in very-high-Rayleigh-number natural- or mixed-convection flows, it is wise to also underrelax the temperature equation and/or density (i.e., use an under-relaxation factor less than 1.0). Conversely, when temperature is not coupled with the momentum equations (or when it is weakly coupled), as in flows with constant density, the under-relaxation factor for temperature can be set to 1.0. For other scalar equations (e.g., swirl, species, mixture fraction and variance) the default under-relaxation may be too aggressive for some problems, especially at the start of the

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24.10 Changing the Courant Number

calculation. You may wish to reduce the factors to 0.8 to facilitate convergence.

User Inputs You can modify the under-relaxation factors in the Solution Controls panel (Figure 24.7.1). Solve −→ Controls −→Solution... You can set the under-relaxation factor for each equation in the field next to its name under Under-Relaxation Factors.

! If you are using the segregated solver, all equations will have an associated underrelaxation factor. If you are using one of the coupled solvers, only those equations that are solved sequentially (see Section 24.1.2) will have under-relaxation factors. If you change under-relaxation factors, but you then want to return to FLUENT’s default settings, you can click the Default button. FLUENT will change the factors to the default values and the Default button will become the Reset button. To get your settings back again, you can click the Reset button.

24.10

Changing the Courant Number

For FLUENT’s coupled solvers, the main control over the time-stepping scheme is the Courant number (CFL). The time step is proportional to the CFL, as defined in Equation 24.4-13. Linear stability theory determines a range of permissible values for the CFL (i.e., the range of values for which a given numerical scheme will remain stable). When you specify a permissible CFL value, FLUENT will compute an appropriate time step using Equation 24.4-13. In general, taking larger time steps leads to faster convergence, so it is advantageous to set the CFL as large as possible (within the permissible range). The stability limits of the coupled implicit and explicit solvers are significantly different. The explicit solver has a more limited range and requires lower CFL settings than does the coupled implicit solver. Appropriate choices of CFL for the two solvers are discussed below.

24.10.1

Courant Numbers for the Coupled Explicit Solver

Linear stability analysis shows that the maximum allowable CFL for the multi-stage scheme used in the coupled explicit solver will depend on the number of stages used and how often the dissipation and viscous terms are updated (see Section 24.19.5). But in general, you can assume that the multi-stage scheme is stable for Courant numbers up to 2.5. This stability limit is often lower in practice because of nonlinearities in the governing equations.


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Using the Solver

The default CFL for the coupled explicit solver is 1.0, but you may be able to increase it for some 2D problems. You should generally not use a value higher than 2.0. If your solution is diverging, i.e., if residuals are rising very rapidly, and your problem is properly set up and initialized, this is usually a good sign that the Courant number needs to be lowered. Depending on the severity of the startup conditions, you may need to decrease the CFL to a value as low as 0.1 to 0.5 to get started. Once the startup transients are reduced you can start increasing the Courant number again.

24.10.2

Courant Numbers for the Coupled Implicit Solver

Linear stability theory shows that the point Gauss-Seidel scheme used in the coupled implicit solver is unconditionally stable. However, as with the explicit solver, nonlinearities in the governing equations will often limit stability. The default CFL for the coupled implicit solver is 5.0. It is often possible to increase the CFL to 10, 20, 100, or even higher, depending on the complexity of your problem. You may find that a lower CFL is required during startup (when changes in the solution are highly nonlinear), but it can be increased as the solution progresses. The coupled AMG solver has the capability to detect divergence of the multigrid cycles within a given iteration. If this happens, it will automatically reduce the CFL and perform the iteration again, and a message will be printed to the screen. Five attempts are made to complete the iteration successfully. Upon successful completion of the current iteration the CFL is returned to its original value and the iteration procedure proceeds as required.

24.10.3

User Inputs

The Courant number is set in the Solution Controls panel (Figure 24.10.1). Solve −→ Controls −→Solution... Enter the value for Courant Number under Solver Parameters. (Note that the panel shown in Figure 24.10.1 is for the coupled explicit solver. For the coupled implicit solver, the Courant Number is the only item that will appear under Solver Parameters.) When you select the coupled explicit solver in the Solver panel, FLUENT will automatically set the Courant Number to 1; when you select the coupled implicit solver, the Courant Number will be changed to 5 automatically.

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24.11 Turning On FAS Multigrid

Figure 24.10.1: The Solution Controls Panel for the Coupled Explicit Solver

24.11

Turning On FAS Multigrid

As discussed in Section 24.5, FAS multigrid is an optional component of the coupled explicit solver. (AMG multigrid is always on, by default.) Since nearly all coupled explicit calculations will benefit from the use of the FAS multigrid convergence accelerator, you should generally set a non-zero number of coarse grid levels before beginning the calculation. For most problems, this will be the only FAS multigrid parameter you will need to set. Should you encounter convergence difficulties, consider applying one of the methods discussed in Section 24.19.4.

! Note that you cannot use FAS multigrid with explicit time stepping (described in Section 24.2.8) because the coarse grid corrections will destroy the time accuracy of the fine grid solution.

24.11.1

Setting Coarse Grid Levels

As discussed in Section 24.5.4, FAS multigrid solves on successively coarser grids and then transfers corrections to the solution back up to the original fine grid, thus increasing the propagation speed of the solution and speeding convergence. The most basic way you can control the multigrid solver is by specifying the number of coarse grid levels to be used.


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Using the Solver

As explained in Section 24.5.4, the coarse grid levels are formed by agglomerating a group of adjacent “fine” cells into a single “coarse” cell. The optimal number of grid levels is therefore problem-dependent. For most problems, you can start out with 4 or 5 levels. For large 3D problems, you may want to add more levels (although memory restrictions may prevent you from using more levels, since each coarse grid level requires additional memory). If you believe that multigrid is causing convergence trouble, you can decrease the number of levels. If FLUENT reaches a coarse grid with one cell before creating as many levels as you requested, it will simply stop there. That is, if you request 5 levels, and level 4 has only 1 cell, FLUENT will create only 4 levels, since levels 4 and 5 would be the same. To specify the number of grid levels you want, set the number of Multigrid Levels in the Solution Controls panel (Figure 24.10.1) under Solver Parameters. Solve −→ Controls −→Solution... You can also set the Max Coarse Levels under FAS Multigrid Controls in the Multigrid Controls panel. Solve −→ Controls −→Multigrid... Changing the number of coarse grid levels in one panel will automatically update the number shown in the other. Coarse grid levels are created when you first begin iterating. If you want to check how many cells are in each level, request one iteration and then use the Grid/Info/Size menu item (described in Section 5.6.1) to list the size of each grid level. If you are satisfied, you can continue the calculation; if not, you can change the number of coarse grid levels and check again. For most problems, you will not need to modify any additional multigrid parameters once you have settled on an appropriate number of coarse grid levels. You can simply continue your calculation until convergence.

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24.12 Setting Solution Limits

24.12

Setting Solution Limits

In order to keep the solution stable under extreme conditions, FLUENT provides limits that keep the solution within an acceptable range. You can control these limits with the Solution Limits panel (Figure 24.12.1). Solve −→ Controls −→Limits...

Figure 24.12.1: The Solution Limits Panel FLUENT applies limiting values for pressure, static temperature, and turbulence quantities. The purpose of these limits is to keep the absolute pressure or the static temperature from becoming 0, negative, or excessively large during the calculation, and to keep the turbulence quantities from becoming excessive. FLUENT also puts a limit on the rate of reduction of static temperature to prevent it from becoming 0 or negative.

! Typically, you will not need to change the default solution limits. If pressure, temperature, or turbulence quantities are being reset to the limiting value repeatedly (as indicated by the appropriate warning messages in the console window), you should check the dimensions, boundary conditions, and properties to be sure that the problem is set up correctly and try to determine why the variable in question is getting so close to zero or so large. You can use the “marking” feature (used to mark cells for adaption) to identify which cells have a value equal to the limit. (Use the Iso-Value Adaption panel, as described in Section 25.6.) In very rare cases, you may need to change the solution limits, but only do so if you are sure that you understand the reason for the solver’s unusual behavior. (For example, you may know that the temperature in your domain will exceed 5000 K. Be sure that any temperature-dependent properties are appropriately defined for high temperatures if you increase the maximum temperature limit.)


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Using the Solver

Limiting the Values of Solution Variables The limiting minimum and maximum values for absolute pressure are shown in the Minimum and Maximum Absolute Pressure fields. If the FLUENT calculation predicts a value less than the Minimum Absolute Pressure or greater than the Maximum Absolute Pressure, the corresponding limiting value will be used instead. Similarly, the Minimum and Maximum Temperature are limiting values for energy calculations. The Maximum Turb. Viscosity Ratio and the Minimum Turb. Kinetic Energy are limiting values for turbulent calculations. If the calculation predicts a k value less than the Minimum Turb. Kinetic Energy, the limiting value will be used instead. For the viscosity ratio limit, FLUENT uses the limiting maximum value of turbulent viscosity (Cµ k 2 /) in the flow field relative to the laminar viscosity. If the ratio calculated by FLUENT exceeds the limiting value, the ratio is set to the limiting value by limiting to the necessary value.

Limiting the Reduction Rate for Temperature In FLUENT’s coupled solvers, the rate of reduction of temperature is controlled by the Positivity Rate Limit. The default value of 0.2, for example, means that temperature is not allowed to decrease by more than 20% of its previous value from one iteration to the next. If the temperature change exceeds this limit, the time step in that cell is reduced to bring the change back into range and a “time step reduced” warning is printed. (This reduced time step will be used for the solution of all variables in the cell, not just for temperature.) Rapid reduction of temperature is an indication that the temperature may become negative. Repeated “time step reduced” warnings should alert you that something is wrong in your problem setup. (If the warning messages stop appearing, the calculation may have “recovered” from the time-step reduction.)

Resetting Solution Limits If you change and save the value of one of the solution limits, but you then want to return to the default limits set by FLUENT, you can reopen the Solution Limits panel and click the Default button. FLUENT will change the values to the defaults and the Default button will become the Reset button. To get your values back again, you can click the Reset button.

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24.13 Initializing the Solution

24.13

Initializing the Solution

Before starting your CFD simulation, you must provide FLUENT with an initial “guess” for the solution flow field. In many cases, you must take extra care to provide an initial solution that will allow the desired final solution to be attained. A real-life supersonic wind tunnel, for example, will not “start” if the back pressure is simply lowered to its operating value; the flow will choke at the tunnel throat and will not transition to supersonic. The same holds true for a numerical simulation: the flow must be initialized to a supersonic flow or it will simply choke and remain subsonic. There are two methods for initializing the solution: • Initialize the entire flow field (in all cells). • Patch values or functions for selected flow variables in selected cell zones or “registers” of cells. (Registers are created with the same functions that are used to mark cells for adaption.)

! Before patching initial values in selected cells, you must first initialize the entire flow field. You can then patch the new values over the initialized values for selected variables.

24.13.1

Initializing the Entire Flow Field

Before you start your calculations or patch initial values for selected variables in selected cells (Section 24.13.2) you must initialize the flow field in the entire domain. The Solution Initialization panel (Figure 24.13.1) allows you to set initial values for the flow variables and initialize the solution using these values. Solve −→ Initialize −→Initialize... You can compute the values from information in a specified zone, enter them manually, or have the solver compute average values based on all zones. You can also indicate whether the specified values for velocities are absolute or relative to the velocity in each cell zone. The steps for initialization are as follows: 1. Set the initial values: • To initialize the flow field using the values set for a particular zone, select the zone name in the Compute From drop-down list. All values under the Initial Values heading will automatically be computed and updated based on the conditions defined at the selected zone. • To initialize the flow field using computed average values, select all-zones in the Compute From drop-down list. FLUENT will compute and update the Initial Values based on the conditions defined at all boundary zones.


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Using the Solver

Figure 24.13.1: The Solution Initialization Panel

• If you wish to change one or more of the values, you can enter new values manually in the fields next to the appropriate variables. If you prefer to enter all values manually, you can do so without selecting a zone in the Compute From list. 2. If your problem involves moving reference frames or sliding meshes, indicate whether the initial velocities are absolute velocities or velocities relative to the motion of each cell zone by selecting Absolute or Relative to Cell Zone under Reference Frame. (If no zone motion occurs in the problem, the two options are equivalent.) The default reference frame for velocity initialization in FLUENT is relative. If the solution in most of your domain is rotating, using the relative option may be better than using the absolute option. 3. Once you are satisfied with the Initial Values displayed in the panel, you can click the Init button to initialize the flow field. If solution data already exist (i.e., if you have already performed some calculations or initialized the solution), you must confirm that it is OK to overwrite those data.

Saving and Resetting Initial Values When you initialize the solution by clicking on Init, the initial values will also be saved; should you need to reinitialize the solution later, you will find the correct values in the panel when you reopen it. If you wish to define initial values now, but you are not yet ready to initialize the solution, you can follow the instructions above for setting the values and then click Apply instead of Init. This will save the currently displayed values

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24.13 Initializing the Solution

without initializing the solution. You can return to the panel later on and perform the initialization. If you accidentally select the wrong zone from the Compute From list or manually set a value incorrectly, you can use the Reset button to reset all fields to their “saved” values. Values are saved each time the panel is opened, before Compute From is executed, and after Init or Apply is executed.

24.13.2

Patching Values in Selected Cells

Once you have initialized (or calculated) the entire flow field, you may patch different values for particular variables into different cells. If you have multiple fluid zones, for example, you may want to patch a different temperature in each one. You can also choose to patch a custom field function (defined using the Custom Field Function Calculator panel) instead of a constant value. If you are patching velocities, you can indicate whether the specified values are absolute velocities or velocities relative to the cell zone’s velocity. All patching operations are performed with the Patch panel (Figure 24.13.2). Solve −→ Initialize −→Patch...

Figure 24.13.2: The Patch Panel

1. Select the variable to be patched in the Variable list. 2. In the Zones To Patch and/or Registers To Patch lists, choose the zone(s) and/or register(s) for which you want to patch a value for the selected variable. 3. If you wish to patch a constant value, simply enter that value in the Value field. If you want to patch a previously-defined field function, turn on the Use Field Function option and select the appropriate function in the Field Function list.


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Using the Solver

4. If you selected a velocity in the Variable list, and your problem involves moving reference frames or sliding meshes, indicate whether the patched velocities are absolute velocities or velocities relative to the motion of each cell zone by selecting Absolute or Relative to Cell Zone under Reference Frame. (If no zone motion occurs in the problem, the two options are equivalent.) The default reference frame for velocity patching in FLUENT is relative. If the solution in most of your domain is rotating, using the relative option may be better than using the absolute option. 5. Click the Patch button to update the flow-field data. (Note that patching will have no effect on the iteration or time-step count.)

Using Registers The ability to patch values in cell registers gives you the flexibility to patch different values within a single cell zone. For example, you may want to patch a certain value for temperature only in fluid cells with a particular range of concentrations for one species. You can create a cell register (basically a list of cells) using the functions that are used to mark cells for adaption. These functions allow you to mark cells based on physical location, cell volume, gradient or isovalue of a particular variable, and other parameters. See Chapter 25 for information about marking cells for adaption. Section 25.10 provides information about manipulating different registers to create new ones. Once you have created a register, you can patch values in it as described above.

Using Field Functions By defining your own field function using the Custom Field Function Calculator panel, you can patch a non-constant value in selected cells. For example, you may want to patch varying species mass fractions throughout a fluid region. To use this feature, simply create the function as described in Section 29.5, and then perform the function-patching operation in the Patch panel, as described above.

Using Patching Later in the Solution Process Since patching affects only the variables for which you choose to change the value, leaving the rest of the flow field intact, you can use it later in the solution process without losing calculated data. (Initialization, on the other hand, resets all data to the initial values.) For example, you might want to start a combustion calculation from a cold-flow solution. You can simply read in (or calculate) the cold-flow data, patch a high temperature in the appropriate cells, and continue the calculation. Patching can also be useful when you are solving a problem using a step-by-step technique, as described in Section 24.19.2.

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24.14 Performing Steady-State Calculations

24.14

Performing Steady-State Calculations

For steady-state calculations, you will request the start of the solution process using the Iterate panel (Figure 24.14.1). Solve −→Iterate...

Figure 24.14.1: The Iterate Panel In this panel, you will supply the number of additional iterations to be performed in the Number of Iterations field. (For unsteady calculation inputs, see Section 24.15.1.) If no calculations have been performed yet, FLUENT will begin calculations starting at iteration 1, using the initial solution. If you are starting from current solution data, FLUENT will begin at the last iteration performed, using the current solution data as its starting point. By default, FLUENT will update the convergence monitors (described in Section 24.16) after each iteration. If you increase the Reporting Interval from the default of 1 you can get reports less frequently. For example, if you set the Reporting Interval to 2, the monitors will print or plot reports at every other iteration. Note that the Reporting Interval also specifies how often FLUENT should check if the solution is converged. For example, if your solution converges after 40 iterations, but your Reporting Interval is set to 50, FLUENT will continue the calculation for an extra 10 iterations before checking for (and finding) convergence. When you click the Iterate button, FLUENT will begin to calculate. During iteration, a Working dialog is displayed. Clicking on the Cancel button or typing in the FLUENT console window will interrupt the iteration, as soon as it is safe to stop. (See below for more details.)

Updating UDF Profiles If you have used a user-defined function (UDF) to define any boundary conditions, properties, etc., you can control the frequency with which the function is updated by modifying


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Using the Solver

the value of the UDF Profile Update Interval. If UDF Profile Update Interval is set to n, the function will be updated after every n iterations. By default, the UDF Profile Update Interval is set to 1. You might want to increase this value if your profile computation is expensive. See the separate UDF Manual for details about creating and using UDFs.

Interrupting Iterations As mentioned above, you can interrupt the calculation by clicking on the Cancel button in the Working dialog box that appears while the solver is calculating. In addition, on most, but not all, computer systems you will be able to interrupt calculations using a control sequence, usually . This allows you to stop the calculation process before proceeding with the remainder of the requested iterations.

Resetting Data After you have performed some iterations, if you decide to start over again from the first iteration (e.g., after making some changes to the problem setup), you can reinitialize the solution using the Solution Initialization panel, as described in Section 24.13.1.

24.15

Performing Time-Dependent Calculations

FLUENT can solve the conservation equations in time-dependent form, to simulate a wide variety of time-dependent phenomena, such as • vortex shedding and other time-periodic phenomena • compressible filling and emptying problems • transient heat conduction • transient chemical mixing and reactions Figures 24.15.1 and 24.15.2 illustrate the time-dependent vortex shedding flow pattern in the wake of a cylinder. Activating time dependence is sometimes useful when attempting to solve steady-state problems which tend toward instability (e.g., natural convection problems in which the Rayleigh number is close to the transition region). It is possible in many cases to reach a steady-state solution by integrating the time-dependent equations. See Section 24.2.8 for details about temporal discretization.

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24.15 Performing Time-Dependent Calculations

1.92e+01 1.76e+01 1.60e+01 1.44e+01 1.28e+01 1.12e+01 9.60e+00 8.00e+00 6.40e+00 4.80e+00 3.20e+00 1.60e+00 0.00e+00

Contours of Stream Function (kg/s) (Time=3.6600e+01)

Figure 24.15.1: Time-Dependent Calculation of Vortex Shedding (t=3.66 sec)

1.92e+01 1.76e+01 1.60e+01 1.44e+01 1.28e+01 1.12e+01 9.60e+00 8.00e+00 6.40e+00 4.80e+00 3.20e+00 1.60e+00 0.00e+00

Contours of Stream Function (kg/s) (Time=4.1600e+01)

Figure 24.15.2: Time-Dependent Calculation of Vortex Shedding (t=41.6 sec)


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Using the Solver

24.15.1

User Inputs for Time-Dependent Problems

To solve a time-dependent problem, you will follow the procedure outlined below: 1. Enable the Unsteady option in the Solver panel (Figure 24.15.3), and specify the desired Unsteady Formulation. Define −→ Models −→Solver...

Figure 24.15.3: The Solver Panel for an Unsteady Calculation The 1st-Order Implicit formulation is sufficient for most problems. If you need improved accuracy, you can use the 2nd-Order Implicit formulation instead. The Explicit formulation (available only if the coupled explicit solver is selected under Solver and Formulation at the top of the panel) is used primarily to capture the transient behavior of moving waves, such as shocks. See Section 24.2.8 for details. When using the segregated solver, you also can select the Use Frozen Flux Formulation? option in your time dependent flow calculations. (see Section 24.3.4). Note that this option is only available for single-phase transient problems that use the segregated solver and do not use a moving/deforming mesh model.

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2. Define all relevant models and boundary conditions. Note that any boundary conditions specified using user-defined functions can be made to vary in time. See the separate UDF Manual for details. 3. If you are using the segregated solver, choose PISO as the Pressure-Velocity Coupling scheme under Discretization in the Solution Controls panel. Solve −→ Controls −→Solution... In general, you will not need to modify the PISO Parameters from their default values. See Section 24.8.2 for more information about using the PISO algorithm.

!

If you are using the LES turbulence model with small time steps, the PISO scheme may be too computationally expensive. It is therefore recommended that you use SIMPLE or SIMPLEC instead of PISO. 4. (optional) If you are using the explicit unsteady formulation or if you are using the adaptive time stepping method (described below and in Section 24.15.2) it is recommended that you enable the printing of the current time (for the explicit unsteady formulation) or the current time step size (for the adaptive time stepping method) at each iteration, using the Statistic Monitors panel. Solve −→ Monitors −→Statistic... Select time (for the current time) or delta time (for the current time step size) in the Statistics list and turn on the Print option. When FLUENT prints the residuals to the console window at each iteration, it will include a column with the current time or the current time step size. 5. (optional) Use the Force Monitors panel or the Surface Monitors panel to monitor (and/or save to a file) time-varying force coefficient values or the average, mass average, integral, or flux of a field variable or function on a surface as it changes with time. See Section 24.16 for details. 6. Set the initial conditions (at time t = 0) using the Solution Initialization panel. Solve −→ Initialize −→Initialize... You can also read in a steady-state data file to set the initial conditions. File −→ Read −→Data... 7. Use the automatic saving feature to specify the file name and frequency with which case and data files should be saved during the solution process. File −→ Write −→Autosave... See Section 3.3.4 for details about the use of this feature. You may also want to request automatic execution of other commands using the Execute Commands panel. See Section 24.18 for details.


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8. (optional) If you want to create a graphical animation of the solution over time, you can use the Solution Animation panel to set up the graphical displays that you want to use in the animation. See Section 24.17 for details. 9. (optional) If you want FLUENT to gather data for time statistics (i.e., time-averaged and root-mean-square values for solution variables) during the calculation, follow these steps: (a) Turn on the Data Sampling for Time Statistics option in the Iterate panel. Solve −→Iterate... Enabling this option will allow you to display and report both the mean and the root-mean-square (RMS) values, as described in Section 24.15.3.

!

Note that gathering data for time statistics is not meaningful inside a moving cell zone (i.e., a sliding zone in a sliding mesh problem). (b) Initialize the flow statistics. Solve −→ Initialize −→Reset Statistics Note that you can also use this menu item to reset the flow statistics after you have gathered some data for time statistics. If you perform, say, 10 time steps with the Data Sampling for Time Statistics option enabled, check the results, and then continue the calculation for 10 more time steps, the time statistics will include the data gathered in the first 10 time steps unless you reinitialize the flow statistics. 10. Specify time-dependent solution parameters and start the calculation, as described below for the implicit and explicit unsteady formulations: • If you have chosen the 1st-Order or 2nd-Order Implicit formulation, the procedure is as follows: (a) Set the time-dependent solution parameters in the Iterate panel (Figure 24.15.4). Solve −→Iterate... Solution parameters for the implicit unsteady formulations are as follows: – Max Iterations per Time Step: When FLUENT solves the time-dependent equations using the implicit formulation, iteration is necessary at each time step. This parameter sets a maximum for the number of iterations per time step. If the convergence criteria are met before this number of iterations is performed, the solution will advance to the next time step. – Time Step Size: The time step size is the magnitude of ∆t. Since the FLUENT formulation is fully implicit, there is no stability criterion that needs to be met in determining ∆t. However, to model transient

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Figure 24.15.4: The Iterate Panel for Implicit Unsteady Calculations phenomena properly, it is necessary to set ∆t at least one order of magnitude smaller than the smallest time constant in the system being modeled. A good way to judge the choice of ∆t is to observe the number of iterations FLUENT needs to converge at each time step. The ideal number of iterations per time step is 10–20. If FLUENT needs substantially more, the time step is too large. If FLUENT needs only a few iterations per time step, ∆t may be increased. Frequently a time-dependent problem has a very fast “startup” transient that decays rapidly. It is thus often wise to choose a conservatively small ∆t for the first 5–10 time steps. ∆t may then be gradually increased as the calculation proceeds. For time-periodic calculations, you should choose the time step based on the time scale of the periodicity. For a rotor/stator model, for example, you might want 20 time steps between each blade passing. For vortex shedding, you might want 20 steps per period. By default, the size of the time step is fixed (as indicated by the selection of Fixed under Time Stepping Method). To have FLUENT modify the size of the time step as the calculation proceeds, select Adaptive and specify the parameters under Adaptive Time Stepping in the expanded Iterate panel.


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Using the Solver

See Section 24.15.2 for details. With the Adaptive time stepping method, the value you specify for the Time Step Size will be the initial size of the time step. As the calculation proceeds, the Time Step Size shown in the Iterate panel will be the size of the current time step. (b) Specify the desired Number of Time Steps in the Iterate panel and click Iterate. As it calculates a solution, FLUENT will print the current time at the end of each time step. • If you have chosen the Explicit unsteady formulation, you will follow a different procedure: (a) Use the default settings for the Solver Parameters in the Solution Controls panel. Solve −→ Controls −→Solution... If you have modified the Solver Parameters, you can click the Default button to retrieve the default settings. (b) Specify the desired Number of Iterations and click Iterate. Solve −→Iterate... Remember that when the explicit unsteady formulation is used, each iteration is a time step. When FLUENT prints the residuals to the console window, it will include a column with the current time (if you requested this in step 4, above). 11. Save the final data file (and case file, if you have modified it) so that you can continue the unsteady calculation later, if desired. File −→ Write −→Data...

Additional Inputs The procedures for setting the reporting interval, updating UDF profiles, interrupting iterations, and resetting data are the same as those for steady-state calculations. See Section 24.14 for details.

! If you are using a user-defined function in your time-dependent calculation, note that, in addition to being updated after every n iterations (where n is the value of the UDF Profile Update Interval), the function will also be updated at the first iteration of each time step.

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24.15.2

Adaptive Time Stepping

As mentioned in Section 24.15.1, it is possible to have the size of the time step change as the calculation proceeds, rather than specifying a fixed size for the entire calculation. This section provides a brief description of the algorithm that FLUENT uses to compute the time step size, as well as an explanation of each of the parameters that you can set to control the adaptive time stepping.

! Adaptive time stepping is available only with the segregated and coupled implicit solvers; it cannot be used with the coupled explicit solver. In addition, it cannot be used with the VOF or discrete phase model.

The Adaptive Time Stepping Algorithm The automatic determination of the time step size is based on the estimation of the truncation error associated with the time integration scheme (i.e., first-order implicit or second-order implicit). If the truncation error is smaller than a specified tolerance, the size of the time step is increased; if the truncation error is greater, the time step size is decreased. An estimation of the truncation error can be obtained by using a predictor-corrector type of algorithm [92] in association with the time integration scheme. At each time step, a predicted solution can be obtained using a computationally inexpensive explicit method (forward Euler for the first-order unsteady formulation, Adams-Bashford for the secondorder unsteady formulation). This predicted solution is used as an initial condition for the time step, and the correction is computed using the non-linear iterations associated with the implicit (segregated or coupled) algorithm. The norm of the difference between the predicted and corrected solutions is used as a measure of the truncation error. By comparing the truncation error with the desired level of accuracy (i.e., the truncation error tolerance), FLUENT is able to adjust the time step size by increasing it or decreasing it.

Specifying Parameters for Adaptive Time Stepping The parameters that control the adaptive time stepping appear in the Iterate panel, as described in Section 24.15.1. These parameters are as follows: Truncation Error Tolerance specifies the threshold value to which the computed truncation error is compared. Increasing this value will lead to an increase in the size of the time step and a reduction in the accuracy of the solution. Decreasing it will lead to a reduction in the size of the time step and an increase in the solution accuracy, although the calculation will require more computational time. For most cases, the default value of 0.01 is acceptable.


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Ending Time specifies an ending time for the calculation. Since the ending time cannot be determined by multiplying the number of time steps by a fixed time step size, you need to specify it explicitly. Minimum/Maximum Time Step Size specify the upper and lower limits for the size of the time step. If the time step becomes very small, the computational expense may be too high; if the time step becomes very large, the solution accuracy may not be acceptable to you. You can set the limits that are appropriate for your simulation. Minimum/Maximum Step Change Factor limit the degree to which the time step size can change at each time step. Limiting the change results in a smoother calculation of the time step size, especially when high-frequency noise is present in the solution. If the time step change factor, f , is computed as the ratio between the specified truncation error tolerance and the computed truncation error, the size of time step ∆tn is computed as follows: • If 1 < f < fmax , ∆tn is increased to meet the desired tolerance. • If 1 < fmax < f , ∆tn is increased, but its maximum possible value is fmax ∆tn−1 . • If fmin < f < 1, ∆tn is unchanged. • If f < fmin < 1, ∆tn is decreased. Number of Fixed Time Steps specifies the number of fixed-size time steps that should be performed before the size of the time step starts to change. The size of the fixed time step is the value specified for Time Step Size in the Iterate panel. It is a good idea to perform a few fixed-size time steps before switching to the adaptive time stepping. Sometimes spurious discretization errors can be associated with an impulsive start in time. These errors are dissipated during the first few time steps, but they can adversely affect the adaptive time stepping and result in extremely small time steps at the beginning of the calculation.

Specifying a User-Defined Time Stepping Method If you want to use your own adaptive time stepping method, instead of the method described above, you can create a user-defined function for your method and select it in the User-Defined Time Step drop-down list. The other inputs under Adaptive Time Stepping will not be used when you select a user-defined function. See the separate UDF Manual for details about creating and using user-defined functions.

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24.15.3

Postprocessing for Time-Dependent Problems

The postprocessing of time-dependent data is similar to that for steady-state data, with all graphical and alphanumeric commands available. You can read a data file that was saved at any point in the calculation (by you or with the autosave option) to restore the data at any of the time levels that were saved. File −→ Read −→Data... FLUENT will label any subsequent graphical or alphanumeric output with the time value of the current data set. If you save data from the force or surface monitors to files (see step 5 in Section 24.15.1), you can read these files back in and plot them to see a time history of the monitored quantity. Figure 24.15.5 shows a sample plot generated in this way.

-5.00e+00 -5.10e+00 -5.20e+00 -5.30e+00 -5.40e+00

Cl

-5.50e+00 -5.60e+00 -5.70e+00 -5.80e+00 -5.90e+00 -6.00e+00 0

Y X

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Time

Z

Cl

Figure 24.15.5: Lift Coefficient Plot for a Time-Periodic Solution

If you enabled the Data Sampling for Time Statistics option in the Iterate panel, FLUENT will compute the time average (mean) and root-mean-squares of the instantaneous values sampled during the calculation. The mean and root-mean-square (RMS) values for all solution variables will be available in the Unsteady Statistics... category of the variable selection drop-down list that appears in postprocessing panels.


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Using the Solver

24.16

Monitoring Solution Convergence

During the solution process you can monitor the convergence dynamically by checking residuals, statistics, force values, surface integrals, and volume integrals. You can print reports of or display plots of lift, drag, and moment coefficients, surface integrations, and residuals for the solution variables. For unsteady flows, you can also monitor elapsed time. Each of these monitoring features is described below.

24.16.1

Monitoring Residuals

At the end of each solver iteration, the residual sum for each of the conserved variables is computed and stored, thus recording the convergence history. This history is also saved in the data file. The residual sum is defined below. On a computer with infinite precision, these residuals will go to zero as the solution converges. On an actual computer, the residuals decay to some small value (“roundoff”) and then stop changing (“level out”). For “single precision” computations (the default for workstations and most computers), residuals can drop as many as six orders of magnitude before hitting round-off. Double precision residuals can drop up to twelve orders of magnitude. Guidelines for judging convergence can be found in Section 24.19.1.

Definition of Residuals for the Segregated Solver After discretization, the conservation equation for a general variable φ at a cell P can be written as X

aP φP =

anb φnb + b

(24.16-1)

nb

Here aP is the center coefficient, anb are the influence coefficients for the neighboring cells, and b is the contribution of the constant part of the source term Sc in S = Sc + SP φ and of the boundary conditions. In Equation 24.16-1, aP =

X

anb − SP

(24.16-2)

nb

The residual Rφ computed by FLUENT’s segregated solver is the imbalance in Equation 24.16-1 summed over all the computational cells P . This is referred to as the “unscaled” residual. It may be written as Rφ =

X

cells P

|

X

anb φnb + b − aP φP |

(24.16-3)

nb

In general, it is difficult to judge convergence by examining the residuals defined by Equation 24.16-3 since no scaling is employed. This is especially true in enclosed flows

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24.16 Monitoring Solution Convergence

such as natural convection in a room where there is no inlet flow rate of φ with which to compare the residual. FLUENT scales the residual using a scaling factor representative of the flow rate of φ through the domain. This “scaled” residual is defined as φ

R =

P

cells P

|

P

anb φnb + b − aP φP | cells P |aP φP |

nb

P

(24.16-4)

For the momentum equations the denominator term aP φP is replaced by aP vP , where vP is the magnitude of the velocity at cell P . The scaled residual is a more appropriate indicator of convergence for most problems, as discussed in Section 24.19.1. This residual is the default displayed by FLUENT. Note that this definition of residual is also used by Fluent Inc.’s structured grid solver FLUENT 4. For the continuity equation, the unscaled residual for the segregated solver is defined as Rc =

X

|rate of mass creation in cell P|

(24.16-5)

cells P

The segregated solver’s scaled residual for the continuity equation is defined as c Riteration N c Riteration 5

(24.16-6)

The denominator is the largest absolute value of the continuity residual in the first five iterations. The scaled residuals described above are useful indicators of solution convergence. Guidelines for their use are given in Section 24.19.1. It is sometimes useful to determine how much a residual has decreased during calculations as an additional measure of convergence. For this purpose, FLUENT allows you to normalize the residual (either scaled or unscaled) by dividing by the maximum residual value after M iterations, where M is set by you in the Residual Monitors panel in the Iterations field under Normalization. φ Riteration N φ ¯ R = φ Riteration M

(24.16-7)

Normalization in this manner ensures that the initial residuals for all equations are of O(1) and is sometimes useful in judging overall convergence. By default, M = 5. You can also specify the normalization factor (the denominator in Equation 24.16-7) manually in the Residual Monitors panel.


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Definition of Residuals for the Coupled Solvers A residual for the coupled solvers is simply the time rate of change of the conserved variable (W). The RMS residual is the square root of the average of the squares of the residuals in each cell of the domain:

R(W) =

v u uX t

∂W ∂t

!2

(24.16-8)

Equation 24.16-8 is the unscaled residual sum reported for all the coupled equations solved by FLUENT’s coupled solvers.

! The residuals for the equations that are solved sequentially by the coupled solvers (turbulence and other scalars, as discussed in Section 24.1.2) are the same as those described above for the segregated solver. In general, it is difficult to judge convergence by examining the residuals defined by Equation 24.16-8 since no scaling is employed. This is especially true in enclosed flows such as natural convection in a room where there is no inlet flow rate of φ with which to compare the residual. FLUENT scales the residual using a scaling factor representative of the flow rate of φ through the domain. This “scaled” residual is defined as R(W)iteration N R(W)iteration 5

(24.16-9)

The denominator is the largest absolute value of the residual in the first five iterations. The scaled residuals described above are useful indicators of solution convergence. Guidelines for their use are given in Section 24.19.1. It is sometimes useful to determine how much a residual has decreased during calculations as an additional measure of convergence. For this purpose, FLUENT allows you to normalize the residual (either scaled or unscaled) by dividing by the maximum residual value after M iterations, where M is set by you in the Residual Monitors panel in the Iterations field under Normalization. Normalization of the residual sum is accomplished by dividing by the maximum residual value after M iterations, where M is set by you in the Residual Monitors panel in the Iterations field under Normalization: R(W)iteration N ¯ R(W) = R(W)iteration M

(24.16-10)

Normalization in this manner ensures that the initial residuals for all equations are of O(1) and is sometimes useful in judging overall convergence.

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By default, M = 5, making the normalized residual equivalent to the scaled residual. You can also specify the normalization factor (the denominator in Equation 24.16-10) manually in the Residual Monitors panel.

Overview of Using the Residual Monitors Panel All inputs controlling the monitoring of residuals are entered using the Residual Monitors panel (Figure 24.16.1). Solve −→ Monitors −→Residual... or Plot −→Residuals...

Figure 24.16.1: The Residual Monitors Panel In general, you will only need to enable residual plotting and modify the convergence criteria using this panel. Additional controls are available for disabling monitoring of particular residuals, and modifying normalization and plot parameters.


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Using the Solver

Printing and Plotting Residuals By default, residual values for all relevant variables are printed in the text (console) window after each iteration. If you wish to disable this printout, turn off Print under Options. To enable the plotting of residuals after each iteration, turn on Plot under Options. Residuals will be plotted in the graphics window (with the window ID set in the Window field) during the calculation. If you wish to display a plot of the current residual history, simply click the Plot push button.

Modifying Convergence Criteria In addition to plotting and printing residual values during the calculation, FLUENT will also check for convergence. If convergence is being monitored, the solution will stop automatically when each variable meets its specified convergence criterion. Convergence checks can be performed only for variables for which you are monitoring residuals (i.e., variables for which the Monitor option is enabled). You can choose whether or not you want to check the convergence for each variable by turning on or off the Check Convergence option for it in the Residual Monitors panel. To modify the convergence criterion for a particular variable, enter a new value in the corresponding Convergence Criterion field.

Storing Residual History Points Residual histories for each variable are automatically saved in the data file, regardless of whether they are being monitored. You can control the number of history points to be stored by changing the Iterations entry under Storage. By default, up to 1000 points will be stored. If more than 1000 iterations are performed (i.e., the limit is reached), every other point will be discarded—leaving 500 history points—and the next 500 points will be stored. When the total hits 1000 again, every other point will again be discarded, etc. If you are performing a large number of iterations, you will lose a great deal of residual history information about the beginning of the calculation. In such cases, you should increase the Iterations value to a more appropriate value. Of course, the larger this number is, the more memory you will need, the longer the plotting will take, and the more disk space you will need to store the data file.

Plot Parameters If you choose to plot the residual values (either interactively during the solution or using the Plot button after calculations are complete), there are several display parameters you can modify.

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In the Window field under Plotting, you can specify the ID of the graphics window in which the plot will be drawn. When FLUENT is iterating, the active graphics window is temporarily set to this window to update the residual plot, and then returned to its previous value. Thus, the residual plot can be maintained in a separate window that does not interfere with other graphical postprocessing. You can modify the number of residual history points to be displayed in the plot by changing the Iterations entry under Plotting. If you specify n points, FLUENT will display the last n history points. Since the y axis is scaled by the minimum and maximum values of all points in the plot, you can zoom in on the end of the residual history by setting Iterations to a value smaller than the number of iterations performed. If, for example, the residuals jumped early in the calculation when you turned on turbulence, that peak broadens the overall range in residual values, making the smaller fluctuations later on almost indistinguishable. By setting the value of Iterations so that the plot does not include that early peak, your y-axis range is better suited to the values that you are interested in seeing. For more information on residual history points, please refer to the discussion of storing residual history points, described earlier in this section. You can also modify the attributes of the plot axes and the residual curves. Click the Axes... or Curves... button to open the Axes panel or Curves panel. See Sections 27.8.8 and 27.8.9 for details.

! Note that entering a value for Iterations under Plotting does not necessarily mean solved iterations but rather stored (or sampled) data points. Note also that the frequency of the data storage will diminish towards the start of the solution as the number of solved iterations increases. Due to this, whenever the stored iterations is greater than the solved iterations, if you plot n iterations, you actually see a history that goes back further than n solved iterations.

Disabling Monitoring If your problem requires the solution of many equations (e.g., turbulence quantities and multiple species), a plot that includes all residuals may be difficult to read. In such cases, you may choose to monitor only a subset of the residuals, perhaps those that affect convergence the most. You can indicate whether or not you want to monitor residuals for each variable by enabling or disabling the relevant check box in the Monitor list of the Residual Monitors panel.

Controlling Normalization By default, scaling of residuals (see Equations 24.16-4 and 24.16-9) is enabled and the default convergence criterion is 10−6 for energy and P-1 equations and 10−3 for all other equations. Residual normalization (i.e., dividing the residuals by the largest value during the first few iterations) is also available but disabled by default.


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Normalization can be used with both scaled and unscaled residuals. Note that if normalization is enabled, the convergence criterion may need to be adjusted appropriately. See Section 24.19.1 for information about judging convergence based on the different types of residual reports. (Both the raw residuals and scaling factors are stored in the data file, so you can switch between scaled and unscaled residuals.) To report unscaled residuals, simply turn off the Scale option under Normalization.

! If you switch from scaled to unscaled residuals (or vice versa) and you are normalizing the residuals (as described below), you must click the Renorm button to recompute the normalization factors. If you wish to normalize the residuals (see Equation 24.16-7 or 24.16-10), turn on the Normalize option under Normalize. The Normalization Factor column will be added to the panel at this time. FLUENT will normalize the printed or plotted residual for each variable by the value indicated as the Normalization Factor for that variable. The default Normalization Factor is the maximum residual value after the first 5 iterations. To use the maximum residual value after a different number of iterations (i.e., specify a different value for M in Equation 24.16-7 or 24.16-10), you can modify the Iterations entry under Normalization. In some cases, the maximum residual may occur sometime after the iteration specified in the Iterations field. If this should occur, you can click the Renorm button to set the normalization factors for all variables to the maximum values in the residual histories. Subsequent plots and printed reports will use the new normalization factor. You can also specify the normalization factor (the denominator in Equation 24.16-7 or 24.16-10) explicitly. To modify the normalization factor for a particular variable, enter a new value in the corresponding Normalization Factor field in the Residual Monitors panel. If you wish to report unnormalized, unscaled residuals (Equation 24.16-3 or 24.16-8), turn off the Normalize and Scale options under Normalization in the Residual Monitors panel. Note that unnormalized, unscaled residuals are stored in the data file regardless of whether the reported residuals are normalized or scaled.

Postprocessing Residual Values If you are having solution convergence difficulties, it is often useful to plot the residual value fields (e.g., using contour plots) to determine where the high residual values are located. When you use one of the coupled solvers, the residual values for all solution variables are available in the Residuals... category in the postprocessing panels. (If you read case and data files into FLUENT, you will need to perform at least one iteration before the residual values are available for postprocessing.) For the segregated solver, however, only the mass imbalance in each cell is available by default. If you want to plot residual value fields for a segregated solver calculation, you will need to do the following:

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1. Read in the case and data files of interest (if they are not already in the current session). 2. Use the expert command in the solve/set/ text menu to enable the saving of residual values. solve −→ set −→expert Among other questions, FLUENT will ask if you want to save cell residuals for postprocessing. Enter yes or y, and keep the default settings for all of the other questions (by pressing the key). 3. Perform at least one iteration. The solution variables for which residual values are available will appear in the Residuals... category in the postprocessing panels. Note that residual values are not available for the radiative transport equations solved by the discrete ordinates radiation model.

24.16.2

Monitoring Statistics

If you are solving a fully-developed periodic flow, you may want to monitor the pressure gradient or the bulk temperature ratio, as discussed in Section 8.3. If you are solving an unsteady flow (especially if you are using the explicit time stepping option), you may want to monitor the “time” that has elapsed during the calculation. The physical time of the flow field starts at zero when you initialize the flow. (See Section 24.15 for details about modeling unsteady flows.) If you are using the adaptive time stepping method described in Section 24.15.2, you may want to monitor the size of the time step, ∆t. You can use the Statistic Monitors panel (Figure 24.16.2) to print or plot these quantities during the calculation. Solve −→ Monitors −→Statistic... The procedure for setting up this monitor is listed below: 1. Indicate the type of report you want by turning on the Print option for a printout or the Plot option for a plot. You can enable these options simultaneously. 2. Select the appropriate quantity in the Statistics list. 3. If you are plotting the quantities, you can set any of the plotting options discussed below.


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Using the Solver

Figure 24.16.2: The Statistic Monitors Panel

Plot Parameters If you choose to plot the statistics, there are several display parameters you can modify. In the First Window field, you can specify the ID of the graphics window in which the plot will be drawn (or in which the first plot will be drawn, if you are plotting more than one quantity.) When FLUENT is iterating, the active graphics window is temporarily set to this window to update the plot, and then returned to its previous value. Thus, the statistics plot can be maintained in a separate window that does not interfere with other graphical postprocessing. Note that additional quantities that you have selected in the Statistics list will be plotted in windows with incrementally higher IDs. You can also modify the attributes of the plot axes and curves. Click the Axes... or Curves... button to open the Axes panel or Curves panel. See Sections 27.8.8 and 27.8.9 for details.

24.16.3

Monitoring Forces and Moments

At the end of each solver iteration, the lift, drag, and/or moment coefficient can be computed and stored to create a convergence history. You can print and plot this convergence data, and also save it to an external file. The external file is written in the FLUENT XY plot file format described in Section 27.8.5. Monitoring forces can be useful when you are calculating external aerodynamics, for example, and you are especially interested in the forces. Sometimes the forces converge before the residuals have dropped three orders of magnitude, so you can save time by stopping the calculation earlier than you would if you were monitoring only residuals. (You should be sure to check the mass flow rate and heat transfer rate as well, using the Flux Reports panel described in Section 28.2, to ensure that the mass and energy are being suitably conserved.)

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! The force and moment coefficients use the reference values described in Section 28.8. Specifically, the force coefficients use the reference area, density, and velocity, and the moment coefficients use the reference area, density, velocity and length.

! Only the processed force coefficient data is saved. If you decide to change any of the parameters controlling the force monitoring, such as the reference values, force vector, moment center, moment axis, or wall zones, you may see a discontinuity in the data: the previous data is not updated. Usually, if you have made changes you will want to delete the previous force coefficient data before continuing to iterate.

Monitoring Forces in Unsteady Flow Calculations If you are calculating unsteady flow, the specified force reports will be updated after each time step, rather than after each iteration. All other features of the force monitor and the related setup procedures are unchanged.

Overview of Using the Force Monitors Panel You can use the Force Monitors panel (Figure 24.16.3) to print, plot, and save the convergence history of the drag, lift, and moment coefficients on specified wall zones. Solve −→ Monitors −→Force...

Figure 24.16.3: The Force Monitors Panel In this panel you will indicate the types of reports that you want (printouts, plots, or files), and specify which coefficients and wall zones are of interest. Additional information will be entered for each coefficient that is monitored. You can also modify the plot parameters.


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Using the Solver

! Remember to click Apply after making the desired modifications to the setup for each coefficient report.

Specifying the Force Coefficient Report For each coefficient that you choose to monitor, you will set all appropriate parameters in the Force Monitors panel and click Apply. You can monitor one, two, or all three of the coefficients (drag, lift, and moment vector component) while iterating. When you select the desired coefficient, the current (or default) panel settings are shown for that coefficient. Clicking the Apply button will save the current panel settings for the selected coefficient. The procedure for specifying a force coefficient report is listed below: 1. Indicate the type of report you want (printout, plot, or file), as described below. 2. If you want to monitor the force or moment on individual walls in a single printout, plot, or file, turn on the Per Zone option. See below for details. 3. Choose the coefficient of interest by selecting Drag, Lift, or Moment in the Coefficient drop-down list. 4. In the Wall Zones list, select the wall zone(s) on which the selected coefficient is to be computed. If you are monitoring more than one coefficient, the selected wall zones are often the same for each coefficient. If you want, however, you can have each coefficient computed on a different set of zones. 5. Depending on the coefficient selected, do one of the following: • If you are monitoring the drag or lift coefficient, enter the X, Y, and Z components of the Force Vector along which the forces will be computed. The Force Vector heading will appear only if you have selected Drag or Lift in the Coefficient drop-down list. By default, drag is computed in the x direction and lift in the y direction. • If you are monitoring the moment coefficient, enter the Cartesian coordinates (X, Y, and Z) of the Moment Center about which moments will be computed. The Moment Center heading will appear only if you have selected Moment in the Coefficient drop-down list. The default moment center is (0,0,0). You will also need to specify which component of the moment vector you wish to monitor. Presently, you can monitor only one component of the moment vector at a time. Select X-Axis, Y-Axis, or Z-Axis in the About drop-down list. (This list is active only if you have selected Moment in the Coefficient drop-down list.) For two dimensional flows, only the moment vector about the z-coordinate axis exists. 6. Click Apply and repeat the process for additional coefficients, if desired.

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Printing, Plotting, and Saving Force Coefficient Histories There are three methods available for reporting the selected force coefficients. To print the coefficient value(s) in the text (console) window after each iteration, turn on the Print option under Options in the Force Monitors panel. To plot the coefficient in the graphics window indicated in Plot Window, turn on the Plot option. If you want to save the values to a file, turn on the Write option and specify the File Name. You can enable any combination of these options simultaneously.

! If you choose not to save the force coefficient data in a file, this information will be lost when you exit the current FLUENT session. If you wish to display a plot of the current force-coefficient history, simply click the Plot button. Plot Parameters If you choose to plot the force coefficients (either interactively during the solution or using the Plot button after calculations are complete), there are several display parameters you can modify. In the Plot Window field, you can specify the ID of the graphics window in which the plot for each force coefficient will be drawn. When FLUENT is iterating, the active graphics window is temporarily set to this window to update the plot, and then returned to its previous value. Thus, the force-coefficient plots can be maintained in separate windows that do not interfere with other graphical postprocessing. You can also modify the attributes of the plot axes and the coefficient curves. The same attributes apply to all force-monitor plots. Click the Axes... or Curves... button to open the Axes panel or Curves panel. See Sections 27.8.8 and 27.8.9 for details.

Monitoring Forces and Moments on Individual Walls By default, FLUENT will compute and monitor the total force or moment for all of the selected walls combined together. If you have selected multiple walls and you want to monitor the force or moment on each wall separately, you can turn on the Per Zone option in the Force Monitors panel. The specified force vector or moment axis will apply to all selected walls. If the monitor results are printed to the console (using the Print option), the force or moment on each wall will be printed in a separate column. If the results are plotted (using the Plot option), a separate curve for each wall will be drawn in the specified plot window. If the results are written to a file (using the Write option), the file will be in a tab-separated column format based on the XY plot file format described in Section 27.8.5.


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Discarding the Force-Monitoring Data Should you decide that the data gathered by the force monitor are not useful (e.g., if you are restarting the calculation or you changed one of the reference values), you can discard the accumulated data by clicking on the Clear button. The Clear button will delete all monitoring data for the coefficient selected in the Coefficient drop-down list, including the associated history file (with the name in the File Name field). When you use the Clear button, you will need to confirm the data discard in a Question dialog box. Only the force-monitoring data is removed using this operation; the solution data is not affected.

24.16.4

Monitoring Surface Integrals

At the end of each solver iteration or time step, the average, mass average, integral, flow rate, or other integral report of a field variable or function can be monitored on a surface. You can print and plot these convergence data, and also save them in an external file. The external file is written in the FLUENT XY plot file format described in Section 27.8.5. The report types available are the same as those in the Surface Integrals panel, as described in Section 28.5. Monitoring surface integrals can be used to check for both iteration convergence and grid independence. For example, you can monitor the average value of a certain variable on a surface. When this value stops changing, you can stop iterating. You can then adapt the grid and reconverge the solution. The solution can be considered grid-independent when the average value on the surface stops changing between adaptions.

Overview of Defining Surface Monitors You can use the Surface Monitors panel (Figure 24.16.4) to create surface monitors and indicate whether and when each one’s history is to be printed, plotted, or saved. The Define Surface Monitor panel (Figure 24.16.5), opened from the Surface Monitors panel, allows you to define what each monitor tracks (i.e., the average, integral, flow rate, mass average, or other integral report of a field variable or function on one or more surfaces).

Defining Surface Monitors You will begin the surface monitor definition procedure in the Surface Monitors panel (Figure 24.16.4). Solve −→ Monitors −→Surface... The procedure is as follows: 1. Increase the Surface Monitors value to the number of surface monitors you wish to specify. As this value is increased, additional monitor entries in the panel will become editable. For each monitor, you will perform the following steps.

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Figure 24.16.4: The Surface Monitors Panel

2. Enter a name for the monitor under the Name heading, and use the Plot, Print, and Write check buttons to indicate the report(s) you want (plot, printout, or file), as described below. 3. Indicate whether you want to update the monitor every Iteration or every Time Step by selecting the appropriate item in the drop-down list below Every. Time Step is a valid choice only if you are calculating unsteady flow. If you specify every Iteration, and the Reporting Interval in the Iterate panel is greater than 1, the monitor will be updated at every reporting interval instead of at each iteration (e.g., for a reporting interval of 2, the monitor will be updated after every other iteration). If you specify every Time Step, the reporting interval will have no effect; the monitor will always be updated after each time step. 4. Click the Define... button to open the Define Surface Monitor panel (Figure 24.16.5). Since this is a modal panel, the solver will not allow you to do anything else until you perform steps 5–10, below. 5. In the Define Surface Monitor panel, choose the integration method for the surface monitor by selecting Integral, Area-Weighted Average, Flow Rate, Mass Flow Rate, Mass-Weighted Average, Sum, Facet Average, Facet Minimum, Facet Maximum, Vertex Average, Vertex Minimum, or Vertex Maximum in the Report Type drop-down list. These methods are described in Section 28.5. 6. In the Surfaces list, choose the surface or surfaces on which you wish to integrate. 7. Specify the variable or function to be integrated in the Report Of drop-down list. First select the desired category in the upper drop-down list. You can then select


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Figure 24.16.5: The Define Surface Monitor Panel

one of the related quantities in the lower list. (See Chapter 29 for an explanation of the variables in the list.) 8. If you are plotting the data or writing them to a file, specify the parameter to be used as the x-axis value (the y-axis value corresponds to the monitored data). In the X Axis drop-down list, select Iteration, Time Step, or Flow Time as the x-axis function against which monitored data will be plotted or written. Time Step and Flow Time are valid choices only if you are calculating unsteady flow. If you choose Time Step, the x axis of the plot will indicate the time step, and if you choose Flow Time, it will indicate the elapsed time. 9. If you are plotting the monitored data, specify the ID of the graphics window in which the plot will be drawn in the Plot Window field. When FLUENT is iterating, the active graphics window is temporarily set to this window to update the plot, and then returned to its previous value. Thus, each surface-monitor plot can be maintained in a separate window that does not interfere with other graphical postprocessing. 10. If you are writing the monitored data to a file, specify the File Name. 11. Remember to click OK in the Surface Monitors panel after you finish defining all surface monitors.

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Printing, Plotting, and Saving Surface Integration Histories There are three methods available for reporting the selected surface integration. To print the surface integration in the text (console) window after each iteration, turn on the Print option in the Surface Monitors panel. To plot the integrated values in the graphics window indicated in Plot Window (in the Define Surface Monitor panel), turn on the Plot option in the Surface Monitors panel. If you want to save the values to a file, turn on the Write option in the Surface Monitors panel and specify the File Name in the Define Surface Monitor panel. You can enable any combination of these options simultaneously.

! If you choose not to save the surface integration data in a file, this information will be lost when you exit the current FLUENT session. Plot Parameters You can modify the attributes of the plot axes and curves used for each surface-monitor plot. Click the Axes... or Curves... button in the Define Surface Monitor panel for the appropriate monitor to open the Axes panel or Curves panel for that surface-monitor plot. See Sections 27.8.8 and 27.8.9 for details.

24.16.5

Monitoring Volume Integrals

At the end of each solver iteration or time step, the volume or the sum, volume integral, volume average, mass integral, or mass average of a field variable or function can be monitored in one or more cell zones. You can print and plot these convergence data, and also save them in an external file. The external file is written in the FLUENT XY plot file format described in Section 27.8.5. The report types available are the same as those in the Volume Integrals panel, as described in Section 28.6. Monitoring volume integrals can be used to check for both iteration convergence and grid independence. For example, you can monitor the average value of a certain variable in a particular cell zone. When this value stops changing, you can stop iterating. You can then adapt the grid and reconverge the solution. The solution can be considered gridindependent when the average value in the cell zone stops changing between adaptions.

Overview of Defining Volume Monitors You can use the Volume Monitors panel (Figure 24.16.6) to create volume monitors and indicate whether and when each one’s history is to be printed, plotted, or saved. The Define Volume Monitor panel (Figure 24.16.7), opened from the Volume Monitors panel, allows you to define what each monitor tracks (i.e., the volume or the sum, integral, or average of a field variable or function in one or more cell zones).


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Using the Solver

Defining Volume Monitors You will begin the volume monitor definition procedure in the Volume Monitors panel (Figure 24.16.6). Solve −→ Monitors −→Volume...

Figure 24.16.6: The Volume Monitors Panel The procedure is as follows: 1. Increase the Volume Monitors value to the number of volume monitors you wish to specify. As this value is increased, additional monitor entries in the panel will become editable. For each monitor, you will perform the following steps. 2. Enter a name for the monitor under the Name heading, and use the Plot, Print, and Write check buttons to indicate the report(s) you want (plot, printout, or file), as described below. 3. Indicate whether you want to update the monitor every Iteration or every Time Step by selecting the appropriate item in the drop-down list below Every. Time Step is a valid choice only if you are calculating unsteady flow. If you specify every Iteration, and the Reporting Interval in the Iterate panel is greater than 1, the monitor will be updated at every reporting interval instead of at each iteration (e.g., for a reporting interval of 2, the monitor will be updated after every other iteration). If you specify every Time Step, the reporting interval will have no effect; the monitor will always be updated after each time step. 4. Click the Define... button to open the Define Volume Monitor panel (Figure 24.16.7). Since this is a modal panel, the solver will not allow you to do anything else until you perform steps 5–10, below.

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Figure 24.16.7: The Define Volume Monitor Panel

5. In the Define Volume Monitor panel, choose the integration method for the volume monitor by selecting Volume, Sum, Volume Integral, Volume-Average, Mass Integral, or Mass-Average in the Report Type drop-down list. These methods are described in Section 28.6. 6. In the Cell Zones list, choose the cell zone(s) on which you wish to integrate. 7. Specify the variable or function to be integrated in the Report Of drop-down list. First select the desired category in the upper drop-down list. You can then select one of the related quantities in the lower list. (See Chapter 29 for an explanation of the variables in the list.) 8. If you are plotting the data or writing them to a file, specify the parameter to be used as the x-axis value (the y-axis value corresponds to the monitored data). In the X Axis drop-down list, select Iteration, Time Step, or Flow Time as the x-axis function against which monitored data will be plotted or written. Time Step and Flow Time are valid choices only if you are calculating unsteady flow. If you choose Time Step, the x axis of the plot will indicate the time step, and if you choose Flow Time, it will indicate the elapsed time. 9. If you are plotting the monitored data, specify the ID of the graphics window in which the plot will be drawn in the Plot Window field. When FLUENT is iterating, the active graphics window is temporarily set to this window to update the plot, and then returned to its previous value. Thus, each volume-monitor plot can be maintained in a separate window that does not interfere with other graphical postprocessing.


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10. If you are writing the monitored data to a file, specify the File Name. 11. Remember to click OK in the Volume Monitors panel after you finish defining all volume monitors.

Printing, Plotting, and Saving Volume Integration Histories There are three methods available for reporting the selected volume integration. To print the volume integration in the text (console) window after each iteration, turn on the Print option in the Volume Monitors panel. To plot the integrated values in the graphics window indicated in Plot Window (in the Define Volume Monitor panel), turn on the Plot option in the Volume Monitors panel. If you want to save the values to a file, turn on the Write option in the Volume Monitors panel and specify the File Name in the Define Volume Monitor panel. You can enable any combination of these options simultaneously.

! If you choose not to save the volume integration data in a file, this information will be lost when you exit the current FLUENT session. Plot Parameters You can modify the attributes of the plot axes and curves used for each volume-monitor plot. Click the Axes... or Curves... button in the Define Volume Monitor panel for the appropriate monitor to open the Axes panel or Curves panel for that volume-monitor plot. See Sections 27.8.8 and 27.8.9 for details.

24.17

Animating the Solution

During the calculation, you can have FLUENT create an animation of contours, vectors, XY plots, monitor plots (residual, statistic, force, surface, or volume), or the mesh (useful primarily for moving mesh simulations). Before you begin the calculation, you will specify and display the variables and types of plots you want to animate, and how often you want plots to be saved. At the specified intervals, FLUENT will display the requested plots, and store each one. When the calculation is complete, you can play back the animation sequence, modify the view (for grid, contour, and vector plots), if desired, and save the animation to a series of hardcopy files or an MPEG file Instructions for defining a solution animation sequence are provided in Section 24.17.1. Sections 24.17.2 and 24.17.3 describe how to play back and save the animation sequences you have created, and Section 24.17.4 describes how to read a previously-saved animation sequence into FLUENT.

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24.17 Animating the Solution

24.17.1

Defining an Animation Sequence

You can use the Solution Animation panel (Figure 24.17.1) to create an animation sequence and indicate how often each frame of the sequence should be created. The Animation Sequence panel (Figure 24.17.2), opened from the Solution Animation panel, allows you to define what each sequence displays (e.g., contours or vectors of a particular variable), where it is displayed, and how each frame is stored. You will begin the animation sequence definition in the Solution Animation panel (Figure 24.17.1). Solve −→ Animate −→Define...

Figure 24.17.1: The Solution Animation Panel The procedure is as follows: 1. Increase the Animation Sequences value to the number of animation sequences you wish to specify. As this value is increased, additional sequence entries in the panel will become editable. For each sequence, you will perform the following steps. 2. Enter a name for the sequence under the Name heading. This name will be used to identify the sequence in the Playback panel, where you can play back the animation sequences that you have defined or read in. This name will also be used as the prefix for the file names if you save the sequence frames to disk. 3. Indicate how often you want to create a new frame in the sequence by setting the interval under Every and selecting Iteration or Time Step in the drop-down list below


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When. (Time Step is a valid choice only if you are calculating unsteady flow.) For example, to create a frame every 10 time steps, you would enter 10 under Every and select Time Step under When. 4. Click the Define... button to open the Animation Sequence panel (Figure 24.17.2).

Figure 24.17.2: The Animation Sequence Panel

5. Define the Sequence Parameters in the Animation Sequence panel. (a) Specify whether you want FLUENT to save the animation sequence frames in memory or on your computer’s hard drive. To save the animation sequence in memory, select In Memory under Storage Type. To save the animation sequence to your computer’s hard drive as a graphics metafile, select Metafile under Storage Type. To save the animation sequence to your computer’s hard drive as a pixmap image, select PPM Image under Storage Type.

!

Note that the FLUENT metafiles created for each frame in the animation sequence contain information about the entire scene, not just the view that is displayed in the plot. As a result, they can be quite large. By default, the files will be stored to disk. If you do not want to use up disk space to store them, you can instead choose to store them in memory. Storing them in memory will, however, reduce the amount of memory available to the solver. Note that the playback of a sequence stored in memory will be faster than one stored to disk.

!

An advantage to saving the animation sequence using the PPM Image option is that you can use the separate pixmap image files for the creation of a single GIF file. GIF file creation can be done quickly with graphics tools provided by other third-party graphics packages such as ImageMagick, i.e., animate or

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convert. For example, if you save the PPM files starting with the string sequence-2, and you are using the ImageMagick software, you can use the convert command with the -adjoin option to create a single GIF file out of the sequence using the following command. convert -adjoin sequence-2_00*.ppm

sequence2.gif

(b) If you selected Metafile or PPM Image under Storage Type, specify the directory where you want to store the files in the Storage Directory field. (This can be a relative or absolute path.) (c) Specify the ID of the graphics window where you want the plot to be displayed in the Window field, and click Set. (The specified window will open, if it is not already open.) When FLUENT is iterating, the active graphics window is set to this window to update the plot. If you want to maintain each animation in a separate window, specify a different Window ID for each. 6. Define the display properties for the sequence. (a) Under Display Type in the Animation Sequence panel, choose the type of display you want to animate by selecting Grid, Contours, Vectors, XY Plot, or Monitor. If you choose Monitor, you can select any of the available types of monitor plots in the Monitor Type drop-down list: Residuals, Force, Statistics, Surface, or Volume. The first time that you select Contours, Vectors, or XY Plot, or one of the monitor types if you select Monitor, FLUENT will open the corresponding panel (e.g., the Contours panel or the Vectors panel) so you can modify the settings and generate the display. To make subsequent modifications to the display settings for any of the display types, click the Properties... button to open the panel for the selected Display Type. (b) Define the display in the panel for the selected Display Type (e.g., the Contours or Solution XY Plot panel), and click Display or Plot.

!

You must click Display or Plot to initialize the scene to be repeated during the calculation. See below for guidelines on defining display properties for grid, contour, and vector displays. 7. Remember to click OK in the Solution Animation panel after you finish defining all animation sequences. Note that, when you click OK in the Animation Sequence panel for a sequence, the Active button for that sequence in the Solution Animation panel will be turned on automatically. You can choose to use a subset of the sequences you have defined by turning off the Active button for those that you currently do not wish to use.


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Guidelines for Defining an Animation Sequence If you are defining an animation sequence containing grid, contour, or vector displays, note the following when you are defining the display: • If you want to include lighting effects in the animation frames, be sure to define the lights before you begin the calculation. See Section 27.2.6 for information about adding lights to the display. • If you want to maintain a constant range of colors in a contour or vector display, you can specify a range explicitly by turning off the Auto Range option in the Contours or Vectors panel. See Section 27.1.2 or 27.1.3 for details. • Scene manipulations that are specified using the Scene Description panel will not be included in the animation sequence frames. View modifications such as mirroring across a symmetry plan will be included.

24.17.2

Playing an Animation Sequence

Once you have defined a sequence (as described in Section 24.17.1) and performed a calculation, or read in a previously created animation sequence (as described in Section 24.17.4), you can play back the sequence using the Playback panel (Figure 24.17.3). Solve −→ Animate −→Playback...

Figure 24.17.3: The Playback Panel

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Under Animation Sequences in the Playback panel, select the sequence you want to play in the Sequences list. To play the animation once through from start to finish, click the “play” button under the Playback heading. (The buttons function in a way similar to those on a standard video cassette player. “Play” is the second button from the right—a single triangle pointing to the right.) To play the animation backwards once, click the “play reverse” button (the second from the left—a single triangle point to the left). As the animation plays, the Frame scale shows the number of the frame that is currently displayed, as well as its relative position in the entire animation. If, instead of playing the complete animation sequence, you want to jump to a particular frame, move the Frame slider bar to the desired frame number, and the frame corresponding to the new frame number will be displayed in the graphics window.

! For smoother animations, turn on the Double Buffering option in the Display Options panel (see Section 27.2.7). This will reduce screen flicker during graphics updates. Additional options for playing back animations are described below.

Modifying the View If you want to replay the animation sequence with a different view of the scene, you can use your mouse to modify (e.g., translate, rotate, zoom) it in the graphics window where the animation is displayed. Note that any changes you make to the view for an animation sequence will be lost when you select a new sequence (or reselect the current sequence) in the Sequences list.

Modifying the Playback Speed Different computers will play the animation sequence at different speeds, depending on the complexity of the scene and the type of hardware used for graphics. You may want to slow down the playback speed for optimal viewing. Move the Replay Speed slider bar to the left to reduce the playback speed (and to the right to increase it).

Playing Back an Excerpt You may sometimes want to play only one portion of a long animation sequence. To do this, you can modify the Start Frame and the End Frame under the Playback heading. For example, if your animation contains 50 frames, but you want to play only frames 20 to 35, you can set Start Frame to 20 and End Frame to 35. When you play the animation, it will start at frame 20 and finish at frame 35.

“Fast-Forwarding” the Animation You can “fast-forward” or “fast-reverse” the animation by skipping some of the frames during playback. To fast-forward the animation, you will need to set the Increment and click the fast-forward button (the last button on the right—two triangles pointing to the


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right). If, for example, your Start Frame is 1, your End Frame is 15, and your Increment is 2, when you click the fast-forward button, the animation will show frames 1, 3, 5, 7, 9, 11, 13 and 15. Clicking on the fast-reverse button (the first button on the left—two triangles pointing to the left) will show frames 15, 13, 11,...1.

Continuous Animation If you want the playback of the animation to repeat continuously, there are two options available. To continuously play the animation from beginning to end (or from end to beginning, if you use one of the reverse play buttons), select Auto Repeat in the Playback Mode drop-down list. To play the animation back and forth continuously, reversing the playback direction each time, select Auto Reverse in the Playback Mode drop-down list. To turn off the continuous playback, select Play Once in the Playback Mode list. This is the default setting.

Stopping the Animation To stop the animation during playback, click the “stop” button (the square in the middle of the playback control buttons). If your animation contains very complicated scenes, there may be a slight delay before the animation stops.

Advancing the Animation Frame by Frame To advance the animation manually frame by frame, use the third button from the right (a vertical bar with a triangle pointing to the right). Each time you click this button, the next frame will be displayed in the graphics window. To reverse the animation frame by frame, use the third button from the left (a left-pointing triangle with a vertical bar). Frame-by-frame playback allows you to freeze the animation at points that are of particular interest.

Deleting an Animation Sequence If you want to remove one of the sequences that you have created or read in, select it in the Sequences list and click the Delete button. If you want to delete all sequences, click the Delete All button.

! Note that if you delete a sequence that has not yet been saved to disk (i.e., if you selected In Memory under Storage Type in the Animation Sequence panel), it will be removed from memory permanently. If you want to keep any animation sequences that are stored only in memory, you should be sure to save them (as described in Section 24.17.3) before you delete them from the Sequences list or exit FLUENT.

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24.17.3

Saving an Animation Sequence

Once you have created an animation sequence, you can save it in any of the following formats: • Solution animation file containing the FLUENT metafiles • Hardcopy files, each containing a frame of the animation sequence • MPEG file containing each frame of the animation sequence Note that, if you are saving hardcopy files or an MPEG file, you can modify the view (e.g., translate, rotate, zoom) in the graphics window where the animation is displayed, and save the modified view instead of the original view.

Solution Animation File If you selected Metafile or PPM Image under Storage Type in the Animation Sequence panel, then FLUENT will save the solution animation file for you automatically. It will be saved in the specified Storage Directory, and its name will be the Name you specified for the sequence, with a .cxa extension (e.g., pressure-contour.cxa). In addition to the .cxa file, FLUENT will also save a metafile with a .hmf extension for each frame (e.g., pressure-contour 0002.hmf). The .cxa file contains a list of the associated .hmf files, and tells FLUENT the order in which to display them. If you selected In Memory under Storage Type, then the solution animation file (.cxa) and the associated metafiles (.hmf) will be lost when you exit from FLUENT, unless you save them as described below. You can save the animation sequence to a file that can be read back into FLUENT (see Section 24.17.4) when you want to replay the animation. As noted in Section 24.17.4, the solution animation file can be used for playback in FLUENT independent of the case and data files that were used to generate it. To save a solution animation file (and the associated metafiles), select Animation Frames in the Write/Record Format drop-down list in the Playback panel, and click the Write button. FLUENT will save a .cxa file, as well as a .hmf file for each frame of the animation sequence. The filename for the .cxa file will be the specified sequence Name (e.g., pressure-contour.cxa), and the filenames for the metafiles will consist of the specified sequence Name followed by a frame number (e.g., pressure-contour 0002.hmf). All of the files (.cxa and .hmf) will be saved in the current working directory.


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Hardcopy File You can also generate a hardcopy file for each frame in the animation sequence. This feature allows you to save your sequence frames to hardcopy files used by an external animation program such as ImageMagick. As noted above, you can modify the view in the graphics window before you save the hardcopy files. To save the animation as a series of hardcopy files, follow these steps: 1. Select Hardcopy Frames in the Write/Record Format drop-down list in the Playback panel. 2. If necessary, click the Hardcopy Options... button to open the Graphics Hardcopy panel and set the appropriate parameters for saving the hardcopy files. (If you are saving hardcopy files for use with ImageMagick, for example, you may want to select the window dump format. See Section 3.12.1 for details.) Click Apply in the Graphics Hardcopy panel to save your modified settings.

!

Do not click the Save... button in the Graphics Hardcopy panel. You will save the hardcopy files from the Playback panel in the next step. 3. In the Playback panel, click the Write button. FLUENT will replay the animation, saving each frame to a separate file. The filenames will consist of the specified sequence Name followed by an animation sequence and a frame number (e.g., pressure-contour 1 0002.ps), and they will all be saved in the current working directory.

MPEG File It is also possible to save all of the frames of the animation sequence in an MPEG file, which can be viewed using an MPEG decoder such as mpeg play. Saving the entire animation to an MPEG file will require less disk space than storing individual window dump files (using the hardcopy method), but the MPEG file will yield lower-quality images. As noted above, you can modify the view in the graphics window before you save the MPEG file. To save the animation to an MPEG file, follow these steps: 1. Select MPEG in the Write/Record Format drop-down list in the Playback panel. 2. Click the Write button. FLUENT will replay the animation and save each frame to a separate scratch file, and then it will combine all the files into a single MPEG file. The name of the MPEG file will be the specified sequence Name with a .mpg extension (e.g., pressure-contour.mpg), and it will be saved in the current working directory.

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24.18 Executing Commands During the Calculation

24.17.4

Reading an Animation Sequence

If you have saved an animation sequence to a solution animation file (as described in Section 24.17.3), you can read that file back in at a later time (or in a different session) and play the animation. Note that you can read a solution animation file into any FLUENT session; you do not need to read in the corresponding case and data files. In fact, you do not need to read in any case and data files at all before you read a solution animation file into FLUENT. To read a solution animation file, click the Read... button in the Playback panel. In the resulting Select File dialog box, specify the name of the file to be read.

24.18

Executing Commands During the Calculation

As described in Sections 24.16 and 24.17, respectively, you can report and monitor various quantities (e.g., residuals, force coefficients) and create animations of the solution while the solver is performing calculations. FLUENT also includes a feature that allows you to define your own command(s) to be executed during the calculation at specified intervals. For example, you can ask FLUENT to export data to a third-party package such as FIELDVIEW after every time step. You will specify a series of text commands or use the GUI to define the steps to be performed.

! If you want to save case or data files at intervals during the calculation, you must use the Autosave Case/Data panel (opened with the File/Write/Autosave... menu item). See Section 3.3.4 for details.

24.18.1

Specifying the Commands to be Executed

You will indicate the command(s) that you want the solver to execute at specified intervals during the calculation using the Execute Commands panel (Figure 24.18.1). Solve −→Execute Commands... The procedure is as follows: 1. Increase the Defined Commands value to the number of commands you wish to specify. As this value is increased, additional command entries will become editable. For each command, you will perform the following steps. 2. Turn on the On check button next to the command if you want it to be executed during the calculation. You may define multiple commands and choose to use only a subset of them by turning off the check button for those that you do not wish to use. 3. Enter a name for the command under the Name heading.


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Using the Solver

Figure 24.18.1: The Execute Commands Panel

4. Indicate how often you want the command to be executed by setting the interval under Every and selecting Iteration or Time Step in the drop-down list below When. (Time Step is a valid choice only if you are calculating unsteady flow.) For example, to execute the command every 10 iterations, you would enter 10 under Every and select Iteration under When.

!

If you specify an interval in iterations, be sure to keep the Reporting Interval in the Iterate panel at its default value of 1. 5. Define the command by entering a series of text commands in the Command field, or by entering the name of a command macro you have defined (or will define) as described in Section 24.18.2.

!

If the command to be executed involves saving a file, see Section 24.18.3 for important information.

24.18.2

Defining Macros

Macros that you define for automatic execution during the calculation can also be used interactively by you during the problem setup or postprocessing. For example, if you define a macro that performs a certain type of adaption after each iteration, you can also use the macro to perform this adaption interactively.

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24.18 Executing Commands During the Calculation

Definition of a macro is accomplished as follows: 1. In the Execute Commands panel, click the Define Macro... button to open the Define Macro panel (Figure 24.18.2). Since this is a “modal” panel, the solver will not allow you to do anything else until you perform step 2, below.

Figure 24.18.2: The Define Macro Panel

2. In the Define Macro panel, specify a Name for the macro (e.g., adapt1) and click OK. (The Define Macro... button in the Execute Commands panel will become the End Macro button.) 3. Perform the steps that you want the macro to perform. For example, if you want the macro to perform gradient adaption, open the Gradient Adaption panel, specify the appropriate adaption function and parameters, and click Adapt to perform the adaption.

!

If the command to be executed involves saving a file, see Section 24.18.3 for important information. 4. When you have completed the steps you wish the macro to perform, click the End Macro button in the Execute Commands panel. As noted above, once you have defined a macro for execution during the calculation, you can use it at any time. If you defined the macro called adapt1 to adapt based on pressure gradient, you can simply type adapt1 in the console (text) window to perform this adaption. This macro is independent of any text menus, so you need not move to a different text menu to use it. Macros can be saved to and read from files. To save all


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macros that are currently defined, use the file/write-macros text command. To read all the macros in a macro file, use the file/read-macros text command.

! A macro, like a journal file, is a simple record/playback function. It will therefore know nothing about the state in which it was recorded or the state in which it is being played back. You must be careful that all surfaces, variables, etc. that are used by the macro have been properly defined when you (or FLUENT) invoke the macro.

24.18.3

Saving Files During the Calculation

If the command to be executed during the calculation involves saving a file, you must include a special character in the file name when you enter it in the Select File dialog box so that the solver will know to assign a new name to each file it saves. You can number the files by iteration number or by time step. (These special characters for numbering files are also useful when you are saving window dumps for use in animations, as described in Section 3.12.1.) See Section 3.1.7 for details about these special characters for filenames.

! If you want to save case or data files at intervals during the calculation, you must use the Autosave Case/Data panel (opened with the File/Write/Autosave... menu item). See Section 3.3.4 for details.

24.19

Convergence and Stability

Convergence can be hindered by a number of factors. Large numbers of computational cells, overly conservative under-relaxation factors, and complex flow physics are often the main causes. Sometimes it is difficult to know whether you have a converged solution. In the following sections, some of the numerical controls and modeling techniques that can be exercised to enhance convergence and maintain stability are examined. • Section 24.19.1: Judging Convergence • Section 24.19.2: Step-by-Step Solution Processes • Section 24.19.3: Modifying Algebraic Multigrid Parameters • Section 24.19.4: Modifying FAS Multigrid Parameters • Section 24.19.5: Modifying Multi-Stage Time-Stepping Parameters You should also refer to Sections 24.7 and 24.8 for information about how the choice of discretization scheme or (for the segregated solver) pressure-velocity coupling scheme can affect convergence. Manipulation of under-relaxation parameters and multigrid settings to enhance convergence is discussed in Sections 24.9 and 24.19.3.

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24.19 Convergence and Stability

24.19.1

Judging Convergence

There are no universal metrics for judging convergence. Residual definitions that are useful for one class of problem are sometimes misleading for other classes of problems. Therefore it is a good idea to judge convergence not only by examining residual levels, but also by monitoring relevant integrated quantities such as drag or heat transfer coefficient. For most problems, the default convergence criterion in FLUENT is sufficient. This criterion requires that the scaled residuals defined by Equation 24.16-4 or 24.16-9 decrease to 10−3 for all equations except the energy and P-1 equations, for which the criterion is 10−6 . Sometimes, however, this criterion may not be appropriate. Typical situations are listed below. • If you make a good initial guess of the flow field, the initial continuity residual may be very small leading to a large scaled residual for the continuity equation. In such a situation it is useful to examine the unscaled residual and compare it with an appropriate scale, such as the mass flow rate at the inlet. • For some equations, such as for turbulence quantities, a poor initial guess may result in high scale factors. In such cases, scaled residuals will start low, increase as non-linear sources build up, and eventually decrease. It is therefore good practice to judge convergence not just from the value of the residual itself, but from its behavior. You should ensure that the residual continues to decrease (or remain low) for several iterations (say 50 or more) before concluding that the solution has converged. Another popular approach to judging convergence is to require that the unscaled residuals drop by three orders of magnitude. FLUENT provides residual normalization for this purpose, as discussed in Sections 24.16.1 and 24.16.1. In this approach the convergence criterion is that the normalized unscaled residuals should drop to 10−3 . However, this requirement may not be appropriate in many cases: • If you have provided a very good initial guess, the residuals may not drop three orders of magnitude. In a nearly-isothermal flow, for example, energy residuals may not drop three orders if the initial guess of temperature is very close to the final solution. • If the governing equation contains non-linear source terms which are zero at the beginning of the calculation and build up slowly during computation, the residuals may not drop three orders of magnitude. In the case of natural convection in an enclosure, for example, initial momentum residuals may be very close to zero because the initial uniform temperature guess does not generate buoyancy. In such a case, the initial nearly-zero residual is not a good scale for the residual.


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• If the variable of interest is nearly zero everywhere, the residuals may not drop three orders of magnitude. In fully-developed flow in a pipe, for example, the cross-sectional velocities are zero. If these velocities have been initialized to zero, initial (and final) residuals are both close to zero, and a three-order drop cannot be expected. In such cases, it is wise to monitor integrated quantities, such as drag or overall heat transfer coefficient, before concluding that the solution has converged. It may also be useful to examine the un-normalized unscaled residual, and determine if the residual is small compared to some appropriate scale. Alternatively, the scaled residual defined by Equation 24.16-4 or 24.16-9 (the default) may be considered. Conversely, it is possible that if the initial guess is very bad, the initial residuals are so large that a three-order drop in residual does not guarantee convergence. This is specially true for k and equations where good initial guesses are difficult. Here again it is useful to examine overall integrated quantities that you are particularly interested in. If the solution is unconverged, you may drop the convergence tolerance, as described in Section 24.16.1.

24.19.2

Step-by-Step Solution Processes

One important technique for speeding convergence for complex problems is to tackle the problem one step at a time. When modeling a problem with heat transfer, you can begin with the calculation of the isothermal flow. To solve turbulent flow, you might start with the calculation of laminar flow. When modeling a reacting flow, you can begin by computing a partially converged solution to the non-reacting flow, possibly including the species mixing. When modeling a discrete phase, such as fuel evaporating from droplets, it is a good idea to solve the gas-phase flow field first. Such solutions generally serve as a good starting point for the calculation of the more complex problems. These step-by-step techniques involve using the Solution Controls panel to turn equations on and off.

Selecting a Subset of the Solution Equations FLUENT automatically solves each equation that is turned on using the Models family of panels. If you specify in the Viscous Model panel that the flow is turbulent, equations for conservation of turbulence quantities are turned on. If you specify in the Energy panel that FLUENT should enable energy, the energy equation is activated. Convergence can be sped up by focusing the computational effort on the equations of primary importance. The Equations list in the Solution Controls panel allows you to turn individual equations on or off temporarily. Solve −→ Controls −→Solution... A typical example is the computation of a flow with heat transfer. Initially, you will define the full problem scope, including the thermal boundary conditions and temperature-

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dependent flow properties. Following the problem setup, you will use the Solution Controls panel to temporarily turn off the energy equation. You can then compute an isothermal flow field, remembering to set a reasonable initial value for the temperature of the fluid.

! This is possible only for the segregated solver; the coupled solvers solve the energy equation together with the flow equations in a coupled manner, so you cannot turn off the energy equation as described above. When the isothermal flow is reasonably well converged, you can turn the energy equation back on. You can actually turn off the momentum and continuity equations while the initial energy field is being computed. When the energy field begins to converge well, you can turn the momentum and continuity equations back on so that the flow pattern can adjust to the new temperature field. The temperature will couple back into the flow solution by its impact on fluid properties such as density and viscosity. The temperature field will have no effect on the flow field if the fluid properties (e.g., density, viscosity) do not vary with temperature. In such cases, you can compute the energy field without turning the flow equations back on again.

! If you have specified temperature-dependent flow properties, you should be sure that a realistic value has been set for temperature throughout the domain before disabling calculation of the energy equation. If an unrealistic temperature value is used, the flow properties dependent on temperature will also be unrealistic, and the flow field will be adversely affected. Instructions for initializing the temperature field or patching a temperature field onto an existing solution are provided in Section 24.13.

Turning Reactions On and Off To solve a species mixing problem prior to solving a reacting flow, you should set up the problem including all of the reaction information, and save the complete case file. To turn off the reaction so that only the species mixing problem can be solved, you can use the Species Model panel to turn off the Volumetric Reactions. Define −→ Models −→Species... Once the species mixing problem has partially converged, you can return to the Species Model panel and turn the Volumetric Reactions option on again. You can then resume the calculation starting from the partially converged data. For combustion problems you may want to patch a hot temperature in the vicinity of the anticipated reactions before you restart the calculation. See Section 24.13.2 for information about patching an initial value for a flow variable.

24.19.3

Modifying Algebraic Multigrid Parameters

The default algebraic multigrid settings are appropriate for nearly all problems, but in rare cases you may need to make minor adjustments. This section describes how to


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analyze the multigrid solver’s performance to determine which parameters should be modified. It also provides examples of suggested settings for particular types of problems and explains how to set the multigrid parameters.

Analyzing the Algebraic Multigrid Solver As mentioned earlier, in most cases the multigrid solver will not require any special attention from you. If, however, you have convergence difficulties or you want to minimize the overall solution time by using more aggressive settings, you can monitor the multigrid solver and modify the parameters to improve its performance. (The instructions below assume that you have already begun calculations, since there is no need to monitor the solver if you do not fit into one of the two categories above.) To determine whether your convergence difficulties can be alleviated by modifying the multigrid settings, you will check if the requested residual reduction is obtained on each grid level. To minimize solution time, you will check to see if switching to a more powerful cycle will result in overall reduction of work by the solver.

Monitoring the Algebraic Multigrid Solver The steps for monitoring the solver are as follows: 1. Set multigrid Verbosity to 1 or 2 in the Multigrid Controls panel. Solve −→ Controls −→Multigrid... 2. Request a single iteration using the Iterate panel. Solve −→Iterate... If you set the verbosity to 2, the information printed in the console (text) window for each equation will include the following: • equation name • equation tolerance (computed by the solver using a normalization of the source vector) • residual value after each fixed multigrid cycle or fine relaxation for the flex cycle • number of equations in each multigrid level, with the zeroth level being the original (finest-level) system of equations Note that the residual printed at cycle or relaxation 0 is the initial residual before any multigrid cycles are performed.

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When verbosity is set to 1, only the equation name, tolerance, and residuals are printed. A portion of a sample printout is shown below: pressure correction equation: tol. 1.2668e-05 0 2.5336e+00 1 4.9778e-01 2 2.5863e-01 3 1.9387e-01 multigrid levels: 0 918 1 426 2 205 3 97 4 45 5 21 6 10 7 4

Interpreting the Algebraic Multigrid Report By default, the flex cycle is used for all equations except pressure correction, which uses a V cycle. Typically, for a flex cycle only a few (5–10) relaxations will be performed at the finest level and no coarse levels will be visited. In some cases one or two coarse levels may be visited. If the maximum number of fine level relaxations is not sufficient, you may want to increase the maximum number (as described in Section 24.19.3) or switch to a V cycle (as described in Section 24.19.3). For pressure correction, a V cycle is used by default. If the maximum number of cycles (30 by default) is not sufficient, you can switch to a W cycle (using the Multigrid Controls panel, as described in Section 24.19.3). Note that for the parallel solver, efficiency may deteriorate with a W cycle. If you are using the parallel solver, you can try increasing the maximum number of cycles by increasing the value of Max Cycles in the Multigrid Controls panel under Fixed Cycle Parameters. Solve −→ Controls −→Multigrid...

Changing the Maximum Number of Relaxations To change the maximum number of relaxations, increase or decrease the value of Max Fine Relaxations or Max Coarse Relaxations in the Multigrid Controls panel (Figure 24.19.1) under Flexible Cycle Parameters. Solve −→ Controls −→Multigrid...


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Using the Solver

Figure 24.19.1: The Multigrid Controls Panel

Specifying the Multigrid Cycle Type By default, the V cycle is used for the pressure equation and the flex cycle is used for all other equations. (See Section 24.5.2 for a description of these cycles.) To change the cycle type for an equation, you will use the top portion of the Multigrid Controls panel (Figure 24.19.1). For each equation, you can choose Flexible, V-Cycle, W-Cycle, or F-Cycle in the adjacent drop-down list.

Setting the Termination and Residual Reduction Parameters When you use the flex cycle for an equation, you can control the multigrid performance by modifying the Termination and/or Restriction criteria for that equation at the top of the Multigrid Controls panel (Figure 24.19.1). Solve −→ Controls −→Multigrid...

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The Restriction criterion is the residual reduction tolerance, β in Equation 24.5-14. This parameter dictates when a coarser grid level must be visited (due to insufficient improvement in the solution on the current level). With a larger value of β, coarse levels will be visited less often (and vice versa). The Termination criterion, α in Equation 24.5-15, governs when the solver should return to a finer grid level (i.e., when the residuals have improved sufficiently on the current level). For the V, W, or F cycle, the Termination criterion determines whether or not another cycle should be performed on the finest (original) level. If the current residual on the finest level does not satisfy Equation 24.5-15, and the maximum number of cycles has not been performed, FLUENT will perform another multigrid cycle. (The Restriction parameter is not used by the V, W, and F cycles.)

Additional Algebraic Multigrid Parameters There are several additional parameters that control the algebraic multigrid solver, but there will usually be no need to modify them. These additional parameters are all contained in the Multigrid Controls panel (Figure 24.19.1). Solve −→ Controls −→Multigrid... Coarsening Parameters For all multigrid cycle types, you can control the maximum number of coarse levels (Max Coarse Levels under Coarsening Parameters) that will be built by the multigrid solver. Sets of coarser simultaneous equations are built until the maximum number of levels has been created, or the coarsest level has only 3 equations. Each level has about half as many unknowns as the previous level, so coarsening until there are only a few cells left will require about as much total coarse-level coefficient storage as was required on the fine mesh. Reducing the maximum coarse levels will reduce the memory requirements, but may require more iterations to achieve a converged solution. Setting Max Coarse Levels to 0 turns off the algebraic multigrid solver. Another coarsening parameter you can control is the increase in coarseness on successive levels. The Coarsen By parameter specifies the number of fine grid cells that will be grouped together to create a coarse grid cell. The algorithm groups each cell with its closest neighbor, then groups the cell and its closest neighbor with the neighbor’s closest neighbor, continuing until the desired coarsening is achieved. Typical values are in the range from 2 to 10, with the default value of 2 giving the best performance, but also the greatest memory use. You should not adjust this parameter unless you need to reduce the memory required to run a problem. Fixed Cycle Parameters For the fixed (V, W, and F) multigrid cycles, you can control the number of pre- and post-relaxations (β1 and β3 in Section 24.5.2). Pre Sweeps sets the number of relaxations


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Using the Solver

to perform before moving to a coarser level. Post Sweeps sets the number to be performed after coarser level corrections have been applied. Normally one post-relaxation is performed and no pre-relaxations are done (i.e., β3 = 1 and β1 = 0), but in rare cases, you may need to increase the value of β1 to 1 or 2.

! If you are using AMG with V-cycle to solve an energy equation with a solid conduction model presented with anisotropic or very high conductivity coefficient, there is a possibility of divergence with a default post-relaxation sweep of 1. In such cases you should increase the post-relaxation sweep (to say 2) in the AMG section for better convergence.

Returning to the Default Multigrid Parameters If you change the multigrid parameters, but you then want to return to FLUENT’s default settings, you can click the Default button in the Multigrid Controls panel. FLUENT will change all settings to the defaults, and the Default button will become the Reset button. To get your settings back again, you can click the Reset button.

24.19.4

Setting FAS Multigrid Parameters

For most calculations, you will not need to modify any FAS multigrid parameters once you have set the number of coarse grid levels. If, however, you encounter convergence difficulties, you may consider the following suggested procedures.

! Recall that FAS multigrid is used only by the coupled explicit solver. Combating Convergence Trouble Some problems may approach convergence steadily at first, but then the residuals will level off and the solution will “get stuck.” In some cases (e.g., long thin ducts), this convergence trouble may be due to multigrid’s slow propagation of pressure information through the domain. In such cases, you should turn off multigrid by setting Multigrid Levels to 0 in the Solution Controls panel (under Solver Parameters). Solve −→ Controls −→Solution...

“Industrial-Strength” FAS Multigrid In some cases, you may find that your problem is converging, but at an extremely slow rate. Such problems can often benefit from a more aggressive form of multigrid, which will speed up the propagation of the solution corrections. For such problems, you can try the “industrial-strength” multigrid settings.

! These settings are very aggressive and assume that the solution information passed through the multigrid levels is somewhat accurate. For this reason, you should only attempt the procedure described here after you have performed enough iterations that

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the solution is off to a good start. Using “industrial-strength” multigrid too early in the calculation process—when the solution is far from correct—will not help convergence and may cause the calculation to become unstable, as very incorrect values are propagated quickly to the original grid. Note also that while these multigrid settings will usually reduce the total number of iterations required to reach convergence, they will greatly increase the computation time for each multigrid cycle. Thus the solver will be performing fewer but longer iterations. The strategy employed is as follows: • Increase the number of iterations performed on each grid level before proceeding to a coarser level • Increase the number of iterations performed on each grid level after returning from a coarser level • Allow full correction transfer from one level to the next finer level, instead of transferring reduced values of the corrections • Do not smooth the interpolated corrections when they are transferred from a coarser grid to a finer grid You can set all of the parameters for this strategy under FAS Multigrid Controls in the Multigrid Controls panel (Figure 24.19.2) and then continue the calculation. Solve −→ Controls −→Multigrid... Increasing the number of iterations performed on each grid level before proceeding to a coarser level (the value of β1 described in Section 24.5.2) will improve the solution passed from each finer grid level to the next coarser grid level. Try increasing the value of Pre Sweeps (under FAS Multigrid Controls, not under Algebraic Multigrid Controls) to 10. Increasing the number of iterations performed on each level after returning from a coarser level will improve the corrections passed from each coarser grid level to the next finer grid level. Errors introduced on the coarser grid levels can therefore be reduced before they are passed further up the grid hierarchy to the original grid. Try increasing the value of Post Sweeps (under FAS Multigrid Controls, not under Algebraic Multigrid Controls) to 10. By default, the full values of the multigrid corrections are not transferred from a coarser grid to a finer grid; only 60% of the value is transferred. This prevents large errors from transferring quickly up to the original grid and causing the calculation to become unstable. It also prevents a “good” solution from propagating quickly to the original grid, however. By increasing the Correction Reduction to 1, you can transfer the full values from coarser to finer grid levels, speeding the propagation of the solution and, usually, the convergence as well.


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Figure 24.19.2: The Multigrid Controls Panel

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When the corrections on a coarse grid are passed back to the next finer grid level, the values are, by default, interpolated and then smoothed. Disabling the smoothing so that the actual value in a coarse grid cell is assigned to the fine grid cells that comprise it can also aid convergence. To turn off smoothing, set Correction Smoothing to 0. Large discontinuities between cells will be smoothed out implicitly as a result of the additional Post Sweeps performed.

Additional Multigrid Parameters There are several additional parameters that control the multigrid solver, but there will usually be no need to modify them. These additional parameters are all contained in the Multigrid Controls panel. Solve −→ Controls −→Multigrid... Specifying the Multigrid Cycle Type By default, the V cycle is used for the flow equations. (See Section 24.5.2 for a description of the available cycles.) To change to a W cycle, you can select it in the drop-down list next to Flow at the top of the Multigrid Controls panel (Figure 24.19.2). Reducing the Time Step for Coarse Grid Levels The Courant Number Reduction (at the bottom of the Multigrid Controls panel) sets the factor by which to reduce the Courant number for coarse grid levels (i.e., every level except the finest). Some reduction of time step (such as the default 0.9) is typically required because the stability limit cannot be determined as precisely on the irregularly shaped coarser grid cells.

24.19.5

Modifying Multi-Stage Time-Stepping Parameters

The most common parameter you will change to control the multi-stage time-stepping scheme is the Courant number. Instructions for modifying the Courant number are presented in Section 24.10, and procedures for modifying other less commonly changed parameters are provided in this section.

Using Residual Smoothing to Increase the Courant Number Implicit residual smoothing (or averaging) is a technique that can be used to reduce the time step restriction of the solver, thereby allowing the Courant number to be increased. The implicit smoothing is implemented with an iterative Jacobi method, as described in Section 24.4.3. You can control residual smoothing in the Solution Controls panel. Solve −→ Controls −→Solution...


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By default, the number of Iterations for Residual Smoothing is set to zero, indicating that residual smoothing is disabled. If you increase the Iterations counter to 1 or more, you can enter the Smoothing Factor. A smoothing factor of 0.5 with 2 passes of the Jacobi smoother is usually adequate to allow the Courant number to be doubled.

Changing the Multi-Stage Scheme It is possible to make several changes to the multi-stage time-stepping scheme itself. You can change the number of stages and set a new multi-stage coefficient for each stage. You can also control whether or not dissipation and viscous stresses are updated at each stage. These changes are made in the Multi-Stage Parameters panel (Figure 24.19.3). Solve −→ Controls −→Multi-Stage...

! You should not attempt to make changes to FLUENT’s multi-stage scheme unless you are very familiar with multi-stage schemes and are interested in trying a different scheme found in the literature.

Figure 24.19.3: The Multi-Stage Parameters Panel

Changing the Coefficients and Number of Stages By default, the FLUENT multi-stage scheme uses 5 stages with coefficients of 0.25, 0.166666, 0.375, 0.5, and 1.0 for the first through fifth stages, respectively. You can decrease the number of stages using the arrow buttons for Number of Stages in the MultiStage Parameters panel. (If you want to increase the number of stages, you will need to use the text-interface command solve/set/multi-stage.) For each stage, you can

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modify the Coefficient. Coefficients must be greater than 0 and less than 1. The final stage should always have a coefficient of 1. Controlling Updates to Dissipation and Viscous Stresses For each stage, you can indicate whether or not artificial dissipation and viscous stresses are evaluated. If a Dissipation box is selected for a particular stage, artificial dissipation will be updated on that stage. If not selected, artificial dissipation will remain “frozen” at the value of the previous stage. If a Viscous box is selected for a particular stage, viscous stresses will be updated on that stage. If not selected, viscous stresses will remain “frozen” at the value of the previous stage. Viscous stresses should always be computed on the first stage, and successive evaluations will increase the “robustness” of the solution process, but will also increase the expense (i.e., increase the CPU time per iteration). For steady problems, the final solution is independent of the stages on which viscous stresses are updated. Resetting the Multi-Stage Parameters If you change the multi-stage parameters, but you then want to return to the default scheme set by FLUENT, you can click the Default button in the Multi-Stage Parameters panel. FLUENT will change the values to the defaults and the Default button will become the Reset button. To get your values back again, you can click the Reset button.


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Chapter 25.

Grid Adaption

The solution-adaptive mesh refinement feature of FLUENT allows you to refine and/or coarsen your grid based on geometric and numerical solution data. In addition, FLUENT provides tools for creating and viewing adaption fields customized to particular applications. The adaption process is described in detail in the following sections. • Section 25.1: Using Adaption • Section 25.2: The Static Adaption Process • Section 25.3: Boundary Adaption • Section 25.4: Gradient Adaption • Section 25.5: Dynamic Gradient Adaption • Section 25.6: Isovalue Adaption • Section 25.7: Region Adaption • Section 25.8: Volume Adaption • Section 25.9: y + and y ∗ Adaption • Section 25.10: Managing Adaption Registers • Section 25.11: Adaption Controls • Section 25.12: Improving the Grid by Smoothing and Swapping


25-1

Grid Adaption

25.1

Using Adaption

Two significant advantages of the unstructured mesh capability in FLUENT are: • The reduced setup time compared to structured grids • The ability to incorporate solution-adaptive refinement of the mesh By using solution-adaptive refinement, you can add cells where they are needed in the mesh, thus enabling the features of the flow field to be better resolved. When adaption is used properly, the resulting mesh is optimal for the flow solution because the solution is used to determine where more cells are added. In other words, computational resources are not wasted by the inclusion of unnecessary cells, as typically occurs in the structured grid approach. Furthermore, the effect of mesh refinement on the solution can be studied without completely regenerating the mesh.

! Any time you perform mesh adaption in a parallel computation, a load balancing step will be performed by FLUENT by default. You can turn off the automatic load balancing by issuing the following command: (disable-load-balance-after-adaption) To return to the default behavior, use the following command: (enable-load-balance-after-adaption) Note however that the automatic load balancing will not occur in conjunction with dynamic adaption. See Section 25.5 for more information on dynamic adaption, and Section 30.5.2 for more information on load balancing in parallel FLUENT.

25.1.1

Adaption Example

One example of how adaption can be used effectively is in the solution of the compressible, turbulent flow through a 2D turbine cascade. The initial mesh, shown in Figure 25.1.1, is quite fine around the blade. The surface node distribution thus provides adequate definition of the blade geometry, and enables the turbulent boundary layer to be properly resolved without further adaption. On the other hand, the mesh on the inlet, outlet, and periodic boundaries is comparatively coarse. To ensure that the flow in the blade passage is appropriately resolved, solution-adaptive refinement was used to create the mesh shown in Figure 25.1.2. Although the procedure for solution adaption will vary according to the flow being solved, the adaption process used for the turbine cascade is described here as an example. Note that while this example involves compressible flow, the general procedure is applicable for incompressible flows as well.

25-2


25.1 Using Adaption

Grid

Figure 25.1.1: Turbine Cascade Mesh Before Adaption

Grid

Figure 25.1.2: Turbine Cascade Mesh After Adaption


25-3

Grid Adaption

1. Display contours of pressure adaption function to determine a suitable refinement threshold. (See Section 25.4.) 2. “Mark” the cells within the refinement threshold, creating a refinement register. (See Sections 25.2.1 and 25.4.) 3. Repeat the process described in steps 1 and 2, using gradients of Mach number as a refinement criterion. 4. To refine in the wake region, use isovalues of total pressure as a criterion. (See Section 25.6.) This causes cells within the boundary layer and the wake to be marked, since these are both regions of high total-pressure loss. 5. Use the Manage Adaption Registers panel to combine the three refinement registers into a single register. (See Section 25.10.) 6. Limit the minimum cell volume for adaption to prevent the addition of cells within the boundary layer, where the mesh was judged to be fine enough already. (See Section 25.11.) 7. Refine the cells contained in the resulting adaption register. (See Section 25.10.) 8. Perform successive smoothing and swapping iterations using the Smooth/Swap Grid panel. (See Section 25.12.) This step is recommended if you are using conformal adaption. As shown in Figure 25.1.2, the effect of refining on gradients is evident in the finer mesh ahead of the leading edge of the blade and within the blade passage. The finer mesh in the wake region is due to the adaption using isovalues of total pressure.

25.1.2

Adaption Guidelines

The advantages of solution-adaptive refinement, when used properly as in the turbine cascade example in Section 25.1.1, are significant. However, the capability must be used carefully to avoid certain pitfalls. Some guidelines for proper usage of solution-adaptive refinement are as follows: • The surface mesh must be fine enough to adequately represent the important features of the geometry. For example, it would be bad practice to place too few nodes on the surface of a highly-curved airfoil, and then use solution refinement to add nodes on the surface. Clearly, the surface will always contain the facets contained in the initial mesh, regardless of the additional nodes introduced by refinement.

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25.1 Using Adaption

• The initial mesh should contain sufficient cells to capture the essential features of the flow field. Suppose, for example, that your intention is to predict the shock forming around a bluff body in supersonic flow. In addition to having sufficient surface resolution to represent the shape of the body, the initial mesh should also contain enough cells so that a reasonable first solution can be obtained. Subsequent gradient adaption can be used to sharpen the shock and establish a gridindependent solution. • A reasonably well-converged solution should be obtained before you perform an adaption. If you adapt to an incorrect solution, cells will be added in the wrong region of the flow. However, you must use careful judgment in deciding how well to converge the solution before adapting, because there is a trade-off between adapting too early to an unconverged solution and wasting time by continuing to iterate when the solution is not changing significantly. Note that this does not directly apply to dynamic adaption, because here the solution is adapted either at every iteration or at every time-step, depending on which solver is being used. • In general, you should write a case and data file before starting the adaption process. Then, if you generate an undesirable mesh, you can restart the process with the saved files. Note that this does not directly apply to dynamic adaption, because here the solution is adapted either at every iteration or at every time-step, depending on which solver is being used. • When performing gradient adaption, you must select suitable variables. For some flows, the choice is clear. For instance, adapting on gradients of pressure is a good criterion for refining in the region of shock waves. In most incompressible flows, however, it makes little sense to refine on pressure gradients. A more suitable parameter in an incompressible flow might be mean velocity gradients. If the flow feature of interest is a turbulent shear flow, it will be important to resolve the gradients of turbulent kinetic energy and turbulent energy dissipation, so these might be appropriate refinement variables. In reacting flows, temperature or concentration (or mole or mass fraction) of reacting species might be appropriate. • Poor adaption practice can have adverse effects. One of the most common mistakes is to over-refine a particular region of the solution domain, causing very large gradients in cell volume. This can adversely affect the accuracy of the solution.


25-5

Grid Adaption

25.2

The Static Adaption Process

The adaption process has been separated into two distinct tasks. First, the individual cells are marked for refinement or coarsening based on the adaption function, which is created from geometric and/or solution data. Next, the cell is refined or considered for coarsening based on these adaption marks. The primary advantages of this modularized approach are the abilities to create sophisticated adaption functions and to experiment with various adaption functions without modifying the existing mesh.

! It is highly recommended that you write a case and data file before starting the adaption process. Then, if you generate an undesirable grid, you can restart the process with the saved files. Two different types of adaption are available in FLUENT: “conformal” and “hanging node” adaption. Hanging node adaption, the default method, is described in Section 25.2.2. Conformal adaption, which is available only for triangular and tetrahedral grids, is described in Section 25.2.3.

25.2.1

Adaption and Mask Registers

Invoking the Mark command creates an adaption register. It is called a register because it is used in a manner similar to the way memory registers are used in calculators. For example, one adaption register holds the result of an operation, another register holds the results of a second operation, and these registers can be used to produce a third register. An adaption register is basically a list of identifiers for each cell in the domain. The identifiers designate whether a cell is neutral (not marked), marked for refinement, or marked for coarsening. The adaption function is used to set the appropriate identifier. For example, to refine the cells based on pressure gradient, the solver computes the gradient adaption function for each cell. The cell value is compared to the refining and coarsening threshold values and assigned the appropriate identifier, specifically for this example: • cell value < coarsen threshold: mark for coarsening • coarsen threshold < cell value < refine threshold: don’t mark, neutral • cell value > refine threshold: mark for refinement The GUI and text interface commands generate adaption registers that designate the cells marked for refinement or coarsening. These registers can be converted to mask registers. Masks, unlike the adaption registers, maintain only two states: ACTIVE and INACTIVE. If the adaption register is converted to a mask, cells marked for refinement become ACTIVE cells, while those that are unmarked or marked for coarsening become INACTIVE. You can use a mask register to limit adaption to cells within a certain region. This process is illustrated below.

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25.2 The Static Adaption Process

Figure 25.2.1 shows a cloud of cells representing an adaption register (shaded cells are marked cells). Figure 25.2.2 illustrates the active cells associated with a mask register. If the mask is applied to (combined with) the adaption register, the new adaption register formed from the combination has the marked cells shown in Figure 25.2.3. (Note that this example does not differentiate between refinement or coarsening marks because the mask is applied to both types of marks.) For more information on combining registers, see Section 25.10.

Figure 25.2.1: Adaption Register with Shaded Cells Representing Marked Cells

Figure 25.2.2: Mask Register with Shaded Cells Representing Active Cells

Figure 25.2.3: New Adaption Register Created from Application of Mask

In summary, adaption registers can be created using geometric data, physical features of the flow field, and combinations of this information. Once created, adaption registers can be listed, displayed, deleted, combined, exchanged, inverted, and changed to mask registers.


25-7

Grid Adaption

25.2.2

Hanging Node Adaption

Grids produced by the hanging node adaption procedure are characterized by nodes on edges and faces that are not vertices of all the cells sharing those edges or faces, as shown in Figure 25.2.4. Hanging node grid adaption provides the ability to operate on grids with a variety of cell shapes, including hybrid grids. However, although the hanging node scheme provides significant grid flexibility, it does require additional memory to maintain the grid hierarchy which is used by the rendering and grid adaption operations.

Hanging Node

Figure 25.2.4: Example of a Hanging Node

Hanging Node Refinement The cells are refined by isotropically subdividing each cell marked for refinement. Figures 25.2.5 and 25.2.6 illustrate the division of the supported cell shapes described below: • A triangle is split into 4 triangles. • A quadrilateral is split into 4 quadrilaterals. • A tetrahedron is split into eight tetrahedra. The subdivision consists of trimming each corner of the tetrahedron, and then subdividing the enclosed octahedron by introducing the shortest diagonal. • A hexahedron is split into 8 hexahedra. • A wedge (prism) is split into 8 wedges. • A pyramid is split into 6 pyramids and 4 tetrahedra. To maintain accuracy, neighboring cells are not allowed to differ by more than one level of refinement. This prevents the adaption from producing excessive cell volume variations (reducing truncation error) and ensures that the positions of the “parent” (original) and “child” (refined) cell centroids are similar (reducing errors in the flux evaluations).

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Triangle

Quadrilateral

Figure 25.2.5: Hanging Node Adaption of 2D Cell Types

Tetrahedron

Hexahedron

Prism/Wedge

Pyramid

Figure 25.2.6: Hanging Node Adaption of 3D Cell Types


25-9

Grid Adaption

Hanging Node Coarsening The mesh is coarsened by reintroducing inactive parent cells, i.e., coalescing the child cells to reclaim the previously subdivided parent cell. An inactive parent cell is reactivated if all its children are marked for coarsening. You will eventually reclaim the original grid with repeated application of the hanging node coarsening. You cannot coarsen the grid any further than the original grid using the hanging node adaption process. Conformal coarsening, however, allows you to remove original grid points to reduce the density of the grid.

25.2.3

Conformal Adaption

The conformal adaption process does not create hanging nodes. Instead, all the cells sharing an edge or face include all the nodes on those entities. The conformal refinement process adds nodes on edges and the conformal coarsening removes nodes and retriangulates the resulting cavity.

! Note that this process should not be used in conjunction with dynamic adaption (described in Section 25.5).

Conformal Refinement To refine the cell, boundary or internal faces (including periodic boundary faces) may be split. Figure 25.2.7 shows how the triangle labeled A would be split for refinement. The cells are refined by splitting the longest edge of the triangle or tetrahedron. This technique has two primary advantages: the process is conservative and does not require interpolation to obtain the solution vector for the new cells, and repeated refinement of a skewed cell does not continue to increase grid skewness.

Figure 25.2.7: Cells are Refined by Bisecting Longest Edge

The present scheme finds the longest edge of any cell marked for refinement. The scheme then visits each of the cells that contain that edge and searches for a longer edge. If any of the neighbor cells has a longer edge, the scheme spins around that new edge searching for yet a longer edge. Once it has arrived at the longest edge, it splits that edge. Although this process maintains the quality of the triangulation with repeated application, it can cause many cells that were not marked for refinement to be split. For

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example, Figure 25.2.8 shows the original cell marked for refinement (marked with an X), and Figure 25.2.9 shows the final mesh created by the refinement process.

Conformal Coarsening The grid is coarsened by removing nodes that are shared by cells marked for coarsening. If all the cells attached to the node are marked for coarsening, the solver attempts to remove the node. The following local retriangulation process is attempted for each of the nodes marked for removal: 1. A list of the cells attached to the marked node is generated. Removing these cells creates a cavity that must be retriangulated. 2. A list of the faces inside the cavity is generated. 3. A list of the faces on the cavity boundary is generated. 4. If the node to be removed is on a boundary, a new boundary triangulation is generated and those faces are added to the list of faces on the cavity. 5. From the list of faces on the cavity, a new Delaunay triangulation is created. (See the Theory chapter in the TGrid User’s Guide for a description of Delaunay triangulation.) 6. If the process is successful, the node, faces, and cells from the original triangulation of the region are deleted. 7. All nodes associated with the cavity are removed from the list of doomed nodes to avoid consecutive coarsening in the same region. 8. The solution variables in the new cells are computed using a volume-weighted average. Figure 25.2.10 illustrates the removal of node n1 and the resulting retriangulation. In this example, the list of cells attached to the node includes c1, c2, c3, c4, and c5; the list of faces inside the cavity includes f 6, f 7, f 8, f 9, and f 10; and the list of faces on the cavity includes f 1, f 2, f 3, f 4, and f 5. The new faces of the triangulation are f 11 and f 12, and the new cells are c6, c7, and c8. Nodes introduced by refinement are called refinement nodes. Nodes that existed in the mesh before refinement are called original nodes. By default, only refinement nodes can be removed in the coarsening process, but you can remove any node by resetting the node flags. For additional information on node flags, see Section 25.11. Presently, the grid-coarsening scheme is implemented only in the 2D version of FLUENT.


25-11

Grid Adaption

Figure 25.2.8: Original Grid With One Cell Marked for Refinement

Figure 25.2.9: Final Grid After Refinement Process

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Figure 25.2.10: The Grid is Coarsened by Removing a Node and Retriangulating the Region

25.2.4

Conformal vs. Hanging Node Adaption

For most problems, the hanging node adaption provides the most flexibility for grid adaption. However, the following points should aid you in selecting the appropriate type of adaption for your specific application. • The conformal adaption method is only valid for tri and tet grids, while the hanging node adaption can be applied to all supported cell shapes. • The hanging node adaption is usually much more local in nature than the conformal adaption. In conformal adaption, many cells in addition to the marked cells may be refined due to the longest edge splitting criteria. For highly graded grids, the initial conformal refinement sweeps tend to exhibit substantial propagation of the cell refinement, sometimes refining the grid many cells away from the actual cell marked for refinement. (Subsequent refinements are usually much more local in nature.) The hanging node scheme only propagates to maintain the refinement level difference, which is much more confined. • The connectivity of the original grid is retained in the hanging node adaption scheme, but the conformal adaption method will modify the connectivity with refinement and coarsening. This could have accuracy implications for grids used in unsteady problems with periodic behavior (e.g., vortex shedding behind a cylinder) if you perform successive refinements and coarsenings. However, only conformal coarsening allows you to coarsen the initial grid, and this is only available in 2D. • The hanging node adaption has a memory penalty associated with maintaining the grid hierarchy and temporarily storing the edges in 3D. The conformal adaption has no memory overhead other than the additional nodes, faces and cells added to increase the grid density. • Conformal adaption should not be used in conjunction with dynamic adaption (described in Section 25.5).


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Grid Adaption

25.3

Boundary Adaption

If more cells are required on a boundary, they can be added using boundary adaption. The boundary adaption function allows you to mark or refine cells in the proximity of the selected boundary zones. The ability to refine the grid near one or more boundary zones is provided because important fluid interactions often occur in these regions, such as the development of strong velocity gradients in the boundary layer near a wall.

25.3.1

Boundary Adaption Example

An example of a grid that can be improved with boundary adaption is shown in Figure 25.3.1. This mesh has only two cells on the vertical face of a step. Boundary adaption on the zone corresponding to the face of the step can be used to increase the number of cells, as shown in Figure 25.3.2. Note that this procedure cannot increase the resolution of a curved surface. Therefore, if more cells are required on a curved surface where the shape of the surface is important, it is preferable to create the mesh with sufficient surface nodes before reading it into the solver.

25.3.2

Steps for Performing Boundary Adaption

Three different methods are available for boundary adaption: • adaption based on a cell’s distance from the boundary, measured in number of cells • adaption based on the normal distance of a cell from the boundary • adaption based on a target boundary volume and growth factor You can make use of any of these methods in the Boundary Adaption panel (Figure 25.3.3). Adapt −→Boundary... The steps for using each method are described below.

Boundary Adaption Based on Number of Cells The general procedure for performing adaption based on a cell’s distance from the boundary in terms of the number of cells is listed below: 1. In the Boundary Adaption panel, select Cell Distance under Options, choose the boundary zones near which you want to refine cells in the Boundary Zones list, and click Apply. 2. Open the Contours panel by clicking on the Contour... button.

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25.3 Boundary Adaption

Grid

Figure 25.3.1: Mesh Before Adaption

Grid

Figure 25.3.2: Mesh After Boundary Adaption


25-15

Grid Adaption

Figure 25.3.3: The Boundary Adaption Panel

3. In the Contours panel, enable Filled contours, disable Node Values, choose Adaption... and Boundary Cell Distance in the Contours Of drop-down list, select the appropriate surfaces (3D only), and click Display to see the location of cells with each value of boundary cell distance. By displaying different ranges of values (as described in Section 27.1.2), you can determine the cell distance of the cells you wish to adapt. 4. In the Boundary Adaption panel, set the Number of Cells to the desired value. If you retain the default value of 1, only those cells that have edges (2D) or faces (3D) on the specified boundary zone(s) (i.e., those cells with a boundary cell distance of 1) will be marked or adapted. If you increase the value to 2, cells with a boundary cell distance of 2 will also be marked/adapted, and so on. 5. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 6. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.

Boundary Adaption Based on Normal Distance The general procedure for performing refinement based on a cell’s normal distance from the boundary is listed below: 1. In the Boundary Adaption panel, select Normal Distance under Options, choose the boundary zones near which you want to refine cells in the Boundary Zones list, and click Apply.

25-16


25.3 Boundary Adaption

2. Open the Contours panel by clicking on the Contour... button. 3. In the Contours panel, enable Filled contours, disable Node Values, choose Adaption... and Boundary Normal Distance in the Contours Of drop-down list, select the appropriate surfaces (3D only), and click Display to see the location of cells with each value of normal distance. By displaying different ranges of values (as described in Section 27.1.2), you can determine the normal distance of the cells you wish to adapt. 4. In the Boundary Adaption panel, set the Distance Threshold to the desired value. Cells with a normal distance to the selected boundary zone(s) less than or equal to this value will be marked or adapted. 5. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 6. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.

Boundary Adaption Based on Target Boundary Volume This boundary adaption allows you to refine cells based on a target boundary cell volume and an exponential growth function. This allows you to produce grids with cells that have the target volume near the selected boundaries and exponentially larger (or smaller) cells as you get further from the boundaries. The cells are marked for refinement based on the following equation: Vn > Vboundary eαd

(25.3-1)

where Vn is the volume of the cell, Vboundary is the specified boundary volume (Boundary Volume), α is the exponential growth factor (Growth Factor), and d is the normal distance of the cell centroid from the selected boundaries. Vboundary eαd is the target volume for a cell. The general procedure for this type of boundary refinement is listed below: 1. In the Boundary Adaption panel, select Volume Distance under Options, set the Boundary Volume and Growth Factor to the desired values, choose the boundary zones in the Boundary Zones list where you want the Boundary Volume to be applied, and click Apply. 2. Open the Contours panel by clicking on the Contour... button.


25-17

Grid Adaption

3. In the Contours panel, enable Filled contours, disable Node Values, choose Adaption... and Boundary Volume Distance in the Contours Of drop-down list, select the appropriate surfaces (3D only), and click Display to see contours of the target volume. You can modify the values of any of the inputs (Boundary Volume, Growth Factor, and/or Boundary Zones), click on Apply in the Boundary Adaption panel, and then redisplay the contour plot to visualize the modified target volume distribution. 4. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 5. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.

25.4

Gradient Adaption

The gradient adaption function allows you to mark cells or adapt the grid based on the gradient (or curvature) of the selected field variables.

25.4.1

Gradient Adaption Approach

The primary goal of solution-adaptive grid refinement is to efficiently reduce the numerical error in the digital solution, with minimal numerical cost. Unfortunately, direct error estimation for point-insertion adaption schemes is difficult because of the complexity of accurately estimating and modeling the error in the adapted grids. In fact, no comprehensive mathematically rigorous theory for error estimation and convergence is available yet for CFD simulations. Assuming the greatest error occurs in high-gradient regions, the readily available physical features of the evolving flow field may be used to drive the grid adaption process. Two approaches for using this information for grid adaption are available in FLUENT: • The first gradient approach is recommended for problems with strong shocks, e.g. supersonic inviscid flows. In this approach, FLUENT multiplies the undivided euclidean norm of the gradient of the selected solution variable by a characteristic length scale [52]. For example, the gradient function in two dimensions has the following form: r

|ei1 | = (Acell ) 2 |∇f |

(25.4-1)

where ei1 is the error indicator, Acell is the cell area, r is the gradient volume weight, and ∇f is the undivided euclidean norm of the gradient of the desired field variable, f . The default value of the gradient volume weight is unity, which corresponds to full volume weighting; a value of zero will eliminate the volume weighting, and values between 0 and 1 will use proportional weighting of the volume.

25-18


25.4 Gradient Adaption

• The second gradient (curvature) approach is recommended for problems with smooth solutions. This is the equidistribution adaption technique formerly used by FLUENT, that multiplies the undivided Laplacian of the selected solution variable by a characteristic length scale [283]. For example, the gradient function in two dimensions has the following form: r

|ei2 | = (Acell ) 2 |∇2 f |

(25.4-2)

where ei2 is the error indicator, Acell is the cell area, r is the gradient volume weight, and ∇2 f is the undivided Laplacian of the desired field variable, f . The default value of the gradient volume weight is unity, which corresponds to full volume weighting; a value of zero will eliminate the volume weighting, and values between 0 and 1 will use proportional weighting of the volume. The length scale is the square (2D) or cube (3D) root of the cell volume. The introduction of this length scale permits resolution of both strong and weak disturbances, increasing the potential for more accurate solutions. You can, however, reduce or eliminate the volume weighting by changing the gradient Volume Weight in the Grid Adaption Controls panel (see Section 25.11 for details). Any of the field variables available for contouring can be used in the gradient adaption function. Interestingly, these scalar functions include both geometric and physical features of the numerical solution. Therefore, in addition to traditional adaption to physical features, such as the velocity, you may choose to adapt to the cell volume field to reduce rapid variations in cell volume. In addition to the Standard (no normalization) approach formerly used by FLUENT, two options are available for Normalization [83]: • Scale, which scales the values of ei1 or ei2 by their average value in the domain, i.e.: |ei | |ei |

(25.4-3)

when using the Scale option, suitable first-cut values for the Coarsen Threshold and the Refine Threshold are 0.3 to 0.5, and 0.7 to 0.9, respectively. Smaller values will result in larger adapted regions. • Normalize, which scales the values of ei1 or ei2 by their maximum value in the domain, therefore always returning a problem-independent range of [0, 1] for any variable used for adaption, i.e.: |ei | max |ei |


(25.4-4)

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Grid Adaption

when using the Normalize option, suitable first-cut values for the Coarsen Threshold and the Refine Threshold are 0.2 to 0.4, and 0.5 to 0.9, respectively. Smaller values will result in larger adapted regions.

25.4.2

Steady Gradient Adaption Example

A good example of the use of steady gradient adaption is the solution of the supersonic flow over a circular cylinder. The initial mesh, shown in Figure 25.4.1, is very coarse, even though it contains sufficient cells to adequately describe the shape of the cylinder. The mesh ahead of the cylinder is too coarse to resolve the shock wave that forms in front of the cylinder. In this instance, because there will be a jump in pressure across the shock, it is clear that pressure is a suitable variable to use in gradient adaption. Several adaptions are necessary, however, before the shock can be properly resolved. The mesh after several adaptions is shown in Figure 25.4.2. A typical application of gradient adaption for an incompressible flow might be a mixing layer, which—like the example above—involves a discontinuity.

Grid

Figure 25.4.1: Bluff-Body Mesh Before Adaption

25.4.3

Steps for Performing Gradient Adaption

You will perform gradient adaption in the Gradient Adaption panel (Figure 25.4.3). Adapt −→Gradient...

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25.4 Gradient Adaption

Grid

Figure 25.4.2: Bluff-Body Mesh After Gradient Adaption

Figure 25.4.3: The Gradient Adaption Panel


25-21

Grid Adaption

The general procedure for performing gradient adaption is listed below: 1. In the Gradient Adaption panel, select the desired solution variable in the Gradients Of drop-down list and click on Compute. 2. Open the Contours panel by clicking on the Contour... button. 3. In the Contours panel, enable Filled contours, disable Node Values, choose Adaption... and Existing Value in the Contours Of drop-down list, select the appropriate surfaces (3D only), and click Display to see the location of cells with each gradient value. By displaying different ranges of values (as described in Section 27.1.2), you can determine the range of gradients for which you want to adapt cells. Note that if you are using normalization, the range for the gradients of any variable will always be [0, 1]. 4. In the Gradient Adaption panel, set the Refine Threshold. Cells with gradient values above this value will be marked or refined. In the Gradient Adaption panel, you will also find the categories Method and Normalization. Curvature is the criterion for adaption formerly used by FLUENT; Gradient is a newer one, which uses the first gradient of a field variable instead of the second gradient (curvature) for adaption. Depending on the problem you are solving, you may want to use one or the other adaption method: • Curvature is recommended for problems with smooth solutions. • Gradient is recommended for problems with strong shocks, e.g. supersonic inviscid flows. Further options are: • Standard meaning that no normalization of the gradient or curvature is performed. This was always the case in Fluent 6.0. • Scale meaning that the gradients or curvature are scaled by the average value in the domain. • Normalize uses a scaling by the maximum value of the variable in the domain, i.e. the gradient or curvature are bounded by [0, 1]. Using either scaling or normalization makes the setting of the refine and coarsen thresholds much simpler, and almost independent of the current solution and specific problem. This is especially important when using the automated dynamic adaption process. 5. If you want to coarsen the grid, set the Coarsen Threshold to a non-zero value. Cells with gradient values below the specified value will be marked or coarsened. Note that if you are using hanging node adaption (the default), you will not be able to create a grid that is coarser than the original grid. For this, you must use

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25.5 Dynamic Gradient Adaption

conformal adaption. Note also that conformal coarsening is only available for 2D or axisymmetric geometries. See Section 25.11 for details. 6. (Optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 7. Click Mark to mark the cells for adaption (refinement/coarsening) by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the adaption immediately. (If you wish to disable refinement or coarsening, or marking for refinement or coarsening, you can turn off the Refine or Coarsen option before marking or adapting.)

25.5

Dynamic Gradient Adaption

In contrast with the static gradient adaption described in Section 25.4, where the adaption of the mesh is performed “by hand,” dynamic gradient adaption is a fully automated process. For time dependent as well as for steady state problems, you can start the solution process without changing the initial settings, i.e. without stopping the iteration process, and setting new refine/coarsen threshold values, thus performing the mesh adaption “by hand.”

25.5.1

Dynamic Gradient Adaption Approach

The dynamic gradient adaption executes the gradient adaption described in Section 25.4 automatically. All options of gradient adaption are also valid for the dynamic gradient adaption, but specific settings are recommended for the dynamic gradient adaption: • The Refine as well as the Coarsen options should be switched on. • Either the Scale or the Normalize option for Normalization should be used. The nonnormalized values of the gradient or the curvature of a variable (obtained by selecting Standard for the Normalization) are generally strongly solution-dependent, and therefore would require re-adjustment of the Coarsen Threshold and Refine Threshold as the solution proceeds. For dynamic adaption, scaling is usually preferred if you wish to resolve regions of minor values of the gradient (or curvature) accurately, in addition to the region of highest gradient (or curvature), because it does not take very high values of the gradient or curvature as much into account as does the normalization. Recommended refine and coarsen threshold values to start with are 0.4, and 0.9, respectively. In general the more refinement you want, the smaller these values should be. • Hanging node adaption only should be used.


25-23

Grid Adaption

• The Min # of Cells and Max # of Cells and the Max Level of Refine or the Min Cell Volume should be set. The limits for the Min # of Cells and Max # of Cells can affect the Coarsen Threshold and Refine Threshold: if either the Min # of Cells or the Max # of Cells are violated, the Coarsen Threshold or the Refine Threshold are adjusted to fulfill the limits for the Min # of Cells or the Max # of Cells. For the Max Level of Refine, the default value of 2 is a good start for most problems. If this is not sufficient, you can increase this value, but keep in mind that even in a 2D problem, the default value of 2 can increase the number of cells by a factor of 16, in the adapted regions. A value of zero leaves this parameter unbounded: in this case you should use a suitable limit for Min Cell Volume. • The Interval between two consecutive automatic mesh adaptions must be specified. Depending on whether you are performing a steady-state or a time-dependent solution, the Interval is specified in iterations or time steps respectively. This value strongly depends on the problem solved and the time step used (where applicable): for (almost) steady state problems, values of 100 or higher are reasonable; for time dependent problems, values of 10 or lower are often required. Note that if you are using the coupled explicit solver with explicit unsteady formulation, your input here will be in number of iterations.

! Note that when the parallel solver is used, there is no automatic load balancing during the dynamic adaption process. Thus you may want to use the execute command functionality to enforce repartitioning after a reasonable number of time steps or iterations. For example you could use the following commands: para/part/method principal-axes para/part/use-stored See also Tutorial 4 for an example of applying dynamic gradient adaption to a FLUENT simulation.

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25.6 Isovalue Adaption

25.6

Isovalue Adaption

Some flows may contain flow features that are easy to identify based on values of a certain quantity. For instance, wakes represent a total pressure deficit, and jets are identifiable by a region of relatively high-velocity fluid. Since it is known that these regions also contain large gradients of important flow quantities (such as k and in turbulent flows) it may be more convenient to perform an isovalue adaption on the relevant flow quantity than to refine on gradients of the individual flow variables. The isovalue adaption function allows you to mark or refine cells inside or outside a specified range of a selected field variable function. The grid can be refined or marked for refinement based on geometric and/or solution vector data. Specifically, any quantity in the display list of field variables can be used for the isovalue adaption. Some examples of how you might use the isovalue marking/adaption feature include the following: • Create masks using coordinate values or the quadric function. • Refine cells that have a velocity magnitude within a specified range. • Mark and display cells with a pressure or continuity residual outside of a desired range to determine where the numerical solution is changing rapidly. The approach used in isovalue adaption function is to compute the specified value for each cell (velocity, quadric function, centroid x coordinate, etc.), and then visit each cell, marking for refinement the cells that have values inside (or outside) the specified ranges.

25.6.1

Isovalue Adaption Example

An example of a problem in which isovalue adaption is useful is shown in Figure 25.6.1. The mesh for an impinging jet is displayed together with contours of x velocity. An isovalue adaption based on x velocity allows refinement of the mesh only in the jet, with the result shown in Figure 25.6.2.

! Caution must be used when adapting to isovalues to prevent large gradients in cell volume. As explained in Section 25.1, this can affect accuracy and impede convergence. One approach to rectifying large gradients in cell volume is to adapt to cell-volume change, as demonstrated in Section 25.8.2.

25.6.2

Steps for Performing Isovalue Adaption

You will perform isovalue adaption in the Iso-Value Adaption panel (Figure 25.6.3). Adapt −→Iso-Value...


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Grid Adaption

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

Contours of X-Velocity (m/s)

Figure 25.6.1: Impinging Jet Mesh Before Adaption Shown Together With Contours of x Velocity

Grid

Figure 25.6.2: Impinging Jet Mesh After Isovalue Adaption

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25.6 Isovalue Adaption

Figure 25.6.3: The Iso-Value Adaption Panel

The general procedure for performing isovalue adaption is listed below: 1. In the Iso-Value Adaption panel, select the desired solution variable in the Iso-Values Of drop-down list and click on Compute to update the Min and Max fields. 2. Choose the Inside or Outside option and set the Iso-Min and Iso-Max values. • If you choose Inside, cells with isovalues between Iso-Min and Iso-Max will be marked or refined. • If you choose Outside, cells with isovalues less than Iso-Min or greater than Iso-Max will be marked or refined. 3. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 4. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.


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Grid Adaption

25.7

Region Adaption

Many mesh generators create meshes with cell volumes that grow very rapidly with distance from boundaries. While this avoids a dense grid as a matter of course, it might also create problems if the mesh is not fine enough to resolve the flow. But if it is known a priori that a finer mesh is required in a certain region of the solution domain, the mesh can be refined using region adaption. The region adaption function marks or refines cells inside or outside a region defined by text or mouse input. Presently, the grid can be refined or marked inside or outside a hexahedron (quadrilateral in 2D), a sphere (circle in 2D), or a cylinder. The regionbased marking/adaption feature is particularly useful for refining regions that intuitively require good resolution: e.g., the wake region of a blunt-body flow field. In addition, you can use the region marking to create mask adaption registers that can be used to limit the extent of the refinement and coarsening.

25.7.1

Defining a Region

The basic approach to the region adaption function is to first define a hexahedral (quadrilateral), spherical (circular), or cylindrical region. You will define the hexahedron (quadrilateral) by entering the coordinates of two points defining the diagonal. The sphere (circle) is defined by entering the coordinates of the center of the sphere and its radius. To define a cylinder, you will specify the coordinates of the points defining the cylinder axis, and the radius. In 3D this will define a cylinder. In 2D, you will have an arbitrarily oriented rectangle with length equal to the cylinder axis length and width equal to the radius. A rectangle defined using the cylinder option differs from one defined with the quadrilateral option in that the former can be arbitrarily oriented in the domain while the latter must be aligned with the coordinate axes. You can either type the exact coordinates into the appropriate real entry fields or select locations with the mouse on displays of the grid or solution field. After the region is defined, each cell that has a centroid inside/outside the specified region is marked for refinement.

25.7.2

Region Adaption Example

Figure 25.7.1 shows a mesh that was created for solving the flow around a flap airfoil. The mesh is very fine near the surface of the airfoil so that the viscous-affected region may be resolved. However, the mesh grows very rapidly away from the airfoil, with the result that the flow separation known to occur on the suction surface of the flap will not be properly predicted. To circumvent this problem, the grid was adapted within circular regions (selected by mouse probe) surrounding the flap. The result is shown in Figure 25.7.2. Note that when the region adaption was performed, the minimum cell volume for adaption was limited (as described in Section 25.11) to prevent the very small cells near the surface from being refined further.

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25.7 Region Adaption

Grid

Figure 25.7.1: Flap-Airfoil Mesh Before Adaption

Grid

Figure 25.7.2: Flap-Airfoil Mesh After Region Adaption


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Grid Adaption

25.7.3

Steps for Performing Region Adaption

You will perform region adaption in the Region Adaption panel (Figure 25.7.3). Adapt −→Region...

Figure 25.7.3: The Region Adaption Panel The general procedure for performing isovalue adaption is listed below: 1. In the Region Adaption panel, choose the Inside or Outside option. • If you choose Inside, cells with centroids within the specified region will be marked or refined. • If you choose Outside, cells with centroids outside the specified region will be marked or refined. 2. Specify the shape of the region. In 2D, you may choose a Quadrilateral, Circle, or Cylinder. In 3D, you may choose a Hexahedron, Sphere, or Cylinder. 3. Define the region by entering values into the panel or by using the mouse. In the panel the inputs are as follows: • To define a hexahedron or quadrilateral, you will input the coordinates of two points defining the box’s diagonal: (Xminimum,Yminimum,Zminimum) and (Xmaximum,Ymaximum, Zmaximum) for a hexahedron, or (Xminimum,Yminimum) and (Xmaximum,Ymaximum) for a quadrilateral.

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25.7 Region Adaption

• To define a sphere or circle, you will input the coordinates of its center— (Xcenter,Ycenter,Zcenter) for a sphere or (Xcenter,Ycenter) for a circle—and its Radius. • To define a cylinder, you will input the minimum and maximum coordinates defining the cylinder axis—(X-Axis Min,Y-Axis Min,Z-Axis Min) and (X-Axis Max,Y-Axis Max,Z-Axis Max) for 3D or (X-Axis Min,Y-Axis Min) and (X-Axis Max,Y-Axis Max) for 2D—as well as the Radius of the cylinder. (In 2D, this will be the width of the resulting rectangle.) To define the region using the mouse, click on the Select Points With Mouse button. Using the mouse probe (the right mouse button, by default), you may select the input coordinates from a display of the grid or solution field. See Section 27.3 for details about mouse button functions.) After you select the points, the values will be loaded automatically into the appropriate fields in the panel. If you want, you can edit these values before marking or adapting. • To define a hexahedron or quadrilateral, you can select the two points of the diagonal in any order. • To define a sphere or circle, first select the location of the centroid and then select a point that lies on the sphere/circle (i.e., a point that is one radius away from the centroid). • To define a cylinder, first select the two points that define the cylinder axis and then select a point that is one radius away from the axis. 4. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 5. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.


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Grid Adaption

25.8

Volume Adaption

As mentioned in Section 25.1, it is best for both accuracy and convergence to have a mesh in which the changes in cell volume are gradual. If the mesh creation or adaption process has resulted in a mesh that does not have this property, the grid can be improved by using volume adaption with the option of refining based on either the cell volume or the change in volume between the cell and its neighbors.

25.8.1

Approach

Marking or refining the grid based on volume magnitude is most often used to remove large cells or to globally refine the mesh. The procedure is to mark for refinement any cell with a volume greater than the specified threshold value. Marking or refining the grid based on the change in cell volume is used to improve the smoothness of the grid. The procedure is to mark for refinement any cell that has a volume change greater than the specified threshold value. The volume change is computed by looping over the faces and comparing the ratio of the cell neighbors to the face. For example, in Figure 25.8.1 the ratio of V1/V2 and the ratio of V2/V1 is compared to the threshold value. If V2/V1, for example, is greater than the threshold, then C2 is marked for refinement.

Figure 25.8.1: The Volume Change is Computed as the Ratio of the Volumes of the Cells Neighboring a Face

25.8.2

Volume Adaption Example

The mesh in Figure 25.8.2 was created for the purpose of computing a turbulent jet. Local refinement was used in TGrid to create a mesh that is fine in the region of the jet, but coarse elsewhere. This created a very sharp change in cell volume at the edge of the jet. To improve the mesh, it was refined using volume adaption with the criterion that the maximum cell volume change should be less than 50%. The minimum cell volume for adaption was also limited. The resulting mesh, after smoothing and swapping, is shown in Figure 25.8.3. It can be seen that the interface between the refined region within the jet and the surrounding mesh is no longer as sharp.

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25.8 Volume Adaption

Grid

Figure 25.8.2: Jet Mesh Before Adaption

Grid

Figure 25.8.3: Jet Mesh After Volume Adaption Based on Change in Cell Volume


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Grid Adaption

25.8.3

Steps for Performing Volume Adaption

You will perform volume adaption in the Volume Adaption panel (Figure 25.8.4). Adapt −→Volume...

Figure 25.8.4: The Volume Adaption Panel The general procedure for performing volume adaption is listed below: 1. In the Volume Adaption panel, specify whether you want to adapt based on volume magnitude or volume change by selecting the Magnitude or Change option. 2. Click on Compute to update the Min and Max fields. These fields will show the range of cell volumes or cell volume changes (defined in Section 25.8.1), depending on your selection in step 1. 3. Set the Max Volume or Max Volume Change value. If you have chosen to adapt based on volume Magnitude, cells that have volumes greater than Max Volume will be marked or refined. If you are adapting based on volume Change, cells with volume changes greater than Max Volume Change will be marked or refined. 4. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 5. Click Mark to mark the cells for refinement by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the refinement immediately.

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25.9 y + and y ∗ Adaption

y + and y ∗ Adaption

25.9

FLUENT provides three different options for near-wall modeling of turbulence (standard wall functions, non-equilibrium wall functions, and the enhanced wall treatment). As described in Section 10.9, there are certain mesh requirements for each of these near-wall modeling options. Since it is often difficult to gauge the near-wall resolution requirements when creating the mesh, y + and y ∗ adaption have been provided to enable you to appropriately refine or coarsen the mesh along the wall during the solution process. If you are using the enhanced wall treatment, you will adapt to y + ; if you are using wall functions, you can adapt to either y + or y ∗ .

25.9.1

Approach

The approach is to compute y + or y ∗ for boundary cells on the specified viscous wall zones, define the minimum and maximum allowable y + or y ∗ , and mark and/or adapt the appropriate cells. Cells with y + or y ∗ values below the minimum allowable threshold will be marked for coarsening and cells with y + or y ∗ values above the maximum allowable threshold will be marked for refinement (unless coarsening or refinement has been disabled).

25.9.2

y + Adaption Example

Figure 25.9.1 shows the mesh for a duct flow, with the top boundary being the wall and the bottom boundary being a symmetry plane. After an initial solution, it was determined that y + values of the cells on the wall boundary were too large, and y + adaption was used to refine them. The resulting mesh is shown in Figure 25.9.2. This figure shows that the height of the cells along the wall boundary has been reduced during the refinement process. However, the cell-size distribution on the wall after refinement is much less uniform than in the original mesh, which is an adverse effect of y + adaption. See Section 10.9 for guidelines on recommended values of y + or y ∗ for different near-wall treatments.

25.9.3

Steps for Performing y + or y ∗ Adaption

You will perform y + or y ∗ adaption in the Y+/Y* Adaption panel (Figure 25.9.3). Adapt −→Y+/Y*... The general procedure for performing y + or y ∗ adaption is listed below: 1. In the Y+/Y* Adaption panel, select Y+ or Y* as the adaption Type. (Select Y+ if you are using the enhanced wall treatment; if you are using wall functions, you can select either type.)


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Grid Adaption

Grid

Figure 25.9.1: Duct-Flow Mesh Before Adaption

Grid

Figure 25.9.2: Duct-Flow Mesh After y + Adaption

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25.9 y + and y ∗ Adaption

Figure 25.9.3: The Y+/Y* Adaption Panel

2. Choose the wall zones for which you want boundary cells to be marked or adapted in the Wall Zones list, and click on Compute to update the Min and Max fields. (Note that the values displayed are the minimum and maximum values for all wall zones, not just those selected.) 3. Set the Min Allowed and Max Allowed. Cells with y + or y ∗ values below Min Allowed will be coarsened or marked for coarsening, and cells with y + or y ∗ values above Max Allowed will be refined or marked for refinement. Note that if you are using hanging node adaption (the default), you will not be able to create a grid that is coarser than the original grid. For this, you must use conformal adaption. Note also that conformal coarsening is only available for 2D or axisymmetric geometries. See Section 25.11 for details. 4. (optional) If you want to set any adaption options (described in Section 25.11), click on the Controls... button to open the Grid Adaption Controls panel. 5. Click Mark to mark the cells for adaption (refinement/coarsening) by placing them in an adaption register (which can be manipulated as described in Section 25.10), or click Adapt to perform the adaption immediately. (If you wish to disable refinement or coarsening, or marking for refinement or coarsening, you can turn off the Refine or Coarsen option before marking or adapting.)


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Grid Adaption

25.10

Managing Adaption Registers

You can manipulate, delete, and display adaption registers that you have created by marking cells for adaption. Since these registers will be used to adapt the grid, the ability to manipulate them provides you with additional control over the adaption process. Management of adaption registers is performed in the Manage Adaption Registers panel (Figure 25.10.1). Adapt −→Manage...

Figure 25.10.1: The Manage Adaption Registers Panel (You can also open this panel by clicking on the Manage... button in any of the adaption panels.) For additional information about registers, see Section 25.2.1.

Overview The creation of hybrid adaption functions is generally motivated by the desire to confine the adaption to a specific region (using masks) and/or create a more accurate error indicator. FLUENT provides a few basic tools to aid in creating hybrid adaption functions. First, you can create the initial adaption registers using geometric and/or solution vector information. After creating the adaption registers, you can manipulate these registers and their associated refinement and coarsening marks. The registers are manipulated by changing the type and/or combining them to create the desired hybrid function. The

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25.10 Managing Adaption Registers

marks are manipulated by using Exchange, Invert, Limit, and Fill operations. Finally, you can delete, display, and most importantly, adapt to the hybrid adaption functions. For example, you can capture the shock wave generated on a wedge in a supersonic flow field by adapting the grid to the gradients of pressure. The pressure gradient near the surface of the wedge, however, is relatively small. You might therefore use the velocity field to resolve the equally important boundary layer near the surface of the wedge. If you adapt to pressure, regions near the surface might be coarsened. If you subsequently adapted to velocity, these same regions might be refined, but the net result would be no gain in resolution. But if you combine the velocity and pressure gradient adaption functions, the new adaption function would allow increased resolution in both regions. The relative weight of the two functions in the hybrid function is determined by the values of the refinement and coarsening thresholds you specify for each of the flow field variables. If, in addition, you decided to refine the shock and boundary layer only near the leading edge of the wedge, you could create a circle at the leading edge of the wedge using the region adaption function, change this new register to a mask, and combine it with the hybrid gradient function.

25.10.1

Manipulating Adaption Registers

There are three basic tools available for modifying and manipulating adaption registers: changing type, combining, and deleting.

Changing Register Types Presently, there are two types of registers: adaption registers and mask registers. The present adaption functions accessed through the GUI and text interface generate adaption registers—i.e., registers that designate the cells marked for refinement or coarsening. These registers can be converted to mask registers, however, by changing their type. Mask registers, unlike the adaption registers, only maintain two states: ACTIVE and INACTIVE. If the adaption register is converted to a mask, the cells marked for refinement are ACTIVE, and all other cells are INACTIVE; i.e., the cells marked for coarsening are ignored. Commonly, the adaption registers converted to masks are those that are generated by adaption functions that mark cells exclusively for refinement, such as region or isovalue adaption functions. The other major difference between adaption and mask registers is the manner in which they are combined. To change the type of one or more registers from adaption to mask, or vice versa, follow these steps: 1. Choose the register(s) in the Registers list. 2. Click on the Change Type button under Register Actions.


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Grid Adaption

The new type of the register (or of the most recently selected or deselected register, if multiple registers are selected) will be shown as the Type under Register Info. You can select each register individually to see what its current type is.

Combining Registers After the individual adaption registers have been created and appropriately modified, these registers are combined to create hybrid adaption functions. Any number of registers can be combined in the following manner: • All adaption registers are combined into a new adaption register. • All mask registers are combined into a new mask register. • The new adaption and mask registers are combined. Any number of adaption registers can be combined in the following manner: • If the cell is marked for refinement in any of the registers, mark the cell for refinement in the new register (bitwise OR). • If the cell is marked for coarsening in all of the registers, mark the cell for coarsening in the new register (bitwise AND). The mask registers are combined in a manner similar to the refinement marks: if any cell is marked ACTIVE, the cell in the new register is marked ACTIVE (bitwise OR). Finally, in the combination of an adaption and mask register, only cells that are marked in the mask register can have an adaption mark in the combined register (bitwise AND). For example, creating an adaption function based on pressure gradient may generate cells marked for refinement and coarsening throughout the entire solution domain. If this register is then combined with a mask register created from cells marked inside a sphere, only the cells inside the sphere will be marked for refinement or coarsening in the new register. The effect of masks depends on the order in which they are applied. For example, consider two adjacent, circular masks. Applying one mask to the adaption register and then applying the other mask to the result of the first combination would give a much different result than applying the combination of the two masks to the initial adaption register. (The second combination results in a greater possible number of marked cells.) To combine two or more registers, follow these steps: 1. Choose the registers in the Registers list.

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2. Click on the Combine button under Register Actions. The selected registers will remain intact, and the register(s) resulting from the combination will be added to the Registers list. In some instances, three new registers may be created: a combination of the adaption registers, a combination of the mask registers, and then a combination of the two combined registers. For more information about combining registers, see Section 25.2.1.

Deleting Registers Any number of adaption registers can be deleted. The primary reason for deleting registers is to discard unwanted adaption registers, reducing possible confusion and the potential for generating undesired results by selecting these castaways. In addition, only 32 adaption registers can exist at one time. You may therefore need to discard unwanted registers to make room for new ones. To permanently remove one or more registers, follow these steps: 1. Choose the register(s) in the Registers list. 2. Click on the Delete button under Register Actions.

25.10.2

Modifying Adaption Marks

The adaption marks are the identifiers that designate whether a cell should be refined, coarsened, or neutral. Presently, four basic tools are provided for modifying the adaption marks: Exchange, Invert, Limit, and Fill operations. The Exchange operation changes all cells marked for refinement into cells marked for coarsening, and all cells originally marked for coarsening into cells marked for refinement. Commonly, this operator is applied to adaption registers that have only refinement marks. For example, the exchange operation can be used to coarsen a rectangular region. First, you create an adaption register that marks a rectangular region of cells for refinement. Next, you use the Exchange operation to modify the cell marks, creating a rectangular region with cells marked for coarsening. The Invert operation can only be used with mask registers. It toggles the mask markings: all cells marked ACTIVE are switched to INACTIVE, and all cells marked INACTIVE are switched to ACTIVE. For example, if you generate a mask that defines a circular region, you can quickly modify the mask to define the region outside of the circle using the Invert operation. The Limit operation applies the present adaption volume limit to the selected adaption register. (For information on adaption limits, see Section 25.11.) Commonly, you would


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Grid Adaption

use this operation to determine the effect of the present limits on the adaption process. You can use the volume limit to create a more uniform mesh by setting the limit to refine only large cells. After all the cells have reached a uniform size, you can continue the refinement process to the desired resolution. Finally, the Fill operation marks for coarsening all cells in the adaption register that are not marked for refinement. You may want to use the Fill operation if you are combining multiple registers to make a new register. When you combine registers, a cell will be marked for coarsening only if it is marked for coarsening in all of the registers. If you create an adaption register with an operation that only marks cells for refinement, but you do not want to prohibit coarsening, you should use the Fill operation before combining the register with any other registers. The steps for modifying adaption marks are as follows: 1. Choose the register(s) in the Registers list. 2. Click on the Exchange, Invert, Limit, or Fill button under Mark Actions.

25.10.3

Displaying Registers

Viewing the cell markings is often helpful in the process of creating hybrid adaption functions. You can plot a marker at the cell centroid and/or a wireframe of the cell to view the state of the cell. By default, the cells marked for refinement are colored in red, and the cells marked for coarsening are marked in cyan. In addition, cells marked ACTIVE in a mask register are also colored red. These are the cells that are marked for adaption, but the final number of cells added or subtracted from the grid will depend on the adaption limits and the grid characteristics. To display a register, follow these steps: 1. Choose the register in the Registers list. 2. If desired, set any of the display options described below by clicking on the Options... button. 3. Click on the Display button.

Adaption Display Options Various aspects of the adaption register display can be modified, such as the wireframe visibility and shading, marker visibility, color, size, and symbol, and whether surface or zone grids are drawn with the display. The adaption register display capability allows you to view the cells that are flagged for adaption. Depending on the dimension of the problem and the number of flagged

25-42



cells, you may wish to customize the adaption display options. For instance, a common method for viewing flagged cells in 2D is to draw the grid and filled wireframes, but this is impractical in 3D. In three dimensions, you may want to plot the centroid markers of the cells with the grid of selected boundary zones. You can display the flagged cells in an adaption or mask register, using markers and/or wireframes. The marker is a symbol placed at the centroid of the cell. There is a refine marker and a coarsen marker. You can change the symbol, color, and size of these markers. A wireframe is composed of the edges of the triangle or tetrahedron. Its color is the same as the respective marker color, and it can be filled, if desired. Finally, portions of the grid can be drawn with the marker symbols or wireframes to aid in evaluating the location of marked cells. All of these options are set in the Adaption Display Options panel (Figure 25.10.2). Adapt −→Display Options...

Figure 25.10.2: The Adaption Display Options Panel (You can also open this panel by clicking on the Options... button in the Manage Adaption Registers panel.) • To enable or disable the display of wireframes for cells marked for refinement/coarsening, turn the Wireframe option on or off under Refine and/or Coarsen. To draw filled wireframes (i.e., using a solid color, instead of the outline) turn on the Filled option. • To enable or disable the display of markers for cells marked for refinement/coarsening, turn the Marker option on or off under Refine and/or Coarsen. If you use markers, you can specify their size in the Size field, and their symbol in the Symbol drop-down list.


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Grid Adaption

• To change the color of the refine or coarsen markers/wireframes, select a new color in the Color drop-down list under Refine or Coarsen. By default, refine markers/wireframes are red and coarsen markers/wireframes are cyan. • To include portions of the grid in the register display, enable the Draw Grid option. The Grid Display panel will appear automatically, and you can set the grid display parameters there. When you click on Display in the Manage Adaption Registers panel, the grid display, as defined in the Grid Display panel, will be included in the register display.

25.10.4

Adapting to Registers

The primary objective is to adapt the grid to efficiently increase the accuracy of the solution. These register tools provide you with the ability to create hybrid adaption functions customized to your flow-field application. Finally, the customized adaption function is used to direct the refinement and coarsening of the grid. To perform the adaption, follow these steps: 1. Choose the register in the Registers list. 2. Click on the Adapt button.

25.11

Grid Adaption Controls

FLUENT allows you to change the adaption type from hanging node to conformal, or place restrictions on the cell zones, the size of cells that can be adapted, and the total number of cells that can be produced from the adaption process. You can also modify the intensity of the volume weighting in the gradient function, restrict the adaption process to refinement and/or coarsening, and control which nodes are eligible for possible elimination from the grid during conformal coarsening. All parameters controlling these aspects of adaption are set in the Grid Adaption Controls panel (Figure 25.11.1). Adapt −→Controls... (You can also open this panel by clicking on the Controls... button in any of the adaption panels.)

! Recall that it is highly recommended that you write a case and data file before starting the adaption process. Then, if you generate an undesirable grid, you can restart the process with the saved files.

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25.11 Grid Adaption Controls

Figure 25.11.1: The Grid Adaption Controls Panel

Controlling the Type of Adaption You can choose to use hanging node or conformal adaption. You can also restrict the adaption process to the addition of grid resolution through refinement and/or the removal of grid density through coarsening. • To use hanging node adaption (the default), select Hanging in the Type frame, and to use conformal adaption, select Conformal. The hanging node and conformal adaption procedures are described in detail in Section 25.2. • To enable/disable refinement, turn the Refine option on or off. • To enable/disable coarsening, turn the Coarsen option on or off.

Limiting Adaption By Zone You can limit the adaption process to specified cell zones. The cells composing the fluid and solid regions of the analysis generally have very different resolution requirements and error indicators. By limiting the adaption to a specific cell zone, you can use different adaption functions to create the optimal grid. To limit the adaption to a particular cell zone (or to particular cell zones), select the cell zones in which you want to perform adaption in the Zones list. By default, adaption will be performed in all cell zones.


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Grid Adaption

Limiting Adaption By Cell Volume or Volume Weight The minimum cell volume limit restricts the refinement process to cells with volumes greater than the limit. You can use this to initiate the refinement process on larger cells, gradually reducing the limit to create a uniform cell size distribution. Set this limit in the Min Cell Volume field. Note that the input that you will give in this field for a 2D axisymmetric problem will be interpreted as the minimum cell area. In addition, the gradient volume weight can be modified. A value of zero eliminates volume weighting, a value of unity uses the entire volume, and values between 0 and 1 scale the volume weighting. Set this value in the Volume Weight field. For more information, see Section 25.4.1.

Limiting the Total Number of Cells The maximum number of cells is a restriction that prevents FLUENT from creating more cells than you consider appropriate for the present analysis. In addition, it saves you the time you might have spent waiting for the grid adaption process to complete the creation of these cells, which could be substantial if you saturate your computer memory resources. This premature termination of the refinement process can, however, produce undesirable grid quality depending on the order in which the cells were visited. The order of visitation is based on the cell arrangement in memory, which in general can be quite random. During the dynamic gradient adaption, the resulting number of cells after adaption is estimated. If this number exceeds the maximum number of cells, both the Coarsen Threshold and the Refine Threshold are updated. This is done to ensure the best possible grid resolution with the specified number of cells. Furthermore, you can specify the minimum number of cells, if dynamic gradient adaption is used. This is particularly helpful if strong structures of the flow that were resolved with the adaption vanished (e.g. left the domain) and you want to resolve the remaining weaker ones, which would otherwise require modifying the Coarsen Threshold and the Refine Threshold. You can set the total number of cells allowed in the grid in the Max # of Cells field. The minimum number of cells in the grid can be set in the Min # of Cells field. The default values of zero places no limits on the number of cells.

Controlling the Levels of Refinement During Hanging Node Adaption You can control the number of levels of refinement used to split cells during non-conformal adaption by setting the Max Level of Refine. The default value of 2 is a good start for most problems. If this is not sufficient, you can increase this value, but keep in mind that even in a 2D problem, the default value of 2 can increase the number of cells by a factor of 16, in the adapted regions. A value of zero leaves this parameter unbounded:

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25.11 Grid Adaption Controls

in this case you should use a suitable limit for Min Cell Volume. See Section 25.2.2 for more information on hanging node adaption. See also Section 25.5.1 for guidelines for limiting cell sizes and number of cells during dynamic gradient adaption.

Controlling Node Removal During Conformal Coarsening You can control the removal of nodes during coarsening by modifying the node removal flags. The node removal flags control which nodes are eligible for possible elimination from the grid. (The node removal flags apply to conformal adaption only. For hanging node adaption, only refinement nodes can be removed during coarsening, and they are always removed.) Nodes introduced by refinement are called refinement nodes, and nodes that existed in the mesh before refinement are called original nodes. FLUENT maintains a section in the case file with the node flags. If this section doesn’t exist (i.e., when you first read a grid), it identifies all nodes as original nodes. In addition, it also distinguishes between nodes on boundary, internal, and periodic zones for both original nodes and nodes created by adaptive refinement. To guarantee that the original shape of the domain boundaries is maintained, usually only nodes introduced by refinement are removed. For example, consider the grid of a rectangular domain. If one of the nodes on the edges of the rectangle is removed the shape is not modified, but if one of the corner nodes of the rectangle is eliminated, the shape is changed from a quadrilateral to a pentagon. You can, however, modify this default behavior by changing the node removal flags. The most common modification is to allow the removal of original internal nodes. Removing internal nodes does not destroy the shape of the boundary. In fact, it can be very helpful if the initial grid has substantial resolution in a region with minor or no changes in physical features.

! As mentioned before, removing original boundary or periodic nodes can alter shape, and in some instances may even destroy topology, producing a worthless grid. Therefore, exercise extreme discretion when removing original boundary and periodic nodes. As always, it is recommended that you write a case and data file before starting the adaption process. Then, if you generate an undesirable grid, you can restart the process with the saved files. By default, only the removal of refinement nodes is allowed, as indicated by the enabled status of Boundary - Refined, Internal - Refined, and Periodic - Refined and the disabled status of Boundary - Original, Internal - Original, and Periodic - Original in the Grid Adaption Controls panel. If you want to disable the removal of these types of nodes, you can do so by turning off the associated check button. Similarly, if you want to enable their removal, turn on the associated check button.


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Grid Adaption

25.12

Improving the Grid by Smoothing and Swapping

Smoothing and face swapping are tools that complement grid adaption, usually increasing the quality of the final numerical mesh. Smoothing repositions the nodes and face swapping modifies the cell connectivity to achieve these improvements in quality.

! Face swapping is applicable only to grids with triangular or tetrahedral cells. Smoothing and swapping are performed using the Smooth/Swap Grid panel (Figure 25.12.1). Adapt −→Smooth/Swap...

Figure 25.12.1: The Smooth/Swap Grid Panel

25.12.1

Smoothing

Two smoothing methods are available in FLUENT: Laplace smoothing and skewnessbased smoothing. The first can be applied to all types of grids, but the second is available only for triangular/tetrahedral meshes.

! For triangular and tetrahedral grids, it is recommended that you always use the skewnessbased smoothing method; reserve the Laplacian method only for quadrilateral and hexahedral grids.

Laplacian Smoothing When you use the Laplace method, a Laplacian smoothing operator is applied to the unstructured grid to reposition nodes. The new node position is the average of the positions of its node neighbors. The relaxation factor (a number between 0.0 and 1.0) multiplies the computed node position increment. A value of zero results in no movement of the node and a value of unity results in movement equivalent to the entire computed

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25.12 Improving the Grid by Smoothing and Swapping

increment. Figure 25.12.2 illustrates the new node position for a typical configuration of quadrilateral cells.

Figure 25.12.2: Result of Smoothing Operator on Node Position (dashed line is original grid and solid line is final grid)

This repositioning strategy tends to improve the skewness of the mesh, but usually relaxes the clustering of node points. In extreme circumstances, the present operator may create grid lines that cross over the boundary, creating negative cell volumes. This is most likely to occur near sharp or coarsely resolved convex corners, especially if you perform multiple smoothing operations with a large relaxation factor. Figure 25.12.3 illustrates an initial tetrahedral grid before one unrelaxed smoothing iteration creates grid lines that cross over each other (Figure 25.12.4).

Figure 25.12.3: Initial Grid Before Smoothing Operation

The default smoothing parameters are designed to improve grid quality with minimal adverse effects, but you should always take the precaution of saving a case file before you smooth your mesh. If you apply a conservative relaxation factor and start with a


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Grid Adaption

Figure 25.12.4: Grid Smoothing Can Cause Grid-Line Crossing

good quality initial grid, the frequency of failure due to smoothing is extremely low in two dimensions. However, corruption of the grid topology occurs much more frequently in three dimensions, particularly with tetrahedral grids. The skewness-based smoothing is recommended for triangular and tetrahedral grids. The smoothing operator can also be applied repeatedly, but as the number of smoothing sweeps increase, the node points have a tendency to pull away from boundaries and the grid tends to lose any clustering characteristics. Steps for Laplacian Smoothing To perform Laplacian smoothing, you will follow these steps: 1. In the Smooth/Swap Grid panel (Figure 25.12.1), select laplace in the Method dropdown list under Smooth. 2. Set the factor by which to multiply the computed position increment for the node in the Relaxation Factor field. The lower the factor, the more reduction in node movement. 3. Specify the number of successive smoothing sweeps to be performed on the grid in the Number of Iterations field. The default value is 4. 4. Click the Smooth button.

Skewness-Based Smoothing When you use skewness-based smoothing, FLUENT applies a smoothing operator to the grid, repositioning interior nodes to lower the maximum skewness of the grid. FLUENT

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will try to move interior nodes to improve the skewness of cells with skewness greater than the specified “minimum skewness.” This process can be very time-consuming, so you should only perform smoothing on cells with high skewness. Improved results can be obtained by smoothing the nodes several times. There are internal checks that will prevent a node from being moved if moving it causes the maximum skewness to increase, but it is common for the skewness of some cells to increase when a cell with a higher skewness is being improved. Thus, you may see the average skewness increase while the maximum skewness is decreasing.

! You should carefully consider whether the improvements to the mesh due to a decrease in the maximum skewness are worth the potential increase in the average skewness. Performing smoothing only on cells with very high skewness (e.g., 0.8 or 0.9) may lessen the adverse effects on the average skewness.

! Skewness-based smoothing is available only for triangular and tetrahedral grids. Steps for Skewness-Based Smoothing To perform skewness-based smoothing, you will follow these steps: 1. In the Smooth/Swap Grid panel (Figure 25.12.1), select skewness in the Method drop-down list under Smooth. 2. Set the minimum cell skewness value for which node smoothing will be attempted in the Minimum Skewness field. FLUENT will try to move interior nodes to improve the skewness of cells with skewness greater than this value. By default, Minimum Skewness is set to 0.4 for 2D and 0.8 for 3D. 3. Specify the number of successive smoothing sweeps to be performed on the grid in the Number of Iterations field. The default value is 4. 4. Click the Smooth button. Skewness-based smoothing should be alternated with face swapping (see Section 25.12.3).

25.12.2

Face Swapping

Face swapping can be used to improve the quality of a triangular or tetrahedral grid.

Triangular Grids The approach for triangular grids is to use the Delaunay circle test to decide if a face shared by two triangular cells should be swapped. A pair of cells sharing a face satisfies the circle test if the circumcircle of one cell does not contain the unshared node of the second cell. Figure 25.12.5 illustrates cell neighbors that do and do not satisfy the circle


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Grid Adaption

Figure 25.12.5: Examples of Cell Configurations That Satisfy and Do Not Satisfy the Circle Test

Figure 25.12.6: The Face is Swapped to Satisfy the Delaunay Circle Test

test. In cases where the circle test is not satisfied, the diagonal or face is swapped, as illustrated in Figure 25.12.6. Repeated application of the face-swapping technique will produce a constrained Delaunay mesh. If a grid is a Delaunay grid, it is a unique triangulation that maximizes the minimum angles in the mesh. Thus, the triangulation tends toward equilateral cells, providing the most equilateral grid for the given node distribution. (See the Theory chapter in the TGrid User’s Guide for more information about Delaunay mesh generation.)

Tetrahedral Grids For tetrahedral grids, face swapping consists of searching for configurations of three cells sharing an edge and converting them into two cells sharing a face to decrease skewness and the cell count. (See Figure 25.12.7.)

Steps for Face Swapping To perform face swapping, simply click on the Swap button until the reported Number Swapped is 0. The Number Visited indicates the total number of faces that were visited and tested for possible face swapping.

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Figure 25.12.7: 3D Face Swapping

25.12.3

Combining Skewness-Based Smoothing and Face Swapping

As mentioned in Section 25.12.1, skewness-based smoothing should usually be alternated with face swapping. Guidelines for this procedure are presented here. 1. Perform 4 smoothing iterations using a Minimum Skewness of 0.8 for 3D, or 0.4 for 2D. 2. Swap until the Number Swapped decreases to 0. 3. For 3D grids, decrease the Minimum Skewness to 0.6 and repeat the smoothing/swapping procedure.


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Grid Adaption

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Chapter 26. Creating Surfaces for Displaying and Reporting Data FLUENT allows you to select portions of the domain to be used for visualizing the flow field. The domain portions are called surfaces, and there are a variety of ways to create them. Surfaces are required for graphical analysis of 3D problems, since you cannot display vectors, contours, etc. or create an XY plot for the entire domain at once. In 2D you can usually visualize the flow field on the entire domain, but to create an XY plot of a variable in a portion of the interior of the domain, you must generate a surface. In addition, in both 2D and 3D, you will need one or more surfaces if you want to generate a surface-integral report. Note that FLUENT will automatically create a surface for each boundary zone in the domain. Surface information is stored in the case file. The following sections explain how to create surfaces, rename, group, and delete them, and determine their sizes. • Section 26.1: Using Surfaces • Section 26.2: Zone Surfaces • Section 26.3: Partition Surfaces • Section 26.4: Point Surfaces • Section 26.5: Line and Rake Surfaces • Section 26.6: Plane Surfaces • Section 26.7: Quadric Surfaces • Section 26.8: Isosurfaces • Section 26.9: Clipping Surfaces • Section 26.10: Transforming Surfaces • Section 26.11: Grouping, Renaming, and Deleting Surfaces


26-1

Creating Surfaces for Displaying and Reporting Data

26.1

Using Surfaces

In order to visualize the internal flow of a 3D problem or create XY plots of solution variables for 3D results, you must select portions of the domain (surfaces) on which the data are to be displayed. Surfaces can also be used for visualizing or plotting data for 2D problems, and for generating surface-integral reports. FLUENT provides methods for creating several kinds of surfaces, and stores all surfaces in the case file. These surfaces and their uses are described briefly below: Zone Surfaces: If you want to create a surface that will contain the same cells/faces as an existing cell/face zone, you can generate a zone surface. This kind of surface is useful for displaying results on boundaries. Partition Surfaces: When you are using the parallel version of FLUENT, you may find it useful to create surfaces that are defined by the boundaries between grid partitions (see Chapter 30 for more information about running the parallel solver). You can then display data on each side of a partition boundary. Point Surfaces: To monitor the value of some variable or function at a particular location in the domain, you can create a surface consisting of a single point. Line and Rake Surfaces: To generate and display pathlines, you must specify a surface from which the particles are released. Line and rake surfaces are well-suited for this purpose and for obtaining data for comparison with wind tunnel data. A rake surface consists of a specified number of points equally spaced between two specified endpoints. A line surface is simply a line that includes the specified endpoints and extends through the domain; data points will be at the centers of the cells through which the line passes, and consequently will not be equally spaced. Plane Surfaces: If you want to display flow-field data on a specific plane in the domain, you can create a plane surface. A plane surface is simply a plane that passes through three specified points. Quadric Surfaces: To display data on a line (2D), plane (3D), circle (2D), sphere (3D), or quadric surface you can specify the surface by entering the coefficients of the quadric function that defines it. This feature provides you with an explicit method for defining surfaces. Isosurfaces: You can use an isosurface to display results on cells that have a constant value for a specified variable. Generating an isosurface based on x, y, or z coordinate, for example, will give you an x, y, or z cross-section of your domain. Generating an isosurface based on pressure will allow you to display data for another variable on a surface of constant pressure.

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26.2 Zone Surfaces

26.2

Zone Surfaces

Zone surfaces are useful for displaying results on boundaries. For example, you may want to plot contours of velocity magnitude at the inlet and outlet of the problem domain, or temperature contours on the domain’s walls. To do so, you need to have a surface that contains the same faces (or cells) as an existing face (or cell) zone. Zone surfaces are created automatically for all boundary face zones in the domain, so you will generally not need to create any zone surfaces unless you accidentally delete one. To create a zone surface, you will use the Zone Surface panel (Figure 26.2.1). Surface −→Zone...

Figure 26.2.1: The Zone Surface Panel The steps for creating the zone surface are as follows: 1. In the Zone list, select the zone for which you want to create a surface. 2. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., zone-surface-6). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 3. Click on the Create button. The new surface name will be added to the Surfaces list in the panel. If you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.3

Partition Surfaces

If you are using the parallel version of FLUENT (see Chapter 30), you may find it useful to create data surfaces defined by the boundaries of grid partitions. As described in Section 30.4, partitioning the grid divides it into groups of cells that can be solved on separate processors when you use a parallel solver. A partition surface will contain faces or cells on the boundary of two grid partitions. For example, you can plot solution values on the partition surface to determine how the solution is changing across a partition interface. Figure 26.3.1 shows cell-partition contours on a partition surface which is overlaid on the grid.

0.00e+00 3.00e-01 6.00e-01 9.00e-01 1.20e+00 1.50e+00 1.80e+00 2.10e+00 2.40e+00 2.70e+00 3.00e+00 Contours of Cell Partition

Figure 26.3.1: Contours of Cell Partitions on Partition Surface Overlaid on Grid

To create a partition surface, you will use the Partition Surface panel (Figure 26.3.2). Surface −→Partition... The steps for creating the partition surface are as follows: 1. Specify the partition boundary you are interested in by indicating the two bordering partitions under the Partitions heading. The boundary that defines the partition surface is the boundary between the “interior partition” and the “exterior partition”. Int Part indicates the ID number of the interior partition (i.e., the partition under consideration), and Ext Part indicates the ID number of the bordering (exterior) partition. The Min and Max fields will indicate the minimum and maximum ID numbers of the grid partitions. (The minimum is always zero, and the maximum

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26.3 Partition Surfaces

Figure 26.3.2: The Partition Surface Panel

is one less than the number of processors.) If there are more than two grid partitions, each interior partition will share boundaries with several exterior partitions. By setting the appropriate values for Int Part and Ext Part, you can create surfaces for any of these boundaries. 2. Choose interior or exterior faces or cells to be contained in the partition surface by turning Cells and Interior on or off under Options. To obtain a surface consisting of cells that are on the “interior” side of the partition boundary, turn on both Cells and Interior. To create one consisting of cells that are on the “exterior” side, turn on Cells and turn off Interior. If you want the surface to contain the faces on the boundary instead of the cells, turn off the Cells option. To have the faces reflect data values for the interior cells, turn the Interior check button on, and to have them reflect values for the exterior cells, turn it off. 3. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., partition-surface-6). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 4. Click on the Create button. The new surface name will be added to the Surfaces list in the panel. If you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.4

Point Surfaces

You may often be interested in displaying results at a single point in the domain. For example, you may want to monitor the value of some variable or function at a particular location. To do this, you must first create a “point” surface, consisting of a single point. When you display node-value data on a point surface, the value displayed will be a linear average of the neighboring node values. If you display cell-value data, the value at the cell in which the point lies will be displayed. To create a point surface, you will use the Point Surface panel (Figure 26.4.1). Surface −→Point...

Figure 26.4.1: The Point Surface Panel The steps for creating the point surface are as follows: 1. Specify the location of the point. There are three different ways to do this: • Enter the coordinates (x0,y0,z0) under Coordinates. • Click on the Select Point With Mouse button and then select the point by clicking on a location in the active graphics window with the mouse-probe button. (See Section 27.3 for information about setting mouse button functions.) • Use the Point Tool option to interactively position a point in the graphics window. You can set the initial location of this point using one of the two methods described above for specifying the point’s position (or you can start from the position defined by the default Coordinates). See Section 26.4.1 for information about using the point tool.

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26.4 Point Surfaces

2. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., point-5). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 3. Click on the Create button to create the new surface. If you want to check that your new surface has been added to the list of all defined surfaces, or you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.

26.4.1

Using the Point Tool

The point tool allows you to interactively fine-tune the definition of a point using graphics. Starting from an initial point, you can translate the point until its position is as desired. For example, if you need to position a point surface at the center of a duct, just past the inlet, you can start with the point tool near the desired location (e.g., on the inlet), and translate it until it is in the proper place. (You may find it helpful to display grid faces to ensure that the point tool is correctly positioned inside the domain.)

Initializing the Point Tool Before turning on the Point Tool option, set the Coordinates to suitable starting values. You can enter values manually, or use the Select Point With Mouse button. Often it is convenient to display the grid for an inlet or isosurface on or near which the point is to be located, and then select a point on that grid to specify the initial position of the point tool. Once you have specified the appropriate Coordinates, activate the tool by turning on the Point Tool option. The point tool, an eight-sided polygon, will appear in the graphics window, as shown in Figure 26.4.2. You can then translate the point tool as described below. The point surface you create will be located at the center of the point tool.

Translating the Point Tool To translate the point tool in the direction along the red axis, click the mouse-probe button (the right button by default—see Section 27.3 for information about changing the mouse functions) anywhere on the gray part of the point tool and drag the mouse until the tool reaches the desired location. Green arrows will show the direction of motion. To translate the tool in the transverse directions (i.e., along either of the other axes), press the key, click the mouse-probe button anywhere on the gray part of the point tool, and drag the mouse until the tool reaches the desired location. Two sets of green arrows will show the possible directions of motion. (In 2D, there will be only one


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Figure 26.4.2: The Point Tool

set of green arrows, since there is only one other direction for translation.) If you find the perspective distracting when performing this type of translation, you can turn it off in the Camera Parameters panel (opened from the Views panel), as described in Section 27.4.2.

Resetting the Point Tool If you “lose” the point tool, or want to reset it for any other reason, you can either click on the Reset button to return the point tool to the default position and start from there, or turn the tool off and reinitialize it as described above. In the default position, the point tool will lie at the center of the domain.

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26.5 Line and Rake Surfaces

26.5

Line and Rake Surfaces

You can create lines and rakes in the domain for releasing particles, obtaining data for comparison with tunnel data, etc. A rake consists of a specified number of points equally spaced between two specified endpoints. A line is simply a line that includes the specified endpoints and extends through the domain; data points will be located where the line intersects the faces of the cell, and consequently may not be equally spaced. To create a line or rake surface, you will use the Line/Rake Surface panel (Figure 26.5.1). Surface −→Line/Rake...

Figure 26.5.1: The Line/Rake Surface Panel The steps for creating the line or rake surface are as follows: 1. Indicate whether you are creating a Line surface or a Rake surface by selecting the appropriate item in the Type drop-down list. 2. If you are creating a rake surface, specify the Number of Points to be equally spaced between the two endpoints. 3. Specify the location of the line or rake surface. There are three different ways to define the location: • Enter the coordinates of the first point (x0,y0,z0) and the last point (x1,y1,z1) under End Points.


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• Click on the Select Points With Mouse button and then select the endpoints by clicking on locations in the active graphics window with the mouse-probe button. (See Section 27.3 for information about setting mouse button functions.) • Use the Line Tool option to interactively position a line in the graphics window. You can set the initial location of this line using one of the two methods described above for specifying endpoints (or you can start from the position defined by the default End Points). See Section 26.5.1 for information about using the line tool. Note that the coordinates of the End Points will be updated automatically when you use the second or third method described above. 4. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., line-5 or rake-6). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 5. Click on the Create button to create the new surface. If you want to check that your new surface has been added to the list of all defined surfaces, or you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.

26.5.1

Using the Line Tool

The line tool allows you to interactively fine-tune the definition of a line or rake using graphics. Starting from an initial line, you can translate, rotate, and resize the line until its position, orientation, and length are as desired. For example, if you need to position a rake surface just inside the inlet to a duct, you can start with the line tool near the desired location (e.g., on the inlet), and translate, rotate, and resize it until you are satisfied. (You may find it helpful to display grid faces to ensure that the line tool is correctly positioned inside the domain.)

Initializing the Line Tool Before turning on the Line Tool option, set the End Points to suitable starting values. You can enter values manually, or use the Select Points With Mouse button. Often it is convenient to display the grid for an inlet or isosurface on or near which you wish to place the line or rake surface and then select two points on that grid to specify the initial position of the line tool. Once you have specified the appropriate End Points, activate the tool by turning on the Line Tool option. The line tool will appear in the graphics window, as shown in Figure 26.5.2.

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26.5 Line and Rake Surfaces

Figure 26.5.2: The Line Tool

You can then translate, rotate, and/or resize the line tool as described below.

Translating the Line Tool To translate the line tool in the direction along the red axis, click the mouse-probe button (the right button by default—see Section 27.3 for information about changing the mouse functions) anywhere on the “line” part of the tool (see note below) and drag the mouse until the tool reaches the desired location. Green arrows will show the direction of motion.

! Do not click on the axes of the line tool that have arrows on the ends. These axes control rotation of the tool. Click only on the portion of the tool that represents the prospective line surface. This portion is designated by the rectangles attached to each end. To translate the tool in the transverse directions (i.e., along either of the axes within the plane perpendicular to the red axis), press the key, click the mouse-probe button anywhere on the “line” part of the tool (see note above), and drag the mouse until the tool reaches the desired location. Two sets of green arrows will show the possible directions of motion. (In 2D, there will be only one set of green arrows, since there is only one other direction for translation.) If you find the perspective distracting when performing this type of translation, you can turn it off in the Camera Parameters panel (opened from the Views panel), as described in Section 27.4.2.


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Rotating the Line Tool To rotate the line tool, you will click the mouse-probe button on one of the white axes with arrows. When you click on one of these axes, a green ribbon will encircle the other arrowed axis, designating it as the axis of rotation. As you drag the mouse along the circle to rotate the tool, the green circle will become yellow.

! Do not click on the red axis to rotate the line tool. Resizing the Line Tool If you plan to generate a rake surface, you can resize the line tool to define the length of the rake. Click the mouse-probe button in one of the white rectangles at the ends of the “line” part of the tool (shown in black in Figure 26.5.2) and drag the mouse to lengthen or shorten the tool. Green arrows will show the direction of stretching/shrinking.

Resetting the Line Tool If you “lose” the line tool, or want to reset it for any other reason, you can either click on the Reset button to return the line tool to the default position and start from there, or turn the tool off and reinitialize it as described above. In the default position, the line tool will lie midway along the x and y lengths of the domain, spanning the z domain extent.

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26.6 Plane Surfaces

26.6

Plane Surfaces

To display flow-field data on a specific plane in the domain, you will use a plane surface. You can create surfaces that cut through the solution domain along arbitrary planes only in 3D; this feature is not available in 2D. There are six types of plane surfaces that you can create: • Intersection of the domain with the infinite plane: This is the default plane surface created. The extents of the plane will be determined by the extents of the domain. Since the plane is slicing through the domain, the data points will, by default, be located where the plane intersects the faces of a cell, and consequently may not be equally spaced. • Bounded plane: This plane will be a bounded parallelepiped, for which 3 of the 4 corners are the 3 points that define the plane equation (or the 4 corners are the corners of the “plane tool”). Like the default plane surface described above, this type of surface will also have unequally spaced data points. • Bounded plane with equally spaced data points: This plane is the same as the bounded plane described above, except you will specify the density of points along the 2 directions of the parallelepiped, creating a uniform distribution of data points. • Plane having a certain normal vector and passing through a specified point: To create this type of plane, you will define a normal vector and a point. A plane with the specified normal and passing through the specified point will be created. • Plane aligned with an existing surface: To create this type of plane, you will define a single point and a surface. A plane parallel to the selected surface and passing through the specified point will be created. • Plane aligned with the view in the graphics window: To create this type of plane, you will define a single point. A plane parallel to the current view in the active graphics window and passing through the specified point will be created. To create a plane surface, you will use the Plane Surface panel (Figure 26.6.1). Surface −→Plane... The steps for creating the plane surface are as follows: 1. Decide which of the six types of planes described above you want to create. If you are creating the default plane type (the intersection of the infinite plane with the domain), go directly to step 2. To create a bounded plane, turn on Bounded under Options. To create a bounded plane with equally spaced data points, turn on both Bounded and Sample Points, and then set the number of data points under


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Figure 26.6.1: The Plane Surface Panel

Sample Density. You will specify the point density in each direction by entering the appropriate values for Edge 1 and Edge 2. (Edge 1 extends from point 0 to point 1, and edge 2 extends from point 1 to point 2. The points are specified in step 2, below.) To define a plane aligned with an existing surface, select Aligned With Surface, and then choose the surface in the Surfaces list and specify a single point using one of the first two methods described below in step 2. To define a plane aligned with the view plane, select Aligned With View Plane, and then choose a single point using one of the first two methods described below in step 2. To define a plane having a certain normal vector and passing through a specified point, select Point And Normal, and then specify the normal vector by entering values in the ix, iy, and iz fields under Normal, and a single point using one of the first two methods described below in step 2.

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26.6 Plane Surfaces

2. Specify the location of the plane surface. There are three different ways to define the location: • Enter the coordinates of the three Points defining the planar surface: (x0,y0,z0), (x1,y1,z1), and (x2,y2,z2). • Click on the Select Points button and then select the three points by clicking on locations in the active graphics window with the mouse-probe button. (See Section 27.3 for information about setting mouse button functions.) • Use the Plane Tool option to interactively position a plane in the graphics window. You can set the initial location of this plane using one of the two methods described above for specifying the defining points (or you can start from the position defined by the default Points). See Section 26.6.1 for information about using the plane tool. Note that the coordinates of the Points will be updated automatically when you use the second or third method described above. 3. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., plane-7). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 4. Click on the Create button to create the new surface. If you want to check that your new surface has been added to the list of all defined surfaces, or you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.

26.6.1

Using the Plane Tool

The plane tool allows you to interactively fine-tune the definition of a plane using graphics. Starting from an initial plane, you can translate, rotate, and resize the plane until its position, orientation, and size are as desired. For example, if you need to position a plane surface at a cross-section of an irregularly-shaped, curved duct, you can start with the plane tool near the desired location, resize it, translate it until it is within the duct walls, and rotate it to the proper orientation. (You may find it helpful to display grid faces to ensure that the plane tool is correctly positioned inside the domain.)

Initializing the Plane Tool Before turning on the Plane Tool option, set the Points to suitable starting values. You can enter values manually, or use the Select Points button. Often it is convenient to display the grid for an inlet or isosurface that is similar to the desired plane surface, and then select three points on that grid to position the initial plane. Once you have specified


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the appropriate Points, activate the tool by turning on the Plane Tool option. The plane tool will appear in the graphics window, as shown in Figure 26.6.2.

Figure 26.6.2: The Plane Tool

You can then translate, rotate, and/or resize the plane tool as described below.

Translating the Plane Tool To translate the plane tool in the direction normal to the plane, click the mouse-probe button (the right button by default—see Section 27.3 for information about changing the mouse functions) anywhere on the gray part of the plane tool and drag the mouse until the tool reaches the desired location. Green arrows will show the direction of motion. To translate the tool in the transverse directions (i.e., along either of the axes that lie within the plane), press the key, click the mouse-probe button anywhere on the gray part of the plane tool, and drag the mouse until the tool reaches the desired location. Two sets of green arrows will show the possible directions of motion. If you find the perspective distracting when performing this type of translation, you can turn it off in the Camera Parameters panel (opened from the Views panel), as described in Section 27.4.2.

Rotating the Plane Tool To rotate the plane tool, you will click the mouse-probe button on one of the white arrows at the tips of the plane’s axes. Clicking on any arrow allows you to rotate the tool about

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26.6 Plane Surfaces

either of the other two axes: when you click on the arrow, two green ribbons will encircle the plane tool, forming circles about each of the two possible axes of rotation. Drag the mouse along the desired circle to rotate the tool. As you do so, the circle along which the tool is rotating will become yellow. The following notes may help you when you are rotating the plane tool: • Once you move your mouse along one circle, you cannot change the direction of rotation unless you release the mouse-probe button and try again. Be careful to start moving your mouse very steadily so that you can choose the correct direction. • Do not click on the red arrow to rotate. • Do not try to rotate by clicking on an arrow that is pointing away from you. It will be very difficult for you to judge which direction of rotation is correct from this point of view. Since there are two arrows on each axis, there will always be an appropriate arrow available. • Do not rotate the plane tool more than 90◦ or so at once. If you rotate the tool by a large angle, the arrow on which you are clicking will begin to point away from you, and you will have trouble controlling the rotation (as discussed in the item above).

Resizing the Plane Tool If you plan to generate a bounded plane, you can resize the plane tool to define the plane’s boundaries. Click the mouse-probe button in one of the white squares at the plane tool’s corners (shown in black in Figure 26.6.2) and drag the mouse to stretch or shrink the tool. Green arrows will show the direction of the plane’s diagonal.

! Be careful not to drag your mouse across any of the axes while resizing the tool. This will flip the tool over and corrupt it. If you accidentally do this, reset the plane tool and start again.

Resetting the Plane Tool If you “lose” the plane tool, or want to reset it for any other reason, you can either click on the Reset Points button to return the plane tool to the default position and start from there, or turn the tool off and reinitialize it as described above. In the default position, the plane tool will lie midway along the x length of the domain, spanning the y and z domain extents.


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26.7

Quadric Surfaces

If you want to display data on a line (2D), plane (3D), circle (2D), sphere (3D), or general quadric surface, you can specify the surface by entering the coefficients of the quadric function that defines it. This feature provides you with an explicit method for defining surfaces. See Sections 26.5 and 26.6 for additional methods for creating line and plane surfaces. To create a quadric surface, you will use the Quadric Surface panel (Figure 26.7.1). Surface −→Quadric...

Figure 26.7.1: The Quadric Surface Panel The steps for creating the quadric surface are as follows: 1. Decide which type of quadric surface you want to create. In 3D, choose Plane, Sphere, or (general) Quadric in the Type drop-down list. In 2D, choose Line, Circle, or Quadric. 2. Specify the defining equation for the surface in SI units. • Line or plane surface: If you have selected Line (in 2D) or Plane (in 3D) as the surface type, the surface will consist of all points on the domain that satisfy the equation ix ∗ x + iy ∗ y + iz ∗ z = distance. You will input ix (the coefficient of x), iy (the coefficient of y), iz (the coefficient of z), and distance (the distance of the line or plane from the origin) in the fields to the right of the Type drop-down list. When you click on the Update button under the

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26.7 Quadric Surfaces

Quadric Function heading, the display of the quadric function coefficients will change to reflect your inputs. • Circle or sphere surface: If you have selected Circle (in 2D) or Sphere (in 3D) as the surface type, the surface will consist of all points on the domain that satisfy the equation (x − x0)2 + (y − y0)2 + (z − z0)2 = r2 . You will input x0,y0,z0 (the x, y, and z coordinates of the sphere or circle’s center) and r2 (the square of the radius) in the fields to the right of the Type drop-down list. When you click on the Update button under the Quadric Function heading, the display of the quadric function coefficients will change to reflect your inputs. • Quadric surface: If you have selected Quadric as the surface type, the surface will consist of all points in the domain that satisfy the general quadric function Q = value. You will input the coefficients of the quadric function Q (the coefficients of the terms x2 , y2 , z2 , xy, yz, zx, x, y, z and the constant term) directly in the Quadric Function box, and you will set value to the right of the Type drop-down list. Note that the Update button will be disabled when you choose this type of surface. 3. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., sphere-slice-7 or quadric-slice-10). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 4. Click on the Create button to create the new surface. If you want to check that your new surface has been added to the list of all defined surfaces, or you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.8

Isosurfaces

If you want to display results on cells that have a constant value for a specified variable, you will need to create an isosurface of that variable. Generating an isosurface based on x, y, or z coordinate, for example, will give you an x, y, or z cross-section of your domain; generating an isosurface based on pressure will allow you to display data for another variable on a surface of constant pressure. You can create an isosurface from an existing surface or from the entire domain.

! Note that you cannot create an isosurface until you have initialized the solution, performed calculations, or read a data file. To create an isosurface, you will use the Iso-Surface panel (Figure 26.8.1). Surface −→Iso-Surface...

Figure 26.8.1: The Iso-Surface Panel The steps for creating the isosurface are as follows: 1. Choose the scalar variable to be used for isosurfacing in the Surface of Constant drop-down list. First, select the desired category in the upper list. You can then select from related quantities from the lower list. (See Chapter 29 for an explanation of the variables in the list.) 2. If you wish to create an isosurface from an existing surface (i.e., generate a new surface of constant x, y, temperature, pressure, etc. that is a subset of another surface), choose that surface in the From Surface list. If you do not select a surface from the list, the isosurfacing will be performed on the entire domain.

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26.8 Isosurfaces

3. Click on the Compute button to calculate the minimum and maximum values of the selected scalar field in the domain or on the selected surface (in the From Surface list). The minimum and maximum values will be displayed in the Min and Max fields. 4. Set the isovalue using one of the following methods. (Note that the second method will allow you to define multiple isovalues in a single isosurface.) • You can set an isovalue interactively by moving the slider with the left mouse button. The value in the Iso-Values field will be updated automatically. This method will also create a temporary isosurface in the graphics window. Using the slider allows you to preview an isosurface before creating it.

!

Even though the isosurface is displayed, it is only a temporary surface. To create an isosurface, use the Create button after deciding on a particular isovalue. • You can type in isovalues in the Iso-Values field directly, separating multiple values by white space. Multiple isovalues will be contained in a single isosurface; i.e., you cannot select subsurfaces within the resulting isosurface. 5. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., z-coordinate-6). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 6. Click on the Create button. The new surface name will be added to the From Surface list in the panel. If you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.9

Clipping Surfaces

If you have created a surface, but you do not want to use the whole surface to display data, you can clip the surface between two isovalues to create a new surface that spans a specified subrange of a specified scalar quantity. The clipped surface consists of those points on the selected surface where the scalar field values are within the specified range. For example, in Figure 26.9.1 the external wall has been clipped to values of x coordinate less than 0 to show only the back half of the wall, allowing you to see the valve inside the intake port.

Figure 26.9.1: External Wall Surface Isoclipped to Values of x Coordinate To clip an existing surface, you will use the Iso-Clip panel (Figure 26.9.2). Surface −→Iso-Clip... The steps for clipping a surface are as follows: 1. Choose the scalar variable on which the clipping will be based in the Clip To Values Of drop-down list. First, select the desired category in the upper list. You can then select from related quantities from the lower list. (See Chapter 29 for an explanation of the variables in the list.) 2. Select the surface to be clipped in the Clip Surface list. 3. Click on the Compute button to calculate the minimum and maximum values of the selected scalar field on the selected surface. The minimum and maximum values will be displayed in the Min and Max fields.

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26.9 Clipping Surfaces

Figure 26.9.2: The Iso-Clip Panel

4. Define the clipping range using one of the following methods. • You can set the upper and lower limits of the clipping range interactively by moving the indicator in each dial (i.e., the dial above the Min or Max field) with the left mouse button. The value in the corresponding Min or Max field will be updated automatically. This method will also create a temporary surface in the graphics window. Using the dials allows you to preview a clipped surface before creating it.

!

Even though the clipped surface is displayed, it is only a temporary surface. To create the new surface, use the Clip button after deciding on the clipping range. • You can type the minimum and maximum values in the clipping range directly in the Min and Max fields. 5. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., clip-density-8). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 6. Click on the Clip button. The new surface name will be added to the Clip Surface list in the panel. (The original surface will remain unchanged.) If you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.10

Transforming Surfaces

You can create a new data surface from an existing surface by rotating and/or translating the original surface. For example, you can rotate the surface of a complicated turbomachinery blade to plot data in the region between blades. You can also create a new surface at a constant normal distance from the original surface. To transform an existing surface to create a new one, you will use the Transform Surface panel (Figure 26.10.1). Surface −→Transform...

Figure 26.10.1: The Transform Surface Panel The steps for transforming a surface are as follows: 1. Select the surface to be transformed in the Transform Surface list. 2. Set the appropriate transformation parameters, as described below. You can perform any combination of translation, rotation, and “isodistancing” on the surface. • Rotation: To rotate a surface, you will specify the origin about which the rotation is performed, and the angle by which the surface is rotated. In the About box under Rotate, you will specify a point, and the origin of the coordinate system for the rotation will be set to that point. (The x, y,

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26.10 Transforming Surfaces

and z directions will be the same as for the global coordinate system.) For example, if you specified the point (1,5,3) in 3D, rotation would be about the x, y, and z axes anchored at (1,5,3). You can either enter the point’s coordinates in the x,y,z fields or click on the Mouse Select button and select a point in the graphics window using the mouse-probe button. (See Section 27.3 for information about mouse button functions.) In the Angles box under Rotate, you will specify the angles about the x, y, and z axes (i.e., the axes of the coordinate system with the origin defined under About) by which the surface is rotated. For 2D problems, you can specify rotation about the z axis only. • Translation: To translate a surface, you will simply define the distance by which the surface is translated in each direction. Set the x, y, and z translation distances under Translate. • Isodistancing: To create a surface positioned at a constant normal distance from the original surface, you need to set only that normal distance between the original surface and the transformed surface. Set the value for d under Iso-Distance. 3. If you do not want to use the default name assigned to the surface, enter a new name under New Surface Name. The default name is the concatenation of the surface type and an integer which is the new surface ID (e.g., transform-9). (If the New Surface Name you enter is the same as the name of a surface that already exists, FLUENT will automatically assign the default name to the new surface when it is created.) 4. Click on the Create button. The new surface name will be added to the Transform Surface list in the panel. (The original surface will remain unchanged.) If you want to delete or otherwise manipulate any surfaces, click on the Manage... button to open the Surfaces panel. See Section 26.11 for details.


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26.11

Grouping, Renaming, and Deleting Surfaces

Once you have created a number of surfaces, you can interactively rename, delete, and group surfaces and obtain information about their components. Grouping surfaces is useful if you want to perform postprocessing on a number of surfaces at a time. For example, you may want to group several wall surfaces together to generate a contour plot of temperature on all walls. To postprocess results on each wall surface individually, you will simply “ungroup” the surfaces. Manipulation of existing surfaces is performed with the Surfaces panel (Figure 26.11.1). Surface −→Manage...

Figure 26.11.1: The Surfaces Panel You can also open this panel by clicking on the Manage... button in one of the surface creation panels described in the previous sections.

Grouping Surfaces As mentioned above, you may want to group several surfaces together in order to perform postprocessing on all of them at once. To create a surface group, select the surfaces to be grouped in the Surfaces list. You can define a new name for the group in the Name field, or you can use the default name, which is the name of the first surface you selected in the Surfaces list. Then click on the Group button. The selected surfaces will disappear from the Surfaces list, and the name of the surface group will be added to the list.

! Note that the Group button will not appear until you have selected at least two surfaces. As soon as you choose a second surface in the Surfaces list, the Rename button will change to the Group button.

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26.11 Grouping, Renaming, and Deleting Surfaces

To ungroup the surfaces, simply select the surface group in the Surfaces list and click on the UnGroup button. The group name will disappear from the list and the names of the original surfaces in the group will reappear in the list.

Renaming Surfaces To change the name of an existing surface, select the surface in the Surfaces list, enter a new name in the Name field, and then click on the Rename button. The new name will replace the old name in the Surfaces list and the surface will be otherwise unchanged. Note that the Rename button will not appear in the panel if you have selected more than one surface. When more than one surface is selected, the Rename button is replaced by the Group button.

Deleting Surfaces If you find that a surface is no longer useful, you may want to delete it to prevent the list of surfaces from becoming too cluttered. Select the surface or surfaces to be deleted in the Surfaces list, and then click on the Delete button. The delete operation is not reversible, so if you want to get a deleted surface back again you will need to recreate it using one of the surface-creation panels described in the previous sections.

Surface Statistics You can also use the Surfaces panel to retrieve topological information about surfaces. Points is the total number of nodes in a surface. 0D Facets is the number of isolated nodes in a surface (i.e., nodes that have no connectivity, such as point surfaces or nodes in a rake), 1D Facets is the number of linear faces (consisting of two connected nodes) in a surface in a 2D problem, and 2D Facets is the number of 2D faces (triangular or quadrilateral) in a surface in a 3D problem. Note that an interior zone surface in a 3D problem consists of 2D facets, and similarly an interior zone surface in a 2D problem consists of 1D facets. These statistics are listed for the surface(s) selected in the Surfaces list. If more than one surface is selected, the sum over all selected surfaces is displayed for each quantity. Note that if you want to check these statistics for a surface that was read from a case file, you will need to first display it.


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Chapter 27.

Graphics and Visualization

Graphics tools available in FLUENT allow you to process the information contained in your CFD solution and easily view the results. The following sections explain how to use these tools to examine your solution. (Note that the procedure for saving hardcopy files of graphics displays is described in Section 3.12.) • Section 27.1: Basic Graphics Generation • Section 27.2: Customizing the Graphics Display • Section 27.3: Controlling the Mouse Button Functions • Section 27.4: Modifying the View • Section 27.5: Composing a Scene • Section 27.6: Animating Graphics • Section 27.7: Creating Videos • Section 27.8: Histogram and XY Plots • Section 27.9: Turbomachinery Postprocessing • Section 27.10: Fast Fourier Transform (FFT) Postprocessing


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27.1

Basic Graphics Generation

In FLUENT you can generate graphics displays showing grids, contours, profiles, vectors, and pathlines. The following sections describe how to create these plots. (Generation of histogram and XY plots is discussed in Section 27.8.)

! If your model includes a discrete phase, you can also display the particle trajectories, as described in Section 21.13.1. • Section 27.1.1: Displaying the Grid • Section 27.1.2: Displaying Contours and Profiles • Section 27.1.3: Displaying Vectors • Section 27.1.4: Displaying Pathlines • Section 27.1.5: Displaying Results on a Sweep Surface

27.1.1

Displaying the Grid

During the problem setup or when you are examining your solution, you may want to look at the grid associated with certain surfaces. You can display the outline of all or part of the domain, as shown in Figure 27.1.1; draw the grid lines (edges), as shown in Figure 27.1.2; draw the solid surfaces (filled grids) for a 3D domain, as shown in Figure 27.1.3; and/or draw the nodes on the domain surfaces, as shown in Figure 27.1.4. See also Section 27.1.5 for information about displaying the grid on a surface that sweeps through the domain.

Steps for Generating Grid or Outline Plots You can draw the grid or outline for all or part of your domain using the Grid Display panel (Figure 27.1.5). Display −→Grid... The basic steps for generating a grid or outline plot are as follows: 1. Choose the surfaces for which you want to display the grid or outline in the Surfaces list. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces of that type will be selected automatically in the Surfaces list (or deselected, if they are all selected already).

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27.1 Basic Graphics Generation

Y Z

X

Grid Outline

Figure 27.1.1: Outline Display

Y Z X

Grid

Figure 27.1.2: Grid Edge Display


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Y X Z

Grid

Figure 27.1.3: Grid Face (Filled Grid) Display

Y X

Z

Node Display

Figure 27.1.4: Node Display

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Figure 27.1.5: The Grid Display Panel

Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). To choose all “outline” surfaces (i.e., surfaces on the outer boundary of the domain), click the Outline button below the Surface Types list. If all outline surfaces are already selected, this will deselect them. To choose all “interior” surfaces, click the Interior button. If all interior surfaces are already selected, this will deselect them. 2. Depending on what you want to draw, do one or more of the following: • To draw an outline of the selected surfaces (as in Figure 27.1.1), select Edges under Options and Outline under Edge Type. If you need more detail in the outline display of a complex geometry, see the description of the Feature option, below. • To draw the grid edges (as in Figure 27.1.2), select Edges under Options and All under Edge Type. • To generate a filled-grid display (as in Figure 27.1.3), select Faces under Options. • To draw the nodes on the selected surfaces (as in Figure 27.1.4), select Nodes under Options.


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3. Set any of the options described below. 4. Click the Display button to draw the specified grid or outline in the active graphics window. If you choose to display filled grids, and you want a smoothly shaded display, you should turn on lighting and select a lighting interpolation method other than Flat in the Display Options panel or the Lights panel. If you display nodes, and you want to change the symbol representing the nodes, you can change the Point Symbol in the Display Options panel. See Section 27.2.7 for details.

Grid and Outline Display Options The options mentioned in the procedure above include modifying the grid colors, adding the outline of important features to an outline display, drawing partition boundaries, and shrinking the faces and/or cells in the display. Modifying the Grid Colors FLUENT allows you to control the colors that are used to render the grids for each zone type or surface. This capability can help you to understand grid plots quickly and easily. To modify the colors, open the Grid Colors panel (Figure 27.1.6) by clicking on the Colors... button in the Grid Display panel.

Figure 27.1.6: The Grid Colors Panel (Note that you can set colors individually for the grids displayed on each surface, using the Scene Description panel.) By default, the Color By Type option is turned on, allowing you to assign colors based on zone type. To change the color used to draw the grid for a particular zone type, select

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the zone type in the Types list and then select the new color in the Colors list. You will see the effect of your change when you next display the grid. Note that the surface type in the Types list applies to all surface grids (i.e., grids that are drawn for surfaces created using the panels opened from the Surface menu) except zone surfaces. If you prefer to use the colors FLUENT assigns by zone ID, then you can display the grid using the Color By ID option. Adding Features to an Outline Display For closed 3D geometries such as cylinders, the standard outline display often will not show enough detail to accurately depict the shape. This is because for each boundary, only those edges on the “outside” of the geometry (i.e., those that are used by only one face on the boundary) are drawn. In Figure 27.1.7, which shows the outline display for a complicated duct geometry, only the inlet and outlet are visible.

Figure 27.1.7: Standard Outline of Complex Duct

You can capture additional features using the Feature option in the Grid Display panel. (See Figure 27.1.8.) Turn on Feature under Edge Type, and then set the Feature Angle. With the default Feature Angle of 20, if the difference between the normal directions of two adjacent faces is more than 20◦ , the edge between those faces will be drawn. Decreasing the Feature Angle will result in more edge lines (i.e., more detail) being added to the outline display. The appropriate angle for your geometry will depend on its curvature and complexity. You can modify the Feature Angle until you find the value that yields the best outline display.


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Figure 27.1.8: Feature Outline of Complex Duct

Drawing Partition Boundaries If you have partitioned your grid for parallel processing, you can add the display of partition boundaries to the grid display by turning on the Partitions option in the Grid Display panel. Shrinking Faces and Cells in the Display If you need to distinguish individual faces or cells in the display, you may want to enlarge the space between adjacent faces or cells by increasing the Shrink Factor in the Grid Display panel. The default value of zero produces a display in which the edges of adjacent faces or cells overlap. A value of 1 creates the opposite extreme: each face or cell is represented by a point and there is considerable space between each one. A small value such as 0.01 may be large enough to allow you to distinguish one face or cell from its neighbor. Displays with different Shrink Factor values are shown in Figures 27.1.9 and 27.1.10. Remember that you must click Display to see the effect of the change in Shrink Factor.

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Figure 27.1.9: Grid Display with Shrink Factor = 0

Figure 27.1.10: Grid Display with Shrink Factor = 0.01


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27.1.2

Displaying Contours and Profiles

FLUENT allows you to plot contour lines or profiles superimposed on the physical domain. Contour lines are lines of constant magnitude for a selected variable (isotherms, isobars, etc.). A profile plot draws these contours projected off the surface along a reference vector by an amount proportional to the value of the plotted variable at each point on the surface. Sample plots are shown in Figures 27.1.11 and 27.1.12. See also Section 27.1.5 for information about displaying contours or profiles on a surface that sweeps through the domain.

6.60e-02 5.80e-02 5.01e-02 4.21e-02 3.41e-02 2.61e-02 1.82e-02 1.02e-02 2.23e-03 -5.75e-03 -1.37e-02

Natural Convection in a Power Bus Configuration Contours of Static Pressure (pascal)

Figure 27.1.11: Contours of Static Pressure

Steps for Generating Contour and Profile Plots You can plot contours or profiles using the Contours panel (Figure 27.1.13). Display −→Contours... The basic steps for generating a contour or profile plot are as follows: 1. Select the variable or function to be contoured or profiled in the Contours Of dropdown list. First select the desired category in the upper list; you may then select a related quantity in the lower list. (See Chapter 29 for an explanation of the variables in the list.)

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1.45e-01 1.20e-01 9.61e-02 7.17e-02 4.74e-02 2.30e-02 -1.34e-03 -2.57e-02 -5.00e-02 -7.44e-02 -9.87e-02

Natural Convection in a Power Bus Configuration Profiles of Y-Velocity (m/s)

Figure 27.1.12: Profile Plot of y Velocity

2. Choose the surface or surfaces on which to draw the contours or profiles in the Surfaces list. For 2D cases, if no surface is selected, contouring or profiling is done on the entire domain. For 3D cases, you must always select at least one surface. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces of that type will be selected automatically in the Surfaces list (or deselected, if they are all selected already). Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 3. Specify the number of contours or profiles in the Levels field. The maximum number of levels allowed is 100. 4. If you are generating a profile plot, turn on the Draw Profiles option. In the resulting Profile Options panel (Figure 27.1.14) you will define the profiles as described below: (a) Set the “zero height” reference value for the profile (Reference Value) and the length scale factor for projection (Scale Factor). Any point on the profile with a value equal to the Reference Value will be plotted exactly on the defining surface. Values greater than the Reference Value will be projected ahead of the surface (in the direction of Projection Dir.) and scaled by Scale Factor),


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Figure 27.1.13: The Contours Panel

and values less than the Reference Value will be projected behind the surface and scaled. These parameters can be used to create fuller profiles when you need to display the variation in a variable which is small compared to the absolute value of the variable. Consider, for example, the display of temperature profiles when the temperature range in the domain is from 300 K to 310 K. The 10 K range in the temperature will be hard to detect when profiles are drawn using the default scaling (which will be based on the absolute magnitude of 310 K). To create a fuller profile, you can set the Reference Value to 300 and the profile Scaling Factor to 5 (for example) to magnify the display of the remaining 10 K range. In subsequent display of the profiles, the reference value of 300 will be effectively subtracted from the data before display so that the temperatures of 300 K will not be offset from the baselines. The profiles will then reflect only the variation of temperature from 300 K. (b) Set the direction in which profiles are projected (Projection Dir.). In 2D, for example, a contour plot of pressure on the entire domain can be projected in the z direction to form a carpet plot, or a contour plot of y velocity on a sequence of y-coordinate slice lines can be projected in the y direction to form a series of velocity profiles (as shown in Figure 27.1.12). (c) Click Apply and close the Profile Options panel.

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Figure 27.1.14: The Profile Options Panel

5. Set any of the options described below. 6. Click the Display button to draw the specified contours or profiles in the active graphics window. The resulting display will include the specified number of contours or profiles of the selected variable, with the magnitude on each one determined by equally incrementing between the values shown in the Min and Max fields.

Contour and Profile Plot Options The options mentioned in the procedure above include drawing color-filled contours/profiles (instead of the default line contours/profiles), specifying a range of values to be contoured or profiled, including portions of the grid in the contour or profile display, choosing node or cell values for display, and storing the contour or profile plot settings. Drawing Filled Contours or Profiles Color-filled contour or profile plots show a contour or profile display containing a continuous color display (see Figure 27.1.15), instead of just drawing lines representing specific values. (Note that a color-filled profile display is often referred to as a “carpet plot”.) To generate a filled contour or profile plot, turn on the Filled option in the Contours panel during step 5 above. To display smoothly shaded filled contours, you must turn on lighting and select a lighting interpolation method other than Flat in the Display Options panel or the Lights panel. Note that you will not get smooth shading of filled contours if the Clip to Range (see below) option is turned on. Smooth shading of filled profiles is not available.


27-13


1.38e+05 1.29e+05 1.20e+05 1.12e+05 1.03e+05 9.43e+04 8.56e+04 7.69e+04 6.82e+04 5.95e+04 X Z

5.09e+04 Y

Fluent Inc. Contours of Static Pressure (pascal) Thu Aug 24 1995

Figure 27.1.15: Filled Contours of Static Pressure

Specifying the Range of Magnitudes Displayed By default, the minimum and maximum values contoured or profiled are set based on the range of values in the entire domain. This means that the color scale will start at the smallest value in the domain (shown in the Min field) and end at the largest value (shown in the Max field). If you are plotting contours or profiles on a subset of the domain (i.e., on a surface), your plot may cover only the midrange of the color scale. For example, if blue corresponds to 0 and red corresponds to 10, and the values on your surface range only from 4 to 6, your plot will contain mostly green contours or profiles, since green is the color at the middle of the default color scale. If you want to focus in on a smaller range of values, so that blue corresponds to 4 and red to 6, you can manually reset the range to be displayed. (You can also use the minimum and maximum values on the selected surfaces—rather than in the entire domain—to determine the range, as described below.) Another reason to manually set the range is if you are interested only in certain values. For example, if you want to determine the region where pressure exceeds a certain value, you can increase the minimum value for display so that the lower pressure values are not displayed. To manually set the contour/profile range, turn off the Auto Range option in the Contours panel. The Min and Max fields will become editable, and you can enter the new range of values to be displayed. To show the default range at any time, click the Compute button and the Min and Max fields will be updated. If you are drawing filled contours or profiles (as described above) you can control whether

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or not values outside the prescribed Min/Max range are displayed. To leave areas in which the value is outside the specified range empty (i.e., draw no contours or profiles), turn on the Clip to Range option. This is the default setting. If you turn Clip to Range off, values below the Min value will be colored with the lowest color on the color scale, and values above the Max value will be colored with the highest color on the color scale. Figures 27.1.16 and 27.1.17 show the results of enabling/disabling the Clip to Range option. You can also choose to base the minimum and maximum values on the range of values on the selected surfaces, rather than in the entire domain. To do this, turn off the Global Range option in the Contours panel. The Min and Max values will be updated when you next click Compute or Display. Including the Grid in the Contour Plot For some problems, especially complex 3D geometries, you may want to include portions of the grid in your contour or profile plot as spatial reference points. For example, you may want to show the location of an inlet and an outlet along with the contours. This is accomplished by turning on the Draw Grid option in the Contours panel. The Grid Display panel will appear automatically when you turn on the Draw Grid option, and you can set the grid display parameters there. When you click Display in the Contours panel, the grid display, as defined in the Grid Display panel, will be included in the contour or profile plot. Choosing Node or Cell Values In FLUENT you can choose to display the computed cell-center values or values that have been interpolated to the nodes. By default, the Node Values option is turned on, and the interpolated values are displayed. For line contours or profiles, node values are always used. If you are displaying filled contours or profiles and you prefer to display the cell values, turn the Node Values option off. Filled contours/profiles of node values will show a smooth gradation of color, while filled contours/profiles of cell values may show sharp changes in color from one cell to the next. If you are plotting contours to show the effect of a porous medium or fan, to depict a shock wave, or to show any other discontinuities or jumps in the plotted variable, you should use cell values; if you use node values in such cases, the discontinuity will be smeared by the node averaging for graphics and will not be shown clearly in the plot. Storing Contour Plot Settings For frequently used combinations of contour variables and options, you can store the information needed to generate the contour plot by specifying a Setup number and setting up the desired information in the Contours panel. When you click on the Display button, the settings for Options, Contours Of, Min, Max, and Surfaces will be saved. You can


27-15


1.30e+05 1.27e+05 1.24e+05 1.21e+05 1.18e+05 1.15e+05 1.12e+05 1.09e+05 1.06e+05 1.03e+05 X Z

1.00e+05 Y


Figure 27.1.16: Filled Contours with Clip to Range On

1.30e+05 1.27e+05 1.24e+05 1.21e+05 1.18e+05 1.15e+05 1.12e+05 1.09e+05 1.06e+05 1.03e+05 X Z

1.00e+05 Y


Figure 27.1.17: Filled Contours with Clip to Range Off

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then change the Setup number to an unused value (i.e., an ID for which no information has been saved) and generate a different contour plot. To generate a plot using the saved setup information, change the Setup number back to the value for which you saved contour information and click Display. You can save up to 10 different setups.

! Note that the number of contour Levels, the surfaces selected for display in the Grid Display panel (when the Draw Grid option is activated), and the settings for profiles in the Profile Options panel (when the Draw Profiles option is activated) will not be saved in the Setup, nor will the Setups be saved in the case file.

27.1.3

Displaying Vectors

You can draw vectors in the entire domain, or on selected surfaces. By default, one vector is drawn at the center of each cell (or at the center of each facet of a data surface), with the length and color of the arrows representing the velocity magnitude (Figure 27.1.18). The spacing, size, and coloring of the arrows can be modified, along with several other vector plot settings. Velocity vectors are the default, but you can also plot vector quantities other than velocity. Note that cell-center values are always used for vector plots; you cannot plot node-averaged values. See also Section 27.1.5 for information about displaying vectors on a surface that sweeps through the domain.

1.45e-01 1.30e-01 1.16e-01 1.01e-01 8.69e-02 7.24e-02 5.79e-02 4.34e-02 2.90e-02 1.45e-02 0.00e+00

Natural Convection in a Power Bus Configuration Velocity Vectors Colored By Velocity Magnitude (m/s)

Figure 27.1.18: Velocity Vector Plot


27-17


Steps for Generating Vector Plots You can plot vectors using the Vectors panel (Figure 27.1.19). Display −→Vectors...

Figure 27.1.19: The Vectors Panel The basic steps for generating a vector plot are as follows: 1. In the Vectors Of drop-down list, select the vector quantity to be plotted. By default, only velocity and relative velocity are available, but you can create your own custom vectors as described below. 2. In the Surfaces list, choose the surface(s) on which you want to display vectors. If you want to display vectors on the entire domain, select none of the surfaces in the list. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces of that type will be selected automatically in the Surfaces list (or deselected, if they are all selected already).

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Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 3. Set any of the options described below. 4. Click the Display button to draw the vectors in the active graphics window.

Displaying Relative Velocity Vectors If you are solving your problem using one or more moving reference frames or moving meshes, you will have the option to display either the absolute vectors or the relative vectors. If you select Velocity (the default) in the Vectors Of list, the vectors will be drawn based on the absolute, stationary reference frame. If you select Relative Velocity, the vectors will be drawn based on the reference frame of the Reference Zone in the Reference Values panel. See Section 28.8.2 for details. (If you are modeling a single rotating reference frame, you need not specify the Reference Zone; the vectors will be drawn based on the rotating reference frame.)

Vector Plot Options The options mentioned in the procedure above include scaling the vector arrows, skipping the display of some vectors, displaying vectors in the plane of the data surface, displaying fixed-length or fixed-color vectors, displaying directional components of the vectors, specifying a range of values to be displayed, coloring the vectors by a different scalar field, including portions of the grid in the vector display, and changing the style of the arrows or the scale of the arrowheads. The most common options are set in the Vectors panel, and others are set in the Vector Options panel (Figure 27.1.20), which you can open by clicking on the Vector Options... button in the Vectors panel. Scaling the Vectors By default, vectors are scaled automatically so that the arrows overlap minimally when no vectors are skipped. (See below for instructions on thinning the vector display.) With the Auto Scale option, you can modify the Scale factor (which is set to 1 by default) to increase or decrease the vector scale from the default “auto scale”. The main advantage of autoscaling is that the vector display with a scale factor of 1 will always be appropriate, regardless of the size of the domain, giving you a better starting point for fine-tuning the vector scale.


27-19


Figure 27.1.20: The Vector Options Panel

If you turn off the Auto Scale option, the vectors will be drawn at their actual sizes scaled by the scale factor (Scale, which is set to 1 by default). The “actual” size of a vector is the magnitude of the vector variable (velocity, by default) at the point where it is drawn. A vector drawn at a point where the velocity magnitude is 100 m/s is drawn 100 m long, whether the domain is 0.1 m or 1000 m. You can modify the vector scale by changing the value of Scale in the Vectors panel until the size of the vectors (i.e., the actual size multiplied by Scale) is satisfactory. Skipping Vectors If your vector display is difficult to understand because there are too many arrows displayed, you can “thin out” the vectors by changing the Skip value in the Vectors panel. By default, Skip is set to 0, indicating that a vector will be drawn for each cell in the domain or for each face on the selected surface (e.g., n vectors). If you increase Skip to 1, every other vector will be displayed, yielding n/2 vectors. If you increase Skip to 2, every third vector will be displayed, yielding n/3 vectors, and so on. The order of faces on the selected surface (or cells in the domain) will determine which vectors are skipped or drawn; thus adaption and reordering will change the appearance of the vector display when a non-zero Skip value is used. Drawing Vectors in the Plane of the Surface For some problems, you may be interested in visualizing velocity (or other vector) components that are normal to the flow. These “secondary flow” components are usually much smaller than the components in the flow direction and are difficult to see when the flow direction components are also visible. To easily view the normal flow components, you can turn on the In Plane option in the Vector Options panel. When this option is on, FLUENT will display only the vector components in the plane of the surface selected for display. If the selected surface is a cross-section of the flow domain, you will be displaying the components normal to the flow. Figure 27.1.21 shows velocity vectors generated using

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the In Plane option. (Note that these vectors have been translated outside the domain, as described in Section 27.5.3, so that they can be seen more easily.)

1.50e+00 1.35e+00 1.20e+00 1.05e+00 8.97e-01 7.48e-01 5.98e-01 4.49e-01 2.99e-01 1.50e-01

Z

X Y

5.23e-04

Velocity Vectors in Plane Colored By Velocity Magnitude (m/s)

Figure 27.1.21: Velocity Vectors Generated Using the In Plane Option

Displaying Fixed-Length Vectors By default, the length of a vector is proportional to its velocity magnitude. If you want all of the vectors to be displayed with the same length, you can turn on the Fixed Length option in the Vector Options panel. To modify the vector length, adjust the value of the Scale factor in the Vectors panel. Displaying Vector Components All Cartesian components of the vectors are drawn by default, so that the arrow points along the resultant vector in physical space. However, sometimes one of the components, say, the x component, is relatively large. In such cases, you may want to suppress the x component and scale up the vectors, in order to visualize the smaller y and z components. To suppress one or more of the vector components, turn off the appropriate button(s) (X, Y, or Z Component) in the Vector Options panel. Specifying the Range of Magnitudes Displayed By default, the minimum and maximum vectors included in the vector display are set based on the range of vector-variable (velocity, by default) magnitudes in the entire domain. If you want to focus in on a smaller range of values, you can restrict the range


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to be displayed. The color scale for the vector display will change to reflect the new range of values. (You can also use the minimum and maximum values on the selected surfaces—rather than on the entire domain—to determine the range, or change the scalar field by which the vectors are colored from velocity magnitude to any other scalar, as described below.) To manually set the range of velocity magnitudes (or the range of whatever scalar field is selected in the Color By drop-down list), turn off the Auto Range option in the Vectors panel. The Min and Max fields will become editable, and you can enter the new range of values to be displayed. For example, if you want to display velocity vectors only in regions where the velocity magnitude exceeds 150 m/s but is less than 300 m/s, you will change the value of Min to 150 and the value of Max to 300. Similarly, if you are coloring the vectors by static pressure, you can choose to display velocity vectors only in regions where the pressure is within a specified range. To show the default range at any time, click the Compute button and the Min and Max fields will be updated. When you restrict the range of vectors displayed, you can also control whether or not values outside the prescribed Min/Max range are displayed. To leave areas in which the value is outside the specified range empty (i.e., draw no vectors), turn on the Clip to Range option. This is the default setting. If you turn Clip to Range off, values below the Min value will be colored with the lowest color on the color scale, and values above the Max value will be colored with the highest color on the color scale. This feature is the same as the one available for displaying filled contours (see Figures 27.1.16 and 27.1.17). You can also choose to base the minimum and maximum values on the range of values on the selected surfaces, rather than the entire domain. To do this, turn off the Global Range option in the Vectors panel. The Min and Max values will be updated when you next click Compute or Display. Changing the Scalar Field Used for Coloring the Vectors If you want to color the vectors by a scalar field other than velocity magnitude (the default), you can select a different variable or function in the Color By drop-down list. Select the desired category in the upper list, and then choose one of the related quantities from the lower list. If you choose static pressure, for example, the length of the vectors will still correspond to the velocity magnitude, but the color of the vectors will correspond to the value of pressure at each point where a vector is drawn. Displaying Vectors Using a Single Color If you want all of the vectors to be the same color, you can select the color to be used in the Color drop-down list in the Vector Options panel. If no color is selected (i.e., if you choose the empty space at the top of the drop-down list—the default selection), the vector color will be determined by the Color By field specified in the Vectors panel. Single-color vectors are useful in displays that overlay contours and vectors.

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Including the Grid in the Vector Plot For some problems, especially complex 3D geometries, you may want to include portions of the grid in your vector plot as spatial reference points. For example, you may want to show the location of an inlet and an outlet along with the vectors. This is accomplished by turning on the Draw Grid option in the Vectors panel. The Grid Display panel will appear automatically when you turn on the Draw Grid option, and you can set the grid display parameters there. When you click Display in the Vectors panel, the grid display, as defined in the Grid Display panel, will be included in the vector plot. Changing the Arrow Characteristics There are five different styles available for drawing the vector arrows. Choose cone, filledarrow, arrow, harpoon, or headless in the Style drop-down list in the Vectors panel. The default arrow style is harpoon. If you choose a vector arrow style that includes heads, you can control the size of the arrowhead by modifying the Scale Head value in the Vector Options panel.

Creating and Managing Custom Vectors In addition to the velocity vector quantity provided by FLUENT, you can also define your own custom vectors to be plotted. This capability is available with the Custom Vectors panel. Any custom vectors that you define will be saved in the case file the next time that you save it. You can also save your custom vectors to a separate file, so that they can be used with a different case file. Creating Custom Vectors To create your own custom vector, you will use the Custom Vectors panel (Figure 27.1.22). This panel allows you to define custom vectors based on existing quantities. Any vectors that you define will be added to the Vectors Of list in the Vectors panel. To open the Custom Vectors panel, click the Custom Vectors... button in the Vectors panel. The steps for creating a custom vector are as follows: 1. Specify the name of the custom vector in the Vector Name field.

!

Be sure that you do not specify a name that is already used for a standard vector (e.g., velocity or relative-velocity). 2. Select the variable or function for the x component of the vector in the X Component drop-down list. First select the desired category in the upper list; you may then


27-23


Figure 27.1.22: The Custom Vectors Panel

select a related quantity in the lower list. (See Chapter 29 for an explanation of the variables in the list.) 3. Repeat the step above to select the variable or function for the y component (and, in 3D, the z component) of the custom vector. 4. Click the Define button. Manipulating, Saving, and Loading Custom Vectors Once you have defined your vectors, you can manipulate them using the Vector Definitions panel (Figure 27.1.23). You can display a vector definition to be sure that it is correct, delete the vector if you decide that it is incorrect and needs to be redefined, or give the vector a new name. You can also save custom vectors to a file or read them from a file. The custom vector file allows you to transfer custom vectors between case files. To open the Vector Definitions panel, click the Manage... button in the Custom Vectors panel. The following actions can be performed in the Vector Definitions panel: • To check the definition of a vector, select it in the Vectors list. Its definition will be displayed in the X Component, Y Component, and Z Component fields at the top of the panel. This display is for informational purposes only; you cannot edit it. If you want to change a vector definition, you must delete the vector and define it again in the Custom Vectors panel. • To delete a vector, select it in the Vectors list and click the Delete button. • To rename a vector, select it in the Vectors list, enter a new name in the Name field, and click the Rename button.

!

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Be sure that you do not specify a name that is already used for a standard vector (e.g., velocity or relative-velocity).



Figure 27.1.23: The Vector Definitions Panel

• To save all the vectors in the Vectors list to a file, click the Save... button, and specify the file name in the resulting Select File dialog box (see Section 2.1.2). • To read custom vectors from a file that you saved as described above, click the Load... button and specify the file name in the resulting Select File dialog box. (Custom vectors are valid Scheme functions, and can also be loaded with the File/Read/Scheme... menu item, as described in Section 3.15.)

27.1.4

Displaying Pathlines

Pathlines are used to visualize the flow of massless particles in the problem domain. The particles are released from one or more surfaces that you have created with the tools in the Surface menu (see Chapter 26). A line or rake surface (see Section 26.5) is most commonly used. Figure 27.1.24 shows a sample plot of pathlines. Note that the display of discrete-phase particle trajectories is discussed in Section 21.13.1.

Steps for Generating Pathlines You can plot pathlines using the Path Lines panel (Figure 27.1.25). Display −→Path Lines... The basic steps for generating pathlines are as follows:


27-25


3.00e+01 2.70e+01 2.40e+01 2.10e+01 1.80e+01 1.50e+01 1.20e+01 9.00e+00 6.00e+00 3.00e+00

Y X Z

0.00e+00

Fluent Inc. Path Lines Colored by Particle Id Tue Aug 29 1995

Figure 27.1.24: Pathline Plot

1. Select the surface(s) from which to release the particles in the Release From Surfaces list. 2. Set the step size and the maximum number of steps. The Step Size sets the length interval used for computing the next position of a particle. (Note that particle positions are always computed when particles enter/leave a cell; even if you specify a very large step size, the particle positions at the entry/exit of each cell will still be computed and displayed.) The value of Steps sets the maximum number of steps a particle can advance. A particle will stop when it has traveled this number of steps or when it leaves the domain. One simple rule of thumb to follow when setting these two parameters is that if you want the particles to advance through a domain of length L, the Step Size times the number of Steps should be approximately equal to L. 3. Set any of the options described below. 4. Click the Display button to draw the pathlines, or click the Pulse button to animate the particle positions. The Pulse button will become the Stop ! button during the animation, and you must click Stop ! to stop the pulsing.

Options for Pathline Plots The options mentioned in the procedure above include the following. You can include the grid in the pathline display, control the style of the pathlines (including the twisting

27-26



Figure 27.1.25: The Path Lines Panel

of ribbon-style pathlines), and color them by different scalar fields and control the color scale. You can also “thin” the pathline display, trace the particle positions in reverse, and draw “oil-flow” pathlines. If you are “pulsing” the pathlines, you can control the pulse mode. In addition to the regular pathline display, you can also generate an XY plot of a specified quantity along the pathline trajectories. Finally, you can choose node or cell values for display (or plotting). Including the Grid in the Pathline Display For some problems, especially complex 3D geometries, you may want to include portions of the grid in your pathline display as spatial reference points. For example, you may want to show the location of an inlet and an outlet along with the pathlines (as in Figure 27.1.24). This is accomplished by turning on the Draw Grid option in the Path Lines panel. The Grid Display panel will appear automatically when you turn on the Draw Grid option, and you can set the grid display parameters there. When you click Display in the Path Lines panel, the grid display, as defined in the Grid Display panel, will be included in the plot of pathlines. Controlling the Pathline Style Pathlines can be displayed as lines (with or without arrows), ribbons, cylinders (coarse, medium, or fine), triangles, spheres, or a set of points. You can choose line, line-arrows,


27-27


point, sphere, ribbon, triangle, coarse-cylinder, medium-cylinder, or fine-cylinder in the Style drop-down list in the Path Lines panel. (Note that pulsing can be done only on point, sphere, or line styles.) Once you have selected the pathline style, click the Style Attributes... button to set the pathline thickness and other parameters related to the selected Style: • If you are using the line or line-arrows style, set the Line Width in the Path Style Attributes panel that appears when you click the Style Attributes... button. For line-arrows you will also set the Arrow Scale, which controls the size of the arrow heads. • If you are using the point style, you will set the Marker Width in the Path Style Attributes panel. The thickness of the pathline will be the thickness of the marker. • If you are using the sphere style, you will set the Diameter and the Detail in the Path Style Attributes panel. The best diameter to use will depend on the dimensions of the domain, the view, and the particle density. However, an adequate starting point would be a diameter on the order of 1/4 of the average cell size or 1/4 step size. Units for the Diameter field correspond to the mesh dimensional units. The level of detail applied to the graphical rendering of the spheres can be controlled using the Detail field in the Path Style Attributes panel. The level of detail uses integer values ranging from 4 to 50. Note that the performance of the graphical rendering will be better when using a small level of detail, i.e., very coarse spheres, such as 6 or 8. The rendering performance significantly decreases with higher levels of detail. You should gradually increase the detail to determine the best-case scenario between performance and quality. Also note that to take full advantage of spherical rendering, lighting should be turned on in the view. The Gouraud setting provides much smoother looking spheres than the Flat setting and better performance than the Phong setting. For more information on lighting, see Section 27.2.6. • If you are using the triangle or any of the cylinder styles, you will set the Width in the Path Style Attributes panel. For triangles, the specified value will be half the width of the triangle’s base, and for cylinders, the value will be the cylinder’s radius. • If you are using the ribbon style, clicking on the Style Attributes... button will open the Ribbon Attributes panel, in which you can set the ribbon’s Width. You can also specify parameters for twisting the ribbon pathlines. In the Twist By dropdown list, you can select a scalar field on which the pathline twisting is based (e.g., helicity). Select the desired category in the upper list and then select a related quantity in the lower list. Note that the twisting may not be displayed smoothly

27-28



because the scalar field by which you are twisting the pathline is calculated at cell centers only (and not interpolated to a particle’s position). The Twist Scale sets the amount of twist for the selected scalar field. To magnify the twist for a field with very little change, increase this factor; to display less twist for a field with dramatic changes, decrease this factor. (When you click Compute, the Max field will be updated to show the range of the Twist By scalar field.) Controlling Pathline Colors By default, the pathlines are colored by the particle ID number. That is, each particle’s path will be a different color. You can also choose the color based on the surface from where the pathlines were released from using the surface ID as the particle variable. You can choose to color the pathlines by any of the scalar fields in the Color By drop-down list. (Select the desired category in the upper list and then select a related quantity in the lower list.) If you color the pathlines by velocity magnitude, for example, each particle’s path will be colored depending on the speed of the particle at each point in the path. The range of values of the selected scalar field will, by default, be the upper and lower limits of that field in the entire domain. The color scale will map to these values accordingly. If you prefer to restrict the range of the scalar field, turn off the Auto Range option (under Options) and set the Min and Max values manually beneath the Color By list. If you color the pathlines by velocity, and you limit the range to values between 30 and 60 m/s, for example, the “lowest” color will be used when the particle speed falls below 30 m/s and the “highest” color will be used when the particle speed exceeds 60 m/s. To show the default range at any time, click the Compute button and the Min and Max fields will be updated. “Thinning” Pathlines If your pathline plot is difficult to understand because there are too many paths displayed, you can “thin out” the pathlines by changing the Skip value in the Path Lines panel. By default, Skip is set to 0, indicating that a pathline will be drawn from each face on the selected surface (e.g., n pathlines). If you increase Skip to 1, every other pathline will be displayed, yielding n/2 pathlines. If you increase Skip to 2, every third pathline will be displayed, yielding n/3, and so on. The order of faces on the selected surface will determine which pathlines are skipped or drawn; thus adaption and reordering will change the appearance of the pathline display when a non-zero Skip value is used. Reversing the Pathlines If you are interested in determining the source of a particle for which you know the final destination (e.g., a particle that leaves the domain through an exit boundary), you can reverse the pathlines and follow them from their destination back to their source. To do this, turn on the Reverse option in the Path Lines panel. All other inputs for defining the pathlines will be exactly the same as for forward pathlines; the only difference is that


27-29


the surface(s) selected in the Release From Surfaces list will be the final destination of the particles instead of their source. Plotting Oil-Flow Pathlines If you want to display “oil-flow” pathlines (i.e., pathlines that are constrained to lie on a particular boundary), turn on the Oil Flow option in the Path Lines panel. You will then need to select a single boundary zone in the On Zone list. The selected zone is the boundary on which the oil-flow pathlines will lie. Controlling the Pulse Mode If you are going to use the Pulse button in the Path Lines panel to animate the pathlines, you can choose one of two pulse modes for the release of particles that follow the pathlines. To release a single wave of particles, select the Single option under Pulse Mode. To release particles continuously from the initial positions, select the Continuous option. Generating an XY Plot Along Pathline Trajectories If you want to generate an XY plot along the trajectories of the pathlines you have defined, turn on the XY Plot option in the Path Lines panel. The Color By drop-down list will be replaced by Y Axis Function and X Axis Function lists. Select the variable to be plotted on the y axis in the Y Axis Function list, and specify whether you want to plot this quantity as a function of the Time elapsed along the trajectory, or the Path Length along the trajectory by selecting the appropriate item in the X Axis Function drop-down list. Specify the Step Size, number of Steps, and other parameters as usual for a standard pathline display. Then click Plot to display the XY plot. Once you have generated an XY plot, you may want to save the plot data to a file. You can read this file into FLUENT at a later time and plot it alone using the File XY Plot panel, as described in Section 27.8.3, or add it to a plot of solution data, as described in Section 27.8.2. To save the plot data to a file, turn on the Write to File option in the Path Lines panel. The Plot button will change to the Write... button. Clicking on the Write... button will open the Select File dialog box, in which you can specify a name and save a file containing the plot data. The format of this file is described in Section 27.8.5. Choosing Node or Cell Values In FLUENT you can determine the scalar field value at a particle location using the computed cell-center values or values that have been interpolated to the nodes. By default, the Node Values option is turned on, and the interpolated values are used. If you prefer to use the cell values, turn the Node Values option off.

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If you are plotting pathlines to show the effect of a porous medium or fan, to depict a shock wave, or to show any other discontinuities or jumps in the plotted variable, you should use cell values; if you use node values in such cases, the discontinuity will be smeared by the node averaging for graphics and will not be shown clearly in the plot.

27.1.5

Displaying Results on a Sweep Surface

Sweep surfaces can be used when you want to examine the grid, contours, or vectors on various sections of the domain without explicitly creating the corresponding surfaces. For example, if you want to display solution results for a 3D combustion chamber, instead of creating numerous surfaces at different cross-sections of the domain, you can use a sweep surface to view the variation of the flow and temperature throughout the chamber.

Steps for Generating a Plot Using a Sweep Surface You can plot grids, contours, or vectors on a sweep surface using the Sweep Surface panel (Figure 27.1.26). Display −→Sweep Surface...

Figure 27.1.26: The Sweep Surface Panel The basic steps for generating a grid, contour, or vector plot using a sweep surface are as follows: 1. Under Sweep Axis, specify the (X, Y, Z) vector representing the axis along which the surface should be swept.


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2. Click Compute to update the Min Value and Max Value to reflect the extents of the domain along the specified axis. 3. Under Display Type, specify the type of display you want to see: Grid, Contours, or Vectors. The first time that you select Contours or Vectors, FLUENT will open the Contours panel or the Vectors panel so you can modify the settings for the display. To make subsequent modifications to the display settings, click the Properties... button to open the Contours or Vectors panel. 4. Move the slider under Value (which indicates the value of x, y, or z) to move the sweep surface through the domain along the specified Sweep Axis. FLUENT will update the grid, contour, or vector display when you release the slider. You can also enter a position in the Value field and press the key to update the display. 5. If you want to save the currently-displayed sweep for a different type of plot (e.g., a pathlines plot with displays on other surfaces, click Create... to (Figure 27.1.27). Enter the Surface Name and click

surface so that you can use it or an XY plot) or combine it open the Create Surface panel OK.

Figure 27.1.27: The Create Surface Panel The surface that is created is an isosurface based on the grid coordinates; the contour or vector settings are not stored in the surface. You can also animate the sweep-surface display, as described below, rather than moving the slide bar yourself.

Animating a Sweep-Surface Display The steps for animating a sweep-surface display are as follows: 1. Specify the Sweep Axis and Display Type as described above. 2. Under Animation, enter the Initial Value and Final Value for the animation. These values correspond to the minimum and maximum values along the Sweep Axis for which you want to animate the display.

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27.2 Customizing the Graphics Display

3. Specify the number of Frames you want to see in the animation. 4. Click Animate.

27.2

Customizing the Graphics Display

There are a number of ways in which you can alter the graphical display once you have generated the basic elements in it (contours, grids, etc.). For example, you can overlay multiple graphics, add descriptive text or lighting to the plot, and modify the captions. These and other customizations are described in this section. • Section 27.2.1: Overlay of Graphics • Section 27.2.2: Opening Multiple Graphics Windows • Section 27.2.3: Controlling Captions • Section 27.2.4: Adding Text to the Graphics Window • Section 27.2.5: Changing the Colormap • Section 27.2.6: Adding Lights • Section 27.2.7: Modifying the Rendering Options

27.2.1

Overlay of Graphics

Normally, you can see only one picture at a time in the graphics window; i.e., as one plot is generated, the previous plot is erased. Sometimes, however, you may want to see two plots overlaid. For example, you may want to plot vectors and pressure contours on the same plot (see Figure 27.2.1). You can do this by turning on the Overlays option (and clicking Apply) in the Scene Description panel. Display −→Scene... Once overlaying is enabled, subsequent graphics that you generate will be displayed on top of the existing display in the active graphics window. To generate a plot without overlays, you must turn off the Overlays option in the Scene Description panel (and remember to click Apply). When you are overlaying multiple graphics, the captions and color scale that will appear in the latest display are those that correspond to the most recently drawn graphic. Note that when overlaying is enabled, it will apply to all graphics windows, including those that are not yet open. Turning overlays on and off does so for all graphics windows, not just for the active window. That is, if you enable overlays, open a new graphics window (as described in Section 27.2.2), and then generate two or more graphics in that window, they will be overlaid.


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1.27e+00 1.15e+00 1.04e+00 9.27e-01 8.13e-01 6.99e-01 5.86e-01 4.72e-01 3.58e-01 2.45e-01 1.31e-01

Fluent Inc. Velocity Vectors and Pressure Contours Tue Aug 29 1995

Figure 27.2.1: Overlay of Velocity Vectors and Pressure Contours

27.2.2

Opening Multiple Graphics Windows

During your FLUENT session, you can open up to 12 graphics windows at one time. The windows are numbered 0 through 11 and the ID number for each window will appear at the top of the frame that surrounds it. The first time you display graphics, window 0 will open automatically. To open an additional window, you can use the Display Options panel (Figure 27.2.2). Display −→Options... Use the up arrow to increment the window ID in the Active Window field under Graphics Window and then click the Open button. To close an open window, increase or decrease the Active Window value to the ID of the window to be closed, and then click the Close button that appears next to the Active Window field. (The Open button will change to the Close button if the Active Window is open.)

Setting the Active Window When you have more than one graphics window open, you must identify the active window so that FLUENT will know which one to draw the plot in. There are two ways to set the active window: you can simply click any mouse button in the desired graphics window, or you can specify the ID for the desired graphics window in the Active Window field (in the Display Options panel) and click the Set button. Regardless of the method

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Figure 27.2.2: The Display Options Panel

used, this window will remain active until you set a new active window.

27.2.3

Controlling Captions

FLUENT graphics include, by default, a caption block that consists of fields of text describing the contents of the graphic, the FLUENT product identification, an axis triad indicating the orientation of the displayed object, and a color key defining the correspondence between each color and the magnitude of the plotted variable. You can turn off the display of the captions and color scale, and/or the axis triad, if you want. You can also edit the captions directly in the graphics window.

Enabling/Disabling the Captions and Color Scale You can disable the display of the captions and the color scale by turning off the Captions Visible option under Captions in the Display Options panel (Figure 27.2.2). Display −→Options... Note that you can use the text interface to enable/disable the captions and color scale individually, and to change the size and position of the captions and color scale. display −→ set −→ windows −→ text −→ display −→ set −→ windows −→ scale −→


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Editing the Captions When captions are displayed in the graphics window, you may choose to modify, delete, or add to the text that appears in the caption box. To do so, click the left mouse button in the desired location. A cursor will appear, and you can then type new text or delete the text that was originally there (using the backspace or delete key). Note that changes to existing text in the caption block will be removed when you draw new graphics in the window (unless you are overlaying multiple graphics in the same window), but text that you add on a previously empty line in the caption block will not be removed until the default caption text makes use of that line.

Adding a Title to the Caption You can define a title for your problem using the title text command: display −→ set −→title The title you define will appear on the top line of the caption, at the far left, in all subsequent plots. It will also be saved in the case file.

! You will need to enclose your title in quotation marks (e.g., "my title"). Enabling/Disabling the Axes You can disable the display of the axis triad by turning off the Axes Visible option under Captions in the Display Options panel (Figure 27.2.2). Display −→Options...

27.2.4

Adding Text to the Graphics Window

There are two ways to add text annotations with optional attachment lines to the graphics windows. You can either use the mouse-annotate function for one of the mouse buttons, or use the Annotate panel. Both of these methods are described in this section. Figure 27.2.3 shows an example of a graphics display with annotated text in it.

Adding Text Using the Annotate Panel Adding text to the graphics window using the Annotate panel (Figure 27.2.4) allows you to control the font and color of the text. Display −→Annotate... The steps for adding text are as follows: 1. Under Font Specification, select the font type in the Name drop-down list, the font weight (Medium or Bold) in the Weight drop-down list, the size (in points) in the

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3.00e+01 2.70e+01 2.40e+01 2.10e+01 1.80e+01 1.50e+01 1.20e+01 9.00e+00 6.00e+00 3.00e+00

Y X Z

0.00e+00

Fluent Inc. Path Lines Colored by Particle Id Tue Aug 29 1995

Figure 27.2.3: Graphics Window with Text Annotation

Figure 27.2.4: The Annotate Panel


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Size drop-down list, the color in the Color drop-down list, and the slant (Regular or Italic) in the Slant drop-down list. 2. Enter the text to be added in the Annotation Text field. 3. Click Add. You will be asked to pick the location in the graphics window where you want to place the text, using the mouse-probe button. (By default, the mouseprobe button is the right button, but you can change this using the Mouse Buttons panel, as described in Section 27.3.) If you click the mouse button once in the desired location, the text will be placed at that point. Dragging the mouse with the mouse-probe button depressed will draw an attachment line from the point where the mouse was first clicked to the point where it was released. The annotation text will be placed at the point where the mouse button was released.

Adding Text Using the mouse-annotate Function To add text annotations to the graphics window using the mouse-annotate function, you must first set the function of one of the mouse buttons to be mouse-annotate in the Mouse Buttons panel. (See Section 27.3 for details about modifying the mouse button functions.) Then, click the mouse-annotate button in the desired location in the graphics window. A cursor will appear and you can type the text directly in the graphics window. Dragging the mouse with the mouse-annotate button depressed will draw an attachment line from the point where the mouse was first clicked to the point where it was released. The cursor will then appear at the point where the mouse button was released. You can use the Annotate panel to edit or delete text added using the mouse, as described below.

Editing Existing Annotation Text Once you have added text to the graphics display, using either the Annotate panel or the mouse-annotate function, you may change the font characteristics of one or more text items, or delete individual text items. To modify or delete existing text, follow these steps: 1. Select the appropriate item in the Names list in the Annotate panel (Figure 27.2.4). When you select a name, the associated text will be displayed in the Annotation Text field, and the Add button will become the Edit button. 2. Modify the Font Specification entries as desired, and click the Edit button to modify the text, or simply click the Delete Text button below the Names list to delete the selected text.

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Note that if you want to make changes to all current annotation text, you can select all of the Names instead of just one in step 1. You can move the text in the same way that you move other geometric objects in the display, using the Scene Description panel and the Transformations panel. See Section 27.5.3 for details.

Clearing Annotation Text Annotation text is associated with the active graphics window and is removed only when the annotations are explicitly cleared. To remove the annotations from the graphics window, you must click the Clear button in the Annotate panel (even if you use the mouse-annotate function to add the text). If you draw new graphics in the window without clearing the annotations, they will remain visible in the new display.

27.2.5

Changing the Colormap

The default colormap used by FLUENT to display graphical data (e.g., vectors) ranges from blue (minimum value) to red (maximum value). Additional predefined colormaps are available, and you can also create custom colormaps. To make any changes to the colormap, you will use the Colormap panel (Figure 27.2.5). Display −→Colormaps...

Figure 27.2.5: The Colormap Panel (When you plot contours, you can temporarily modify the number of colors in the colormap by changing the number of contour levels in the Contours panel; you will only need to use the Colormap panel if you wish to change other characteristics of the colormap.)

! Note that if you are using a gray-scale colormap and you wish to save a gray-scale hardcopy, you should actually save a color hardcopy. When you save a gray-scale hardcopy,


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FLUENT uses an internal gray scale, not the gray scale specified by the colormap. If you save a color hardcopy, the colormap you selected (i.e., your gray scale) will be used.

Predefined Colormaps The following colormaps are automatically available in FLUENT: bgr: Blue represents the minimum value, green the middle, and red the maximum value. Colors in between are interpolated from blue to green, and from green to red. (This is the default colormap.) bgrb: Blue represents the minimum and maximum values, and green and red are values 1/3 and 2/3 of the maximum value, respectively. Colors in between are interpolated from blue to green, from green to red, and from red to blue. blue: The minimum value is represented by blue-black, and the maximum value by pure blue. cyan-yellow: Cyan represents the minimum value and yellow represents the maximum value. fea: Blue represents the minimum value and red represents the maximum value. The colors in between are those used in third-party finite element analysis packages. gray: Black is used for the minimum value and white for the maximum value. green: The minimum value is represented by green-black, and the maximum value by pure green. purple-magenta: Purple represents the minimum value and magenta represents the maximum value. red: The minimum value is represented by red-black, and the maximum value by pure red. rgb: Red represents the minimum value, green the middle, and blue the maximum value. Colors in between are interpolated from red to green, and from green to blue. The number of colors interpolated between the colors in the scale name (e.g., between purple and magenta) will depend on the size of the colormap.

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Selecting a Colormap The procedure for selecting a new colormap to be used in graphics displays is as follows: 1. In the Colormap panel (Figure 27.2.5), select the desired colormap in the Currently Defined drop-down list. This list will contain all of the colormaps predefined by FLUENT as well as any custom colormaps that you have created as described below. 2. Set any of the options described below. 3. Click Apply to update the current graphics display with the new colormap. All future displays will use the newly selected colormap and options. Specifying the Colormap Size and Scale Once you have selected the desired colormap from the Currently Defined list, you may modify the Colormap Size. This value is the number of distinct colors in the color scale. You can also choose to use a logarithmic scale instead of a decimal scale by turning on the Log Scale option. With a log scale, the color used in the graphics display will represent the log of the value at that location in the domain. The values represented by the colors will, therefore, increase exponentially. Changing the Number Format You can change the format of the labels that define the color divisions at the left of the graphics window using the controls under the Number Format heading in the Colormap panel. • To display the real value with an integral and fractional part (e.g., 1.0000), select float in the Type drop-down list. You can set the number of digits in the fractional part by changing the value of Precision. • To display the real value with a mantissa and exponent (e.g., 1.0e-02), select exponential in the Type drop-down list. You can define the number of digits in the fractional part of the mantissa in the Precision field. • To display the real value with either float or exponential form, depending on the size of the number and the defined Precision, choose general in the Type drop-down list.


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Creating a Customized Colormap You can create your own colormap by manipulating the “anchor colors” and the colormap size. A color scale is created by linear interpolation between the anchor colors. The color, number, and position of the anchor colors will therefore control the description of the colormap. By increasing the colormap size, you can increase the total number of colors and obtain a color scale that changes more gradually. The procedure you will follow is listed below: 1. In the Colormap panel, click the Edit... button to open the Colormap Editor panel (Figure 27.2.6).

Figure 27.2.6: The Colormap Editor Panel

2. In the Colormap Editor panel, select a color scale in the Currently Defined list as your starting point. The colors in the scale will be displayed at the top of the panel. A white bar below a color is an “anchor point” indicating that this color is an “anchor color”. 3. If you want to add more colors to the color scale, increase the Colormap Size; to use fewer colors, decrease this value. When you use the counter arrows (or type in

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a value and press ), the color scale display at the top of the panel will be updated immediately.

!

The total number of colors must not be less than the number of anchor points. 4. To obtain the desired color scale interpolation, manipulate the anchor colors as needed: • To add an anchor point, click any mouse button on the black space directly below the desired anchor color (or click on the color itself). A white bar will appear below the color to identify it as an anchor color, and the color will automatically be selected for color-definition modification. • To remove an anchor point, click on the white bar below the anchor color. The white bar will disappear and the color scale will be updated to reflect the new interpolation. • To select a current anchor color in order to modify its color definition, click on the color itself at the top of the panel. • To modify the color of the selected anchor color, you can change either the red/green/blue components (choose RGB, the default) or the hue/saturation/value components (choose HSV). HSV is recommended if you plan to record the graphics display on video, as it allows you to create a more subtle gradation of color and reduce the tendency of bright colors to “bleed”. Move the Red, Green, and Blue or Hue, Sat, and Value sliders to obtain the desired color. The color scale at the top of the panel will be updated automatically to show the effect of your change.

!

It is a good idea to note the original value of a color component before moving the slider so that you will be able to return to it if you change your mind. (See Section 2.1.3 for instructions on using a scale slider.) If you make a mistake while modifying the color scale, you can start over by selecting the starting-point colormap in the Currently Defined list. 5. If you want to change the default name of the new colormap, enter the new name in the Name field. By default, custom color maps are called cmap-0, cmap-1, etc. 6. Click OK to save the new colormap. The colormap name will now appear in the Currently Defined list in the Colormap panel and can be selected for use in the graphics display. Custom colormap definitions will be saved in the case file.

27.2.6

Adding Lights

In FLUENT you can add lights with a specified color and direction to your display. These lights can enhance the appearance of the display when it contains 3D geometries. By


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default one light is defined. You can turn on the effect of the existing light(s) using the Display Options panel or the Lights panel, and you can add new lights using the Lights panel.

Turning on Lighting Effects with the Display Options Panel To turn on the effect of lighting, you can use the Display Options panel. Display −→Options... If you turn on the Lights On option under Lighting Attributes and click the Apply button, you will see the lighting effects in the active graphics window. To turn off the lighting effects, simply turn off the Lights On option and click Apply. You can also choose the method to be used in lighting interpolation; select Flat, Gouraud, or Phong in the Lighting drop-down list. (Flat is the most basic method: there is no interpolation within the individual polygonal facets. Gouraud and Phong have smoother gradations of color because they interpolate on each facet.)

Turning on Lighting Effects with the Lights Panel You can also turn on lighting effects using the Lights panel (Figure 27.2.7). Display −→Lights... For constant lighting effects in the direction of the view, turn on the Headlight On option in the Lights panel. This option has the effect of a light source directly in front of the model, no matter what orientation the model is viewed in. To disable this feature, turn off the Headlight On option in the Lights panel. In the Lighting Method drop-down list, choose Flat, Gouraud, or Phong to enable the appropriate lighting method. (These methods are described above.) To disable lighting, select Off in the list. To see the lighting effects in the active graphics window, click the Apply button.

Defining Light Sources You can control individual lights in the Lights panel (Figure 27.2.7). The Lights panel allows you to create a light and then turn it off without deleting it. In this way, you can retain lights that you have defined previously but do not wish to use at present. Display −→Lights... (You can also open the Lights panel by clicking on the Lights... button in the Display Options panel.) By default, light 0 is defined to be dark gray with a direction of (1,1,1). A light source is a distant light, similar to the sun. The direction (1,1,1) means that the rays from the

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Figure 27.2.7: The Lights Panel

light will be parallel to the vector from (1,1,1) to the origin. To create an additional light (e.g., light 1), follow the steps listed below. 1. Increase Light ID to a new value (e.g., 1). 2. Turn on the Light On check button. 3. Define the light color by entering a descriptive string (e.g., lavender) in the Color field, or by moving the Red, Green, and Blue sliders to obtain the desired color. The default color for all lights is dark gray. 4. Specify the light direction by doing one of the following: • Enter the (X,Y,Z) Cartesian components under Direction. • Click the middle mouse button in the desired location on the sphere under Active Lights. (You can also move the light along the circles on the surface of the sphere by dragging the mouse while holding down the middle button.) You can rotate the sphere by pressing the left mouse button and moving the mouse (like a trackball). • Use your mouse to change the view in the graphics window so that your position in reference to the geometry is the position from which you would like a light to shine. Then click the Use View Vector button to update the X,Y,Z fields with the appropriate values for your current position and update the graphics display with the new light direction. This method is convenient


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if you know where you want a light to be, but you are not sure of the exact direction vector. 5. Repeat steps 1–4 if you want to add more lights. 6. When you have defined all the lights you want, click Apply to save their definitions. Removing a Light To remove a light, enter the ID number of the light to be removed in the Light ID field and then turn off the Light On button. When a light is turned off, its definition is retained, so you can easily add it to the display again at a later time by turning on the Light On button. For example, you may want to define three different lights to be used in different scenes. You can define each of them, and then turn on only one or two at a time, using the Light ID field and the Light On button. Once you have made all the desired modifications to the lights, remember to click the Apply button to save the changes. Resetting the Light Definitions If you have made changes to the light definitions, but you have not yet clicked on Apply, you can reset the lights by clicking on the Reset button. All lighting characteristics will revert to the last saved state (i.e., the lighting that was in effect the last time you opened the panel or clicked on Apply).

27.2.7

Modifying the Rendering Options

Depending on the objects in your display window and what kind of graphics hardware and software you are using, you may want to modify some of the rendering parameters listed below. All are listed under the Rendering heading in the Display Options panel (Figure 27.2.8). Display −→Options... After making a change to any of these rendering parameters, click the Apply button to re-render the scene in the active graphics window with the new attributes. To see the effect of the new attributes on another graphics window, you must redisplay it or make it the active window (see Section 27.2.2) and click Apply again. Line Width: By default, all lines drawn in the display have a thickness of 1 pixel. If you want to increase the thickness of the lines, increase the value of Line Width. Point Symbol: By default, nodes displayed on surfaces and data points on line or rake surfaces are represented in the display by a + sign inside a circle. If you want to modify this representation (e.g., to make the nodes easier to see), you can select a different symbol in the Point Symbol drop-down list.

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Figure 27.2.8: The Display Options Panel

Wireframe Animation: When you use the mouse to modify the view in the display, a wireframe representation will be displayed for all geometry during the mouse manipulation. If your computer has a graphics accelerator, you may want to disable this feature by turning off the Wireframe Animation option. Turning this option off when your computer does not have a graphics accelerator may make mouse manipulation very slow. Double Buffering: Enabling the Double Buffering option can dramatically reduce screen flicker during graphics updates. Note, however, that if your display hardware does not support double buffering and you turn this option on, double buffering will be done in software. Software double buffering uses extra memory. Outer Face Culling: This option allows you to turn off the display of outer faces in wall zones. Outer Face Culling is useful for displaying both sides of a slit wall. By default, when you display a slit wall, one side will “bleed” through to the other. When you turn on the Outer Face Culling option, the display of a slit wall will show each side distinctly as you rotate the display. This option can also be useful for displaying two-sided walls (i.e., walls with fluid or solid cells on both sides). Hidden Line Removal: If you do not use hidden line removal, FLUENT will not try to determine which lines in the display are behind others; it will display all of them, and a cluttered display will result for most 3D grid displays. For most 3D problems, therefore, you should turn on the Hidden Line Removal option. You should turn this option off (for optimal performance) if you are working with a 2D problem or with geometries that do not overlap.


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Hidden Surface Removal: If you do not use hidden surface removal, FLUENT will not try to determine which surfaces in the display are behind others; it will display all of them, and a cluttered display will result for most 3D grid displays. For most 3D problems, therefore, you should turn on the Hidden Surface Removal option. You should turn this option off (for optimal performance) if you are working with a 2D problem or with geometries that do not overlap. You can choose one of the following methods for performing hidden surface removal in the Hidden Surface Method drop-down list. These options vary in speed and quality, depending on the device you are using. Hardware Z-buffer is the fastest method if your hardware supports it. The accuracy and speed of this method is hardware-dependent. Note that if this method is not available on your computer, selecting it will cause the Software Z-buffer method to be used. Painters will show fewer edge-aliasing effects than Hardware-Z-buffer. This method is often used instead of Software-Z-buffer when memory is limited. Software Z-buffer is the fastest of the accurate software methods available (especially for complex scenes), but it is memory-intensive. Z-sort only is a fast software method, but it is not as accurate as Software-Z-buffer.

Graphics Device Information If you need to know which graphics driver you are using and what graphics hardware it recognizes, you can click the Info button in the Display Options panel. The graphics device information will be printed in the text (console) window.

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27.3 Controlling the Mouse Button Functions

27.3

Controlling the Mouse Button Functions

A convenient feature of FLUENT is that it allows you to assign a specific function to each of the mouse buttons. According to your specifications, clicking a mouse button in the graphics window will cause the appropriate action to be taken. These functions apply only to the graphics windows; they are not active when an XY plot or histogram is displayed. (See Section 27.8.1 for information about the use of mouse buttons in these plots.) Clicking any mouse button in a graphics window will make that window the active window.

Button Functions The predefined button functions available are listed below: mouse-rotate allows you to rotate the view by dragging the mouse across the screen. Dragging horizontally rotates the object about the screen’s y axis; vertical mouse movement rotates the object about the screen’s x axis. The function completes when the mouse button is released or the cursor leaves the graphics window. mouse-dolly allows you to translate the view by dragging the mouse while holding down the button. The function completes when the mouse button is released or the cursor leaves the graphics window. mouse-zoom allows you to draw a zoom box, anchored at the point at which the button was pressed, by dragging the mouse with the button held down. When you release the button, if the dragging was from left to right, a magnified view of the area within the zoom box will fill the window. If the dragging was from right to left, the area of the window is shrunk to fit into the zoom box, resulting in a “zoomed out” view. If the mouse button is simply clicked (not dragged), the selected point becomes the center of the window. mouse-roll-zoom allows you to rotate or zoom the view, depending on the direction in which you drag the mouse. If you drag the mouse horizontally, the display will rotate about the axis normal to the screen. If you drag it vertically, the display will be magnified (if you drag it down) or shrunk (if you drag it up). The function completes when the mouse button is released or the cursor leaves the graphics window. Note that this function is similar to the function of the right mouse button in GAMBIT. mouse-probe allows you to select items from the graphics windows and request information about displayed scenes. If the probe function is turned off and you click the mouse-probe button in the graphics window, only the identity of the item on which you clicked will be printed out in the console window. If the probe function is turned on, more detailed information about a selected item will be printed out.


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mouse-annotate allows you to insert text into the graphics window. If the mouse button is dragged, an attachment line is drawn. When the button is released (after dragging or clicking), a cursor is displayed in the graphics window, and you can enter your text. When you are finished, press or move the cursor out of the graphics window. To modify or remove annotated text and attachment lines, use the Clear button in the Annotate panel, as described in Section 27.2.4.

Modifying the Mouse Button Functions Mouse button functions are specified in the Mouse Buttons panel (Figure 27.3.1). Display −→Mouse Buttons...

Figure 27.3.1: The Mouse Buttons Panel For each mouse button (Left, Middle, and Right), select the desired function in the dropdown list. The functions are listed above. If you assign the probe function to one of the buttons, select on or off as the Probe status. The new button functions take effect as soon as you click OK. That is, you do not have to redraw the graphics window to use the new functions; the appropriate function will be executed when a mouse button is subsequently clicked in a graphics window. The default button functions are as follows: Button Left Middle Right

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2D mouse-dolly mouse-zoom mouse-probe

3D mouse-rotate mouse-zoom mouse-probe


27.4 Modifying the View

27.4

Modifying the View

FLUENT allows you to control the view of the scene that is displayed in the graphics window. You can modify the view by scaling, centering, rotating, translating, or zooming the display. You can also save a view that you have created, or restore or delete a view that you saved earlier. These operations are performed in the Views panel (Figure 27.4.1) or with the mouse.

! You can revert to the previous view using the keyboard command -L while the graphics window has the main focus. You can also use the text command view last from the top level of the text command tree. You can use the command to revert to any of the past 20 views.

27.4.1

Scaling, Centering, Rotating, Translating, and Zooming the Display

Scaling and centering the display is accomplished using the Views panel (Figure 27.4.1). Display −→Views...

Figure 27.4.1: The Views Panel You can rotate, translate, and zoom the graphics display using either the mouse or the Camera Parameters panel (Figure 27.4.2), which is opened from the Views panel.

Scaling and Centering You can scale and center the current display without changing its orientation by clicking on the Auto Scale button in the Views panel.


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Figure 27.4.2: The Camera Parameters Panel

Rotating the Display In 3D you can rotate the display in any direction, using either the mouse or the Camera Parameters panel. In 2D you can rotate the display about the axis normal to the screen, using either the mouse or the Camera Parameters panel. To rotate a 3D display with the mouse, you will use the button with the mouse-rotate function (the left button, by default). (See Section 27.3 for information about changing the mouse functions.) Click and drag the left mouse button in the graphics window to rotate the geometry in the display. You can also click and drag the left mouse button on the (x,y,z) graphics triad in the lower left corner to rotate the display. If you press the key when you first click the mouse button to begin the rotation, the rotation will be constrained to a single direction (e.g., you can rotate about the screen’s horizontal axis without changing the position relative to the vertical axis). If you want to constrain the rotation of a 3D display to be about the axis normal to the screen, you can also use the mouse-roll-zoom function described below for 2D cases. To rotate a 3D display using the Camera Parameters panel (Figure 27.4.2) you will use the dial and the scales below it and to its left: • To rotate about the horizontal axis at the center of the screen, move the slider on the scale to the left of the dial up or down (see Section 2.1.3 for instructions on using the scale). • To rotate about the vertical axis at the center of the screen, move the slider on the scale below the dial to the left or right. • To rotate about the axis at the center of and perpendicular to the screen, click the left mouse button on the indicator in the dial and drag it around the dial.

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! Note that the position of the slider or the dial indicator does not reflect the cumulative rotation about the axis; the slider or indicator will return to its original position when you release the mouse button. To rotate a 2D display about the axis normal to the screen, you can use the dial in the Camera Parameters panel, as described above for 3D cases. If you want to rotate with the mouse instead, you can use the mouse-roll-zoom function. (See Section 27.3 for information about enabling this optional function.) Click the appropriate mouse button and drag the mouse to the left for clockwise rotation, or to the right for counter-clockwise rotation. Spinning the Display with the Mouse When you use the mouse for rotation, you have the option to “push” the display into a continuous spin. This feature can be used in conjunction with video recording, or simply for interactive viewing of the domain from different angles. To activate this option, use the auto-spin? text command: display −→ set −→ rendering-options −→auto-spin? Then display the graphics (or, if the graphics are already displayed, you can click the Apply button in the Display Options panel). The mouse-rotate button will then have two uses: • To perform the standard rotation, stop dragging the mouse before you release the mouse-rotate button. • To start the continuous spin, release the mouse-rotate button while you are still dragging the mouse. The display will continue to rotate on its own until you click any mouse button in the graphics window again. The speed of the rotation will depend on how fast you are dragging the mouse when you release the button. For smoother rotation, turn on the Double Buffering option in the Display Options panel (see Section 27.2.7). This will reduce screen flicker during graphics updates.

Translating the Display By default the left mouse button is set to mouse-dolly in 2D. (See Section 27.3 for information about changing the mouse functions.) Click and drag the left mouse button in the graphics window to translate the geometry in the display. In 3D, you can either change one of the button functions to mouse-dolly and follow the instructions above for 2D, or use the mouse-zoom button (the middle button by default). Click the middle button once on the point in the display that you want to move to the center of the screen. FLUENT will redisplay the graphic with that point in the center of the window. (Note that this method can also be used in 2D.)


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Zooming the Display In both 2D and 3D you will use the mouse button with the mouse-zoom function (the middle button by default) or the mouse-roll-zoom function (see Section 27.3 for information about enabling this optional function), or the Camera Parameters panel to magnify and shrink the display. With the mouse-zoom function, click the middle mouse button and drag it from left to right (creating a “zoom box”) to magnify the display. Figure 27.4.3 displays the correct dragging of the mouse, from upper left to lower right on the display, in order to zoom. (You can also drag from lower left to upper right.) After you release the mouse button, FLUENT will redisplay the graphic, filling the graphics window with the portion of the display that previously occupied the zoom box. Click the middle mouse button and drag it from right to left to shrink the display. Figure 27.4.4 displays the correct dragging of the mouse, from lower right to upper left on the display, in order to “de-zoom”. (You can also drag from upper right to lower left.) After you release the mouse button, FLUENT will redisplay the graphic, shrinking the graphical display by the ratio of sizes of the zoom box you created and the previous display. With the mouse-roll-zoom function, click the appropriate mouse button and drag the mouse down to zoom in continuously, or up to zoom out. In the Camera Parameters panel (Figure 27.4.2), use the scale to the right of the dial to zoom the display. Move the slider bar up to zoom in and down to zoom out.

27.4.2

Controlling Perspective and Camera Parameters

Perspective and other camera parameters are defined in the Camera Parameters panel, which you can open by clicking on the Camera... button in the Views panel (Figure 27.4.1). Display −→Views...

Perspective and Orthographic Views You may choose to display either an orthographic view or a perspective view of your graphics. To show a perspective view (the default), select Perspective in the Projection drop-down list in the Camera Parameters panel (Figure 27.4.2). To turn off perspective, select Orthographic in the Projection drop-down list.

Modifying Camera Parameters Instead of translating, rotating, and zooming the display as described in Section 27.4.1, you may sometimes want to modify the “camera” through which you are viewing the graphics display.

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click here

drag direction

release region to be zoomed

Figure 27.4.3: Zooming In (Magnifying the Display)

release

drag direction

click here region to be un-zoomed

Figure 27.4.4: Zooming Out (Shrinking the Display)


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The camera is defined by four parameters: position, target, up vector, and field, as illustrated in Figure 27.4.5. “Position” is the camera’s location. “Target” is the location of the point the camera is looking at, and “up vector” indicates to the camera which way is up. “Field” indicates the field of view (width and height) of the display. view plane

up vector position target x field

y field

Figure 27.4.5: Camera Definition

To modify the camera’s position, select Position in the Camera drop-down list and specify the X, Y, and Z coordinates of the desired point. To modify the target location, select Target in the Camera drop-down list and specify the coordinates of the desired point. Select Up Vector to change the up direction. The up vector is the vector from (0,0,0) to the specified (X,Y,Z) point. Finally, to change the field of view, select Field in the Camera list and enter the X (horizontal) and Y (vertical) field distances.

! Click Apply after you change each camera parameter (Position, Target, Up Vector, and Field).

27.4.3

Saving and Restoring Views

After you make changes to the view shown in your graphics window, you may want to save the view so that you can return to it later. Several default views are predefined for you, and can be easily restored. All saving and restoring functions are performed with the Views panel (Figure 27.4.1). Display −→Views...

! Note that settings for mirroring and periodic repeats are not saved in a view. Restoring the Default View When experimenting with different view manipulation techniques, you may accidentally “lose” your geometry in the display. You can easily return to the default (front) view by clicking on the Default button in the Views panel.

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Saving Views Once you have created a new view that you want to save for future use, enter a name for it in the Save Name field in the Views panel and click the Save button. Your new view will be added to the list of Views, and you can restore it later as described below. If a view with the same name already exists, you will be asked in a Question dialog box if it is OK to overwrite the existing view. If you overwrite one of the default views (top, left, right, front, etc.), be sure to save it in a view file if you wish to use it in a later session. (Although all views are saved to the case file, the default views are recomputed automatically when a case file is read in. Any custom view with the same name as a default view will be overwritten at that time.) As mentioned above, all defined views will be saved in the case file when you write one. If you plan to use your views with another case file, you can write a “view file” containing just the views. You can read this view file into another solver session involving a different case file and restore any of the defined views, as described below. To save a view file, click the Write... button in the Views panel. In the resulting Write Views panel (Figure 27.4.6), select the views you want to save in the Views To Save list and click OK. You will then use the Select File dialog box to specify the file name and save the view file.

Figure 27.4.6: The Write Views Panel

Reading View Files If you have saved views to a view file (as described above), you can read them into your current solver session by clicking on the Read... button in the Views panel, and indicating the name of the view file in the resulting Select File dialog box. If a view that you read has the same name as a view that already exists, you will be asked in a Question dialog box if it is OK to overwrite (i.e., replace) the existing view.


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Restoring Views You can restore any of the predefined views, views you have saved, or views that you have read from a view file. Select the view in the Views list and click the Restore button, or just double-click the desired view in the Views list.

Deleting Views If you decide that you no longer want to keep a particular view, you can delete it by selecting it in the Views list and clicking on the Delete button. Use this option carefully, so that you do not accidentally delete one of the predefined views.

27.4.4

Mirroring and Periodic Repeats

If you model the problem domain as a subset of your geometry using symmetry or periodic boundaries, you can display results on the complete geometry by mirroring or repeating the domain. For example, only one half of the annulus shown in Figure 27.4.7 was modeled, but the graphics are displayed on both halves. You can also define mirror planes or periodic repeats just for graphical display, even if you did not model your problem using symmetry or periodic boundaries.

4.86e-02 4.14e-02 3.42e-02 2.69e-02 1.97e-02 1.25e-02 5.28e-03 -1.94e-03 -9.16e-03 -1.64e-02 -2.36e-02

Fluent Inc. Contours of Static Pressure (pascal) Tue Aug 29 1995

Figure 27.4.7: Mirroring Across a Symmetry Boundary

Display of symmetry and periodic repeats is controlled in the Views panel (Figure 27.4.8). Display −→Views...

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Figure 27.4.8: The Views Panel

For a periodic domain, specify the number of times to repeat the modeled portion by increasing the value of Periodic Repeats. If, for example, you modeled a 90◦ sector of a duct and you wanted to display results on the entire duct, you would set the number of Periodic Repeats to 3. For a symmetric domain, all symmetry boundaries will be listed in the Mirror Planes list. Select one or more of these boundaries as the plane(s) about which to mirror the display. When you click Apply in the Views panel the graphics display will immediately be updated to show the requested mirroring or periodic repeats.

Periodic Repeats Just for Graphics To define graphical periodicity for a non-periodic domain, follow these steps: 1. Click the Define... button under Periodic Repeats in the Views panel. 2. In the resulting Graphics Periodicity panel (Figure 27.4.9), specify Rotational or Translational as the Periodic Type. 3. For translational periodicity, specify the Translation distance of the repeated domain in the X, Y, and Z directions. For rotational periodicity, specify the axis about which the periodicity is defined and the Angle by which the domain is rotated to create the periodic repeat. For 3D problems, the axis of rotation is the vector passing through the specified Axis Origin and parallel to the vector from (0,0,0) to the (X,Y,Z) point specified under Axis Direction. For 2D problems, you will specify only the Axis Origin; the axis of rotation is the z-direction vector passing through the specified point.


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Figure 27.4.9: The Graphics Periodicity Panel

4. Click OK in the Graphics Periodicity panel. 5. In the Views panel, specify the number of Periodic Repeats and click Apply, as described above. You can delete the definition of any periodicity you have defined for graphics by clicking on the Reset button in the Graphics Periodicity panel.

Mirroring Just for Graphics To define a mirror plane for a non-symmetric domain, follow the procedure below: 1. Click the Define Plane... button under Mirror Planes in the Views panel. 2. In the resulting Mirror Planes panel (Figure 27.4.10), set the coefficients of X, Y, and Z and the Distance (of the plane from the origin) in the following equation for the mirror plane: Ax + By + Cz = distance 3. Click the Add button to add the defined plane to the Mirror Planes list. When you are done creating mirror planes, click OK. The newly defined plane(s) will now appear in the Mirror Planes list in the Views panel. To include the mirroring in the display, select the plane(s) and click Apply, as described above. If you want to delete a mirror plane that you have defined, select it in the Mirror Planes list in the Mirror Planes panel and click the Delete button. When you click OK in this panel, the deleted plane will be removed permanently from the Mirror Planes list in the Views panel.

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27.5 Composing a Scene

Figure 27.4.10: The Mirror Planes Panel

27.5

Composing a Scene

Once you have displayed some geometric objects (grids, surfaces, contours, vectors, etc.) in your graphics window, you may want to move them around and change their characteristics to increase the effectiveness of the scene displayed. You can use the Scene Description panel (Figure 27.5.1) and the Display Properties panel (Figure 27.5.2) and Transformations panel (Figure 27.5.4), which are opened from within it, to rotate, translate, and scale each object individually, as well as change the color and visibility of each object. Display −→Scene...

Figure 27.5.1: The Scene Description Panel


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The IsoValue panel (Figure 27.5.5), which is also opened from within the Scene Description panel, allows you to change the isovalue of a selected isosurface. The Pathline Attributes panel (Figure 27.5.6) lets you set some pathline attributes. The ability to make geometric objects visible and invisible is especially useful when you are creating an animation (see Section 27.6) because it allows you to add or delete objects from the scene one at a time. The ability to change the color and position of an object independently of the others in the scene is also useful for setting up animations, as is the ability to change isosurface isovalues. You will find the features in the Scene Description panel useful even when you are not generating animations because they allow you to manage your graphics window efficiently. (Note that you cannot use the Scene Description panel to control XY plot and histogram displays.) Note that the Time Step... option is not available in FLUENT. (It is available only for the Fluent Inc. postprocessing program, FLUENT/Post. See the FLUENT/Post User’s Guide for details.) The procedure for overlaying graphics, which uses the Scene Description panel, is described in Section 27.2.1.

27.5.1

Selecting the Object(s) to be Manipulated

In order to manipulate the objects in the scene, you will begin by selecting the object or objects of interest in the Names list in the Scene Description panel (Figure 27.5.1). The Names list is a list of the geometric objects that currently exist in the scene (including those that are presently invisible). If you select more than one object at a time, any operation (transformation, color specification, etc.) will apply to all the selected objects. You can also select objects by clicking on them in the graphics display using the mouse-probe button, which is, by default, the right mouse button. (See Section 27.3 for information about mouse button functions.) To deselect a selected object, simply click on its name in the Names list. When you select one or more objects (either in the Names list or in the display), the Type field will report the type of the selected object(s). Possible types for a single object include grid, surface, contour, vector, path, and text (i.e., annotation text). This information is especially helpful when you need to distinguish two or more objects with the same name. When more than one object is selected, the type displayed is Group.

27.5.2

Changing an Object’s Display Properties

To enhance the scene in the graphics window, you can change the color, visibility, and other display properties of each geometric object in the scene. You can specify different colors for displaying the edges and faces of a grid object to show the underlying mesh (edges) when the faces of the grid are filled and shaded. You can also make a selected object temporarily invisible. If, for example, you are displaying the entire grid for a complicated problem, you can make objects visible or invisible to display only certain

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boundary zones of the grid without regenerating the grid display using the Grid Display panel. You can also use the visibility controls to manipulate geometric objects for efficient graphics display or for the creation of animations. These features, plus several others, are available in the Display Properties panel (Figure 27.5.2).

Figure 27.5.2: The Display Properties Panel

To set the display properties described above, select one or more objects in the Names list in the Scene Description panel and then click the Display... button to open the Display Properties panel for that object or group of objects.

Controlling Visibility There are several ways for you to control the visibility of an object. All visibility options are listed under the Visibility heading in the Display Properties panel. • To make the selected object(s) invisible, turn off the Visible option. To “undo” invisibility, simply turn the Visible option on again. • To turn the effect of lighting for the selected object(s) on or off, use the Lighting check button. You can choose to have lighting affect only certain objects instead of all of them. Note that if Lighting is turned on for an object such as a contour or vector plot, the colors in the plot will not be exactly the same as those in the colormap at the left of the display.


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• To toggle the filled display of faces for the selected grid or surface object(s), use the Faces option. Turning Faces on here has the same effect as turning it on for the entire grid in the Grid Display panel. • To turn the display of outer edges on or off, use the Outer Faces option. This option is useful for displaying both sides of a slit wall. By default, when you display a slit wall, one side will “bleed” through to the other. When you turn off the Outer Faces option, the display of a slit wall will show each side distinctly as you rotate the display. This option can also be useful for displaying two-sided walls (i.e., walls with fluid or solid cells on both sides). • To turn the display of interior and exterior edges of the geometric object(s) on or off, use the Edges option. • To turn the display of the outline of the geometric object(s) on or off, use the Perimeter Edges check button. • To toggle the display of feature lines (described in Section 27.1.1), if any, for the selected object(s), use the Feature Edges option. • To toggle the display of the lines (if any) in the geometric object(s), use the Lines check button. Pathlines, line contours, and vectors are “lines”. • To toggle the display of nodes (if any) in the geometric object(s), use the Nodes check button. Once you have set the appropriate display parameters, click the Apply button to update the graphics display.

Controlling Object Color and Transparency The Display Properties panel also lets you control an object’s color and how transparent it is. All color and transparency options are listed under the Colors heading. • To modify the color of faces, edges, or lines in the selected object(s), choose facecolor, edge-color, line-color, or node-color in the Color drop-down list. The Red, Green, and Blue color scales will show the RGB components of the face, edge or line color, which you can modify by moving the sliders on the color scales. When you are satisfied with the color specification, click Apply to save it and update the display. The ability to set the colors for faces and edges can be useful when you wish to have a filled display for the grid or surface, but you also want to be able to see the grid lines. You can achieve this effect by specifying different colors for the faces and the edges.

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• To set the relative transparency of an object, select face-color in the Color dropdown list. Move the slider on the Transparency scale and click the Apply button to update the graphics display. An object with a transparency of 0 is opaque, and an object with a transparency of 100 is transparent. By specifying a high transparency value for the walls of a pipe, for example, you will be able to see contours that you have displayed on cross-sections inside the pipe. (This feature is available on all platforms when the software z buffer is used for hidden surface removal, but if your display hardware supports transparency, it will be more efficient to use the hardware z buffer as the hidden surface method instead. You can select these methods in the Display Options panel, as described in Section 27.2.7.)

! If you save a hardcopy of a display with transparent surfaces, you should not set the File Type in the Graphics Hardcopy panel to Vector.

27.5.3

Transforming Geometric Objects in a Scene

When you are composing a scene in your graphics window, you might find it helpful to move a particular object from its original position or to increase or decrease its size. For example, if you have displayed contours or vectors on cross-sections of an internal flow domain (such as a pipe), you might want to translate these cross-sections so that they will appear outside of the pipe, where they can be seen and interpreted more easily. Figure 27.5.3 shows such an example.

1.50e+00 1.35e+00 1.20e+00 1.05e+00 8.97e-01 7.48e-01 5.98e-01 4.49e-01 2.99e-01 1.50e-01

Z

X Y

5.23e-04

Velocity Vectors in Plane Colored By Velocity Magnitude (m/s)

Figure 27.5.3: Velocity Vectors Translated Outside the Domain for Better Viewing


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You can also move an object by rotating it about the x, y, or z axis. If you want to display one object more prominently than the others, you can scale its size. If your geometry is rotating or has rotational symmetry, you can display the meridional view. All of these capabilities are available in the Transformations panel (Figure 27.5.4).

Figure 27.5.4: The Transformations Panel To perform the transformations described above, select one or more objects in the Names list in the Scene Description panel and then click the Transform... button to open the Transformations panel for that object or group of objects.

Translating Objects To translate the selected object(s), enter the translation distance in each direction in the X, Y, and Z real number fields under Translate. (Note that you can check the domain extents in the Scale Grid panel or the Iso-Surface panel.) Translations are not cumulative, so you can easily return to a known state. To return to the original position, simply enter 0 in all three real number fields.

Rotating Objects To rotate the selected object(s), enter the number of degrees by which to rotate about each axis in the X, Y, and Z integer number fields under Rotate By. (You can enter any value between −360 and 360.) By default, the rotation origin will be (0,0,0). If you want to spin an object about its own origin, or about some other point, specify the X, Y, and Z coordinates of that point under Rotate About. Rotations are not cumulative, so you can easily return to a known state. To return to the original position, simply enter 0 in all three integer number fields under Rotate By.

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Scaling Objects To scale the selected object(s), enter the amount by which to scale in each direction in the X, Y, and Z real number fields under Scale. To avoid distortion of the object’s shape, be sure to specify the same value for all three entries. Scaling is not cumulative, so you can easily return to a known state. To return the object to its original size, simply enter 1 in all three real number fields.

Displaying the Meridional View To display the meridional view of the selected object(s), turn on the Meridional option. This option is available only for 3D models. It is applicable to cases with a defined axis of rotation and is especially useful in turbomachinery applications. The meridional transformation projects the selected entities onto a surface of constant angular coordinate, θ. The resultant projection thus lies in an (r, ζ) plane where ζ is in the direction of the rotation axis and r is normal to it. The value of θ used for the projection is taken as that corresponding to the minimum (r, ζ) point of the entity.

27.5.4

Modifying Isovalues

One convenient feature that you can use to generate effective animations is the ability to generate surfaces with intermediate values between two isosurfaces with different isovalues. If the surfaces have contours, vectors, or pathlines displayed on them, FLUENT will generate and display contours, vectors, or pathlines on the intermediate surfaces that it creates.

Steps for Modifying Isovalues You can modify an isosurface’s isovalue directly by selecting it in the Scene Description panel’s Names list or indirectly by selecting an object displayed on the isosurface. Then click the IsoValue... button to open the IsoValue panel (Figure 27.5.5) for the selected object. Note that this button is available only if the geometric object selected in the Names list is an isosurface or a object on an isosurface (contour on an isosurface, for example); otherwise it is grayed out. In the IsoValue panel, set the new isovalue in the IsoValue field, and click Apply. Contours, vectors, or pathlines that were displayed on the original isosurface will be displayed for the new isovalue.

An Example of Isovalue Modification for an Animation The ability to generate intermediate surfaces with data displayed on them is especially convenient if you want to create an animation that shows data on successive slices of the problem domain. For example, if you have solved the flow through a pipe junction


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Figure 27.5.5: The IsoValue Panel

and you want to create an animation that moves through one of the pipes (along the y axis) and displays pressure contours on several cross-sections, you can use the following procedure: 1. Generate a surface of constant y coordinate (such as the y coordinate at the pipe inlet) using the Iso-Surface panel. 2. Use the Contours panel to generate contours of static pressure on this isosurface and manipulate the graphics display to the desired view. 3. Open the Animate panel and create key frame 1. 4. In the Scene Description panel, select the contour in the Names list and click the IsoValue... button to open the IsoValue panel. 5. Change the value of the isovalue to the y coordinate at the other end of the pipe, and click Apply. You will see the contours of static pressure at the new y coordinate. 6. Set key frame 10 in the Animate panel. 7. Play back the animation. When you play back the animation, FLUENT will create the intermediate frames showing contours of static pressure on the slices between the two ends of the pipe. Ten slices will be shown in succession, all with contours displayed on them. Using the Sweep Surface panel to animate the display of contours or vectors on a surface that sweeps through the domain may be more convenient than the procedure described above. See Section 27.1.5 for details.

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27.5.5

Modifying Pathline Attributes

If you are creating animations of existing pathlines, you may want to change the number of steps used in the computation of the pathlines. This allows you to animate pathlines advancing through the domain. To do so, select the pathlines in the Names list in the Scene Description panel and then click the Path Attr... button to open the Pathline Attributes panel (Figure 27.5.6).

Figure 27.5.6: The Pathline Attributes Panel In the Pathline Attributes panel, set the new maximum number of steps for pathline computation (Max Steps). After you change the value and click Apply, the selected pathline will be recomputed and redrawn.

An Example of Pathline Modification for an Animation You can use the following procedure to animate pathlines from step 2 to step 101 (for example): 1. Generate the plot of pathlines using the Path Lines panel. 2. In the Scene Description panel, select the pathlines in the Names list and click the Path Attr... button to open the Pathline Attributes panel. 3. Change the value of the maximum number of steps to 2, and click Apply. 4. Open the Animate panel and create key frame 1. 5. In the Pathline Attributes panel, change the value of the maximum number of steps to 101, and click Apply. 6. Set key frame 100 in the Animate panel. 7. Play back the animation. When you play back the animation, FLUENT will animate the pathlines so that they advance one step in each frame.


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27.5.6

Deleting an Object from the Scene

If you are composing a complex scene with overlays and find that you no longer want to keep one of the objects, it is possible to delete it without affecting any of the other objects in the scene. The ability to delete individual objects is especially useful if you have overlays on and you generate an unwanted object (e.g., if you generate contours of the wrong variable). You can simply delete the unwanted object and continue your scene composition, instead of starting over from the beginning. Note that it is also possible to make objects temporarily invisible, as described in Section 27.5.2. Object deletion is performed in the Scene Description panel (Figure 27.5.1). To delete an object from the scene, select it in the Names list and then click the Delete Geometry button. The selected name will disappear from the Names list, and the display will be updated immediately.

27.5.7

Adding a Bounding Frame

FLUENT allows you to add a bounding frame around your displayed domain. You may also include measure markings on the bounding frame to indicate the length, height, and/or width of the domain, as shown in Figure 27.5.7.

1.1

1.2 -0.85

3.2

Y X Z

Figure 27.5.7: Graphics Display with Bounding Frame

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To add a bounding frame to your display, you will follow the procedure below: 1. Click the Frame Options... button in the Scene Description panel (Figure 27.5.1) to open the Bounding Frame panel (Figure 27.5.8).

Figure 27.5.8: The Bounding Frame Panel

2. Under Frame Extents in the Bounding Frame panel, select Domain or Display to indicate whether the bounding frame should encompass the domain extents or only the portion of the domain that is shown in the display. 3. In the Axes portion of the Bounding Frame panel, specify the frame boundaries and measurements to be shown in the display: • Indicate the bounding plane(s) (e.g., the x-z and y-z planes shown in Figure 27.5.7) to be displayed by clicking on the white square on the appropriate plane of the box shown under the Axes heading. (You can use any of the mouse buttons.) The square will turn red to indicate that the associated bounding plane will be displayed in the graphics window. • Specify where you would like to see the measurement annotations by clicking on the appropriate edge of the box. The edge will turn red to indicate that the markings will be displayed along that edge of the displayed geometry.

!

If you have trouble determining which square or edge corresponds to which location in your domain, you can easily find out by displaying one or two bounding planes to get your bearings. You can then select the appropriate objects to obtain the final display. 4. Click the Display button to update the display with the current settings. If you are not satisfied with the frame, repeat steps 2 and/or 3 and click Display again. 5. Once you are satisfied with the bounding frame that is displayed, click OK to close the Bounding Frame panel and save the frame settings for future displays.


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6. If you wish to include the bounding frame in all subsequent displays, turn on the Draw Frame option in the Scene Description panel and click Apply. If this option is not enabled, the bounding box will appear only in the current display; it will not be redisplayed when you generate a new display (unless you have overlays enabled). The bounding planes and axis annotations will appear in the Names list of the Scene Description panel, and you can manipulate them in the same way as any other geometric object in the display. For example, you can use the Display Properties panel to change the face color of a bounding plane or to make it transparent (see Section 27.5.2).

27.6

Animating Graphics

To generate animations that progress from one static view of the graphics display to the next, you can set up “key frames” (individual static images) using the Animate panel (Figure 27.6.1). Display −→Scene Animation...

Figure 27.6.1: The Animate Panel You can compose a scene in the graphics window and define it as a single key frame. Then, modify the scene by moving or scaling objects, making some objects invisible or visible, changing colors, changing the view, or making other changes, and define the new scene as another key frame. FLUENT can then interpolate smoothly between the two frames that you defined, creating a specified number of intermediate frames. Another method of generating animations is to automatically generate surfaces with intermediate values between two isosurfaces with different isovalues. See Section 27.5.4

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27.6 Animating Graphics

for details. See Section 27.1.5 for information about displaying the grid, contours, or vectors on a surface that sweeps through the domain. If you want to create a graphical animation of the solution over time, you can use the Solution Animation panel to set up the graphical displays that you want to use in the animation. See Section 24.17 for details.

27.6.1

Creating an Animation

You can define any number of key frames (up to 3000) to create your animation. By assigning the appropriate numbers to the key frames, you provide the information FLUENT needs to create the correct number of intermediate frames. For example, to create a simple animation that begins with a front view of an object, moves to a side view, and ends with a rear view of the object, you would follow the procedure outlined below: 1. Determine the number of frames that you want in the animation. For this example, consider the animation to be 31 frames. 2. Determine the number of key frames that you need to specify. In this example, you will specify three: one showing the front view, one showing the side view, and one showing the rear view. 3. Determine the appropriate key frame numbers to assign to the 3 specified frames. Here, the front view will be specified as key frame 1, the side view will be key frame 16, and the rear view will be key frame 31. 4. Compose the scenes for each view to be used as a key frame. You can use the Scene Description panel (see Section 27.5) and the Views panel (see Section 27.4) to modify the display, and any other panels or commands to create contours, vectors, pathlines, etc. to be included in each scene. After you complete each scene, create the appropriate key frame by setting the Frame number and clicking on the Add button under Key Frames in the Animate panel. (See Section 27.6.5 for special considerations related to key frame definition.)

!

Be sure to change the Frame number before clicking on the Add button, or you will overwrite the last key frame that you created. You can check any of the key frames that you have created by selecting it in the Keys list. The selected key frame will be displayed in the graphics window. 5. When you complete the animation, you can play it back as described in Section 27.6.2 and/or save it as described in Section 27.6.3.

Deleting Key Frames If, during the creation of your animation, you want to remove one of the key frames that you have defined, select the key frame in the Keys list and click the Delete button. If you want to delete all key frames and start over again, click the Delete All button.


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27.6.2

Playing an Animation

Once you have defined the key frames (as described in Section 27.6.1) or read in a previously created animation file (as described in Section 27.6.4), you can play back the animation and FLUENT will interpolate between the frames that you specified to complete the animation. To play the animation once through from start to finish, click the “play” button under the Playback heading in the Animate panel. (The buttons function in a way similar to those on a standard video cassette player. “Play” is the second button from the right—a single triangle pointing to the right.) To play the animation backwards once, click the “play reverse” button (the second from the left—a single triangle point to the left). As the animation plays, the Frame scale shows the number of the frame that is currently displayed, as well as its relative position in the entire animation. If, instead of playing the complete animation, you want to jump to a particular key frame, move the Frame slider bar to the desired frame number, and the frame corresponding to the new frame number will be displayed in the graphics window. Additional options for playing back animations are described below. Be sure to check Section 27.6.5 as well for important notes about playing back animations.

Playing Back an Excerpt You may sometimes want to play only one portion of a long animation. To do this, you can modify the Start Frame and the End Frame under the Playback heading in the Animate panel. For example, if your animation contains 50 frames, but you want to play only frames 20 to 35, you can set Start Frame to 20 and End Frame to 35. When you play the animation, it will start at frame 20 and finish at frame 35.

“Fast-Forwarding” the Animation You can “fast-forward” or “fast-reverse” the animation by skipping some of the frames during playback. To fast-forward the animation, you will need to set the Increment and click the fast-forward button (the last button on the right—two triangles pointing to the right). If, for example, your Start Frame is 1, your End Frame is 15, and your Increment is 2, when you click the fast-forward button, the animation will show frames 1, 3, 5, 7, 9, 11, 13 and 15. Clicking on the fast-reverse button (the first button on the left—two triangles pointing to the left) will show frames 15, 13, 11,...1.

Continuous Animation If you want the playback of the animation to repeat continuously, there are two options available. To continuously play the animation from beginning to end (or from end to beginning, if you use one of the reverse play buttons), select Auto Repeat in the Playback

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Mode drop-down list in the Animate panel. To play the animation back and forth continuously, reversing the playback direction each time, select Auto Reverse in the Playback Mode drop-down list. To turn off the continuous playback, select Play Once in the Playback Mode list. This is the default setting.

Stopping the Animation To stop the animation during playback, click the “stop” button (the square in the middle of the playback control buttons). If your animation contains very complicated scenes, there may be a slight delay before the animation stops.

Advancing the Animation Frame by Frame To advance the animation manually frame by frame, use the third button from the right (a vertical bar with a triangle pointing to the right). Each time you click this button, the next frame will be displayed in the graphics window. To reverse the animation frame by frame, use the third button from the left (a left-pointing triangle with a vertical bar). Frame-by-frame playback allows you to freeze the animation at points that are of particular interest.

27.6.3

Saving an Animation

Once you have created your animation, you can save it in any of the following formats: • Animation file containing the key frame descriptions • Hardcopy files, each containing a frame of the animation • MPEG file containing each frame of the animation • Video (see Section 27.7)

Animation File You can save the key frame definitions to a file that can be read back into FLUENT (see Section 27.6.4) when you want to replay the animation. Since the animation file will contain only the key frame definitions, you must be sure that you have a case and data file containing the necessary surfaces and other information referred to by the key frame descriptions. To write an animation file, select Key Frames in the Write/Record Format drop-down list in the Animate panel, and click the Write... button. In the resulting Select File dialog box, specify the name of the file and save it.


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Hardcopy File You can also generate a hardcopy file for each frame in the animation. This feature allows you to save your animation frames to hardcopy files used by an external animation program such as ImageMagick. To save the animation as a hardcopy file, follow these steps: 1. Select Hardcopy Frames in the Write/Record Format drop-down list in the Animate panel. 2. If necessary, click the Hardcopy Options... button to open the Graphics Hardcopy panel and set the appropriate parameters for saving the hardcopy files. (If you are saving hardcopy files for use with ImageMagick, for example, you may want to select the window dump format. See Section 3.12.1 for details.) Click Apply in the Graphics Hardcopy panel to save your modified settings.

!

Do not click the Save... button in the Graphics Hardcopy panel. You will save the hardcopy files from the Animate panel in the next step. 3. In the Animate panel, click the Write... button. In the resulting Select File dialog box, specify the filename and click OK to save the files. (See Section 3.12.1 for information about specifying filenames that increment automatically as additional hardcopies are saved.) FLUENT will replay the animation, saving each frame to a separate file.

MPEG File It is also possible to save all of the frames of the animation in an MPEG file, which can be viewed using an MPEG decoder such as mpeg play. Saving the entire animation to an MPEG file will require less disk space than storing the individual window dump files (using the hardcopy method), but the MPEG file will yield lower-quality images. To save the animation to an MPEG file, follow these steps: 1. Select MPEG in the Write/Record Format drop-down list in the Animate panel. 2. In the Animate panel, click the Write... button. In the resulting Select File dialog box, specify the filename and click OK to save the files. FLUENT will replay the animation and save each frame to a separate scratch file, and then it will combine all the files into a single MPEG file.

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27.6.4

Reading an Animation File

If you have saved the key frames defining an animation to an animation file (as described in Section 27.6.3), you can read that file back in at a later time (or in different session) and play the animation. Before reading in an animation file, be sure that the current case and data contain the surfaces and any other information that the key frame description refers to. To read an animation file, click the Read... button in the Animate panel. In the resulting Select File dialog box, specify the name of the file to be read.

27.6.5

Notes on Animation

When you are creating and playing back animations, please note the following: • For smoother animations, turn on the Double Buffering option in the Display Options panel (see Section 27.2.7). This will reduce screen flicker during graphics updates. • When you are defining key frames, you must create all geometric objects that will be used in the animation before you create any key frames. You cannot create a key frame using one set of geometric objects and then generate a new geometry (such as a vector plot) and include that in another key frame. Create all geometric objects first, and then use the Display Properties panel to control the visibility of the objects in each key frame (see Section 27.5.2). • A single animation sequence can contain up to 3000 key frames. • When you play back an animation, the colormap used will be the one that is currently active, not the one that was active during “recording.”


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27.7

Creating Videos

Tools are available for creating videos from FLUENT. This section is a guide to video creation using the new video capabilities. It assumes that you have a ready-to-use video system, and that you are familiar with this system, including the special video hardware and software installed on your computer. The main use for this feature is to record an animation that you have created using the Animate panel (as described in Section 27.6). This section will describe issues involved in recording animations to video, the kind of video equipment you will need, and the procedures for creating a video using FLUENT.

! Video creation is not currently available in Windows versions of FLUENT. 27.7.1

Recording Animations To Video

Recording an animation involves copying the computer-generated images to videotape so that you can view the animation with a VCR, or another type of tape player. This task is not an easy one, as there are several issues that should be addressed in order to create an acceptable video. A couple of these issues are described in the following sections.

Computer Image vs. Video Image The computer monitor uses a different video signal than the video tape recorder (VTR). Most computers use an RGB-component, non-interlaced signal with high resolution and a high refresh rate. A VTR typically uses a standard broadcast video signal (such as NTSC or PAL), which has an interlaced, composite signal with lower resolution and a lower refresh rate. In order to send the computer image to the VTR for recording, the computer has to produce a video signal in the proper format. This requires extra hardware, which, in many cases, converts RGB component video to standard broadcast video, resulting in a lower quality image. A solution to this problem is to make sure that the image you are recording does not have small text, or too much small detail that will be hard to see on video. Sometimes it is best to zoom in on an area of interest in a large image and animate just that portion. Another problem is that RGB-component video has a larger color space (or color gamut) than standard broadcast video. This means that some colors may get “clipped” when an image is converted to broadcast video, resulting in washed-out colors, or color bleeding. The solution is to try to make sure that the colors fall within the color space of the video format, and are not oversaturated. Some picture controls that can help you do this are available in FLUENT. These controls will be discussed in Section 27.7.3.

Real-Time vs. Frame-By-Frame If the images in the animation can be rendered fast enough on the computer screen, it may be possible to record the animation in real-time. This is as simple as placing the video tape recorder (VTR) in record mode, and playing the animation on the computer

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27.7 Creating Videos

screen. This also requires scan-converting hardware that will convert the scan lines of the computer screen to a video signal sent to the VTR. In many cases, however, the animation cannot be played back on the computer screen in real-time. To create a video that plays the animation at a desirable speed, the animation must be recorded frame-by-frame. This involves sending one frame to the VTR, instructing it to record the frame at a specific point on the tape, then backing up the VTR to repeat the procedure with the next frame. This process takes quite a bit longer than real-time recording, but the result can be a much smoother video animation.

27.7.2

Equipment Required

In general, recording an animation to video requires a system with the following hardware components: Computer with video hardware to produce the video signal. Editing VTR (video tape recorder) that supports frame-accurate recording. VTR Controller which enables computer software to control the recording process. Two VTR controller models are supported by FLUENT: the V-LAN controller developed by Videomedia, Inc., and the MiniVAS/MiniVAS-2 controller developed by the V.A.S. Group. FLUENT assumes that your recording system is set up as shown in Figure 27.7.1 for a system with a V-LAN controller or as shown in Figure 27.7.2 for a system with a MiniVAS controller.

27.7.3

Recording an Animation with FLUENT

The steps for recording an animation using FLUENT are as follows: 1. Create an animation. 2. Open a connection to the VTR controller. 3. Set up your recording session. 4. Check the picture quality. 5. Make sure your tape is formatted (preblacked). 6. Start the recording session. Each step is described in detail in the following sections.


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RS-232

Computer

V-LAN Controller

Editing VTR

Video Composite Video

Figure 27.7.1: Recording System with V-LAN Controller

RS-232

Computer

MiniVAS Controller

Editing VTR

Video Composite Video

Figure 27.7.2: Recording System with MiniVAS/MiniVAS-2 Controller

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Create an Animation When recording animations to video, you must first create your animation. It’s also a good idea to play it back a couple times to make sure you are satisfied with it, and to save the animation key frame definitions to a file for later use (see Section 27.6.1). When you are ready to record the animation, you can select Video in the Write/Record Format drop-down list found in the Animate panel. When you do so, the name of the Write... button will change to Record..., and you can click Record... to display the Video Control panel (Figure 27.7.3) used for video creation. This panel can also be displayed by selecting the Video Control... menu item in the Display pull-down menu.

Figure 27.7.3: The Video Control Panel

Open a Connection to the VTR Controller The steps for connecting to your VTR controller are as follows: 1. Select the protocol used by your VTR controller using the Protocol drop-down list. 2. Check the settings for your VTR controller by clicking on the Settings... button. For V-LAN, this will display the V-LAN Settings panel, and for MiniVAS, it will display the MiniVAS Settings panel.


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3. Select the RS-232 serial port used to connect the VTR controller to your computer. Usually, the serial port is identified by a file name such as /dev/ttyd1 for serial port 1, and /dev/ttyd2 for serial port 2. If this is the case on your system, you can simply set the value of Port #; otherwise, you can type a new file name in the Serial Port text entry. Make sure that you have the proper UNIX read/write permissions for the file. 4. Open a connection to the VTR controller by clicking the Open button. If successful, a line will be printed out in the console window that reports the VTR controller protocol version and the VTR device ID.

Set Up Your Recording Session Once you have established a connection to the VTR controller, you can set up your recording session. There are three types of recording sessions, as described below: Preblack is the process of formatting a tape by laying down a time code onto the tape. A tape must be formatted before any frame-accurate editing, including frame-byframe animation, can be performed. During this process, one usually records a black video signal onto the tape as well, thus the name “preblack”. When you select this option, the current graphics window will be cleared to black. You can use the window to send your black video signal to the VTR.

!

Remember that when you preblack a previously formatted tape, a new time code will be written and any previously recorded video will be destroyed. Live Action allows you to record a live FLUENT session which can be used for demonstration. This option requires your computer’s video hardware to have a scan converter that will send the computer display image to your VTR system. Animation will play an animation that you have created, and record it onto your VTR system. The Options... button in the Video Control panel is used to display the Animation Recording Options panel (Figure 27.7.4): There are three parts to setting up your animation recording session: 1. Select the recording source. 2. Choose real-time or frame-by-frame recording. 3. Set the video frame hold counts.

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Figure 27.7.4: The Animation Recording Options Panel

Select the Recording Source There are two possible video sources that can be used for recording an animation: Screen and Hardcopy. The choice of video source depends on what your video hardware/software provides. Here is a description of each: Screen can be used if your computer’s video hardware can send all or a portion of the computer screen as a video signal to the VTR using a scan converter and associated software. With this option, you are responsible for setting up the scan converter and sending the video signal to the VTR. Hardcopy instructs FLUENT to create a hardcopy of each frame of animation and send the hardcopy file to the computer’s video hardware using a system command. This option assumes that your computer’s video system includes a frame buffer that can store an image and send it as a video signal to the video recording system. When using the hardcopy option, a shell script will be called that will send the hardcopy file to the video frame buffer. The default setting is videocmd, which is a shell script that is included in your FLUENT distribution. It is located in path/Fluent.Inc/bin, where path is the directory in which you have placed the release directory, Fluent.Inc. This shell script will execute your system’s command to send an image file to the video frame buffer. The script videocmd is set up to call the SGI system command memtovid. If you have a different system, you must copy the shell script videocmd to a new file and modify it to perform the proper task on your system (see the comments in videocmd for


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details). You can specify the name of your shell script using the Video Command text entry in the Animation Recording Options panel. In order to send a hardcopy file of the proper format to the video frame buffer, you must set up the hardcopy format using the Graphics Hardcopy panel, which can be displayed by clicking the Hardcopy Options... button in the Animation Recording Options panel. If you choose to perform a window dump to create the hardcopy file, the default window dump command used will also be videocmd. You can change this setting to use your own command. After setting the hardcopy options, click Apply instead of Save... in the Graphics Hardcopy panel to apply the change. Once you have set up the hardcopy format and system command, you can test the configuration by sending the picture in the current graphics window to the video frame buffer. This is done by clicking on Preview in the Animation Recording Options panel. (Note that this is another way to send a black video signal to your VTR when you are preblacking a tape). Choose Real-Time or Frame-By-Frame Recording There are two methods for recording an animation: real-time and frame-by-frame. These methods are described below: Real-Time can be used if the animation playback speed is fast enough to provide a reasonably smooth animation in real-time. This is only available if the selected record source is Screen. In this mode, FLUENT will simply turn VTR recording on, play the animation, then stop the recording. Frame-By-Frame is used to produce a higher-quality video animation by recording one frame at a time. For each animation frame, this method will 1) play the frame on the screen (and generate the hardcopy file, if needed), 2) preroll the VTR, and 3) record the frame. If the animation has 50 frames, this procedure is repeated 50 times, i.e., 50 record passes are made. This is the recommended method, because the real-time playback of the animation will usually be too slow and choppy. When recording in frame-by-frame mode, there is an optional setting called Frames/Pass, which can be used to try and speed up the frame-by-frame recording process. It specifies the number of animation frames recorded to tape per record pass. If the animation is long enough (200 frames or more), you can try setting this value to 2 or higher. For example, if you set this value to 2 for a 202-frame animation, it will record animation frame 1 during the first pass, frames 2 and 102 during the second pass, frames 3 and 103 during the third pass, and so on. This is possible only if the animation frames can be rendered in time to be inserted onto the tape during a record pass, so use this setting with caution.

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Set the Video Frame Hold Counts The video standard NTSC has a frame rate of 30 frames/sec (and the PAL standard has a rate of 25 frames/sec). At the NTSC rate, a 150-frame animation will take only 5 seconds to play. To stretch out the animation, you can record the same animation frame over 2 or more video frames. This is done by setting video frame hold counts for the beginning, middle, and end of the animation, using the Animation Recording Options panel controls described below: Begin Hold specifies the number of video frames to hold the first animation frame. It helps to hold the first frame for about 5 seconds (150 video frames for NTSC, or 125 for PAL) so that the viewer can get accustomed to the picture before the animation begins. Frame Hold specifies the number of video frames to hold each animation frame, other than the first and last. To slow down your recorded animation, try setting this value to 2 or 3. End Hold specifies the number of video frames to hold the last animation frame. You may want to hold the last animation frame for about 5 seconds to provide closure.

Check the Picture Quality As described in Section 27.7.1, there are several sacrifices made when sending a computer image to video, including loss of color and resolution. Some steps can be taken to minimize the problem using the Picture Options panel (Figure 27.7.5). Display this panel by clicking the Picture... button in the Video Control panel. Color Use these controls to ensure that all colors fall into the proper color space for your video device. Also, for best results, set the saturation and brightness levels to 80% or less. Window Size If you have a scan converter that converts a portion of the computer screen, you can set the graphics window to a particular pixel size to match the scan converter’s window size. You can also create a margin around the picture in the window to keep unwanted parts of the screen (such as the window border) out of the video image.

Make Sure Your Tape is Formatted (Preblacked) Before you can start the recording session, you need to make sure the tape has been preblacked with a time code or frame code. When you start with a brand new tape, you need to take time out and preblack the whole tape first. This can be done using the following steps:


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Figure 27.7.5: The Picture Options Panel

1. Rewind the tape to the beginning. 2. Select a preblack recording session by clicking on the Preblack radio button in the Video Control panel. 3. Send the VTR a black video signal using a scan converter or a hardcopy by clicking on the Preview button in the Animation Recording Options panel. 4. Click the Preblack button in the VTR Controls section of the Video Control panel to start the preblacking.

Start the Recording Session Make sure you have the proper recording session selected. If you are recording an animation, the Animation radio button should be selected. To start recording onto tape, you must first go to the “in point” on tape where you want the recording to begin. With a blank tape, it is important to start at about 20 seconds into the tape, so the VTR has a chance to preroll up to the in point. You can use the VTR button controls to position the tape, but an easier way to go to a certain point is to type the time code or frame code in the Time or Frame counter and press the key. For example, a time code of 00:02:36:07 is 2 minutes, 36 seconds, and 7 frames. In order to go to this position on the tape, you can enter the time code as 2:36:07, leaving out the leading zeros, or you can simply enter 23607, leaving out the leading zeros and colons.

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27.8 Histogram and XY Plots

Once your tape is at the start position for your recording session, click the Record button to start recording.

27.7.4

General Information

For other sources of information on video creation, check out these web sites on the Internet: • San Diego Supercomputer Center (SDSC) http://vis.sdsc.edu • Army High Performance Computing Research Center (AHPCRC) http://www.arc.umn.edu

27.8

Histogram and XY Plots

In addition to the many graphics tools already discussed, FLUENT also provides tools that allow you to generate XY plots and histograms of solution, file, and residual data. You can modify the colors, titles, legend, and axis and curve attributes to customize your plots. The following sections describe the XY and histogram plotting features in FLUENT. • Section 27.8.1: Plot Types • Section 27.8.2: XY Plots of Solution Data • Section 27.8.3: XY Plots of File Data • Section 27.8.4: XY Plots of Circumferential Averages • Section 27.8.5: XY Plot File Format • Section 27.8.6: Residual Plots • Section 27.8.7: Solution Histograms • Section 27.8.8: Modifying Axis Attributes • Section 27.8.9: Modifying Curve Attributes

27.8.1

Plot Types

Data can be plotted in XY (abscissa/ordinate) form or histogram form. Each form is described below.


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XY Plots An XY (abscissa/ordinate) plot is a line and/or symbol chart of data. Virtually any defined variable or function is accessible for this type of plot. Furthermore, you may read in an externally-generated data file in order to compare your results with experimental data. You can also use the XY-plot facility to plot out the residual histories of variables, or the time histories if you have a transient problem. FLUENT provides tools for controlling many aspects of the XY plot, including background color, legend, and axis and curve attributes. Figure 27.8.1 shows a sample XY plot.

Zones/Surfaces symmetry-3 wall-4

7.00e-02 6.00e-02 5.00e-02 4.00e-02

Static Pressure (pascal)

3.00e-02 2.00e-02 1.00e-02 -2.24e-10 -1.00e-02 -0.08

-0.06

-0.04

-0.02 -1.79e-09

0.02

0.04

0.06

0.08

Position (m)

Static Pressure

Figure 27.8.1: Sample XY Plot

To differentiate the data being displayed, you can customize the pattern, color and weight of the data lines and the shape, color, and size of the data markers. When an XY plot is displayed in the graphics window, you can use any of the mouse buttons to add text annotations to the plot. (See Section 27.2.4 for more information about the mouse-annotate function.) In addition, you can use any of the mouse buttons to move and resize the legend box.

Histograms A histogram plot is a bar chart of data. It is a representation of a frequency of distribution by means of rectangles of widths representing class intervals and with areas proportional to the corresponding frequencies. When a histogram plot is displayed in the graphics window, you can use any of the mouse buttons to add text annotations to the plot. (See

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Section 27.2.4 for more information about the mouse-annotate function.) Figure 27.8.2 shows a sample histogram.

25 22.5 20 17.5 15 12.5 10 7.5 5 2.5 0 0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

Density (kg/m3)

Histogram of Density

Figure 27.8.2: Sample Histogram

See Section 28.7 for information about printing histogram reports. For more information on histogram plots, see Section 27.8.7.

27.8.2

XY Plots of Solution Data

You can produce a very sophisticated XY plot by using data from several zones, surfaces, or files and modifying the axis and curve attributes. Using the capability for loading external data files, you can create plots that compare your FLUENT results with data from other sources. To get further information about the solution, you can investigate the frequency of distribution of the data using a histogram (see Section 27.8.7).

Steps for Generating Solution XY Plots You can create an XY plot of solution data using the Solution XY Plot panel (Figure 27.8.3). Plot −→XY Plot...


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Figure 27.8.3: The Solution XY Plot Panel

The basic steps for generating a solution XY plot are as follows: 1. Specify the variables(s) you are plotting: • To plot a variable on the y axis as a function of position on the x axis, turn on the Position on X Axis option and choose the variable to be plotted on the y axis in the Y Axis Function drop-down list. Select a category from the upper list and then choose the desired quantity in the lower list. (See Chapter 29 for an explanation of the variables in the list.) • To plot a variable on the x axis as a function of position on the y axis, turn on the Position on Y Axis option and choose the variable to be plotted on the x axis in the X Axis Function drop-down list. • To plot one variable as a function of another, turn off both the Position on X Axis and Position on Y Axis options and select the variables to be plotted in the X Axis Function and Y Axis Function drop-down lists. 2. Specify the plot direction: • To plot a variable as a function of position along a specified direction vector, select Direction Vector in the X Axis Function or Y Axis Function drop-down list (whichever is the position axis), and specify the components of the direction vector for plotting under Plot Direction. The position axis of the plot is indicated by the selection of Position on X Axis or Position on Y Axis. The positions plotted will have coordinate values that correspond to the dot product

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of the data coordinate vector with the plot direction vector. For example, if you are plotting a variable at the pressure outlet of the geometry shown in Figure 27.8.4, you would specify the Plot Direction vector (1,0,0) since you are interested in how the variable changes as a function of x. Figure 27.8.5 shows the resulting XY plot. (If you specified (0,1,0) as the plot direction, all variable values would be plotted at the same position (see Figure 27.8.6), since the y value is the same at every point on the pressure outlet.) • It is also possible to plot a variable as a function of position along the length of a specified curvilinear surface. The curvilinear surface must be piecewise linear and it cannot contain more than one closed curve, such as a complete circle. To plot a variable in this way, select Curve Length in the X Axis Function or Y Axis Function drop-down list (whichever is the position axis). Then specify the plot direction along the surface: to plot the variable along the direction of increasing curve length, select Default under Plot Direction; to plot the variable in the direction of decreasing surface length, select Reverse. To check the direction in which the variable will be plotted along a surface, select the surface in the Surfaces list and click Show under Plot Direction. FLUENT will display the selected surface in the graphics window, marking the start of the surface with a blue dot and the end of the surface with a red dot. FLUENT will also display arrows on the surface showing the direction in which the variable will be plotted. 3. Choose the surface(s) on which to plot data in the Surfaces list. Note that if you are plotting a variable as a function of position along the length of a curvilinear surface, you can select only one surface in the Surfaces list. 4. Set any of the options described below, or modify the attributes of the axes or curves as described in Sections 27.8.8 and 27.8.9. 5. Click the Plot button to generate the XY plot in the active graphics window. Note that you can use any of the mouse buttons to annotate the XY plot (see Section 27.2.4) or move the plot legend from its default position in the upper left corner of the graphics window.

Options for Solution XY Plots The options mentioned in the procedure above include the following. You can include data from an external file in the solution XY plot to compare your results with experimental data. You can also choose node or cell values to be plotted, and save the plot data to a file.


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Fluent Inc. Grid Thu Aug 31 1995

Figure 27.8.4: Geometry Used for XY Plot

pressure-outlet-6 3.00e+02

2.50e+02

2.00e+02

dyn-head

1.50e+02

1.00e+02

5.00e+01

0.00e+00 48

50

52

54

56

58

60

62

64

Position (in)

Fluent Inc. Dynamic Head Thu Aug 31 1995

Figure 27.8.5: Data Plotted at Outlet Using a Plot Direction of (1,0,0)

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pressure-outlet-6 3.00e+02

2.50e+02

2.00e+02

dyn-head

1.50e+02

1.00e+02

5.00e+01

0.00e+00 64

64

64

Position (in)

Fluent Inc. Dynamic Head Thu Aug 31 1995

Figure 27.8.6: Data Plotted at Outlet Using a Plot Direction of (0,1,0)

Including External Data in the Solution XY Plot To add external data to your XY plot for comparison with your results, you must first ensure that any external data files are in the format described in Section 27.8.5. You can then load the file(s) by clicking on the Load File... button and specifying the file(s) to be read in the resulting Select File dialog box (see Section 2.1.2). Once a file has been loaded, its title will appear in the File Data list. You can choose the data file(s) to be included in your plot from the titles in this list. To remove a file from the File Data list, select it and then click the Free Data button. Choosing Node or Cell Values In FLUENT you can choose to display the computed cell-center values or values that have been interpolated to the nodes. By default, the Node Values option is turned on, and the interpolated values are displayed. If you prefer to display the cell values, turn the Node Values option off. Node-averaged data curves may be somewhat smoother than curves for cell values. If you are displaying the XY plot to show the effect of a porous medium or fan, to depict a shock wave, or to show any other discontinuities or jumps in the plotted variable, you should use cell values; if you use node values in such cases, the discontinuity will be smeared by the node averaging for graphics and will not be shown clearly in the plot.


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Saving the Plot Data to a File Once you have generated an XY plot, you may want to save the plot data to a file. You can read this file into FLUENT at a later time and plot it alone using the File XY Plot panel, as described in Section 27.8.3, or add it to a plot of solution data, as described above. To save the plot data to a file, turn on the Write to File option in the Solution XY Plot panel. The Plot button will change to the Write... button. Clicking on the Write... button will invoke the Select File dialog box, in which you can specify a name and save a file containing the plot data. The format of this file is described in Section 27.8.5. To sort the saved plot data in order of ascending x axis value, turn on the Order Points option in the Solution XY Plot panel before you click the Write... button. This option is available only when the Write to File option is turned on.

27.8.3

XY Plots of File Data

In addition to plots of FLUENT data, you can also plot the data contained in external files. The File XY Plot panel allows you to display data read from external files in an abscissa/ordinate plot form. The format of the plot file is described in Section 27.8.5.

Steps for Generating XY Plots of Data in External Files You can create an XY plot of data contained in one or more external files using the File XY Plot panel (Figure 27.8.7). Plot −→File...

Figure 27.8.7: The File XY Plot Panel

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The steps for generating a file XY plot are as follows: 1. Load each external data file (with the format described in Section 27.8.5) by entering its name in the text field beneath the Files list and clicking on the Add... button (or pressing ). If you click Add... without specifying a name under Files (or if you specify an incorrect or duplicate name), a Select File dialog box will appear and you can specify one or more files there. When a file is loaded, its name will appear in the Files list and its title will appear in the Legend Entries list. Data in all loaded files will be plotted, so if you decide not to include one of the loaded files in the plot you must select it and click the Delete button to remove it. 2. Set any of the options described below, or modify the attributes of the axes or curves as described in Sections 27.8.8 and 27.8.9. 3. Click the Plot button to generate an XY plot of the data associated with all loaded files.

Options for File XY Plots The options mentioned in the procedure above include the following. You can change the plot title, legend title, or legend entry. Changing the Plot Title The plot title will appear in the caption box at the bottom of the graphics window. You can modify the plot title by changing the entry in the Plot Title text box in the File XY Plot panel (or by editing the caption box manually, as described in Section 27.2.3). Changing the Legend Entry When you plot data from a single file, the y axis of the plot will be labeled by the “legend entry.” To modify this label, click on the text in the Legend Entries list, edit the text that appears in the text field below the list, and then click the Change Legend Entry button (or hit ). When you next plot the data, the new legend entry will appear in the plot. Changing the Legend Title When you plot data from more than one file, a legend will appear in the upper left corner of the graphics window. By default, the legend will have no title. If you want to add a title, enter it in the Legend Title text field. The title will appear above the legend the next time you plot the data. Note that you can use any of the mouse buttons to annotate the plot (see Section 27.2.4) or move the legend from its default position.


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27.8.4

XY Plots of Circumferential Averages

You can also generate a plot of circumferential averages in FLUENT. This allows you to find the average value of a quantity at several different radial or axial positions in your model. FLUENT computes the average of the quantity over a specified circumferential area, and then plots the average against the radial or axial coordinate.

Steps for Generating an XY Plot of Circumferential Averages You can generate an XY plot of circumferential averages in the radial direction using the circum-avg-radial text command: plot −→circum-avg-radial or you can use the circum-avg-axial text command to generate an average in the axial direction: plot −→circum-avg-axial The steps for generating an XY plot of circumferential averages are as follows: 1. Specify the variable to be averaged by typing its name when FLUENT prompts you for averages of. You can press to see a list of available variables. 2. Choose the surface on which to plot data by typing its name when FLUENT prompts you for on surface.

!

Use the Grid Display panel to see a list of surfaces on which you can plot data. (Pressing will not show a list of available surfaces.) 3. Specify the number of bands to be created. (The default number of bands is 5.) FLUENT will create circumferential bands by iso-clipping the specified surface into equal bands of radial or axial coordinate. An example of the iso-clips created is shown in Figure 27.8.8. (The radial or axial coordinate is derived from the rotation axis of the Reference Zone specified in the Reference Values panel.) FLUENT then computes the average of the variable for each band using the area-weighted average described in Section 28.5.1. Finally, it plots the average of the variable as a function of radial or axial coordinate. Figure 27.8.9 shows an example of an XY plot of circumferential averages using radial coordinates. When the circumferential average plot is generated, FLUENT also creates a new surface called radial-bands or axial-bands, which contains the iso-clips described above (see Figure 27.8.8). You can use this surface to generate other XY plots. For more information on the creation and manipulation of surfaces, see Chapter 26.

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iso-clips

X Z

Y

Iso-Clips for Circumferential Average

Figure 27.8.8: Iso-Clips Created For Circumferential Averaging

1.02e+05 1.02e+05 1.02e+05 1.01e+05 1.00e+05

Total Pressure

1.00e+05 9.95e+04 9.90e+04 9.85e+04 9.80e+04 9.75e+04 0.17

X

Y

0.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

0.26

Radius

Z

Circumferential Averages

Figure 27.8.9: XY Plot of Circumferential Averages


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Customizing the Appearance of the Plot If you want to customize the appearance of the axes or curves in a circumferential average plot, you can save the plot data to a file (using the plot-to-file text command, as described below), read the file into FLUENT and plot it again (using the File XY Plot panel, as described in Section 27.8.3), and then use the Axes and Curves panels (as described in Sections 27.8.8 and 27.8.9) to modify the appearance of the plot. To save the plot data to a file, first use the plot-to-file text command to specify the name of the file. plot −→ file-set −→plot-to-file Then generate the circumferential average XY plot as described above. FLUENT will display the plot in the graphics window, and also save the plot data to the specified file.

27.8.5

XY Plot File Format

The XY file format read or written by FLUENT includes the following information: • The title of the plot • The label for the abscissa and the ordinate • Cortex variables and pairs of abscissa/ordinate data for each curve in the plot The following sample file illustrates the XY file format: (title "Velocity Magnitude") (labels "Position" "Velocity Magnitude") ((xy/key/label "pressure-inlet-8") (xy/key/visible? #t) (xy/line/pattern "--") 0.0000 230.097 0.0625 160.551 0.1250 149.205 ... 0.5000 183.007 ) Similar to the case file format, parentheses bound the various pieces of information in the formatted, ASCII file. The title (title " ") and labels (labels " ") must be first in the file, then each curve has information in the form ((cxvar value) x y x y x y ...), where there may be zero or more Cortex variables defined for each curve.

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You do not have to include Cortex variables to import your XY data. For example, you may wish to import experimental data to compare with the FLUENT solution. The following example would use the default Cortex variables in the code to define the data. After you import the file into FLUENT, you could then use the Axes panel and the Curves panel to customize the XY plot, as described in Sections 27.8.8 and 27.8.9. (title "Experiment, Run 11") (labels "X, m" "Cp") ( 0 1.5 1.5 1.3 3.2 1.5 5.1 1.2 )

27.8.6

Residual Plots

Residual history can be displayed using an XY plot. The abscissa of the plot corresponds to the number of iterations and the ordinate corresponds to the log-scaled residual values. To plot the current residual history, click the Plot button in the Residual Monitors panel. Plot −→Residuals... For additional information about using the Residual Monitors panel to plot residuals, see Section 24.16.1.

27.8.7

Solution Histograms

Histograms can be displayed in a graphics window using a bar chart (or printed in the console window, as described in Section 28.7). The abscissa of the chart is the desired solution quantity and the ordinate is the percentage of the total number of cells.

Steps for Generating Histogram Plots You can create a histogram plot of solution data using the Solution Histogram panel (Figure 27.8.10). Plot −→Histogram... The steps for generating a histogram plot are as follows: 1. Choose the scalar quantity to be plotted in the Histogram Of drop-down list. Select a category in the upper list and then select the desired quantity in the lower list. (See Chapter 29 for an explanation of the variables in the list.)


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Figure 27.8.10: The Solution Histogram Panel

2. Set the number of data intervals that will be plotted in the histogram in the Divisions field. By default there will be 10 intervals (“bars”) in the histogram plot. If you want to resolve the histogram plot to finer intervals, increase the number of Divisions. You may want to click the Compute button to update the Min and Max fields when you are trying to decide how many divisions to plot. 3. Set the option described below, if desired, or modify the attributes of the axes or curves as described in Sections 27.8.8 and 27.8.9. 4. Click the Plot button to generate the histogram plot in the active graphics window.

Options for Histogram Plots Other than the axis and curve attribute controls mentioned in the procedure above, the only option for histogram plotting is the ability to specify a subrange of values to be plotted. Specifying the Range of Values Plotted By default, the range of values included in the histogram plot is automatically set to the range of values in the entire domain for the selected variable. If you want to focus in on a smaller range of values, you can restrict the range to be displayed. To manually set the range of values, turn off the Auto Range option in the Solution Histogram panel. The Min and Max fields will become editable, and you can enter the new range of values to be plotted. To show the default range at any time, click the Compute button and the Min and Max fields will be updated.

27.8.8

Modifying Axis Attributes

You can modify the appearance of the XY and histogram plot axes by changing the parameters that control the labels, scale, range, numbers, and major and minor rules.

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For each type of plot (solution XY, file XY, residual, histogram, etc.), you can set different axis parameters in the Axes panel (Figure 27.8.11). Note that the title following Axes in the panel indicates which plot environment you are changing (e.g., the Axes - Solution XY Plot panel controls axis parameters for solution XY plots).

Figure 27.8.11: The Axes Panel

To open the Axes panel for a particular plot type, click the Axes... button in the appropriate panel (e.g., the Solution XY Plot, File XY Plot, or Residual Monitors panel).

Using the Axes Panel The Axes panel allows you to independently control the characteristics of the ordinate (y axis) and abscissa (x axis) on an XY plot or histogram. To set parameters for one axis or the other, you will follow the procedure below: 1. Choose the axis for which you want to modify the attributes by selecting X or Y under Axis. 2. Set the desired parameters. 3. Click Apply and then choose the other axis and repeat the steps, if desired. Your changes to the axis attributes will appear in the graphics window the next time you generate a plot.


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Changing the Axis Label If you want to modify the label for the axis, you can do so by editing the Label text field in the Axes panel. Changing the Format of the Data Labels You can change the format of the labels that define the primary data divisions on the axes using the controls under the Number Format heading in the Axes panel. • To display the real value with an integral and fractional part (e.g., 1.0000), select float in the Type drop-down list. You can set the number of digits in the fractional part by changing the value of Precision. • To display the real value with a mantissa and exponent (e.g., 1.0e-02), select exponential in the Type drop-down list. You can define the number of digits in the fractional part of the mantissa in the Precision field. • To display the real value with either float or exponential form, depending on the size of the number and the defined Precision, choose general in the Type drop-down list. Choosing Logarithmic or Decimal Scaling By default, decimal scaling is used for both axes (except for the y axis in residual plots, which uses a log scale). If you want to change to a logarithmic scale, turn on the Log option in the Axes panel. To return to a decimal scale, turn off the Log option. Note that when you are using the logarithmic scale, the Range values are the exponents; to specify a logarithmic range from 1 to 10000, for example, you will specify a minimum value of 1 and a maximum value of 4. Resetting the Range of the Axis By default, the extents of the axis will range from the minimum value plotted to the maximum value plotted. If you want to change the range or extents of the axis, you can do so by turning off the Auto Range option in the Axes panel and setting the new Minimum and Maximum values for the Range. This feature is useful when you are generating a series of plots and you want the extents of one or both of the axes to be the same, even if the range of plotted values differs. (For example, if you are generating plots of temperature on several different wall zones, you might want the minimum and maximum temperature on the y axis to be the same in every plot so that you can easily compare one plot with another. You would determine a temperature range that includes the temperatures on all walls, and use that as the range for the y axis in each plot.)

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Controlling the Major and Minor Rules FLUENT allows you to display major and/or minor rules on the axes. Major and minor rules are the horizontal or vertical lines that mark, respectively, the primary and secondary data divisions and span the whole plot window to produce a “grid.” To add major or minor rules to the plot, turn on the Major Rules or Minor Rules option. You can then specify a color and weight for each type of rule. Under the Major Rules or Minor Rules heading, select the desired color for the lines in the Color drop-down list and specify the line thickness in the Weight field. A line of weight 1.0 is normally 1 pixel wide. A weight of 2.0 would make the line twice as thick (i.e., 2 pixels wide).

27.8.9

Modifying Curve Attributes

The data curves in XY plots and histograms can be represented by any combination of lines and markers. You can modify the attributes of the curves, including the patterns, weights, and colors of the lines, and the symbols, sizes, and colors of the markers. For each type of plot (solution XY, file XY, residual, histogram, etc.), you can set different curve parameters in the Curves panel (Figure 27.8.12). Note that the title following Curves in the panel indicates which plot environment you are changing (e.g., the Curves - Solution XY Plot panel controls curve parameters for solution XY plots).

Figure 27.8.12: The Curves Panel To open the Curves panel for a particular plot type, click the Curves... button in the appropriate panel (e.g., Solution XY Plot, File XY Plot, or Residual Monitors panel).

Using the Curves Panel The Curves panel allows you to independently control the characteristics of each data curve in an XY plot or histogram. To set parameters for a curve, you will follow the procedure below:


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1. Specify the curve for which you want to modify the attributes by increasing or decreasing the Curve # counter. The curves are numbered sequentially, starting from 0. For example, if you were plotting flow-field values on two surfaces, the first surface would be curve 0, and the second, curve 1. If the plot contains only one curve, the Curve # is set to 0 and is not editable. 2. Set the desired line and/or marker parameters as described below. 3. Click Apply and then choose another Curve # and repeat the steps, if desired. Your changes to the curve attributes will appear in the graphics window the next time you generate a plot. Changing the Line Style You can control the pattern, color, and weight of the line using the controls under the Line Style heading: • To set the line pattern for the curve, choose one of the items in the Pattern dropdown list. Except for center and phantom lines, the list displays examples of the pattern choices. A center line alternates a very long dash and a short dash and a phantom line alternates a very long dash and a double short dash. Note that selecting the second item in the drop-down list, represented by 4 short dashes, will result in a solid-line curve.

!

If you do not want the data points to be connected by any type of line (i.e., if you plan to use just markers), select the “blank” choice, which is the first item in the Pattern list. • To set the color of the line, pick one of the choices in the Color drop-down list. • To define the line thickness, set the value of Weight. A line weight of 1.0 is normally 1 pixel wide. Therefore, a weight of 2.0 would make the line twice as thick (i.e., 2 pixels wide).

Changing the Marker Style You can control the symbol, color, and size for the data marker using the controls under the Marker Style heading: • To set the symbol used to mark data, choose one of the items in the Symbol dropdown list. The list displays examples of the symbol choices. For example, in plotting pressure-coefficient data on the upper and lower surfaces of an airfoil, the symbol /*\ (filled-in upward-pointing triangle) could be used for the marker representing

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27.9 Turbomachinery Postprocessing

the upper surface data, and the symbol \*/ (filled-in downward-pointing triangle) could be used for the marker representing the lower surface data.

!

If you do not want the data points to be represented by markers (i.e., if you plan to use just a line connecting the data points), select the “blank” choice, which is the first item in the Style list. • To set the color of the marker, pick one of the choices in the Color drop-down list. • To define the size of the data marker, set the value of Size. A symbol of size 1.0 is 3.0% of the height of the display screen, except for the “.” symbol, which is always one pixel.

Previewing the Curve Style To see what a particular setting will look like in the plot, you can preview it in the Sample window of the Curves panel. A single marker and/or line will be shown with the specified style attributes.

27.9

Turbomachinery Postprocessing

In addition to the many graphics tools already discussed, FLUENT also provides turbomachinery-specific postprocessing features which can be accessed once you have defined the topology of the problem. Information on postprocessing for turbomachinery applications is provided in the following sections: • Section 27.9.1: Defining the Turbomachinery Topology • Section 27.9.2: Generating Reports of Turbomachinery Data • Section 27.9.3: Displaying Turbomachinery Averaged Contours • Section 27.9.4: Displaying Turbomachinery 2D Contours • Section 27.9.5: Generating Averaged XY Plots of Turbomachinery Solution Data • Section 27.9.6: Globally Setting the Turbomachinery Topology • Section 27.9.7: Turbomachinery-Specific Variables

27.9.1

Defining the Turbomachinery Topology

In order to establish the turbomachinery-specific coordinate system used in subsequent postprocessing functions, FLUENT requires you to define the topology of the flow domain. The procedure for defining the topology is described below, along with details about the boundary types.


27-105


! Note that the current implementation of the turbomachinery topology definition for postprocessing is no longer limited to one row of blades at a time. If your geometry contains multiple rows of blades, you can define all turbomachinery topologies simultaneously. You can name and/or manage all topologies and perform various turbomachinery postprocessing tasks on a single topology or on all topologies at once. To define the turbomachinery topology in FLUENT, you will use the Turbo Topology panel (Figure 27.9.1). Define −→Turbo Topology...

Figure 27.9.1: The Turbo Topology Panel The steps for defining topology for your turbomachinery application are as follows: 1. Select a boundary type under Boundaries (e.g., Hub in Figure 27.9.1). The boundary types are described in detail below. 2. In the Surfaces list, choose the surface(s) that represent the boundary type you selected in step 1. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces of that type will be selected

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automatically in the Surfaces list (or deselected, if they are all selected already). Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 3. Repeat the steps above for all the boundary types that are relevant for your model. 4. Enter a name in the Turbo Topology Name field or keep the default name. 5. Click Define to complete the definition of the boundaries. FLUENT will inform you that the turbomachinery postprocessing functions have been activated, and the Turbo menu will appear in FLUENT’s menu bar at the top of the console window. 6. To view a defined topology, select the topology from the Turbo Topology Name dropdown list and click Display. The defined topology is shown in the active graphics window. This allows you to visually check the boundaries to ensure that you have defined them correctly. 7. To edit a defined topology, select the topology from the Turbo Topology Name drop-down list, make the appropriate changes and click Modify. 8. To remove a defined topology, select the topology from the Turbo Topology Name drop-down list and click Delete. Note that the topology setup that you define will be saved to the case file when you save the current model. Thus, if you read this case back into FLUENT, you do not need to set up the topology again.

Boundary Types The boundaries for the turbomachinery topology are as follows (see Figure 27.9.2): Hub is the wall zone(s) forming the lower boundary of the flow passage (generally toward the axis of rotation of the machine). Casing is the wall zone(s) forming the upper boundary of the flow passage (away from the axis of rotation of the machine). Theta Periodic is the periodic boundary zone(s) on the circumferential boundaries of the flow passage.


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Theta Min and Theta Max are the wall zones at the minimum and maximum angular (θ) positions on a circumferential boundary. Inlet is the inlet zone(s) through which the flow enters the passage. Outlet is the outlet zone(s) through which the flow exits the passage. Blade is the wall zone(s) that defines the blade(s) (if any). Note that these zones cannot be attached to the circumferential boundaries. For this situation, use Theta Min and Theta Max to define the blade. TOP view of passage theta periodic (periodic boundaries)

inlet

outlet

blade theta min (wall) theta max (wall)

Figure 27.9.2: Turbomachinery Boundary Types

27.9.2

Generating Reports of Turbomachinery Data

Once you have defined your turbomachinery topologies, as described in Section 27.9.1, you can report a number of turbomachinery quantities, including mass flow, swirl number, torque, and efficiencies. To report turbomachinery quantities in FLUENT, you will use the Turbo Report panel (Figure 27.9.3). Turbo −→Report... The procedure for using this panel is as follows: 1. Under Averages, specify whether you want to report Mass Weighted or Area Weighted averages.

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Figure 27.9.3: The Turbo Report Panel


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2. Under Turbo Topology, specify a predefined turbomachinery topology from the drop-down list. 3. Click Compute. FLUENT will compute the turbomachinery quantities as described below, and display their values. 4. If you want to save the reported values to a file, click Write... and specify a name for the file in the resulting Select File dialog box.

Computing Turbomachinery Quantities Mass Flow The mass flow rate through a surface is defined as follows: m ˙ =

Z

A

(ρ~v · n ˆ )dA

(27.9-1)

where A is the area of the inlet or outlet, ~v is the velocity vector, ρ is the fluid density, and n ˆ is a unit vector normal to the surface. Swirl Number The swirl number is defined as follows: Z

rvθ (~v · n ˆ ) dS

r

vz (~v · n ˆ ) dS

SW =

S Z

(27.9-2)

S

where r is the radial coordinate (specifically, the radial distance from the axis of rotation), vθ is the tangential velocity, ~v is the velocity vector, n ˆ is a unit vector normal to the surface, S denotes the inlet or outlet, and 1Z r= rdS S S

(27.9-3)

Average Total Pressure The area-averaged total pressure is defined as follows: Z

pt =

A

pt dA (27.9-4)

A

where pt is the total pressure and A is the area of the inlet or outlet.

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The mass-averaged total pressure is defined as follows: Z

pt = ZA

(ρpt |~v · n ˆ |)dA (27.9-5)

A

(ρ |~v · n ˆ |)dA

where pt is the total pressure, A is the area of the inlet or outlet, ~v is the velocity vector, ρ is the fluid density, and n ˆ is a unit vector normal to the surface. Average Total Temperature The area-averaged total temperature is defined as follows: Z

Tt =

A

Tt dA (27.9-6)

A

where Tt is the total temperature and A is the area of the inlet or outlet. The mass-averaged total temperature is defined as follows: Z

T t = ZA

(ρTt |~v · n ˆ |)dA

A

(27.9-7) (ρ |~v · n ˆ |)dA

where Tt is the total temperature, A is the area of the inlet or outlet, ~v is the velocity vector, ρ is the fluid density, and n ˆ is a unit vector normal to the surface. Average Flow Angles The area-averaged flow angles are defined as follows: Z

A αr = tan−1  Z



A



vθ dA 

vz dA

 

(27.9-8)

in the radial direction, and Z

ZA αθ = tan−1   

A




vr dA 

vz dA

 

(27.9-9)

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in the tangential direction, where vz , vr , and vθ represent the axial, radial, and tangential velocities, respectively. The mass-averaged flow angles are defined as follows: Z

A αr,m = tan−1  Z



A



(ρvr )dA 

(ρvz )dA

 

(27.9-10)

in the radial direction, and Z

A αθ,m = tan−1  Z



A



(ρvθ )dA 

(ρvz )dA

 

(27.9-11)

in the tangential direction. Passage Loss Coefficient The engineering loss coefficient is defined as follows: pt,i − pt,o 1 ρv 2i 2

KL =

(27.9-12)

where pt,i is the mass-averaged total pressure at the inlet, pt,o is the mass-averaged total pressure at the outlet, ρ is the density of the fluid, and v i is the mass-averaged velocity magnitude at the inlet. The normalized loss coefficient is defined as follows: KL,n =

pt,i − pt,o pt,i − ps,o

(27.9-13)

where ps,o is the mass-averaged static pressure at the outlet. Axial Force The axial force on the rotating parts is defined as follows: Fa =

Z S

(τ · n ˆ ) dS · a ˆ

(27.9-14)

where S represents the surfaces comprising all rotating parts, τ is the total stress tensor (pressure and viscous stresses), n ˆ is a unit vector normal to the surface, and a ˆ is a unit vector parallel to the axis of rotation.

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Torque The torque on the rotating parts is defined as follows: T =

Z S

ˆ )) dS · a ˆ (~r × (τ · n

(27.9-15)

where S represents the surfaces comprising all rotating parts, τ is the total stress tensor, n ˆ is a unit vector normal to the surface, ~r is the position vector, and a ˆ is a unit vector parallel to the axis of rotation. Efficiencies for Pumps and Compressors The definitions of the efficiencies for compressible and incompressible flows in pumps and compressors are described in this section. Efficiencies for turbines are described later in this section. Consider a pumping or compression device operating between states 1 and 2 as illustrated in Figure 27.9.4. Work input to the device is required to achieve a specified compression of the working fluid.

1

2

Work input to rotor

Figure 27.9.4: Pump or Compressor

Assuming that the processes are steady state, steady flow, and that the mass flow rates are equal at the inlet and outlet of the device (no film cooling, bleed air removal, etc.), the efficiencies for incompressible and compressible flows are as described below. Incompressible Flows For devices such as liquid pumps and fans at low speeds, the working fluid can be treated as incompressible. The efficiency of a pumping process with an incompressible working fluid is defined as the ratio of the head rise achieved by the fluid to the power supplied to the rotor/impeller. This can be expressed as follows: η=


Q(pt2 − pt1 ) Tω

(27.9-16)

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where Q pt T ω

= = = =

volumetric flow rate total pressure net torque acting on the rotor/impeller rotational speed

This definition is sometimes called the “hydraulic efficiency”. Often, other efficiencies are included to account for flow leakage (volumetric efficiency) and mechanical losses along the transmission system between the rotor and the machine providing the power for the rotor/impeller (mechanical efficiency). Incorporating these losses then yields a total efficiency for the system. Compressible Flows For gas compressors that operate at high speeds and high pressure ratios, the compressibility of the working fluid must be taken into account. The efficiency of a compression process with a compressible working fluid is defined as the ratio of the work required for an ideal (reversible) compression process to the actual work input. This assumes the compression process occurs between states 1 and 2 for a given pressure ratio. In most cases, the pressure ratio is the total pressure at state 2 divided by the total pressure at state 1. If the process is also adiabatic, then the ideal state at 2 is the isentropic state. From the foregoing definition, the efficiency for an adiabatic compression process can be written as ηc =

ht2,i − ht1 ht2 − ht1

(27.9-17)

where ht1 ht2 ht2,i

= = =

total enthalpy at 1 actual total enthalpy at 2 isentropic total enthalpy at 2

If the specific heat is constant, Equation 27.9-17 can also be expressed as ηc =

Tt2,i − Tt1 Tt2 − Tt1

(27.9-18)

where Tt1 Tt2 Tt2,i

= = =

total temperature at 1 actual total temperature at 2 isentropic total temperature at 2

Using the isentropic relation

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Tt2,i = Tt1

pt2 pt1

! γ−1 γ

(27.9-19)

where γ is the ratio of specific heats specified in the Reference Values panel. the efficiency can be written in the compact form

Tt1 ηc =

"

pt2 pt1

#

γ−1 γ

−1

(27.9-20)

Tt2 − Tt1

Note that this definition requires data only for the actual states 1 and 2. Compressor designers also make use of the polytropic efficiency when comparing one compressor with another. The polytropic efficiency is defined as follows:

ηc,p =

γ−1 ln ppt2 γ t1 Tt2 ln Tt1

(27.9-21)

Efficiencies for Turbines Consider a turbine operating between states 1 and 2 in Figure 27.9.5. Work is extracted from the working fluid as it expands through the turbine. Assuming that the processes are steady state, steady flow, and that the mass flow rates are equal at the inlet and outlet of the device (no film cooling, bleed air removal, etc.), turbine efficiencies for incompressible and compressible flows are as described below.

1

2

Work output from rotor

Figure 27.9.5: Turbine


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Incompressible Flows The efficiency of a turbine with an incompressible working fluid is defined as the ratio of the work delivered to the rotor to the energy available from the fluid stream. This ratio can be expressed as follows: η=

Tω Q(pt1 − pt2 )

(27.9-22)

where Q pt T ω

= = = =

volumetric flow rate total pressure net torque acting on the rotor/impeller rotational speed

Note the similarity between this definition and the definition of incompressible compression efficiency (Equation 27.9-16). As with hydraulic pumps and compressors, other efficiencies (e.g., volumetric and mechanical efficiencies) can be defined to account for other losses in the system. Compressible Flows For high-speed gas turbines operating at large expansion pressure ratios, compressibility must be accounted for. The efficiency of an expansion process with a compressible working fluid is defined as the ratio of the actual work extracted from the fluid to the work extracted from an ideal (reversible) process. This assumes that the expansion process occurs between states 1 and 2 for a given pressure ratio. In contrast to the compression process, the pressure ratio for expansion is the total pressure at state 1 divided by the total pressure at state 2. If the process is also adiabatic, then the ideal state at 2 is the isentropic state. From the foregoing definition, the efficiency for an adiabatic expansion process through a turbine can be written as ηc =

ht1 − ht2 ht1 − ht2,i

(27.9-23)

where ht1 ht2 ht2,i

= = =

total enthalpy at 1 actual total enthalpy at 2 isentropic total enthalpy at 2

If the specific heat is constant, Equation 27.9-23 can also be expressed as ηe =

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Tt1 − Tt2 Tt1 − Tt2,i

(27.9-24)



where Tt1 Tt2 Tt2,i

= = =

total temperature at 1 actual total temperature at 2 isentropic total temperature at 2

Using the isentropic relation Tt1 = Tt2,i

pt1 pt2

! γ−1 γ

(27.9-25)

the expansion efficiency can be written in the compact form Tt1 − Tt2

ηe =

"

Tt1 1 −

pt2 pt1

γ−1 γ

#

(27.9-26)

Note that this definition requires data only for the actual states 1 and 2. As with compressors, one may also define a polytropic efficiency for turbines. The polytropic efficiency is defined as follows:

ηe,p =

27.9.3

Tt1 Tt2 γ−1 pt1 ln γ pt2

ln

(27.9-27)

Displaying Turbomachinery Averaged Contours

Turbo averaged contours are generated as projections of the values of a variable averaged in the circumferential direction and visualized on an r-z plane. A sample plot is shown in Figure 27.9.7.

Steps for Generating Turbomachinery Averaged Contour Plots You can display contours using the Turbo Averaged Contours panel (Figure 27.9.6). Turbo −→Averaged Contours... The basic steps for generating a turbo averaged contour plot are as follows: 1. Select All or a specific predefined turbomachinery topology from the Turbo Topology drop down list. 2. Select the variable or function to be displayed in the Contours Of drop-down list. First select the desired category in the upper list; you may then select a related quantity in the lower list. (See Section 27.9.7 for a list of turbomachinery-specific variables, and see Chapter 29 for an explanation of the variables in the list.)


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Figure 27.9.6: The Turbo Averaged Contours Panel

3. Specify the number of contours in the Levels field. The maximum number of levels allowed is 100. 4. Set any of the options described below. 5. Click the Display button to draw the specified contours in the active graphics window. The resulting display will include the specified number of contours of the selected variable, with the magnitude on each one determined by equally incrementing between the values shown in the Min and Max fields. Note that the Min and Max values displayed in the panel are the minimum and maximum averaged values. These limits will in general be different from the global Domain Min and Domain Max, which are also displayed for your reference (see Figure 27.9.6).

Contour Plot Options The options mentioned in the procedure above include drawing color-filled contours (instead of line contours), specifying a range of values to be contoured, and storing the contour plot settings. These options are the same as those in the standard Contours panel. See Section 27.1.2 for details about using them.

27.9.4

Displaying Turbomachinery 2D Contours

In postprocessing a turbomachinery solution, it is often desirable to display contours on surfaces of constant pitchwise, spanwise, or meridional coordinate, and then project

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1.80e+00

1.63e+00

1.45e+00

1.28e+00

1.10e+00

Y 9.24e-01

Z

X

Averaged Turbo Contour - pressure (atm) (atm)

Figure 27.9.7: Turbo Averaged Filled Contours of Static Pressure

these contours onto a plane. This permits easier evaluation of the contours, especially for surfaces that are highly three-dimensional.

Steps for Generating Turbo 2D Contour Plots You can display contours using the Turbo 2D Contours panel (Figure 27.9.8). Turbo −→2D Contours... The basic steps for generating a turbo 2D contour plot are as follows: 1. Specify a specific predefined turbomachinery topology using the Turbo Topology drop-down list. 2. Specify whether you want to generate the contour plot on a surface of constant pitchwise value, spanwise value, or meridional value by selecting Pitchwise Value, Spanwise Value, or Meridional Value under Surface of Constant. 3. Enter a value for the fractional distance along the surface where you want to create the contour plot in the Fractional Distance field. The definition of the fractional distance depends on your selection under Surface of Constant: • If you selected Pitchwise Value in step 1, the fractional distance is Blade to Blade (fractional distance between the two blades). • If you selected Spanwise Value, the fractional distance is Hub to Casing.


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Figure 27.9.8: The Turbo 2D Contours Panel

• If you selected Meridional Value, the fractional distance is Inlet to Outlet. 4. Select the variable or function to be displayed in the Contours Of drop-down list. First select the desired category in the upper list; you may then select a related quantity in the lower list. (See Section 27.9.7 for a list of turbomachinery-specific variables, and see Chapter 29 for an explanation of the variables in the list.) 5. Specify the number of contours in the Levels field. The maximum number of levels allowed is 100. 6. Select the Projection Type. The choices are Axial, Radial, and Normalized Coordinates. 7. Set any of the options described below. 8. Click the Display button to draw the specified contours in the active graphics window. The resulting display will include the specified number of contours of the selected variable, with the magnitude on each one determined by equally incrementing between the values shown in the Min and Max fields.

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Contour Plot Options The options mentioned in the procedure above include drawing color-filled contours (instead of line contours), specifying a range of values to be contoured, and storing the contour plot settings. These options are the same as those in the standard Contours panel. See Section 27.1.2 for details about using them.

27.9.5

Generating Averaged XY Plots of Turbomachinery Solution Data

When comparing numerical solutions of turbomachinery problems to experimental data, it is often useful to plot circumferentially averaged quantities in the spanwise and meridional directions. This section describes how to do this in FLUENT.

Steps for Generating Turbo Averaged XY Plots To create an XY plot of circumferentially averaged solution data, you will use the Turbo Averaged XY Plot panel (Figure 27.9.9). Turbo −→Averaged XY Plot...

Figure 27.9.9: The Turbo Averaged XY Plot Panel The basic steps for generating a turbo averaged XY plot are as follows: 1. Select the variable or function to be plotted in the Y Axis Function drop-down list. First select the desired category in the upper list; you may then select a related quantity in the lower list. (See Section 27.9.7 for a list of turbomachinery-specific variables, and see Chapter 29 for an explanation of the variables in the list.) 2. Select All or a specific predefined turbomachinery topology from the Turbo Topology drop down list.


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3. Select the variable or function to be plotted in the X Axis Function drop-down list. The choices are Hub to Casing Distance and Meridional Distance. 4. Specify the desired value in the Fractional Distance field. The definition of the fractional distance depends on your selection of X Axis Function: • If you selected Hub to Casing Distance, the fractional distance is Inlet to Outlet. • If you selected Meridional Distance, the fractional distance is Hub to Casing. 5. (optional) Modify the attributes of the axes or curves as described in Sections 27.8.8 and 27.8.9. 6. Click the Plot button to generate the XY plot in the active graphics window. Note that you can use any of the mouse buttons to annotate the XY plot (see Section 27.2.4). If you wish to write the XY data to a file, follow these steps instead of Step 5 above: 1. Turn on the Write to File option. The Plot button will change to the Write... button. 2. Click Write.... 3. In the resulting Select File dialog box, specify a name for the plot file and save it.

27.9.6

Globally Setting the Turbomachinery Topology

In some cases, i.e., iso-surface creation, FLUENT allows you to globally set the current turbomachinery topology for your model using the Turbo Options panel (Figure 27.9.10). Turbo −→Options...

Figure 27.9.10: The Turbo Options Panel To set the current topology, select a topology from the Current Topology drop-down list and select OK.

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27.10 Fast Fourier Transform (FFT) Postprocessing

27.9.7

Turbomachinery-Specific Variables

The following turbomachinery-specific variables are available in FLUENT: • Meridional Coordinate • Abs Meridional Coordinate • Spanwise Coordinate • Abs (H-C) Spanwise Coordinate • Abs (C-H) Spanwise Coordinate • Pitchwise Coordinate • Abs Pitchwise Coordinate These variables are contained in the Grid... category of the variable selection drop-down list. See Chapter 29 for their definitions.

27.10

Fast Fourier Transform (FFT) Postprocessing

When trying to interpret time-sequence data from a transient solution, it is often useful to look at the data’s spectral (frequency) attributes. For instance, you may wish to determine the major vortex-shedding frequency from the time-history of the drag force on a body recorded during a FLUENT simulation. Or, you may want to compute the spectral distribution of static pressure data recorded at a particular location on a body surface. Similarly, you may need to compute the spectral distribution of turbulent kinetic energy using data for fluctuating velocity components. To interpret some of these time dependent data, you need to perform Fourier transform analysis. In essence, the Fourier transform enables you to take any time dependent data and resolve it into an equivalent summation of sine and cosine waves. FLUENT allows you to analyze your time dependent data using the Fast Fourier Transform (FFT) algorithm. Information on using the FFT algorithm in FLUENT is provided in the following sections: • Section 27.10.1: Limitations of the FFT Algorithm • Section 27.10.2: Windowing • Section 27.10.3: Fast Fourier Tranform • Section 27.10.4: Using the FFT Utility


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27.10.1

Limitations of the FFT Algorithm

• The FLUENT FFT module can only read inputs files in the FLUENT monitor and x-y file formats. • The FLUENT FFT module assumes that the input data have been sampled at equal intervals and are consecutive (in the order of increasing time).

27.10.2

Windowing

The discrete FFT algorithm is based on the assumption that the time-sequence data passed to the FFT corresponds to a single period of a periodically repeating signal. Since, in most situations, the first and the last data points will not coincide, the repeating signal implied in the assumption can often have a large discontinuity. The large discontinuity produces high-frequency components in the resulting Fourier modes, causing an aliasing error. You can condition the input signal before the transform by “windowing” it, in order to avoid this problem. Suppose that we have N consecutive discrete (time-sequence) data sampled with a constant interval, ∆t: φk ≡ φ(tk ),

tk ≡ k ∆t,

k = 0, 1, 2, ..., N − 1

(27.10-1)

Windowing is done by multiplying the original input data (φj ) by a window function, Wj : φ˜j = φj Wj

j = 0, 1, 2, ..., N − 1

(27.10-2)

FLUENT offers four different window functions. Hamming’s window: Wj =

(

0.54 − 0.46 cos(8πj/N ) 1

j ≤ N/8, j ≥ 7N/8 N/8 < j < 7N/8

(27.10-3)

Hanning’s window: Wj =

(

0.5(1 − cos(8πj/N )) 1

Barlett’s window: Wj =

   8j/N  

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8(1 − j/N ) 1

j ≤ N/8, j ≥ 7N/8 N/8 < j < 7N/8

(27.10-4)

j ≤ N/8 j ≥ 7N/8 N/8 < j < 7N/8

(27.10-5)



Blackman’s window: Wj =

(

0.42 − 0.5 cos(8πj/N ) + 0.08 cos(16πj/N ) 1

j ≤ N/8, j ≥ 7N/8 N/8 < j < 7N/8

(27.10-6)

These window functions preserve a large fraction (3/4) of the original data, affecting 1/4 of the data on both ends only.

27.10.3

Fast Fourier Transform (FFT)

The Fourier transform utility in FLUENT allows you to compute the Fourier transform of a signal, φ(t), a real-valued function, from a finite number of its sampled points. The discrete Fourier transform of φk is defined by:

φk =

N −1 X

φˆn e2πikn/N

k = 0, 1, 2, ...N − 1

(27.10-7)

n=0

where φˆn are the discrete Fourier coefficient which can be obtained from: −1 1 NX φˆn = φk e−2πikn/N N k=0

n = 0, 1, 2, ...N − 1

(27.10-8)

Equation 27.10-7 and Equation 27.10-8 form a Fourier transform pair that allows us to determine one from the other. Note that when we follow the convention of varying n from 0 to N-1 in Equation 27.10-7 or Equation 27.10-8 instead of from −N/2 to N/2, the range of index 1 ≤ n ≤ N/2 − 1 corresponds to positive frequencies, and the range of index N/2 + 1 ≤ n ≤ N − 1 corresponds to negative frequencies. n = 0 still corresponds to zero frequency. For the actual calculation of the transforms, FLUENT adopts the so-called fast Fourier transform (FFT) algorithm which significantly reduces operation counts in comparison to the direct transform. Furthermore, unlike most FFT algorithms in which the number of data should be a power of 2, the FFT utility in FLUENT employs a prime-factor algorithm[268]. The number of data points permissible in the prime-factor FFT algorithm is any products of mutually prime factors from the set 2,3,4,5,7,8,9,11,13,16, with a maximum value of 720720 = 5 × 7 × 9 × 11 × 13 × 16. Thus, the prime-factor FFT preserves the original data better than the conventional FFT. Just prior to computing the transform, FLUENT determines the largest permissible number of data points based on the prime factors, discarding the rest of the data.


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27.10.4

Using the FFT Utility

The FLUENT FFT utility is available through the Fourier Transform (Spectral Analysis) panel (Figure 27.10.1). To access the Fourier Transform (Spectral Analysis) panel, select the FFT... option under the Plot menu. Plot −→FFT... Note that the FFT utility options described in this section are also available in the plot/fft command in the text interface. plot −→fft

Loading a File for Spectral Analysis FFT analysis requires an input signal data file consisting of time-sequence data. To load an input signal data file into the Fourier Transform (Spectral Analysis) panel, click the Load Input File button. This displays a file selection dialog box where you can browse through your file directories and locate your data file containing your time-sequence data. Once the file is located and selected, click OK to dismiss the file selection dialog and load the data file into the Fourier Transform (Spectral Analysis) panel (Figure 27.10.1).

Figure 27.10.1: The Fourier Transform (Spectral Analysis) Panel

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To remove a file from the Files list, select it and then click the Free Data button.

Customizing the Input With the input signal data file loaded into the Fourier Transform (Spectral Analysis) panel, you may want to customize the input signal data set. You can customize the input signal by clicking the Plot/Prune Input Signal button. This displays the Plot/Prune Input Signal panel (Figure 27.10.2).

Figure 27.10.2: The Plot/Prune Input Signal Panel

The Plot/Prune Input Signal panel allows you to analyze a portion of the input signal, view input signal statistics (minimum, maximum, mean, and variance), and set title and label information for the input signal data file. Customizing the Input Signal Data Set By default, the Process the whole data option is turned on so that the entire data set is analyzed. To analyze a portion of the input signal, turn off the Process the whole data option and specify the data range by entering Min and Max values under X-axis Range. The Set Defaults button will reset the original values for the Min and Max fields under X-axis Range and turn on the Process the whole data option.


27-127


Viewing Data Statistics To aid in the signal analysis, whether for the entire input signal or for a certain range of data, the Signal Statistics portion of the Plot/Prune Input Signal panel displays signal information such as minimum, maximum, and average signal values, as well as signal variance. Customizing Titles and Labels You can create a new title or edit the original title for the input signal plot by entering a text string in the Signal Plot Title text box. Likewise, you can create a new axis label or edit the original axis label by entering a text string into either the Y-axis Label text box or the X-axis Label text box. Applying the Changes in the Input Signal Data Apply any changes you have made in the Plot/Prune Input Signal panel and view a plot of the input signal by clicking the Apply/Plot Signal button.

Customizing the Output In most practical applications with CFD data, you may want to find out how much power or energy is contained in a certain frequency range, but do not want to distinguish positive and negative frequency. In recognition of this, all the outputs from the FFT module in FLUENT pertain to one-sided spectra for the range of positive frequency. The Fourier Transform (Spectral Analysis) panel, Figure 27.10.1, lets you set several different functions for the x and y axes, apply different FFT windowing techniques, and set various output options. Specifying a Function for the Y-Axis You can choose the y-axis function using the Y Axis Function drop-down list. Available options for the y-axis functions are: Power Spectral Density is defined by: E(fn ) = |φˆ0 |2 E(fn ) = 2 |φˆn |2

n = 1, 2, ..., N/2

(27.10-9)

Magnitude or amplitude, is the square-root of the power spectral density,

A(fn ) ≡

27-128

q

E(fn )

n = 0, 1, 2, ..., N/2

(27.10-10)



Sound Pressure Level in dB For either general or acoustic data, when the sampled data is pressure (e.g., static pressure or sound pressure), you can compute the power in decibel units using:

Lsp (fn ) = 10 log10

p02 (fn ) 2 Pref

(dB)

(27.10-11)

where p02 (fn ) is the power spectral density of the pressure fluctuation and Pref is the reference acoustic power that is currently hardwired to a value appropriate for air ( i.e., 4 × 10−10 W or 1.3649 × 10−9 Btu/h). Sound Amplitude in dB is exactly a one-half of the sound pressure level in Equation 27.10-11. This quantity is also applicable for acoustics analysis.

Asp (fn ) = 10 log10

v u 02 u p (fn ) t 2 Pref

(dB)

(27.10-12)

Further graphical customizations for the y-axis are available by clicking the Axes... button. For more information, see Section 27.8.8. Specifying a Function for the X-Axis There are three options for the x-axis function you can choose from. They are all related to the discrete frequencies at which the Fourier coefficients are computed. You can apply specific analytic functions for the x-axis using the X Axis Function drop-down list. Available options for the x-axis functions are: Frequency is defined as:

fn =

1 n N ∆t

n = 0, 1, 2, ..., N/2

(27.10-13)

where N is the number of data points used in the FFT. Strouhal Number is the non-dimensionalized version of the frequency defined in Equation 27.10-13:

Stn ≡

fn Lref Uref

(27.10-14)

where Lref and Uref are the reference length and velocity scales specified via the Report/Reference Values panel.


27-129


Frequency Index is the index n(= 0, 1, 2, ..., N/2) in Equation 27.10-13. Further graphical customizations for the x-axis are available by clicking the Axes... button. For more information, see Section 27.8.8. Specifying Output Options You can write out the FFT data directly to a file by choosing the Write FFT to File option under Options in the Fourier Transform (Spectral Analysis) panel. Once the Write FFT to File option is selected, click the Write FFT button to display a file selection dialog box where you can choose a file and/or a location to hold the FFT data. Further customizations for how the FFT data is displayed are available by clicking the Curves... button. For more information, see Section 27.8.9. Specifying a Windowing Technique You can use the various windowing techniques described in Section 27.10.2 by selecting any of the Window options in the Fourier Transform (Spectral Analysis) panel. By default, None is selected so that no windowing technique is applied. Specifying Labels and Titles You can assign a title for your FFT plot using the Plot Title text field. By default, FLUENT prepends the string “Spectral Analysis of” to the title of the input data file. You can also assign y-axis and x-axis labels for your FFT plot using the Y-axis Label and X-axis Label text fields, respectively. By default, FLUENT assigns the Y-axis Label and the X-axis Label to the particular selection of Y-axis Function and X-axis Function.

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Chapter 28.

Alphanumeric Reporting

FLUENT provides tools for computing and reporting integral quantities at surfaces and boundaries. These tools enable you to find the mass flow rate and heat transfer rate through boundaries, the forces and moments on boundaries, and the area, integral, flow rate, average, and mass average (among other quantities) on a surface or in a volume. In addition, you can print histograms of geometric and solution data, set reference values for the calculation of non-dimensional coefficients, and compute projected surface areas. You can also print or save a summary report of the models, boundary conditions, and solver settings in the current case. These features are described in the following sections. • Section 28.1: Reporting Conventions • Section 28.2: Fluxes Through Boundaries • Section 28.3: Forces on Boundaries • Section 28.4: Projected Surface Area Calculations • Section 28.5: Surface Integration • Section 28.6: Volume Integration • Section 28.7: Histogram Reports • Section 28.8: Reference Values • Section 28.9: Summary Reports of Case Settings Reporting tools for the discrete phase are described in Section 21.13.

28.1

Reporting Conventions

For 2D problems, FLUENT computes all integral quantities per unit depth. For axisymmetric problems, all integral quantities are computed for an angle of 2π radians.


28-1


28.2

Fluxes Through Boundaries

For selected boundary zones, you can compute the following quantities: • The mass flow rate through a boundary is computed by summing the dot product of the density times the velocity vector and the area projections over the faces of the zone. • The total heat transfer rate through a boundary is computed by summing the total heat transfer rate, q = qc +qr , over the faces, where qc is the convective heat transfer rate and qr is the radiation heat transfer rate. The computation of the heat transfer through the face depends on the specified boundary condition. For example, the conduction heat transfer on a constant-temperature wall face would be the product of the thermal conductivity with the dot product of the area projection and the temperature gradient. For flow boundaries, the total heat transfer rate is the flow rate of the conserved quantity. Depending on the models that are being used, the total heat transfer rate may include the convective flow of sensible or total enthalpy, diffusive flux of energy, etc. • The radiation heat transfer rate through a boundary is computed by summing the radiation heat transfer rate qr over the faces. The computation of the radiation heat transfer depends on the radiation model used. For example, you might use flux reporting to compute the resulting mass flow through a duct with pressure boundaries specified at the inlet and exit.

Flux Reporting with Particles and Volumetric Sources Note that the reported mass and heat balances address only flow that enters or leaves the domain through boundaries; they do not include the contributions from user-defined volumetric sources or particle injections. For this reason, a mass or heat imbalance may be reported. To determine if a solution involving a discrete phase is converged, you can compare this imbalance with the change in mass flow or heat content computed in the particle tracking summary report. The net flow rate or heat transfer rate reported in the Flux Reports panel should be nearly equal to the Change in Mass Flow or Heat Content in the summary report generated from the Particle Tracks panel.

28.2.1

Generating a Flux Report

To obtain a report of mass flow rate, heat transfer rate, or radiation heat transfer rate on selected boundary zones, use the Flux Reports panel (Figure 28.2.1). Report −→Fluxes... The steps for generating the report are as follows:

28-2


28.2 Fluxes Through Boundaries

Figure 28.2.1: The Flux Reports Panel

1. Specify which flux computation you are interested in by selecting Mass Flow Rate, Total Heat Transfer Rate, or Radiation Heat Transfer Rate under Options. 2. In the Boundaries list, choose the boundary zone(s) on which you want to report fluxes. If you want to select several boundary zones of the same type, you can select that type in the Boundary Types list instead. All of the boundaries of that type will be selected automatically in the Boundaries list (or deselected, if they are all selected already). Another shortcut is to specify a Boundary Name Pattern and click Match to select boundary zones with names that match the specified pattern. For example, if you specify wall*, all boundaries whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all boundaries whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 3. Click on the Compute button. The Results list will display the results of the selected flux computation for each selected boundary zone, and the box below the Results list will show the summation of the individual zone flux results. Note that the fluxes are reported exactly as computed by the solver. Therefore, they are inherently more accurate than those computed with the Flow Rate option in the Surface Integrals panel (described in Section 28.5).


28-3


28.3

Forces on Boundaries

You can compute and report the forces along a specified vector and the moments about a specified center for selected wall zones. This feature can be used, for example, to report aerodynamic coefficients such as lift, drag, and moment coefficient for an airfoil calculation.

28.3.1

Computing Forces and Moments

The forces on a wall zone are computed by summing the dot product of the pressure and viscous forces on each face with the specified force vector. In addition to the actual pressure, viscous, and total forces, the associated force coefficients are also computed, using the reference values specified in the Reference Values panel (as described in Section 28.8). The force coefficient is defined as force divided by 21 ρv 2 A, where ρ, v, and A are the density, velocity, and area explicitly specified in the Reference Values panel. Finally, the summations of the pressure, viscous, and total forces for all the selected wall zones are presented in both dimensional form and as non-dimensional coefficients. The moment vector about a specified center is computed by summing the product of the force vectors for each face with the moment vector—i.e., summing the forces on each face about the moment center. In addition to the actual components of the pressure, viscous, and total moment, the moment coefficients are also printed. The moment coefficient is defined as the moment divided by the product of the reference dynamic pressure, reference area, and the reference length. Finally, the summations of the pressure, viscous, and total moments for all the selected wall zones are presented in both dimensional form and as non-dimensional coefficients. To reduce round-off error, a reference pressure (also specified in the Reference Values panel) is used to normalize the cell pressure for computation of the pressure force. For example, the net pressure force vector is computed as the vector sum of the individual force vectors for each face:

F~p = − = −

n X i=1 n X i=1

(p − pref )Aˆ n pAˆ n + pref

n X

(28.3-1) Aˆ n

(28.3-2)

i=1

where n is the number of faces, A is the area of the face, and n ˆ is the unit normal to the face. This normalization has implications when computing total force coefficients for open domains. For closed domains, the additional term introduced by the reference pressure cancels, but for open domains the pressure normalization introduces a net force equivalent to the product of the projected area of the missing portion of the domain and the specified reference pressure.

28-4


28.3 Forces on Boundaries

28.3.2

Generating a Force or Moment Report

To obtain a report for selected wall zones of forces along a specified vector or moments about a specified center, use the Force Reports panel (Figure 28.3.1). Report −→Forces...

Figure 28.3.1: The Force Reports Panel The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Forces or Moments under Options. 2. If you choose a force report, specify the X, Y, and Z components of the Force Vector along which the forces will be computed. If you choose a moment report, specify the X, Y, and Z coordinates of the Moment Center about which the moments will be computed. 3. In the Wall Zones list, choose the wall zone(s) on which you want to report the force or moment information. A shortcut that may be useful if you have a large number of wall zones is to specify a Wall Name Pattern and click Match to select wall zones with names that match the specified pattern. For example, if you specify out*, all walls whose names begin with out (e.g., outer-wall-top, outside-wall) will be selected automatically. If they are all selected already, they will be deselected. If you specify out?, all walls whose names consist of out followed by a single character will be selected (or deselected, if they are all selected already).


28-5


4. Click on the Print button. In the console (text) window, the pressure, viscous (if appropriate), and total forces or moments, and the pressure, viscous, and total force or moment coefficients along the specified force vector or about the specified moment center will be printed for the selected wall zones. The summations of the coefficients and the forces or moments for all selected wall zones will be printed at the end of the report.

28.4

Projected Surface Area Calculations

You can use the Projected Surface Areas panel (Figure 28.4.1) to compute an estimated area of the projection of selected surfaces along the x, y, or z axis (i.e., onto the yz, xz, or xy plane). Report −→Projected Areas...

Figure 28.4.1: The Projected Surface Areas panel The procedure for calculating the projected area is as follows: 1. Select the Projection Direction (X, Y, or Z). 2. Choose the surface(s) for which the projected area is to be calculated in the Surfaces list. 3. Set the Min Feature Size to the length of the smallest feature in the geometry that you want to resolve in the area calculation. (You can just use the default value to start with, if you are not sure of the size of the smallest geometrical feature.) 4. Click on Compute. The area will be displayed in the Area box and in the console window.

28-6


28.5 Surface Integration

5. To improve the accuracy of the area calculation, reduce the Min Feature Size by half and recompute the area. Repeat this step until the computed Area stops changing (or you reach memory capacity). This feature is available only for 3D domains.

28.5

Surface Integration

You can compute the area or mass flow rate, or the integral, area-weighted average, flow rate, mass-weighted average, sum, facet average, facet maximum, facet minimum, vertex average, vertex minimum, and vertex maximum for a selected field variable on selected surfaces in the domain. These surfaces are sets of data points created by FLUENT for each of the zones in your model, or defined by you using the methods described in Chapter 26. Since a surface can be arbitrarily positioned in the domain, the value of a variable at each data point is obtained by linear interpolation of node values. For some variables, these node values are computed explicitly by the solver. For others, however, only cell-center values are computed, and the node values are obtained by averaging of the cell values. These successive interpolations can lead to small errors in the surface integration reports. (Chapter 29 provides information on which variables have computed node values.) Example uses of several types of surface integral reports are given below: • Area: You can compute the area of a velocity inlet zone, and then estimate the velocity from the mass flow rate: v=

m ˙ ρA

(28.5-1)

• Area-weighted average: You can find the average value on a solid surface, such as the average heat flux on a heated wall with a specified temperature. • Mass average: You can find the average value on a surface in the flow, such as average enthalpy at a velocity inlet. • Mass flow rate: You can compute the mass flow rate through a velocity inlet zone, and then estimate the velocity from the area, as described above. • Flow rate: To calculate the heat transfer rate through a surface, you can calculate the flow rate of enthalpy. • Integral: You can use integrals for more complex calculations, which may involve the use of the Custom Field Function Calculator panel, described in Section 29.5, to calculate a function that requires integral computations (e.g., swirl number).


28-7


28.5.1

Computing Surface Integrals

Area The area of a surface is computed by summing the areas of the facets that define the surface. Facets on a surface are either triangular or quadrilateral in shape. Z

dA =

n X

|Ai |

(28.5-2)

i=1

Integral An integral on a surface is computed by summing the product of the facet area and the selected field variable, such as density or pressure. Each facet is associated with a cell in the domain. If the facet is the result of an isovalue cut through the cell, the field variable assigned to the facet is the associated cell value. If the facet is on a boundary surface, an interpolated face value is used for the integration instead of the cell value. This is done to improve the accuracy of the calculation, and to ensure that the result matches the boundary conditions specified on the boundary and the fluxes reported on the boundary. Z

φdA =

n X

φi |Ai |

(28.5-3)

i=1

Area-Weighted Average The area-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and facet area by the total area of the surface: n 1Z 1X φdA = φi |Ai | A A i=1

(28.5-4)

Flow Rate The flow rate of a quantity through a surface is computed by summing the product of density and the selected field variable with the dot product of the facet area vector and the facet velocity vector: Z

~= φρ~v · dA

n X

~i φi ρi v~i · A

(28.5-5)

i=1

28-8



Mass Flow Rate The mass flow rate through a surface is computed by summing the product of density with the dot product of the facet area vector and the facet velocity vector: Z

n X

~= ρ~v · dA

~i ρi v~i · A

(28.5-6)

i=1

Mass-Weighted Average The mass-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and the absolute value of the dot product of the facet area and momentum vectors by the summation of the absolute value of the dot product of the facet area and momentum vectors (surface mass flux): n X ~ i φ ρ v ~ · A i i i ~ φρ ~v · dA i=1 Z = n X ~ ρ ~v · dA ~ i ρi v~i · A

Z

(28.5-7)

i=1

Sum The sum of a specified field variable on a surface is computed by summing the value of the selected variable at each facet: n X

φi

(28.5-8)

i=1

Facet Average The facet average of a specified field variable on a surface is computed by dividing the summation of the cell values of the selected variable at each facet by the total number of facets: n X

φi

i=1

n

(28.5-9)

Facet Minimum The facet minimum of a specified field variable on a surface is the minimum cell value of the selected variable on the surface.


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Facet Maximum The facet maximum of a specified field variable on a surface is the maximum cell value of the selected variable on the surface.

Vertex Average The vertex average of a specified field variable on a surface is computed by dividing the summation of the node values of the selected variable at each node by the total number of nodes: n X

φi

i=1

n

(28.5-10)

Vertex Minimum The vertex minimum of a specified field variable on a surface is the minimum node value of the selected variable on the surface.

Vertex Maximum The vertex maximum of a specified field variable on a surface is the maximum node value of the selected variable on the surface.

28.5.2

Generating a Surface Integral Report

To obtain a report for selected surfaces of the area or mass flow rate or the integral, flow rate, sum, facet maximum, facet minimum, vertex maximum, vertex minimum, or mass-, area-, facet-, or vertex-averaged quantity of a specified field variable, use the Surface Integrals panel (Figure 28.5.1). Report −→Surface Integrals... The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Area, Integral, AreaWeighted Average, Flow Rate, Mass Flow Rate, Mass-Weighted Average, Sum, Facet Average, Facet Minimum, Facet Maximum, Vertex Average, Vertex Minimum, or Vertex Maximum in the Report Type drop-down list. 2. If you are generating a report of area or mass flow rate, skip to the next step. Otherwise, use the Field Variable drop-down lists to select the field variable to be used in the surface integrations. First, select the desired category in the upper

28-10



Figure 28.5.1: The Surface Integrals Panel

drop-down list. You can then select a related quantity from the lower list. (See Chapter 29 for an explanation of the variables in the list.) 3. In the Surfaces list, choose the surface(s) on which to perform the surface integration. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces of that type will be selected automatically in the Surfaces list (or deselected, if they are all selected already). Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 4. Click on the Compute button. Depending on the type of report you have selected, the label for the result will change to Area, Integral, Area-Weighted Average, Flow Rate, Mass Flow Rate, Mass-Weighted Average, Sum of Facet Values, Average of Facet Values, Minimum of Facet Values, Maximum of Facet Values, Average of Surface Vertex Values, Minimum of Vertex Values, or Maximum of Vertex Values, as appropriate.


28-11


Note the following items: • Mass averaging “weights” toward regions of higher velocity (i.e., regions where more mass crosses the surface). • Flow rates reported using the Surface Integrals panel are not as accurate as those reported with the Flux Reports panel (described in Section 28.2). • The facet and vertex average options are recommended for zero-area surfaces.

28.6

Volume Integration

The volume, sum, volume integral, volume-weighted average, mass integral, and massweighted average can be obtained for a selected field variable in selected cell zones in the domain. Example uses of the different types of volume integral reports are given below: • Volume: You can compute the total volume of a fluid region. • Sum: You can add up the discrete-phase mass or energy sources to determine the net transfer from the discrete phase. You can also sum user-defined sources of mass or energy. • Volume integral: For quantities that are stored per unit volume, you can use volume integrals to determine the net value (e.g., integrate density to determine mass). • Volume-weighted average: You can obtain volume averages of mass sources, energy sources, or discrete-phase exchange quantities. • Mass integral: You can determine the total mass of a particular species by integrating its mass fraction. • Mass-weighted average: You can find the average value (such as average temperature) in a fluid zone.

28.6.1

Computing Volume Integrals

Volume The volume of a surface is computed by summing the volumes of the cells that comprise the zone: Z

dV =

n X

|Vi |

(28.6-1)

i=1

28-12


28.6 Volume Integration

Sum The sum of a specified field variable in a cell zone is computed by summing the value of the selected variable at each cell in the selected zone: n X

φi

(28.6-2)

i=1

Volume Integral A volume integral is computed by summing the product of the cell volume and the selected field variable: Z

φdV =

n X

φi |Vi |

(28.6-3)

i=1

Volume-Weighted Average The volume-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and cell volume by the total volume of the cell zone: n 1 Z 1 X φdV = φi |Vi | V V i=1

(28.6-4)

Mass-Weighted Integral The mass-weighted integral is computed by summing the product of density, cell volume, and the selected field variable: Z

φρdV =

n X

φi ρi |Vi |

(28.6-5)

i=1

Mass-Weighted Average The mass-weighted average of a quantity is computed by dividing the summation of the product of density, cell volume, and the selected field variable by the summation of the product of density and cell volume: Z Z

n X

φρdV = ρdV

φi ρi |Vi |

i=1 n X

(28.6-6) ρi |Vi |

i=1


28-13


28.6.2

Generating a Volume Integral Report

To obtain a report for selected cell zones of the volume or the sum, volume integral, volume-weighted average, mass-weighted integral, or mass-weighted average quantity of a specified field variable, use the Volume Integrals panel (Figure 28.6.1). Report −→Volume Integrals...

Figure 28.6.1: The Volume Integrals Panel The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Volume, Sum, Volume Integral, Volume-Average, Mass Integral, or Mass-Average under Options. 2. If you are generating a report of volume, skip to the next step. Otherwise, use the Field Variable drop-down lists to select the field variable to be used in the integral, sum, or averaged volume integrations. First, select the desired category in the upper drop-down list. You can then select a related quantity from the lower list. (See Chapter 29 for an explanation of the variables in the list.) 3. In the Cell Zones list, choose the zones on which to compute the volume, sum, volume integral, volume-weighted average, mass integral, or mass-averaged quantity. 4. Click on the Compute button. Depending on the type of report you have selected, the label for the result will change to Total Volume, Sum, Total Volume Integral, Volume-Weighted Average, Total Mass-Weighted Integral, or Mass-Weighted Average, as appropriate.

28-14


28.7 Histogram Reports

28.7

Histogram Reports

In FLUENT, you can print geometric and solution data in the console (text) window in histogram format or plot a histogram in the graphics window. Graphical display of histograms and the procedures for defining a histogram are discussed in Section 27.8.7. The number of cells, the range of the selected variable or function, and the percentage of the total number of cells in the interval will be reported, as in the example below: 0 cells below 1.195482 (0 %) 2 cells between 1.195482 and 1.196048 (4.1666667 1 cells between 1.196048 and 1.196614 (2.0833333 0 cells between 1.196614 and 1.19718 (0 %) 0 cells between 1.19718 and 1.197746 (0 %) 2 cells between 1.197746 and 1.198312 (4.1666667 1 cells between 1.198312 and 1.198878 (2.0833333 6 cells between 1.198878 and 1.199444 (12.5 %) 9 cells between 1.199444 and 1.20001 (18.75 %) 25 cells between 1.20001 and 1.200576 (52.083333 2 cells between 1.200576 and 1.201142 (4.1666667 0 cells above 1.201142 (0 %)

%) %)

%) %)

%) %)

To generate such a printed histogram, use the Solution Histogram panel. Report −→Histogram... Follow the instructions in Section 27.8.7 for generating histogram plots, but click on Print instead of Plot to create the report.


28-15


28.8

Reference Values

You can control the reference values that are used in the computation of derived physical quantities and non-dimensional coefficients. These reference values are used only for postprocessing. Some examples of the use of reference values include the following: • Force coefficients use the reference area, density, and velocity. In addition, the pressure force calculation uses the reference pressure. • Moment coefficients use the reference length, area, density and velocity. In addition, the pressure force calculation uses the reference pressure. • Reynolds number uses the reference length, density, and viscosity. • Pressure and total pressure coefficients use the reference pressure, density, and velocity. • Entropy uses the reference density, pressure, and temperature. • Skin friction coefficient uses the reference density and velocity. • Heat transfer coefficient uses the reference temperature. • Turbomachinery efficiency calculations use the ratio of specific heats.

28.8.1

Setting Reference Values

To set the reference quantities used for computing normalized flow-field variables, use the Reference Values panel (Figure 28.8.1). Report −→Reference Values... You can input the reference values manually or compute them based on values of physical quantities at a selected boundary zone. The reference values to be set are Area, Density, Enthalpy, Length, Pressure, Temperature, Velocity, dynamic Viscosity, and Ratio Of Specific Heats. For 2D problems, an additional quantity, Depth, can also be defined. This value will be used for reporting fluxes and forces. (Note that the units for Depth are set independently from the units for length in the Set Units panel.) If you want to compute reference values from the conditions set on a particular boundary zone, select the zone in the Compute From drop-down list. Note, however, that depending on the boundary condition used, only some of the reference values may be set. For example, the reference length and area will not be set by computing the reference values from a boundary condition; you will need to set these manually. To set the values manually, simply enter the value for each under the Reference Values heading.

28-16


28.8 Reference Values

Figure 28.8.1: The Reference Values Panel

28.8.2

Setting the Reference Zone

If you are solving a flow involving multiple reference frames or sliding meshes, you can plot velocities and other related quantities relative to the motion of a specified “reference zone”. Choose the desired zone in the Reference Zone drop-down list. Changing the reference zone allows you to plot velocities (and total pressure, temperature, etc.) relative to the motion of different zones. See Chapter 9 for details about postprocessing of relative quantities.


28-17


28.9

Summary Reports of Case Settings

You may sometimes find it useful to get a report of the current settings in your case. In FLUENT, you can list the settings for physical models, boundary conditions, material properties, and solver controls. This report allows you to get an overview of your current problem definition quickly, instead of having to check the settings in each panel.

28.9.1

Generating a Summary Report

To generate a summary report you will use the Summary panel (Figure 28.9.1). Report −→Summary...

Figure 28.9.1: The Summary Panel The steps are as follows: 1. Select the information you would like to see in the report (Models, Boundary Conditions, Solver Controls, and/or Material Properties) in the Report Options list. 2. To print the information to the FLUENT console window, click on the Print button. To save the information to a text file, click on the Save... button and specify the filename in the resulting Select File dialog box.

28-18


Chapter 29.

Field Function Definitions

You must select flow variables for a number of tasks in FLUENT. The values are computed and placed in temporary memory that is allocated for storing the results for each cell. For example, the Compute command associated with a panel that contains the field variable drop-down list calculates the values of the selected function and places them into temporary storage. Sections 29.1 and 29.2 provide some general information related to the field variables. In Section 29.3, the variables are listed by category in Tables 29.3.1–29.3.12. These tables will also indicate when each variable will be available. Section 29.4 contains an alphabetical listing of the variables along with their definitions. All variables appear as they would in the variable selection drop-down lists that are contained in many of the FLUENT panels. Section 29.5 explains how you can calculate your own field function. • Section 29.1: Node and Cell Values • Section 29.2: Velocity Reporting Options • Section 29.3: Field Variables Listed by Category • Section 29.4: Alphabetical Listing of Field Variables and Their Definitions • Section 29.5: Custom Field Functions

29.1

Node and Cell Values

Two types of field values are available for postprocessing: node values and cell values. For the following discussion, “surface” refers to a collection of facets, lines or points that are created and manipulated in the Surface menu. In most cases, these surfaces are created by computing intersections of constant isovalues with the domain cells or with existing surfaces.

29.1.1

Cell Values

FLUENT stores most variables in cells. For postprocessing, the entire region contained within the cell has this value. A surface cell value is the value of the cell that has been intersected by a surface facet or line, or that contains a surface point. Since surface facets and lines are created from the intersection of isovalues and the existing grid cells, this is a unique definition. On a boundary, the cell value is the value in the cell adjacent to the boundary.


29-1


29.1.2

Node Values

Node values are explicitly defined or obtained by averaging the cell data. Various boundary conditions impose values of field variables at the domain boundaries, so grid node values on these boundary zones are defined explicitly. In addition, for several variables (e.g., node coordinates) explicit node values are available at all nodes. For most variables, however, the grid node values are computed by averaging the data of all the cells that share the node. Computation of node values is performed in two steps: 1. Values at all nodes are initialized to the average of the surrounding cell values. 2. At boundaries, these node values are overwritten with the boundary values (if available). (Variables for which explicit node values are available at boundaries are indicated by bnv in Tables 29.3.1–29.3.12.) For example, in Figure 29.1.1, the value at node n1 will be computed from the average of the values in the surrounding cells (c1–c6), and the value at node n2 will be the specified boundary value (not the average of the values in cells c1, c6, and c7), if there are explicit boundary values available for the variable in question.

c4 c3

c5 n1

c2

c6 c1 n2

c7 boundary

Figure 29.1.1: Computing Node Values

! Note that explicit boundary node values are not available for custom field functions. The values of the nodes on surfaces are interpolated from the grid node data by linear interpolation. For zone surfaces the nodes on the surface and the zone correspond, so the values are identical. For isofacets and isolines, the values are interpolated from the grid nodes on the face intersected by the isovalue. For isopoints, the value is interpolated from all the grid nodes of the cell containing the point.

29-2


29.2 Velocity Reporting Options

29.2

Velocity Reporting Options

The following methods are available for reporting velocities: • Cartesian velocities: These velocities are based on the Cartesian coordinate system used by the geometry. To report Cartesian velocities, select X Velocity, Y Velocity, or Z Velocity. This is the most common type of velocity reported. • Cylindrical velocities: These velocities are the axial, radial, and tangential components based on the following coordinate systems: – For axisymmetric problems, in which the rotation axis must be the x axis, the x direction is the axial direction and the y direction is the radial direction. (If you model axisymmetric swirl, the swirl direction is the tangential direction.) – For 2D problems involving a single cell zone, the z direction is the axial direction, and its origin is specified in the Fluid panel. – For 3D problems involving a single cell zone, the coordinate system is defined by the rotation axis and origin specified in the Fluid panel. – For problems involving multiple zones (e.g., multiple reference frames or sliding meshes), the coordinate system is defined by the rotation axis specified in the Fluid (or Solid) panel for the “reference zone”. The reference zone is chosen in the Reference Values panel, as described in Section 28.8. Recall that for 2D problems, you will specify only the axis origin; the z direction is always the axial direction. For all of the above definitions of the cylindrical coordinate system, positive radial velocities point radially out from the rotation axis, positive axial velocities are in the direction of the rotation axis vector, and positive tangential velocities are based on the right-hand rule using the positive rotation axis. To report cylindrical velocities, select Axial Velocity, Radial Velocity, etc. Figure 29.2.1 illustrates the cylindrical velocities available for different types of domains: For 3D problems, you can report axial, radial, and tangential velocities. For 2D problems, radial and tangential velocities are available. For axisymmetric problems, you can report axial and radial velocities, and if you are modeling axisymmetric swirl you can also report the swirl velocity (which is equivalent to the tangential velocity). • Relative velocities: These velocities are based on the coordinate system and motion of a moving reference frame. They are useful when you are modeling your flow using a rotating reference frame, a mixing plane, multiple reference frames, or sliding meshes. (See Chapter 9 for information about modeling flow in moving zones.) To report relative velocities, select Relative X Velocity, Relative Y Velocity, Relative Radial Velocity, etc. (Note that you can report relative velocities for both Cartesian and cylindrical components.)


29-3

Field Function Definitions axial tangential

radial tangential

radial rotation axis

rotation axis origin

radial

rotation axis

axial tangential (swirl)

Figure 29.2.1: Cylindrical Velocity Components in 3D, 2D, and Axisymmetric Domains

If you are using a single rotating reference frame, the relative velocity values will be reported with respect to the moving frame. If you are using multiple reference frames, mixing planes, or sliding meshes, you will need to specify the frame to which you want the velocities to be relative by choosing the appropriate cell zone as the Reference Zone in the Reference Values panel (see Section 28.8). The axis of rotation for each cell zone is defined in the associated Fluid panel or Solid panel. (See Section 6.17.1 or 6.18.1 for details.) Note that if your problem does not involve any moving zones, relative and absolute velocities will be equivalent. Note that relative velocities can also be used to compute stagnation quantities (total pressure and total temperature), and that the cylindrical coordinate systems described in the second item above are used for defining the Axial Coordinate and Radial Coordinate as well.

29-4


29.3 Field Variables Listed by Category

29.3

Field Variables Listed by Category

In Tables 29.3.1–29.3.12, the following restrictions apply to marked variables: 2d 2da 2dasw 3d bnv cpl cv dil do dpm dtrm e edc emm ewt gran h2o id ke kw les melt mix mp nox np nv p p1

available only for 2D flows available only for 2D axisymmetric flows (with or without swirl) available only for 2D axisymmetric swirl flows available only for 3D flows node values available at boundaries available only in the coupled solvers available only for cell values (Node Values option turned off) not available with full multicomponent diffusion available only when the discrete ordinates radiation model is used available only for coupled discrete phase calculations available only when the discrete transfer radiation model is used available only for energy calculations available only with the EDC model for turbulence-chemistry interaction available only when the Eulerian multiphase model is used available only with the enhanced wall treatment available only if a granular phase is present available only when the mixture contains water available only when the ideal gas law is enabled for density available only when one of the k- turbulence models is used available only when one of the k-ω turbulence models is used available only when the LES turbulence model is used available only when the melting and solidification model is used available only when the multiphase mixture model is used available only for multiphase models available only for NOx calculations not available in parallel solvers uses explicit node value function available only in parallel solvers available only when the P-1 radiation model is used


29-5


pdf pmx ppmx r rad rc rsm s2s sa seg sp sr soot stat stcm t turbo udm uds v

available available available available available available available available available available available available available available available available available available available available

only only only only only only only only only only only only only only only only only only only only

for non-premixed combustion calculations for premixed combustion calculations for partially premixed combustion calculations when the Rosseland radiation model is used for radiation heat transfer calculations for finite-rate reactions when the Reynolds stress turbulence model is used when the surface-to-surface radiation model is used when the Spalart-Allmaras turbulence model is used in the segregated solver for species calculations for surface reactions for soot calculations with data sampling for unsteady statistics for stiff chemistry calculations for turbulent flows when a turbomachinery topology has been defined when a user-defined memory location is used when a user-defined scalar is used for viscous flows

Table 29.3.1: Pressure and Density Categories Category Pressure...

Density...

29-6

Variable Static Pressure (bnv, nv) Pressure Coefficient Dynamic Pressure Absolute Pressure (bnv, nv) Total Pressure (bnv, nv) Relative Total Pressure Density Density All



Table 29.3.2: Velocity Category Category Velocity...


Variable Velocity Magnitude (bnv, nv, mp) X Velocity (bnv, nv, mp) Y Velocity (bnv, nv, mp) Z Velocity (3d, bnv, nv, mp) Swirl Velocity (2dasw, bnv, nv, mp) Axial Velocity (2da or 3d, mp) Radial Velocity (mp) Stream Function (2d, nv,mp) Tangential Velocity Mach Number (id) Relative Velocity Magnitude (bnv, nv) Relative X Velocity (bnv, nv) Relative Y Velocity (bnv, nv) Relative Z Velocity (3d, bnv, nv) Relative Axial Velocity (2da) Relative Radial Velocity (2da) Relative Swirl Velocity (2dasw, bnv, nv) Relative Tangential Velocity (2d or 3d) Relative Mach Number (id) Grid X-Velocity (nv) Grid Y-Velocity (nv) Grid Z-Velocity (3d, nv) Velocity Angle Relative Velocity Angle Vorticity Magnitude (v) Helicity (v, 3d) X-Vorticity (v, 3d) Y-Vorticity (v, 3d) Z-Vorticity (v, 3d) Cell Reynolds Number (v) Preconditioning Reference Velocity (cpl)

29-7


Table 29.3.3: Temperature, Radiation, and Solidification/Melting Categories Category Variable Temperature... Static Temperature (e, nv) Total Temperature (e, bnv, nv) Enthalpy (e, nv, mp) Relative Total Temperature (e) Rothalpy (e, nv) Fine Scale Temperature (edc, nv) Wall Temperature (Outer Surface) (e, v, cv) Wall Temperature (Inner Surface) (e, v, cv) Total Enthalpy (e, mp) Total Enthalpy Deviation (e, mp) Entropy (e) Total Energy (e, mp) Internal Energy (e) Radiation... Absorption Coefficient (r, p1, do, or dtrm) Scattering Coefficient (r, p1, or do) Refractive Index (do) Radiation Temperature (p1 or do) Incident Radiation (p1 or do) Incident Radiation (Band n) (do (non-gray)) Surface Cluster ID (s2s) Solidification/ Liquid Fraction (melt) Melting... Contact Resistivity (melt) X Pull Velocity (melt (if calculated)) Y Pull Velocity (melt (if calculated)) Z Pull Velocity (melt (if calculated), 3d) Axial Pull Velocity (melt (if calculated), 2da) Radial Pull Velocity (melt (if calculated), 2da) Swirl Pull Velocity (melt (if calculated), 2dasw)

29-8



Category Turbulence...


Table 29.3.4: Turbulence Category Variable Turbulent Kinetic Energy (k) (ke, kw, or rsm; bnv, nv, emm) UU Reynolds Stress (rsm) VV Reynolds Stress (rsm) WW Reynolds Stress (rsm) UV Reynolds Stress (rsm) UW Reynolds Stress (rsm, 3d) VW Reynolds Stress (rsm, 3d) Turbulence Intensity (ke, kw, or rsm) Turbulent Dissipation Rate (Epsilon) (ke or rsm; bnv, nv, emm) Specific Dissipation Rate (Omega) (kw) Production of k (ke, kw, or rsm, emm) Modified Turbulent Viscosity (sa) Turbulent Viscosity (t, emm) Effective Viscosity (t) Turbulent Viscosity Ratio (ke, kw, rsm, or sa) Subgrid Turbulent Kinetic Energy (les) Subgrid Turbulent Viscosity (les) Subgrid Effective Viscosity (les) Subgrid Turbulent Viscosity Ratio (les) Effective Thermal Conductivity (t, e) Effective Prandtl Number (t, e) Wall Ystar (ke, kw, or rsm; cv) Wall Yplus (t, cv, emm) Turbulent Reynolds Number (Re y) (ke or rsm; ewt)

29-9


Table 29.3.5: Species, Reactions, Pdf, and Premixed Combustion Categories Category Species...

Reactions...

Pdf...

Premixed Combustion...

29-10

Variable Mass fraction of species-n (sp, pdf, or ppmx; nv) Mole fraction of species-n (sp, pdf, or ppmx) Molar Concentration of species-n (sp, pdf, or ppmx) Lam Diff Coef of species-n (sp, dil) Eff Diff Coef of species-n (t, sp, dil) Thermal Diff Coef of species-n (sp) Enthalpy of species-n (sp) species-n Source Term (rc, cpl) Surface Deposition Rate of species-n (sr) Surface Coverage of species-n (sr) Relative Humidity (sp, pdf, or ppmx; h2o) Time Step Scale (sp, stcm) Fine Scale Mass fraction of species-n (edc) Fine Scale Transfer Rate (edc) 1-Fine Scale Volume Fraction (edc) Rate of Reaction-n (rc) Arrhenius Rate of Reaction-n (rc) Turbulent Rate of Reaction-n (rc, t) Mean Mixture Fraction (pdf or ppmx; nv) Secondary Mean Mixture Fraction (pdf or ppmx; nv) Mixture Fraction Variance (pdf or ppmx; nv) Secondary Mixture Fraction Variance (pdf or ppmx; nv) Fvar Prod (pdf or ppmx) Fvar2 Prod (pdf or ppmx) Scalar Dissipation (pdf or ppmx) Progress Variable (pmx or ppmx; nv) Damkohler Number (pmx or ppmx) Stretch Factor (pmx or ppmx) Turbulent Flame Speed (pmx or ppmx) Static Temperature (pmx or ppmx) Product Formation Rate (pmx or ppmx) Laminar Flame Speed (pmx or ppmx) Critical Strain Rate (pmx or ppmx) Adiabatic Flame Temperature (pmx or ppmx) Unburnt Fuel Mass Fraction (pmx or ppmx)



Table 29.3.6: NOx, Soot, and Unsteady Statistics Categories Category NOx...

Soot...

Unsteady Statistics...


Variable Mass fraction of NO (nox) Mass fraction of HCN (nox) Mass fraction of NH3 (nox) Mole fraction of NO (nox) Mole fraction of HCN (nox) Mole fraction of NH3 (nox) NO Density (nox) HCN Density (nox) NH3 Density (nox) Variance of Temperature (nox) Variance of Species (nox) Variance of Species 1 (nox) Variance of Species 2 (nox) Mass fraction of soot (soot) Mass fraction of nuclei (soot) Mole fraction of soot (soot) Soot Density (soot) Mean quantity-n (stat) RMS quantity-n (stat)

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Table 29.3.7: Phases, Discrete Phase Model, Granular Pressure, and Granular Temperature Categories Category Variable Phases... Volume fraction (mp) Discrete Phase Model... DPM Mass Source (dpm) DPM Erosion (dpm, cv) DPM Accretion (dpm, cv) DPM X Momentum Source (dpm) DPM Y Momentum Source (dpm) DPM Z Momentum Source (dpm, 3d) DPM Swirl Momentum Source (dpm, 2dasw) DPM Sensible Enthalpy Source (dpm, e) DPM Enthalpy Source (dpm, e) DPM Absorption Coefficient (dpm, rad) DPM Emission (dpm, rad) DPM Scattering (dpm, rad) DPM Burnout (dpm, sp, e) DPM Evaporation/Devolatilization (dpm, sp, e) DPM Concentration (dpm) DPM species-n Source (dpm, sp, e) Granular Pressure... Granular Pressure (emm, gran) Granular Temperature... Granular Temperature (emm, gran)

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Table 29.3.8: Properties, Wall Fluxes, User Defined Scalars, and User Defined Memory Categories Category Variable Properties... Molecular Viscosity (v, mp) Diameter (mix, emm) Granular Conductivity (mix, emm, gran) Thermal Conductivity (e, v) Specific Heat (Cp) (e) Specific Heat Ratio (gamma) (id) Gas Constant (R) (id) Molecular Prandtl Number (e, v) Mean Molecular Weight (seg, pdf) Sound Speed (id) Wall Fluxes... Wall Shear Stress (v, cv, emm) X-Wall Shear Stress (v, cv, emm) Y-Wall Shear Stress (v, cv, emm) Z-Wall Shear Stress (v, 3d, cv, emm) Axial-Wall Shear Stress (2da, cv) Radial-Wall Shear Stress (2da, cv) Swirl-Wall Shear Stress (2dasw, cv) Skin Friction Coefficient (v, cv, emm) Total Surface Heat Flux (e, v, cv) Radiation Heat Flux (rad, cv) Absorbed Radiation Flux (Band-n) do,cv Reflected Radiation Flux (Band-n) do, cv Transmitted Radiation Flux (Band-n) do, cv Surface Incident Radiation (do, cv) Surface Heat Transfer Coef. (e, v, cv) Surface Nusselt Number (e, v, cv) Surface Stanton Number (e, v, cv) User Defined Scalars... Scalar-n (uds, nv) Diffusion Coef. of Scalar-n (uds) User Defined Memory... udm-n (udm)


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Table 29.3.9: Cell Info, Grid, and Adaption Categories Category Cell Info...

Grid...

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Variable Cell Partition (np) Active Cell Partition (p) Stored Cell Partition (p) Cell Id (p) Cell Element Type Cell Zone Type Cell Zone Index Partition Neighbors X-Coordinate (nv) Y-Coordinate (nv) Z-Coordinate (3d, nv) Axial Coordinate (nv) Angular Coordinate (3d, nv) Radial Coordinate (nv) X Surface Area Y Surface Area Z Surface Area (3d) X Face Area Y Face Area Z Face Area (3d) Cell Equiangle Skew Cell Equivolume Skew Cell Volume 2D Cell Volume (2da) Cell Wall Distance Face Handedness Face Squish Index Cell Squish Index



Table 29.3.10: Grid Category (Turbomachinery-Specific Variables) and Adaption Category Category Variable Grid... Meridional Coordinate (nv, turbo) Abs Meridional Coordinate (nv, turbo) Spanwise Coordinate (nv, turbo) Abs (H-C) Spanwise Coordinate (nv, turbo) Abs (C-H) Spanwise Coordinate (nv, turbo) Pitchwise Coordinate (nv, turbo) Abs Pitchwise Coordinate (nv, turbo) Adaption... Adaption Function Adaption Curvature Adaption Space Gradient Existing Value Boundary Cell Distance Boundary Normal Distance Boundary Volume Distance (np) Cell Volume Change Cell Surface Area Cell Warpage Cell Children Cell Refine Level

Table 29.3.11: Residuals Category Category Residuals...


Variable Mass Imbalance Pressure Residual (cpl) X-Velocity Residual (cpl; 2d or 3d) Y-Velocity Residual (cpl; 2d or 3d) Z-Velocity Residual (cpl, 3d) Axial-Velocity Residual (cpl, 2da) Radial-Velocity Residual (cpl, 2da) Swirl-Velocity Residual (cpl, 2dasw) Temperature Residual (cpl, e) Species-n Residual (cpl, sp)

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Table 29.3.12: Derivatives Category Category Derivatives...

29-16

Variable Strain Rate (v) dX-Velocity/dx dY-Velocity/dx dZ-Velocity/dx (3d) dAxial-Velocity/dx (2da) dRadial-Velocity/dx (2da) dSwirl-Velocity/dx (2dasw) d species-n/dx (cpl, sp) dX-Velocity/dy dY-Velocity/dy dZ-Velocity/dy (3d) dAxial-Velocity/dy (2da) dRadial-Velocity/dy (2da) dSwirl-Velocity/dy (2dasw) d species-n/dy (cpl, sp) dX-Velocity/dz (3d) dY-Velocity/dz (3d) dZ-Velocity/dz (3d) d species-n/dz (cpl, sp, 3d) dOmega/dx (2dasw) dOmega/dy (2dasw) dp-dX (seg) dp-dY (seg) dp-dZ (seg, 3d)


29.4 Alphabetical Listing of Field Variables and Their Definitions

29.4

Alphabetical Listing of Field Variables and Their Definitions

Below, the variables listed in Tables 29.3.1–29.3.12 are defined. For some variables (such as residuals) a general definition is given under the category name, and variables in the category are not listed individually. When appropriate, the unit quantity is included, as it appears in the Quantities list in the Set Units panel. Abs (C-H) Spanwise Coordinate (in the Grid... category) is the dimensional coordinate in the spanwise direction, from casing to hub. Its unit quantity is length. Abs (H-C) Spanwise Coordinate (in the Grid... category) is the dimensional coordinate in the spanwise direction, from hub to casing. Its unit quantity is length. Abs Meridional Coordinate (in the Grid... category) is the dimensional coordinate that follows the flow path from inlet to outlet. Its unit quantity is length. Abs Pitchwise Coordinate (in the Grid... category) is the dimensional coordinate in the circumferential (pitchwise) direction. Its unit quantity is angle. Absolute Pressure (in the Pressure... category) is equal to the operating pressure plus the gauge pressure. See Section 7.12 for details. Its unit quantity is pressure. Absorbed Radiation Flux (Band-n) (in the Wall Fluxes... category) is the amount of radiative heat flux absorbed by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux. Absorption Coefficient (in the Radiation... category) is the property of a medium that describes the amount of absorption of thermal radiation per unit path length within the medium. It can be interpreted as the inverse of the mean free path that a photon will travel before being absorbed (if the absorption coefficient does not vary along the path). The unit quantity for Absorption Coefficient is length-inverse. Active Cell Partition (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file. See Section 30.4.3 for more information. Adaption... includes field variables that are commonly used for adapting the grid. For information about solution adaption, see Chapter 25. Adaption Function (in the Adaption... category) can be either the Adaption Space Gradient or the Adaption Curvature, depending on the settings in the Gradient Adaption


29-17


panel. For instance, the Adaption Curvature is the undivided Laplacian of the values in temporary cell storage. To display contours of the Laplacian of pressure, for example, you first select Static Pressure, click the Compute (or Display) button, select Adaption Function, and finally click the Display button. Adaption Space Gradient (in the Adaption... category) is the first derivative of the desired field variable. r

|ei1 | = (Acell ) 2 |∇f |

(29.4-1)

Depending on the settings in the Gradient Adaption panel, this equation will either be scaled or normalized. Recommended for problems with shock waves (i.e., supersonic, inviscid flows). For more information, see Section 25.4.1. Adaption Curvature (in the Adaption... category) is the second derivative of the desired field variable. r

|ei2 | = (Acell ) 2 |∇2 f |

(29.4-2)

Depending on the settings in the Gradient Adaption panel, this equation will either be scaled or normalized. Recommended for smooth solutions (i.e., viscous, incompressible flows). For more information, see Section 25.4.1. Adiabatic Flame Temperature (in the Premixed Combustion... category) is the adiabatic temperature of burnt products in a laminar premixed flame (Tb in Equation 15.2-21). Its unit quantity is temperature. Arrhenius Rate of Reaction-n (in the Reactions... category) is given by the following expression (see Equation 13.1-7 for definitions of the variables shown here): 

ˆ r = Γ kf,r R

Nr Y

j=1

0 ηj,r

[Cj,r ]

− kb,r

Nr Y

j=1

00 ηj,r

[Cj,r ]

 

The reported value is independent of any particular species, and has units of kgmol/m3 -s. To find the rate of production/destruction for a given species i due to reaction r, 00 0 multiply the reported reaction rate for reaction r by the term Mi (νi,r − νi,r ), where 00 0 Mi is the molecular weight of species i, and νi,r and νi,r are the stoichiometric coefficients of species i in reaction r. Angular Coordinate (in the Grid... category) is the angle between the radial vector and the position vector. The radial vector is obtained by transforming the default radial vector(y-axis) by the same rotation that was applied to the default axial vector (zaxis ). This assumes that, after the transformation, the default axial vector (z-axis)

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becomes the reference axis. The angle is positive in the director of cross-product between reference axis and radial vector. Axial Coordinate (in the Grid... category) is the distance from the origin in the axial direction. The axis origin and (in 3D) direction is defined for each cell zone in the Fluid or Solid panel. The axial direction for a 2D model is always the z direction, and the axial direction for a 2D axisymmetric model is always the x direction. The unit quantity for Axial Coordinate is length. Axial Pull Velocity (in the Solidification/Melting... category) is the axial-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity. Axial Velocity (in the Velocity... category) is the component of velocity in the axial direction. (See Section 29.2 for details.) For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Its unit quantity is velocity. Axial-Wall Shear Stress (in the Wall Fluxes... category) is the axial component of the force acting tangential to the surface due to friction. Its unit quantity is pressure. Boundary Cell Distance (in the Adaption... category) is an integer that indicates the approximate number of cells from a boundary zone. Boundary Normal Distance (in the Adaption... category) is the distance of the cell centroid from the closest boundary zone. Boundary Volume Distance (in the Adaption... category) is the cell volume distribution based on the Boundary Volume, Growth Factor, and normal distance from the selected Boundary Zones defined in the Boundary Adaption panel. See Section 25.3 for details. Cell Children (in the Adaption... category) is a binary identifier based on whether a cell is the product of a cell subdivision in the hanging-node adaption process (value = 1) or not (value = 0). Cell Element Type (in the Cell Info... category) is the integer cell element type identification number. Each cell can have one of the following element types: triangle tetrahedron quadrilateral hexahedron pyramid wedge


1 2 3 4 5 6

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Cell Equiangle Skew (in the Grid... category) is a nondimensional parameter calculated using the normalized angle deviation method, and is defined as "

qmax − qe qe − qmin max , 180 − qe qe

#

(29.4-3)

where qmax = largest angle in the face or cell qmin = smallest angle in the face or cell qe = angle for an equiangular face or cell (e.g., 60 for a triangle and 90 for a square) A value of 0 indicates a best case equiangular cell, and a value of 1 indicates a completely degenerate cell. Degenerate cells (slivers) are characterized by nodes that are nearly coplanar (collinear in 2D). Cell Equiangle Skew applies to all elements. Cell Equivolume Skew (in the Grid... category) is a nondimensional parameter calculated using the volume deviation method, and is defined as optimal-cell-size − cell-size optimal-cell-size

(29.4-4)

where optimal-cell-size is the size of an equilateral cell with the same circumradius. A value of 0 indicates a best case equilateral cell and a value of 1 indicates a completely degenerate cell. Degenerate cells (slivers) are characterized by nodes that are nearly coplanar (collinear in 2D). Cell Equivolume Skew applies only to triangular and tetrahedral elements. Cell Id (in the Cell Info... category) is a unique integer identifier associated with each cell. Cell Info... includes quantities that identify the cell and its relationship to other cells. Cell Partition (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells. Cell Refine Level (in the Adaption... category) is an integer that indicates the number of times a cell has been subdivided in the hanging node adaption process, compared with the original grid. For example, if one quad cell is split into four quads, the Cell Refine Level for each of the four new quads will be 1. If the resulting four quads are split again, the Cell Refine Level for each of the resulting 16 quads will be 2.

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Cell Reynolds Number (in the Velocity... category) is the value of the Reynolds number in a cell. (Reynolds number is a dimensionless parameter that is the ratio of inertia forces to viscous forces.) Cell Reynolds Number is defined as Re ≡

ρud µ

(29.4-5)

where ρ is density, u is velocity magnitude, µ is the effective viscosity (laminar plus turbulent), and d is Cell Volume1/2 for 2D cases and Cell Volume1/3 in 3D or axisymmetric cases. Cell Squish Index (in the Grid... category) is a measure of the quality of a mesh, and is calculated from the dot products of each vector pointing from the centroid of a cell toward the center of each of its faces, and the corresponding face area vector as 



~ i · ~rc0/xf A i  max 1 − ~ i ||~rc0/xf | i |A

(29.4-6)

i

Therefore, the worst cells will have a Cell Squish Index close to 1. Cell Surface Area (in the Adaption... category) is the total surface area of the cell, and is computed by summing the area of the faces that compose the cell. Cell Volume (in the Grid... category) is the volume of a cell. In 2D the volume is the area of the cell multiplied by the unit depth. For axisymmetric cases, the cell volume is calculated using a reference depth of 1 radian. The unit quantity of Cell Volume is volume. 2D Cell Volume (in the Grid... category) is the two-dimensional volume of a cell in an axisymmetric computation. For an axisymmetric computation, the 2D cell volume is scaled by the radius. Its unit quantity is area. Cell Volume Change (in the Adaption... category) is the maximum volume ratio of the current cell and its neighbors. Cell Wall Distance (in the Grid... category) is the distribution of the normal distance of each cell centroid from the wall boundaries. Its unit quantity is length. Cell Warpage (in the Adaption... category) is the square root of the ratio of the distance between the cell centroid and cell circumcenter and the circumcenter radius: warpage =


s

|~rcentroid − ~rcircumcenter | Rcircumcenter

(29.4-7)

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Cell Zone Index (in the Cell Info... category) is the integer cell zone identification number. In problems that have more than one cell zone, the cell zone ID can be used to identify the various groups of cells. Cell Zone Type (in the Cell Info... category) is the integer cell zone type ID. A fluid cell has a type ID of 1, a solid cell has a type ID of 17, and an exterior cell (parallel solver) has a type ID of 21. Contact Resistivity (in the Solidification/Melting... category) is the additional resistance at the wall due to contact resistance. It is equal to Rc (1 − β)/h, where Rc is the contact resistance, β is the liquid fraction, and h is the cell height of the walladjacent cell. The unit quantity for Contact Resistivity is thermal-resistivity. Critical Strain Rate (in the Premixed Combustion... category) is a parameter that takes into account the stretching and extinction of premixed flames (gcr in Equation 15.2-13). Its unit quantity is time-inverse. Custom Field Functions... are scalar field functions defined by you. You can create a custom function using the Custom Field Function Calculator panel. All defined custom field functions will be listed in the lower drop-down list. See Section 29.5 for details. Damkohler Number (in the Premixed Combustion... category) is a nondimensional parameter that is defined as the ratio of turbulent to chemical time scales. Density... includes variables related to density. Density (in the Density... category) is the mass per unit volume of the fluid. Plots or reports of Density include only fluid cell zones. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. The unit quantity for Density is density. Density All (in the Density... category) is the mass per unit volume of the fluid or solid material. Plots or reports of Density All include both fluid and solid cell zones. The unit quantity for Density All is density. Derivatives... are the viscous derivatives. For example, dX-Velocity/dx is the first derivative of the x component of velocity with respect to the x-coordinate direction. You can compute first derivatives of velocity, angular velocity, and pressure in the segregated solver, and first derivatives of velocity, angular velocity, temperature, and species in the coupled solvers. Diameter (in the Properties... category) is the diameter of particles, droplets, or bubbles of the secondary phase selected in the Phase drop-down list. Its unit quantity is length. Diffusion Coef. of Scalar-n (in the User Defined Scalars... category) is the diffusion coefficient for the nth user-defined scalar transport equation. See the separate UDF manual for details about defining user-defined scalars.

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Discrete Phase Model... includes quantities related to the discrete phase model. Chapter 21 for details about this model.

See

DPM Absorption Coefficient (in the Discrete Phase Model... category) is the absorption coefficient for discrete-phase calculations that involve radiation (a in Equation 11.3-1). Its unit quantity is length-inverse. DPM Accretion (in the Discrete Phase Model... category) is the accretion rate calculated at a wall boundary: Raccretion =

N X m ˙p

p=1

Aface

(29.4-8)

where m ˙ p is the mass flow rate of the particle stream, and Aface is the area of the wall face where the particle strikes the boundary. This item will appear only if the optional erosion/accretion model is enabled. See Section 21.7.6 for details. The unit quantity for DPM Accretion is mass-flux. DPM Burnout (in the Discrete Phase Model... category) is the exchange of mass from the discrete to the continuous phase for the combustion law (Law 5) and is proportional to the solid phase reaction rate. The burnout exchange has units of mass-flow. DPM Concentration (in the Discrete Phase Model... category) is the total concentration of the discrete phase. Its unit quantity is density. DPM Emission (in the Discrete Phase Model... category) is the amount of radiation emitted by a discrete-phase particle per unit volume. Its unit quantity is heat-generationrate. DPM Enthalpy Source (in the Discrete Phase Model... category) is the exchange of enthalpy (sensible enthalpy plus heat of formation) from the discrete phase to the continuous phase. The exchange is positive when the particles are a source of heat in the continuous phase. The unit quantity for DPM Enthalpy Source is power. DPM Erosion (in the Discrete Phase Model... category) is the erosion rate calculated at a wall boundary face: Rerosion =

N X m ˙ p f (α)

p=1

Aface

(29.4-9)

where m ˙ p is the mass flow rate of the particle stream, α is the impact angle of the particle path with the wall face, f (α) is the function specified in the Wall panel, and Aface is the area of the wall face where the particle strikes the boundary. This item will appear only if the optional erosion/accretion model is enabled. See Section 21.7.6 for details. The unit quantity for DPM Erosion is mass-flux.


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DPM Evaporation/Devolatilization (in the Discrete Phase Model... category) is the exchange of mass, due to droplet-particle evaporation or combusting-particle devolatilization, from the discrete phase to the evaporating or devolatilizing species. If you are not using the non-premixed combustion model, the mass source for each individual species (DPM species-n Source, below) is also available; for nonpremixed combustion, only this sum is available. The unit quantity for DPM Evaporation/Devolatilization is mass-flow. DPM Mass Source (in the Discrete Phase Model... category) is the total exchange of mass from the discrete phase to the continuous phase. The mass exchange is positive when the particles are a source of mass in the continuous phase. If you are not using the non-premixed combustion model, DPM Mass Source will be equal to the sum of all species mass sources (DPM species-n Source, below); if you are using the non-premixed combustion model, it will be equal to DPM Burnout plus DPM Evaporation/Devolatilization. The unit quantity for DPM Mass Source is mass-flow. DPM Scattering (in the Discrete Phase Model... category) is the scattering coefficient for discrete-phase calculations that involve radiation (σs in Equation 11.3-1). Its unit quantity is length-inverse. DPM Sensible Enthalpy Source (in the Discrete Phase Model... category) is the exchange of sensible enthalpy from the discrete phase to the continuous phase. The exchange is positive when the particles are a source of heat in the continuous phase. Its unit quantity is power. DPM species-n Source (in the Discrete Phase Model... category) is the exchange of mass, due to droplet-particle evaporation or combusting-particle devolatilization, from the discrete phase to the evaporating or devolatilizing species. (The name of the species will replace species-n in DPM species-n Source.) These species are specified in the Set Injection Properties panel, as described in Section 21.9.5. The unit quantity is mass-flow. Note that this variable will not be available if you are using the non-premixed combustion model; use DPM Evaporation/Devolatilization instead. DPM Swirl Momentum Source (in the Discrete Phase Model... category) is the exchange of swirl momentum from the discrete phase to the continuous phase. This value is positive when the particles are a source of momentum in the continuous phase. The unit quantity is force. DPM X, Y, Z Momentum Source (in the Discrete Phase Model... category) are the exchange of x-, y-, and z-direction momentum from the discrete phase to the continuous phase. These values are positive when the particles are a source of momentum in the continuous phase. The unit quantity is force. Dynamic Pressure (in the Pressure... category) is defined as q ≡ 12 ρv 2 . Its unit quantity is pressure.

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Eff Diff Coef of species-n (in the Species... category) is the sum of the laminar and turbulent diffusion coefficients of a species into the mixture: Di,m +

µt ρSct

(The name of the species will replace species-n in Eff Diff Coef of species-n.) The unit quantity is mass-diffusivity. Effective Prandtl Number (in the Turbulence... category) is the ratio µeff cp /keff , where µeff is the effective viscosity, cp is the specific heat, and keff is the effective thermal conductivity. Effective Thermal Conductivity (in the Properties... category) is the sum of the laminar and turbulent thermal conductivities, k+kt , of the fluid. A large thermal conductivity is associated with a good heat conductor and a small thermal conductivity with a poor heat conductor (good insulator). Its unit quantity is thermal-conductivity. Effective Viscosity (in the Turbulence... category) is the sum of the laminar and turbulent viscosities of the fluid. Viscosity, µ, is defined by the ratio of shear stress to the rate of shear. Its unit quantity is viscosity. Enthalpy (in the Temperature... category) is defined differently for compressible and incompressible flows, and depending on the solver and models in use. For compressible flows, H=

X

Yj H j

(29.4-10)

j

and for incompressible flows, H=

X j

Yj H j +

p ρ

(29.4-11)

where Yj and Hj are, respectively, the mass fraction and enthalpy of species j. (See Enthalpy of species-n, below). For the segregated solver, the second term on the right-hand side of Equation 29.4-11 is included only if the pressure work term is included in the energy equation (see Section 11.2.1). For adiabatic non-premixed combustion cases, Enthalpy reports the adiabatic value based on the local mean mixture fraction. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. The unit quantity for Enthalpy is specific-energy.


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Enthalpy of species-n (in the Species... category) is defined differently depending on the solver and models options in use. The quantity: Hj =

Z

T

Tref,j

cp,j dT + h0j (Tref,j )

(29.4-12)

where h0j (Tref,j ) is the formation enthalpy of species j at the reference temperature Tref,j ), is reported only for non-adiabatic PDF cases, or if the coupled solver is selected. The quantity: hj =

Z

T

Tref

cp,j dT

(29.4-13)

where Tref = 298.15K, is reported in all other cases. The unit quantity for Enthalpy of species-n is specific-energy. Entropy (in the Temperature... category) is a thermodynamic property defined by the equation Z δQ (29.4-14) ∆S ≡ rev T where “rev” indicates an integration along a reversible path connecting two states, Q is heat, and T is temperature. For compressible flows, entropy is computed using the equation " # p/pref s = cv −1 (29.4-15) (ρ/ρref )γ where cv is computed from R/(γ − 1), and the reference pressure and density are defined in the Reference Values panel. For incompressible flow, the entropy is computed using the equation s = cp

T −1 Tref

(29.4-16)

where cp is the specific heat at constant pressure and Tref is defined in the Reference Values panel. The unit quantity for entropy is specific-heat. Existing Value (in the Adaption... category) is the value that presently resides in the temporary space reserved for cell variables (i.e., the last value that you displayed or computed). Face Handedness (in the Grid... category) is a parameter that is equal to one in cells that are adjacent to left-handed faces, and zero elsewhere. It can be used to locate mesh problems.

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Face Squish Index (in the Grid... category) is a measure of the quality of a mesh, and is calculated from the dot products of each face area vector, and the vector that connects the centroids of the two adjacent cells as 1−

~ i · ~rc0/c1 A ~ i ||~rc0/c1 | |A

(29.4-17)

Therefore, the worst cells will have a Face Squish Index close to 1. Fine Scale Mass Fraction of species-n (in the Species... category) is the term Yi∗ in Equation 13.1-30. Fine Scale Temperature (in the Temperature... category) is the temperature of the fine scales, which is calculated from the enthalpy when the reaction proceeds over the time scale (τ ∗ in Equation 13.1-29), governed by the Arrhenius rates of Equation 13.1-7. Its unit quantity is temperature. Fine Scale Transfer Rate (in the Species... category) is the transfer rate of the fine scales, which is equal to the inverse of the time scale (τ ∗ in Equation 13.1-29). Its unit quantity is time-inverse. 1-Fine Scale Volume Fraction (in the Species... category) is a function of the fine scale volume fraction (ξ ∗ in Equation 13.1-28). The quantity is subtracted from unity to make it easier to interpret. Fvar Prod (in the Pdf... category) is the production term in the mixture fraction variance equation solved in the non-premixed combustion model (i.e., the last two terms in Equation 14.1-5). Fvar2 Prod (in the Pdf... category) is the production term in the secondary mixture fraction variance equation solved in the non-premixed combustion model. See Equation 14.1-5. Gas Constant (R) (in the Properties... category) is the gas constant of the fluid. Its unit quantity is specific-heat. Granular Conductivity (in the Properties... category) is equivalent to the diffusion coefficient in Equation 22.4-57. For more information, see Section 22.4.6. Its unit quantity is kg/m-s. Granular Pressure... includes quantities for reporting the solids pressure for each granular phase (ps in Equation 22.4-46). See Section 22.4.4 for details. Its unit quantity is pressure. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.


29-27


Granular Temperature... includes quantities for reporting the granular temperature for each granular phase (Θs in Equation 22.4-57). See Section 22.4.6 for details. Its unit quantity is m2 /s2 . For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Grid... includes variables related to the grid. Grid X-Velocity, Grid Y-Velocity, Grid Z-Velocity (in the Velocity... category) are the vector components of the grid velocity for moving-grid problems (rotating or multiple reference frames, mixing planes, or sliding meshes). Its unit quantity is velocity. HCN Density (in the NOx... category) is the mass per unit volume of HCN. The unit quantity is density. The HCN Density will appear only if you are modeling fuel NOx . See Section 18.1.5 for details. Helicity (in the Velocity... category) is defined by the dot product of vorticity and the velocity vector. H = (∇ × V~ ) · V~ (29.4-18) It provides insight into the vorticity aligned with the fluid stream. Vorticity is a measure of the rotation of a fluid element as it moves in the flow field. Incident Radiation (in the Radiation... category) is the total radiation energy, G, that arrives at a location per unit time and per unit area: G=

Z

IdΩ

(29.4-19)

Ω=4π

where I is the radiation intensity and Ω is the solid angle. G is the quantity that the P-1 radiation model computes. For the DO radiation model, the incident radiation is computed over a finite number of discrete solid angles, each associated with a vector direction. The unit quantity for Incident Radiation is heat-flux. Incident Radiation (Band n) (in the Radiation... category) is the radiation energy contained in the wavelength band ∆λ for the non-gray DO radiation model. Its unit quantity is heat-flux. Internal Energy (in the Temperature... category) is the summation of the kinetic and potential energies of the molecules of the substance (in the absence of chemical or nuclear reactions) per unit volume. It is defined as e = cv T . Its unit quantity is specific-energy. Lam Diff Coef of species-n (in the Species... category) is the laminar diffusion coefficient of a species into the mixture, Di,m . Its unit quantity is mass-diffusivity. Laminar Flame Speed (in the Premixed Combustion... category) is the propagation speed of laminar premixed flames (Ul in Equation 15.2-4). Its unit quantity is velocity.

29-28



Liquid Fraction (in the Solidification/Melting... category) is the liquid fraction β computed by the solidification/melting model:

β=

β=

∆H =0 L

if

T < Tsolidus

β=

∆H =1 L

if

T > Tliquidus

∆H T − Tsolidus = L Tliquidus − Tsolidus

if

Tsolidus < T < Tliquidus

(29.4-20)

Mach Number (in the Velocity... category) is the ratio of velocity and speed of sound. Mass fraction of HCN, Mass fraction of NH3, Mass fraction of NO (in the NOx... category) are the mass of HCN, the mass of NH3 , and the mass of NO per unit mass of the mixture (e.g., kg of HCN in 1 kg of the mixture). The Mass fraction of HCN and the Mass fraction of NH3 will appear only if you are modeling fuel NOx . See Section 18.1.5 for details. Mass fraction of nuclei (in the Soot... category) is the number of particles per unit mass of the mixture (in units of particles ×1015 /kg) The Mass fraction of nuclei will appear only if you use the two-step soot model. See Section 18.2 for details. Mass fraction of soot (in the Soot... category) is the mass of soot per unit mass of the mixture (e.g., kg of soot in 1 kg of the mixture). See Section 18.2 for details. Mass fraction of species-n (in the Species... category) is the mass of a species per unit mass of the mixture (e.g., kg of species in 1 kg of the mixture). Mean quantity-n (in the Unsteady Statistics... category) is the time-averaged value of a solution variable (e.g., Static Pressure). See Section 24.15.3 for details. Meridional Coordinate (in the Grid... category) is the normalized (dimensionless) coordinate that follows the flow path from inlet to outlet. Its value varies from 0 to 1. Mixture Fraction Variance (in the Pdf... category) is the variance of the mixture fraction solved for in the non-premixed combustion model. This is the second conservation equation (along with the mixture fraction equation) that the non-premixed combustion model solves. (See Section 14.1.2.) Modified Turbulent Viscosity (in the Turbulence... category) is the transported quantity ν˜ that is solved for in the Spalart-Allmaras turbulence model (see Equation 10.3-1). The turbulent viscosity, µt , is computed directly from this quantity using the relationship given by Equation 10.3-2. Its unit quantity is viscosity.


29-29


Molar Concentration of species-n (in the Species... category) is the moles per unit volume of a species. Its unit quantity is concentration. Mole fraction of species-n (in the Species... category) is the number of moles of a species in one mole of the mixture. Mole fraction of HCN, Mole fraction of NH3, Mole fraction of NO (in the NOx... category) are the number of moles of HCN, NH3 , and NO in one mole of the mixture. The Mole fraction of HCN and the Mole fraction of NH3 will appear only if you are modeling fuel NOx . See Section 18.1.5 for details. Mole fraction of soot (in the Soot... category) is the number of moles of soot in one mole of the mixture. Molecular Prandtl Number (in the Properties... category) is the ratio cp µlam /klam . Molecular Viscosity (in the Properties... category) is the laminar viscosity of the fluid. Viscosity, µ, is defined by the ratio of shear stress to the rate of shear. Its unit quantity is viscosity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. For granular phases, this is equivalent to the solids shear viscosity µs in Equation 22.4-51. NH3 Density, NO Density (in the NOx... category) are the mass per unit volume of NH3 and NO. The unit quantity for each is density. The NH3 Density will appear only if you are modeling fuel NOx . See Section 18.1.5 for details. NOx... contains quantities related to the NOx model. See Section 18.1 for details about this model. Partition Boundary Cell Distance (in the Grid... category) is the smallest number of cells which must be traversed to reach the nearest partition (interface) boundary. Partition Neighbors (in the Cell Info... category) is the number of adjacent partitions (i.e., those that share at least one partition boundary face (interface)). It gives a measure of the number of messages that will have to be generated for parallel processing. Pdf... contains quantities related to the non-premixed combustion model, which is described in Chapter 14. Phases... contains quantities for reporting the volume fraction of each phase. See Chapter 22 for details. Pitchwise Coordinate (in the Grid... category) is the normalized (dimensionless) coordinate in the circumferential (pitchwise) direction. Its value varies from 0 to 1. Preconditioning Reference Velocity (in the Velocity... category) is the reference velocity used in the coupled solver’s preconditioning algorithm. See Section 24.4.2 for details.

29-30



Premixed Combustion... contains quantities related to the premixed combustion model, which is described in Chapter 15. Pressure... includes quantities related to a normal force per unit area (the impact of the gas molecules on the surfaces of a control volume). Pressure Coefficient (in the Pressure... category) is a dimensionless parameter defined by the equation Cp =

(p − pref ) qref

(29.4-21)

where p is the static pressure, pref is the reference pressure, and qref is the reference dynamic pressure defined by 12 ρref vref 2 . The reference pressure, density, and velocity are defined in the Reference Values panel. Product Formation Rate (in the Premixed Combustion... category) is the source term in the progress variable transport equation (Sc in Equation 15.2-1). Its unit quantity is time-inverse. Production of k (in the Turbulence... category) is the rate of production of turbulence kinetic energy (times density). Its unit quantity is turb-kinetic-energy-production. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Progress Variable (in the Premixed Combustion... category) is a normalized mass fraction of the combustion products (c = 1) or unburnt mixture products (c = 0), as defined by Equation 15.2-2. Properties... includes material property quantities for fluids and solids. Radial Coordinate (in the Grid... category) is the length of the radius vector in the polar coordinate system. The radius vector is defined by a line segment between the node and the axis of rotation. You can define the rotational axis in the Fluid panel. (See also Section 29.2.) The unit quantity for Radial Coordinate is length. Radial Pull Velocity (in the Solidification/Melting... category) is the radial-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity. Radial Velocity (in the Velocity... category) is the component of velocity in the radial direction. (See Section 29.2 for details.) The unit quantity for Radial Velocity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Radial-Wall Shear Stress (in the Wall Fluxes... category) is the radial component of the force acting tangential to the surface due to friction. Its unit quantity is pressure.


29-31


Radiation... includes quantities related to radiation heat transfer. See Section 11.3 for details about the radiation models available in FLUENT. Radiation Heat Flux (in the Wall Fluxes... category) is the rate of radiation heat transfer through the control surface. It is calculated by the solver according to the specified radiation model. Heat flux out of the domain is negative, and heat flux into the domain is positive. The unit quantity for Radiation Heat Flux is heat-flux. Radiation Temperature (in the Radiation... category) is the quantity θR , defined by θR = (

G 1/4 ) 4σ

(29.4-22)

where G is the Incident Radiation. The unit quantity for Radiation Temperature is temperature. Rate of Reaction-n (in the Reactions... category) is the effective rate of progress of nth reaction. For the finite-rate model, the value is the same as the Arrhenius Rate of Reaction-n. For the eddy-dissipation model, the value is equivalent to the Turbulent Rate of Reaction-n. For the finite-rate/eddy-dissipation model, it is the lesser of the two. Reactions... includes quantities related to finite-rate reactions. See Chapter 13 for information about modeling finite-rate reactions. Reflected Radiation Flux (Band-n) (in the Wall Fluxes... category) is the amount of radiative heat flux reflected by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux. Refractive Index (in the Radiation... category) is a nondimensional parameter defined as the ratio of the speed of light in a material to that in vacuum. See Section 11.3.6 for details. Relative Axial Velocity (in the Velocity... category) is the axial-direction component of the velocity relative to the reference frame motion. See Section 29.2 for details. The unit quantity for Relative Axial Velocity is velocity. Relative Humidity (in the Species... category) is the ratio of the partial pressure of the water vapor actually present in an air-water mixture to the saturation pressure of water vapor at the mixture temperature. FLUENT computes the saturation pressure, p, from the following equation [211]: p ln pc

29-32

!

=

8 X Tc −1 × Fi [a (T − Tp )]i−1 T i=1

(29.4-23)



where

pc Tc F1 F2 F3 F4 F5 F6 F7 F8 a Tp

= = = = = = = = = = = =

22.089 MPa 647.286 K −7.4192420 2.9721000 × 10−1 −1.1552860 × 10−1 8.6856350 × 10−3 1.0940980 × 10−3 −4.3999300 × 10−3 2.5206580 × 10−3 −5.2186840 × 10−4 0.01 338.15 K

Relative Mach Number (in the Velocity... category) is the nondimensional ratio of the relative velocity and speed of sound. Relative Radial Velocity (in the Velocity... category) is the radial-direction component of the velocity relative to the reference frame motion. (See Section 29.2 for details.) The unit quantity for Relative Radial Velocity is velocity. Relative Swirl Velocity (in the Velocity... category) is the tangential-direction component of the velocity relative to the reference frame motion, in an axisymmetric swirling flow. (See Section 29.2 for details.) The unit quantity for Relative Swirl Velocity is velocity. Relative Tangential Velocity (in the Velocity... category) is the tangential-direction component of the velocity relative to the reference frame motion. (See Section 29.2 for details.) The unit quantity for Relative Tangential Velocity is velocity. Relative Total Pressure (in the Pressure... category) is the stagnation pressure computed using relative velocities instead of absolute velocities; i.e., for incompressible flows the dynamic pressure would be computed using the relative velocities. (See Section 29.2 for more information about relative velocities.) The unit quantity for Relative Total Pressure is pressure. Relative Total Temperature (in the Temperature... category) is the stagnation temperature computed using relative velocities instead of absolute velocities. (See Section 29.2 for more information about relative velocities.) The unit quantity for Relative Total Temperature is temperature. Relative Velocity Angle (in the Velocity... category) is similar to the Velocity Angle except that it uses the relative tangential velocity, and is defined as −1

tan

relative-tangential-velocity − axial-velocity

!

(29.4-24)

Its unit quantity is angle.


29-33


Relative Velocity Magnitude (in the Velocity... category) is the magnitude of the relative velocity vector instead of the absolute velocity vector. The relative velocity (w) ~ is the difference between the absolute velocity (~v ) and the grid velocity. For simple rotation, the relative velocity is defined as ~ × ~r w ~ ≡ ~v − Ω

(29.4-25)

~ is the angular velocity of a rotating reference frame about the origin and where Ω ~r is the position vector. (See also Section 29.2.) The unit quantity for Relative Velocity Magnitude is velocity. Relative X Velocity, Relative Y Velocity, Relative Z Velocity (in the Velocity... category) are the x-, y-, and z-direction components of the velocity relative to the reference frame motion. (See Section 29.2 for details.) The unit quantity for these variables is velocity. Residuals... contains different quantities for the segregated and coupled solvers: In the coupled solvers, this category includes the corrections to the primitive variables pressure, velocity, temperature, and species, as well as the time rate of change of the corrections to these primitive variables for the current iteration (i.e., residuals). Corrections are the changes in the variables between the current and previous iterations and residuals are computed by dividing a cell’s correction by its physical time step. The total residual for each variable is the summation of the Euler, viscous, and dissipation contributions. The dissipation components are the vector components of the flux-like, face-based dissipation operator. In the segregated solver, only the Mass Imbalance in each cell is reported (unless you have requested others, as described in Section 24.16.1). At convergence, this quantity should be small compared to the average mass flow rate. RMS quantity-n (in the Unsteady Statistics... category) is the root mean squared value of a solution variable (e.g., Static Pressure). See Section 24.15.3 for details. Rothalpy (in the Temperature... category) is defined as I =h+

w 2 u2 − 2 2

(29.4-26)

where h is the enthalpy, w is the relative velocity magnitude, and u is the magnitude of the rotational velocity ~u = ω ~ × ~r. Scalar-n (in the User Defined Scalars... category) is the value of the nth scalar quantity you have defined as a user-defined scalar. See the separate UDF manual for more information about user-defined scalars.

29-34



Scalar Dissipation (in the Pdf... category) is one of two parameters that describes the species mass fraction and temperature for a laminar flamelet in mixture fraction spaces. It is defined as χ = 2D|∇f |2

(29.4-27)

where f is the mixture fraction and D is a representative diffusion coefficient (see Section 14.4.3 for details). Its unit quantity is time-inverse. Scattering Coefficient (in the Radiation... category) is the property of a medium that describes the amount of scattering of thermal radiation per unit path length for propagation in the medium. It can be interpreted as the inverse of the mean free path that a photon will travel before undergoing scattering (if the scattering coefficient does not vary along the path). The unit quantity for Scattering Coefficient is length-inverse. Secondary Mean Mixture Fraction (in the Pdf... category) is the mean ratio of the secondary stream mass fraction to the sum of the fuel, secondary stream, and oxidant mass fractions. It is the secondary-stream conserved scalar that is calculated by the non-premixed combustion model. See Section 14.1.2. Secondary Mixture Fraction Variance (in the Pdf... category) is the variance of the secondary stream mixture fraction that is solved for in the non-premixed combustion model. See Section 14.1.2. Skin Friction Coefficient (in the Wall Fluxes... category) is a nondimensional parameter defined as the ratio of the wall shear stress and the reference dynamic pressure Cf ≡

τw 1 ρ v2 2 ref ref

(29.4-28)

where τw is the wall shear stress, and ρref and vref are the reference density and velocity defined in the Reference Values panel. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Solidification/Melting... contains quantities related to solidification and melting. Soot... contains quantities related to the Soot model, which is described in Section 18.2. Soot Density (in the Soot... category) is the mass per unit volume of soot. The unit quantity is density. See Section 18.1.5 for details. SoundqSpeed (in the Properties... category) is the acoustic speed. It is computed from γp . Its unit quantity is velocity. ρ Spanwise Coordinate (in the Grid... category) is the normalized (dimensionless) coordinate in the spanwise direction, from hub to casing. Its value varies from 0 to 1.


29-35


species-n Source Term (in the Species... category) is the source term in each of the species transport equations due to reactions. The unit quantity is always kg/m3 -s. Species... includes quantities related to species transport and reactions. Specific Dissipation Rate (Omega) (in the Turbulence... category) is the rate of dissipation of turbulence kinetic energy in unit volume and time. Its unit quantity is timeinverse. Specific Heat (Cp) (in the Properties... category) is the thermodynamic property of specific heat at constant pressure. It is defined as the rate of change of enthalpy with temperature while pressure is held constant. Its unit quantity is specific-heat. Specific Heat Ratio (gamma) (in the Properties... category) is the ratio of specific heat at constant pressure to the specific heat at constant volume. Stored Cell Partition (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file.See Section 30.4.3 for more information. Static Pressure (in the Pressure... category) is the static pressure of the fluid. It is a gauge pressure expressed relative to the prescribed operating pressure. The absolute pressure is the sum of the Static Pressure and the operating pressure. Its unit quantity is pressure. Static Temperature (in the Temperature... and Premixed Combustion... categories) is the temperature that is measured moving with the fluid. Its unit quantity is temperature. Note that Static Temperature will appear in the Premixed Combustion... category only for adiabatic premixed combustion calculations. See Section 15.3.7.

29-36



Strain Rate (in the Derivatives... category) relates shear stress to the viscosity. Also called the shear rate (γ˙ in Equation 7.3-17), the strain rate is related to the second invariant of the rate-of-deformation tensor D. Its unit quantity is time-inverse. In 3D Cartesian coordinates, the strain rate, S, is defined as

S

2

"

∂u = ∂x " ∂v ∂x " ∂w ∂x

!

∂u ∂u ∂u + + ∂x ∂x ∂y ! ∂v ∂u ∂v + + ∂x ∂y ∂y ! ∂w ∂u ∂w + + ∂x ∂z ∂y

!

!#

∂u ∂v ∂u ∂u ∂w + + + + ∂y ∂x ∂z ∂z ∂x ! !# ∂v ∂v ∂v ∂v ∂w + + + + ∂y ∂y ∂z ∂z ∂y ! !# ∂w ∂v ∂w ∂w ∂w + + + ∂y ∂z ∂z ∂z ∂z (29.4-29)

For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Stream Function (in the Velocity... category) is formulated as a relation between the streamlines and the statement of conservation of mass. A streamline is a line that is tangent to the velocity vector of the flowing fluid. For a 2D planar flow, the stream function, ψ, is defined such that ρu ≡

∂ψ ∂y

ρv ≡ −

∂ψ ∂x

(29.4-30)

where ψ is constant along a streamline and the difference between constant values of stream function defining two streamlines is the mass rate of flow between the streamlines. The accuracy of the stream function calculation is determined by the text command /display/set/n-stream-func. Stretch Factor (in the Premixed Combustion... category) is a nondimensional parameter that is defined as the probability of unquenched flamelets (G in Equation 15.2-10). Subgrid Turbulent Kinetic Energy (in the Turbulence... category) is the turbulence kinetic energy per unit mass of the unresolved eddies, ks , calculated using the LES turbulence model. It is defined as ks =

νt2 L2s

(29.4-31)

Its unit quantity is turbulent-kinetic-energy.


29-37


Subgrid Turbulent Viscosity (in the Turbulence... category) is the turbulent (dynamic) viscosity of the fluid calculated using the LES turbulence model. It expresses the proportionality between the anisotropic part of the subgrid-scale stress tensor and the rate-of-strain tensor. (See Equation 10.7-7.) Its unit quantity is viscosity. Subgrid Turbulent Viscosity Ratio (in the Turbulence... category) is the ratio of the subgrid turbulent viscosity of the fluid to the laminar viscosity, calculated using the LES turbulence model. Surface Cluster ID (in the Radiation... category) is used to view the distribution of surface clusters in the domain. Each cluster has a unique integer number (ID) associated with it. Surface Deposition Rate of species-n (in the Species... category) is the amount of a surface species that is deposited on the substrate. Its unit quantity is mass-flux. Surface Coverage of species-n (in the Species... category) is the amount of a surface species that is deposited on the substrate at a specific point in time. Surface Heat Transfer Coef. (in the Wall Fluxes... category) is defined by the equation heff =

q Twall − Tref

(29.4-32)

where q is the convective heat flux, Twall is the wall temperature, and Tref is reference temperature defined in the Reference Values panel. Its unit quantity is heat-transfercoefficient. Surface Incident Radiation (in the Wall Fluxes... category) is the net incoming radiation heat flux on a surface. Its unit quantity is heat-flux. Surface Nusselt Number (in the Wall Fluxes... category) is a local nondimensional coefficient of heat transfer defined by the equation heff Lref (29.4-33) k where heff is the heat transfer coefficient, Lref is the reference length defined in the Reference Values panel, and k is the molecular thermal conductivity. Nu =

Surface Stanton Number (in the Wall Fluxes... category) is a nondimensional coefficient of heat transfer defined by the equation St =

heff ρref vref cp

(29.4-34)

where heff is the heat transfer coefficient, ρref and vref are reference values of density and velocity defined in the Reference Values panel, and cp is the specific heat at constant pressure.

29-38



Swirl Pull Velocity (in the Solidification/Melting... category) is the tangential-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity. Swirl Velocity (in the Velocity... category) is the tangential-direction component of the velocity in an axisymmetric swirling flow. See Section 29.2 for details. The unit quantity for Swirl Velocity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Swirl-Wall Shear Stress (in the Wall Fluxes... category) is the swirl component of the force acting tangential to the surface due to friction. Its unit quantity is pressure. Tangential Velocity (in the Velocity... category) is the velocity component in the tangential direction. (See Section 29.2 for details.) The unit quantity for Tangential Velocity is velocity. Temperature... indicates the quantities associated with the thermodynamic temperature of a material. Thermal Conductivity (in the Properties... category) is a parameter (k) that defines the conduction rate through a material via Fourier’s law (q = −k∇T ). A large thermal conductivity is associated with a good heat conductor and a small thermal conductivity with a poor heat conductor (good insulator). Its unit quantity is thermal-conductivity. Thermal Diff Coef of species-n (in the Species... category) is the thermal diffusion coefficient for the nth species (DT,i in Equations 7.7-1, 7.7-3, and 7.7-7). Its unit quantity is viscosity. Time Step (in the Residuals... category) is the local time step of the cell, ∆t, at the current iteration level. Its unit quantity is time. Time Step Scale (in the Species... category) is the factor by which the time step is reduced for the stiff chemistry solver (available in the coupled solver only). The time step is scaled down based on an eigenvalue and positivity analysis. Total Energy (in the Temperature... category) is the total energy per unit mass. Its unit quantity is specific-energy. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Total Enthalpy (in the Temperature... category) is defined as H + 12 v 2 where H is the Enthalpy and v is the velocity magnitude. Its unit quantity is specific-energy. For multiphase models, this value corresponds to the selected phase in the Phase dropdown list.


29-39


Total Enthalpy Deviation (in the Temperature... category) is the difference between Total Enthalpy and the reference enthalpy, H + 12 v 2 − Href , where Href is the reference enthalpy defined in the Reference Values panel. The unit quantity for Total Enthalpy Deviation is specific-energy. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Total Pressure (in the Pressure... category) is the pressure at the thermodynamic state that would exist if the fluid were brought to zero velocity and zero potential. For compressible flows, the total pressure is computed using isentropic relationships. For constant cp , this reduces to: γ − 1 2 γ/(γ−1) M (29.4-35) 2 where p is the static pressure, γ is the ratio of specific heats, and M is the Mach number. For incompressible flows (constant density fluid), we use Bernoulli’s equation, p0 = p + pdyn , where pdyn is the local dynamic pressure. Its unit quantity is pressure.

p0 = p 1 +

Total Surface Heat Flux (in the Wall Fluxes... category) is the rate of total heat transfer through the control surface. It is calculated by the solver according to the boundary conditions being applied at that surface. By definition, heat flux out of the domain is negative, and heat flux into the domain is positive. The unit quantity for Total Surface Heat Flux is heat-flux. Total Temperature (in the Temperature... category) is the temperature at the thermodynamic state that would exist if the fluid were brought to zero velocity. For compressible flows, the total temperature is computed from the total enthalpy using the current cp method (specified in the Materials panel). For incompressible flows, the total temperature is equal to the static temperature. The unit quantity for Total Temperature is temperature. Transmitted Radiation Flux (Band-n) (in the Wall Fluxes... category) is the amount of radiative heat flux transmitted by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux. Turbulence... includes quantities related to turbulence. See Chapter 10 for information about the turbulence models available in FLUENT. Turbulence Intensity (in the Turbulence... category) is the ratio of the magnitude of the RMS turbulent fluctuations to the reference velocity:

I=

q

2 k 3

vref

(29.4-36)

where k is the turbulence kinetic energy and vref is the reference velocity specified in the Reference Values panel. The reference value specified should be the mean

29-40



velocity magnitude for the flow. Note that turbulence intensity can be defined in different ways, so you may want to use a custom field function for its definition. See Section 29.5 for more information. Turbulent Dissipation Rate (Epsilon) (in the Turbulence... category) is the turbulent dissipation rate. Its unit quantity is turbulent-energy-diss-rate. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Turbulent Flame Speed (in the Premixed Combustion... category) is the turbulent flame speed computed by FLUENT using Equation 15.2-4. Its unit quantity is velocity. Turbulent Kinetic Energy (k) (in the Turbulence... category) is the turbulence kinetic energy per unit mass defined as 1 k = u0i u0i (29.4-37) 2 Its unit quantity is turbulent-kinetic-energy. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Turbulent Rate of Reaction-n (in the Reactions... category) is the rate of progress of the nth reaction computed by Equation 13.1-25 or 13.1-26. For the “eddy-dissipation” model, the value is the same as the Rate of Reaction-n. For the “finite-rate” model, the value is zero. Turbulent Reynolds Number (Re y) (in the Turbulence... category) is a nondimensional quantity defined as √ ρd k µlam

(29.4-38)

where k is turbulence kinetic energy, d is the distance to the nearest wall, and µlam is the laminar viscosity. Turbulent Viscosity (in the Turbulence... category) is the turbulent viscosity of the fluid computed using the turbulence model. Its unit quantity is viscosity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Turbulent Viscosity Ratio (in the Turbulence... category) is the ratio of turbulent viscosity to the laminar viscosity. udm-n (in the User Defined Memory... category) is the value of the quantity in the nth user-defined memory location. Unburnt Fuel Mass Fraction (in the Premixed Combustion... category) is the mass fraction of unburnt fuel. This function is available only for non-adiabatic models.


29-41


Unsteady Statistics... includes mean and root mean square (RMS) values of solution variables derived from transient flow calculations. User Defined Memory... includes quantities that have been allocated to a user-defined memory location. See the separate UDF Manual for details about user-defined memory. User-Defined Scalars... includes quantities related to user-defined scalars. See the separate UDF Manual for information about using user-defined scalars. UU Reynolds Stress (in the Turbulence... category) is the u0 2 stress. UV Reynolds Stress (in the Turbulence... category) is the u0 v 0 stress. UW Reynolds Stress (in the Turbulence... category) is the u0 w0 stress. Variance of Species (in the NOx... category) is the variance of the mass fraction of a selected species in the flow field. It is calculated from Equation 18.1-86. Variance of Species 1, Variance of Species 2 (in the NOx... category) are the variances of the mass fractions of the selected species in the flow field. They are each calculated from Equation 18.1-86. Variance of Temperature (in the NOx... category) is the variance of the normalized temperature in the flow field. It is calculated from Equation 18.1-86. Velocity... includes the quantities associated with the rate of change in position with time. The instantaneous velocity of a particle is defined as the first derivative of the position vector with respect to time, d~r/dt, termed the velocity vector, ~v . Velocity Angle (in the Velocity... category) is defined as follows: For a 2D model, y-velocity-component x-velocity-component

−1

tan

!

(29.4-39)

For a 2D or axisymmetric model, −1

tan

radial-velocity-component axial-velocity-component

!

(29.4-40)

For a 3D model, −1

tan

tangential-velocity-component axial-velocity-component

!

(29.4-41)

Its unit quantity is angle.

29-42



Velocity Magnitude (in the Velocity... category) is the speed of the fluid. Its unit quantity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Volume fraction (in the Phases... category) is the volume fraction of the selected phase in the Phase drop-down list. Vorticity Magnitude (in the Velocity... category) is the magnitude of the vorticity vector. Vorticity is a measure of the rotation of a fluid element as it moves in the flow field, and is defined as the curl of the velocity vector: ξ = ∇ × V~

(29.4-42)

VV Reynolds Stress (in the Turbulence... category) is the v 0 2 stress. VW Reynolds Stress (in the Turbulence... category) is the v 0 w0 stress. Wall Fluxes... includes quantities related to forces and heat transfer at wall surfaces. Wall Shear Stress (in the Wall Fluxes... category) is the force acting tangential to the surface due to friction. Its unit quantity is pressure. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Wall Temperature (Inner Surface) (in the Temperature... category) is the temperature on the inner surface of a wall (corresponding to the side of the wall surface away from the adjacent fluid or solid cell zone). Note that wall thermal boundary conditions are applied on this surface. See also Figure 6.13.2. The unit quantity for Wall Temperature (Inner Surface) is temperature. Wall Temperature (Outer Surface) (in the Temperature... category) is the temperature on the outer surface of a wall (corresponding to the side of the wall surface toward the adjacent fluid or solid cell zone). Note that wall thermal boundary conditions are applied on the Inner Surface. See also Figure 6.13.2. The unit quantity for Wall Temperature (Outer Surface) is temperature. Wall Yplus (in the Turbulence... category) is a nondimensional parameter defined by the equation y+ =

ρuτ yP µ

(29.4-43)

q

where uτ = τw /ρw is the friction velocity, yP is the distance from point P to the wall, ρ is the fluid density, and µ is the fluid viscosity at point P . See Section 10.8 for details. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.


29-43


Wall Ystar (in the Turbulence... category) is a nondimensional parameter defined by the equation 1/2

ρCµ1/4 kP yP y = µ ∗

(29.4-44)

where kP is the turbulence kinetic energy at point P , yP is the distance from point P to the wall, ρ is the fluid density, and µ is the fluid viscosity at point P . See Section 10.8 for details. WW Reynolds Stress (in the Turbulence... category) is the w0 2 stress. X-Coordinate, Y-Coordinate, Z-Coordinate (in the Grid... category) are the Cartesian coordinates in the x-axis, y-axis, and z-axis directions respectively. The unit quantity for these variables is length. X Face Area, Y Face Area, Z Face Area (in the Grid... category) are the components of the boundary face area vectors accumulated to the boundary cells, for the zones selected in the Boundary Zones list contained in the Boundary Adaption panel. The face areas are calculated only on the zones selected, and in order to make your selection active, you need to click the Mark button in the Boundary Adaption panel. Note that if the Boundary Zones list is empty, all boundary zones will be used. The face area calculations are done as in X Surface Area, Y Surface Area, Z Surface Area (see below), except the area values in the cells with more than one boundary face are not summed to obtain the cell values. Instead, the area value relative to the last visited face of each cell (resulting from your selection of Boundary Zones) is taken as the cell value. X Pull Velocity, Y Pull Velocity, Z Pull Velocity (in the Solidification/Melting... category) are the x, y, and z components of the pull velocity for the solid material in a continuous casting process. The unit quantity for each is velocity. X Surface Area, Y Surface Area, Z Surface Area (in the Grid... category) are the components of the boundary face area vectors accumulated to the boundary cells. The surface area is accumulated for all boundary faces. For each boundary face zone, the component of the face area in the relevant direction (x, y, or z) is accumulated as the cell value of the adjoining cell. For those cells having more than one boundary face, the cell value is the sum (accumulation) of all the face area values. In most circumstances, the X Surface Area, Y Surface Area, Z Surface Area are used for flux and surface integration. In the few instances where area accumulation must be avoided, you can mark the zones of interest and use X Face Area, Y Face Area, Z Face Area (see above) for flux and integral calculations.

29-44


29.5 Custom Field Functions

X Velocity, Y Velocity, Z Velocity (in the Velocity... category) are the components of the velocity vector in the x-axis, y-axis, and z-axis directions, respectively. The unit quantity for these variables is velocity. For multiphase models, these values correspond to the selected phase in the Phase drop-down list. X-Vorticity, Y-Vorticity, Z-Vorticity (in the Velocity... category) are the x, y, and z components of the vorticity vector. X-Wall Shear Stress, Y-Wall Shear Stress, Z-Wall Shear Stress (in the Wall Fluxes... category) are the x, y, and z components of the force acting tangential to the surface due to friction. The unit quantity for these variables is pressure. For multiphase models, these valuescorrespond to the selected phase in the Phase drop-down list.

29.5

Custom Field Functions

In addition to the basic field variables provided by FLUENT (and described in Section 29.4), you can also define your own field functions to be used in conjunction with any of the commands that use these variables (contour and vector display, XY plots, etc.). This capability is available with the Custom Field Function Calculator panel. You can use the default field variables, previously defined calculator functions, and calculator operators to create new functions. (Several sample functions are described in Section 29.5.3.) Any field functions that you define will be saved in the case file the next time that you save it. You can also save your custom field functions to a separate file (as described in Section 29.5.2), so that they can be used with a different case file.

! Note that all custom field functions are evaluated and stored in SI units. Any solverdefined flow variables that you use in your field-function definition will be automatically converted if they are not already in SI units, but you must be careful to enter constants in the appropriate units. Note also that explicit node values are not available for custom field functions; all node values for these functions will be computed by averaging the values in the surrounding cells, as described in Section 29.1.2.

29.5.1

Creating a Custom Field Function

To create your own field function, you will use the Custom Field Function Calculator panel (Figure 29.5.1). This panel allows you to define field functions based on existing functions, using simple calculator operators. Any functions that you define will be added to the list of default flow variables and other field functions provided by the solver. Define −→Custom Field Functions...


29-45


! Recall that you must enter all constants in the function definition in SI units.

Figure 29.5.1: The Custom Field Function Calculator Panel

The steps for creating a custom field function are as follows: 1. Use the calculator buttons and the Field Functions list and Select button to specify the function definition, as described below. (As you select each item from the Field Functions list or click a button in the calculator keypad, its symbol will appear in the Definition text entry box. You cannot edit the contents of this box directly; if you want to delete part of a function, use the DEL button on the keypad.) 2. Specify the name of the function in the New Function Name field.

!

Be sure that you do not specify a name that is already used for a standard field function (e.g., velocity-magnitude); you can see a complete list of the predefined field functions in FLUENT by selecting the display/contours text command and viewing the available choices for contours of. 3. Click the Define button. When you click Define, the solver will create the function and add it to the list of Custom Field Functions within the drop-down list of available field functions. The Define push button is grayed out after you create a new function or if the Definition text entry box is empty. Should you decide to rename or delete the function after you have completed the definition, you can do so in the Field Function Definitions panel, which you can open by clicking on the Manage... push button. See Section 29.5.2 for details.

29-46



Using the Calculator Buttons Your function definition can include many basic calculator operations (e.g., addition, subtraction, multiplication, square root). When you select a calculator button (by clicking on it), the appropriate symbol will appear in the Definition text entry box. The meaning of the buttons is straightforward; they are similar to the buttons you would find on any standard calculator. You should, however, note the following: • The CE/C button will clear the entire Definition and the New Function Name, if you have entered one. The DEL button will delete only the last entry in the Definition text entry box. You can use DEL to delete characters one at a time, starting with the last one entered. • To obtain the inverse trigonometric functions arcsin, arccos, and arctan, click the INV button before selecting sin, cos, or tan. • The ABS button yields the absolute value of the number that follows it, and the log button yields the natural logarithm of the following number. • The PI button represents π and the e button represents the base of the natural logarithm system (which is approximately equal to 2.71828).

Using the Field Functions List Your function definition can also include any of the field functions defined by the solver (and listed in Section 29.4) or by you. To include one of these variables/functions in your function definition, select it in the Field Functions drop-down list and then click the Select button below the list. The symbol for the selected item will appear in the Definition text entry box (e.g., p will appear if you select Static Pressure).

29.5.2

Manipulating, Saving, and Loading Custom Field Functions

Once you have defined your field functions, you can manipulate them using the Field Function Definitions panel (Figure 29.5.2). You can display a function definition to be sure that it is correct, delete the function if you decide that it is incorrect and needs to be redefined, or give the function a new name. You can also save custom field functions to a file or read them from a file. The custom field function file allows you to transfer your custom functions between case files. To open the Field Function Definitions panel, click the Manage... button in the Custom Field Function Calculator panel. The following actions can be performed in the Field Function Definitions panel:


29-47


Figure 29.5.2: The Field Function Definitions Panel

• To check the definition of a function, select it in the Field Functions list. Its definition will be displayed in the Definition field. This display is for informational purposes only; you cannot edit it. If you want to change a function definition, you must delete the function and define it again in the Custom Field Function Calculator panel. • To delete a function, select it in the Field Functions list and click the Delete button. • To rename a function, select it in the Field Functions list, enter a new name in the Name field, and click the Rename button.

!

Be sure that you do not specify a name that is already used for a standard field function (e.g., velocity-magnitude); you can see a complete list of the predefined field functions in FLUENT by selecting the display/contours text command and viewing the available choices for contours of. • To save all of the functions in the Field Functions list to a file, click the Save... button and specify the file name in the resulting Select File dialog box (see Section 2.1.2). • To read custom field functions from a file that you saved as described above, click the Load... button and specify the file name in the resulting Select File dialog box. (Custom field function files are valid Scheme functions, and can also be loaded with the File/Read/Scheme... menu item, as described in Section 3.15.)

29-48



29.5.3

Sample Custom Field Functions

When you are checking the results of your simulation, you may find it useful to define some of the following field functions: • To define a function that determines the ratio of static pressure to inlet total pressure, use the relationship R=

p + pop pto + pop

(29.5-1)

where p is the static pressure calculated by the solver, pto is the inlet total pressure, and pop is the operating pressure for the problem. Use the solver-defined function Static Pressure for p, and the numerical value that you specified for Gauge Total Pressure in the Pressure Inlet panel for pto . Specify the value of the operating pressure to be the value that you set in the Operating Conditions panel. As discussed in Section 7.12, all pressures in FLUENT are gauge pressures relative to the operating pressure. If the operating pressure is zero, as is generally the case for compressible flow calculations, the expression for the pressure ratio reduces to PR =

p pto

(29.5-2)

• To define a function that determines the critical velocity ratio v/a∗ , a parameter that is sometimes used in turbomachinery calculations, use the relationship v = a∗

"

!

γ+1 1 − PR(γ−1)/γ γ−1

#1/2

(29.5-3)

In this relationship, a∗ is the critical velocity (i.e., the velocity that would occur for the same stagnation conditions if M = 1), γ is the ratio of specific heats, and PR is the pressure ratio defined in Equation 29.5-2 for which you created your own function. For γ, ratio of specific heats, select Specific Heat Ratio (gamma) in the Properties... category. To include PR, select Custom Field Functions... in the first drop-down list under Field Functions, and then select from the second list the function name that you assigned PR. • Suppose you have swirling flow in a pipe, aligned with the z axis, and you want to calculate the flow rate of angular momentum through a cross-sectional plane: Z

~ ρrvθ~v · dA

(29.5-4)

You can create a function for the product rvθ , where r is the Radial Coordinate and vθ is the Tangential Velocity. Then use the Surface Integrals panel to compute the flow rate of this quantity.


29-49


29-50


Chapter 30.

Parallel Processing

The following sections describe the parallel-processing features of FLUENT. • Section 30.1: Introduction to Parallel Processing • Section 30.2: Starting the Parallel Version of the Solver • Section 30.3: Using a Parallel Network of Workstations • Section 30.4: Partitioning the Grid • Section 30.5: Checking and Improving Parallel Performance • Section 30.6: Running Parallel FLUENT under SGE • Section 30.7: Running Parallel FLUENT under LSF

30.1

Introduction to Parallel Processing

The FLUENT serial solver manages file input and output, data storage, and flow field calculations using a single solver process on a single computer. FLUENT’s parallel solver allows you to compute a solution by using multiple processes that may be executing on the same computer, or on different computers in a network. Figures 30.1.1 and 30.1.2 illustrate the serial and parallel FLUENT architectures. Parallel processing in FLUENT involves an interaction between FLUENT, a host process, and a set of compute-node processes. FLUENT interacts with the host process and the collection of compute nodes using a utility called cortex that manages FLUENT’s user interface and basic graphical functions. Parallel FLUENT splits up the grid and data into multiple partitions, then assigns each grid partition to a different compute process (or node). The number of partitions is an integral multiple of the number of compute nodes available to you (e.g., 8 partitions for 1, 2, 4, or 8 compute nodes). The compute-node processes can be executed on a massively-parallel computer, a multiple-CPU workstation, or a network of workstations using the same or different operating systems.

! In general, as the number of compute nodes increases, turnaround time for the solution will decrease. However, parallel efficiency decreases as the ratio of communication to computation increases, so you should be careful to choose a large enough problem for the parallel machine.


30-1

Parallel Processing

CORTEX

Solver File Input/Output

Disk

Data: Cell Face Node

Figure 30.1.1: Serial FLUENT Architecture

FLUENT uses a host process that does not contain any grid data. Instead, the host process only interprets commands from FLUENT’s graphics-related interface, cortex. The host distributes those commands to the other compute nodes via a socket communicator to a single designated compute node called compute-node-0. This specialized compute node distributes the host commands to the other compute nodes. Each compute node simultaneously executes the same program on its own data set. Communication from the compute nodes to the host is possible only through compute-node-0 and only when all compute nodes have synchronized with each other. Each compute node is virtually connected to every other compute node, and relies on its “communicator” to perform such functions as sending and receiving arrays, synchronizing, performing global operations (such as summations over all cells), and establishing machine connectivity. A FLUENT communicator is a message-passing library. For example, the message-passing library could be a vendor implementation of the Message Passing Interface (MPI) standard, as depicted in Figure 30.1.2. All of the parallel FLUENT processes (as well as the serial process) are identified by a unique integer ID. The host collects messages from compute-node-0 and performs operations (such as printing, displaying messages, and writing to a file) on all of the data, in the same way as the serial solver.

Recommended Usage of Parallel FLUENT The recommended procedure for using parallel FLUENT is as follows: 1. Start up the parallel solver and spawn additional compute nodes (if necessary). See Sections 30.2 and 30.3 for details.

30-2


30.1 Introduction to Parallel Processing

CORTEX

HOST

File Input/Output

Disk

FLUENT MPI

COMPUTE NODES Compute Node 0


Compute Node 1

FLUENT MPI

Socket

FLUENT MPI


MP Data: Cell Face Node

FLUENT MPI

Compute Node 2

FLUENT MPI


Compute Node 3

Figure 30.1.2: Parallel FLUENT Architecture


30-3

Parallel Processing

2. Read your case file and have FLUENT partition the grid automatically upon loading it. It is best to partition after the problem is set up, since partitioning has some model dependencies (e.g., adaption on non-conformal interfaces, sliding-mesh and shell-conduction encapsulation). Note that there are other approaches for partitioning, including manual partitioning in either the serial or the parallel solver. See Section 30.4 for details. 3. Review the partitions and perform partitioning again, if necessary. See Section 30.4.5 for details on checking your partitions. 4. Calculate a solution. See Section 30.5 for information on checking and improving the parallel performance.

30.2

Starting the Parallel Version of the Solver

The way you start the parallel version of FLUENT depends on whether you are using a dedicated parallel machine or a workstation cluster.

30.2.1

Starting the Parallel Solver on a UNIX System

You can run FLUENT on a UNIX dedicated parallel machine or a network of UNIX workstations. The procedures for starting these versions are described in this section.

Running on a Multiprocessor UNIX Machine To run FLUENT on a dedicated parallel machine (i.e., a multiprocessor workstation or a massively parallel machine), type the usual startup command without a version (i.e., fluent), and then use the Select Solver panel (Figure 30.2.1) to specify the parallel architecture and version information. File −→Run... 1. Under Versions, specify the 3D or 2D single- or double-precision version by turning the 3D and Double Precision options on or off, and turn on the Parallel option. 2. Under Options, select the message-passing library in the Communicator drop-down list. The Default library is recommended, because it selects the library that should provide the best overall parallel performance for your dedicated parallel machine. If you prefer to select a specific library, you can choose either Vendor MPI or Shared Memory MPI (MPICH). Vendor MPI selects the message-passing library optimized by your hardware vendor. If the parallel toolkit supplied by your hardware vendor is installed on your machine, FLUENT will detect it automatically when the Default option is selected. Shared Memory MPI (MPICH) selects the MPICH messagepassing library, a public-domain version of MPI.

30-4


30.2 Starting the Parallel Version of the Solver

Figure 30.2.1: The Select Solver Panel

3. Set the number of CPUs in the Processes field. 4. Click the Run button to start the parallel version. No additional setup is required once the solver starts. If you prefer to start the parallel version from the command line, you can type fluent version -tn [-pcomm] [-loadhost] [-pathpath] where version is 2d, 3d, 2ddp, or 3ddp, and n is replaced by the number of CPUs to be used. The remaining arguments are optional, as indicated by the square brackets around them. (If you enter one or more of these optional arguments, do not include the square brackets.) comm is replaced by the name of the parallel communication library, host is replaced by the hostname of the machine to launch the compute nodes (by default, it is set to the machine you’re using when entering this command), and path is replaced by the root path to the Fluent.Inc installation directory.

! In general, you will need to specify -pcomm only if you want to override the default communication library (which should provide best overall parallel performance). The available communicators for dedicated parallel UNIX machines are listed below, along with their associated communication libraries, the corresponding syntax, and the supported architectures:


30-5

Parallel Processing

net

socket

smpi shared memory MPI (MPICH)

nmpi network MPI (MPICH)

vmpi vendor MPI

-pnet

aix51, aix51 64, alpha, hpux11, hpux11 64, irix65, irix65 mips4, irix65 mips4 64, power3, power3 64, ultra, ultra 64, hpux11 ia64, and fujitsu pp -psmpi aix51, aix51 64, alpha, hpux11, irix65 mips4, irix65 mips4 64, power3, power3 64, ultra, and ultra 64 -pnmpi aix51, alpha, hpux11, irix65 mips4, irix65 mips4 64, power3, ultra, and ultra 64 -pvmpi aix51, aix51 64, alpha, hpux11, hpux11 64, irix65 mips4, irix65 mips4 64, power3, ultra, ultra 64, hpux11 ia64, and fujitsu pp

See step 2, above, for a description of these libraries.

Running on a UNIX Workstation Cluster To run FLUENT on a network of UNIX workstations, type the usual startup command without a version (i.e., fluent), and then use the Select Solver panel (Figure 30.2.1) to specify the parallel architecture and version information. File −→Run... 1. Under Versions, specify the 3D or 2D single- or double-precision version by turning the 3D and Double Precision options on or off, and turn on the Parallel option. 2. Under Options, select the Socket message-passing library in the Communicator dropdown list.

!

When you start the parallel network version, you must select Socket or Network MPI (MPICH) in the Communicator drop-down list, unless the vendor MPI library (described earlier in this section) supports clustering. If you keep the Default option, one of the MPI parallel versions will start instead, and you will be unable to spawn additional compute nodes. 3. Set the number of initial compute node processes to spawn on the host machine in the Processes field. You can start with 1 or 0 nodes and spawn the rest later on, as described in Section 30.3.1.

30-6



4. (optional) Specify the name of a file containing a list of machines, one per line, in the Hosts File field. If the number of Processes is set to 0, FLUENT will spawn a compute node on each machine listed in the file. 5. Click the Run button to start the parallel network version. If you prefer to start the parallel network version from the command line, you can type fluent version -t1 -pnet (to use the socket communicator) or fluent version -t1 -pnmpi (to use the network MPI communicator) to start the solver with 1 compute node on the host workstation. You can then spawn additional processes on remote workstations using the Network Configuration panel, as described in Section 30.3.1. You can type fluent version -t0 -pnet [-cnf=hostsfile] (to use the socket communicator) or fluent version -t0 -pnmpi [-cnf=hostsfile] (to use the network MPI communicator) to start a host process that controls compute nodes situated on remote machines. If the optional -cnf=hostsfile is specified, a compute node will be spawned on each machine listed in the file hostsfile. (If you enter this optional argument, do not include the square brackets.) Otherwise, you can spawn the processes as described in Section 30.3.1.

30.2.2

Starting the Parallel Solver on a LINUX System

You can run FLUENT on a LINUX dedicated parallel machine or a network of LINUX workstations. The procedures for starting these versions are described in this section.

Running on a Multiprocessor LINUX Machine To run FLUENT on a dedicated parallel machine (i.e., a multiprocessor workstation or a massively parallel machine), type the usual startup command without a version (i.e., fluent), and then use the Select Solver panel (Figure 30.2.1) to specify the parallel architecture and version information. File −→Run... 1. Under Versions, specify the 3D or 2D single- or double-precision version by turning the 3D and Double Precision options on or off, and turn on the Parallel option.


30-7

Parallel Processing

2. Under Options, select the message-passing library in the Communicator drop-down list. The Default library is recommended, because it selects the library that should provide the best overall parallel performance for your dedicated parallel machine. If you prefer to select a specific library, you can choose either Vendor MPI or Shared Memory MPI (MPICH). Vendor MPI selects the message-passing library optimized by your hardware vendor. If the parallel toolkit supplied by your hardware vendor is installed on your machine, FLUENT will detect it automatically when the Default option is selected. Shared Memory MPI (MPICH) selects the MPICH messagepassing library, a public-domain version of MPI. 3. Set the number of CPUs in the Processes field. 4. Click the Run button to start the parallel version. No additional setup is required once the solver starts. If you prefer to start the parallel version from the command line, you can type fluent version -tn [-pcomm] [-loadhost] [-pathpath] where version is 2d, 3d, 2ddp, or 3ddp, and n is replaced by the number of CPUs to be used. The remaining arguments are optional, as indicated by the square brackets around them. (If you enter one or more of these optional arguments, do not include the square brackets.) comm is replaced by the name of the parallel communication library, host is replaced by the hostname of the machine to launch the compute nodes (by default, it is set to the machine you’re using when entering this command), and path is replaced by the root path to the Fluent.Inc installation directory.

! In general, you will need to specify -pcomm only if you want to override the default communication library (which should provide best overall parallel performance). The available communicators for dedicated parallel lnx86 LINUX machines are listed below, along with the associated communication libraries and corresponding syntax: net smpi nmpi ssh myrinet scampi scyld

socket shared memory MPI (MPICH) network MPI (MPICH secure shell MPI (MPICH) vendor MPI vendor MPI vendor MPI

-pnet -psmpi -pnmpi -pnmpissh -pgmpi -pscampi -pbeo

FLUENT supplies the necessary components for the ssh, nmpi, smpi, and net communicators. As for the rest, you need to contact the vendor directly. See step 2, above, for a description of these libraries.

30-8



Running on a LINUX Workstation Cluster To run FLUENT on a network of LINUX workstations, type the usual startup command without a version (i.e., fluent), and then use the Select Solver panel (Figure 30.2.1) to specify the parallel architecture and version information. File −→Run... 1. Under Versions, specify the 3D or 2D single- or double-precision version by turning the 3D and Double Precision options on or off, and turn on the Parallel option. 2. Under Options, select the Socket message-passing library in the Communicator dropdown list.

!

When you start the parallel network version, you must select Socket or Network MPI (MPICH) in the Communicator drop-down list, unless the vendor MPI library (described earlier in this section) supports clustering. If you keep the Default option, one of the MPI parallel versions will start instead, and you will be unable to spawn additional compute nodes. 3. Set the number of initial compute node processes to spawn on the host machine in the Processes field. You can start with 1 or 0 nodes and spawn the rest later on, as described in Section 30.3.1. 4. (optional) Specify the name of a file containing a list of machines, one per line, in the Hosts File field. If the number of Processes is set to 0, FLUENT will spawn a compute node on each machine listed in the file. 5. Click the Run button to start the parallel network version. If you prefer to start the parallel network version from the command line, you can type fluent version -t1 -pnet (to use the socket communicator) or fluent version -t1 -pnmpi (to use the network MPI communicator) to start the solver with 1 compute node on the host workstation. You can then spawn additional processes on remote workstations using the Network Configuration panel, as described in Section 30.3.1. You can type fluent version -t0 -pnet [-cnf=hostsfile] (to use the socket communicator) or fluent version -t0 -pnmpi [-cnf=hostsfile]


30-9

Parallel Processing

(to use the network MPI communicator) to start a host process that controls compute nodes situated on remote machines. If the optional -cnf=hostsfile is specified, a compute node will be spawned on each machine listed in the file hostsfile. (If you enter this optional argument, do not include the square brackets.) Otherwise, you can spawn the processes as described in Section 30.3.1.

30.2.3

Starting the Parallel Solver on a Windows System

You can run FLUENT on a Windows dedicated parallel machine or a network of Windows machines. The procedures for starting these versions are described in this section.

Running on a Multiprocessor Windows Machine On a Windows system, you can start the dedicated parallel version of FLUENT from the MS-DOS Command Prompt window. To start the parallel version on x processors, type fluent version -tx at the prompt, replacing version with the solver version (2d, 3d, 2ddp, or 3ddp) and x with the number of processors (e.g., fluent 3d -t3 to run the 3D version on 3 processors). (See Section 1.5.3 for information about modifying your user environment if the fluent command is not recognized.)

Running on a Windows Cluster There are several ways to run FLUENT in parallel on a network of Windows machines: using one of the communicators that is included with the FLUENT distribution, or using either a vendor-supplied or a public domain message-passing interface. The available communicators for dedicated parallel ntx86 Windows machines, the associated communication libraries for them, and the corresponding syntax are listed below: net smpi nmpi vmpi

RSHD shared memory MPI (MPICH) network MPI (MPICH) vendor MPI

-pnet -psmpi -pnmpi -pvmpi

See the installation instructions for Windows parallel for details about obtaining and installing one of these programs. The startup instructions below assume that you have properly set up the necessary software, based on the appropriate installation instructions.

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Starting the RSHD-Based Parallel Version of FLUENT If you are using the RSHD software for network communication, type the following in an MS-DOS Command Prompt window: fluent version -tnprocs -pnet [-cnf=hostfile] -pathsharename where • version must be replaced by the version of FLUENT you want to run (2d, 3d, 2ddp, or 3ddp). • -pathsharename specifies the shared network name for the Fluent.Inc directory in UNC form. For example, if FLUENT has been installed on computer1, then you should replace sharename by the UNC name for the shared directory, \\computer1\fluent.inc. • -cnf=hostfile (optional) specifies the hostfile, which contains a list of the computers on which you want to run the parallel job. If the hostfile is not located in the directory where you are typing the startup command, you will need to supply the full pathname to the file. (If you include the -cnf option, do not include the square brackets; see the example below.) You can use a plain text editor like Notepad to create the hostfile. The only restriction on the filename is that there should be no spaces in it. For example, hosts.txt is an acceptable hostfile name, but my hosts.txt is not. Your hostfile (e.g., hosts.txt) might contain the following entries: computer1 computer2

!

The first computer in the list must be the name of the local computer you are working on. The last entry must be followed by a blank line. If a computer in the network is a multiprocessor, you can list it more than once. For example, if computer1 has 2 CPUs, then, to take advantage of both CPUs, the hosts.txt file should list computer1 twice: computer1 computer1 computer2 If you do not include the -cnf option, FLUENT will start nprocs (see below) processes on the computer where you type the startup command. You can then use the Network Configuration panel in FLUENT to interactively spawn additional nodes on the cluster. See Section 30.3 for details.


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• -tnprocs specifies the number of processes to use. If the -cnf option is present, the hostfile argument is used to determine which computers to use for the parallel job. For example, if there are 10 computers listed in the hostfile and you want to run a job with 5 processes, set nprocs to 5 (i.e., -t5) and FLUENT will use the first 5 machines listed in the hostfile. You can use the Network Configuration panel to kill processes or spawn additional processes after startup. See Section 30.3 for details. As an example, the full command line to start a 3D RSHD-based parallel job on the first 3 computers listed in a hostfile called hosts.txt is as follows: fluent 3d -t3 -pnet -cnf=hosts.txt -path\\computer1\fluent.inc

Starting the MPI-Based Parallel Version of FLUENT If you are using either vendor-supplied or public domain MPI software for network communication, type the following in an MS-DOS Command Prompt window: fluent version -tnprocs -pcomm -cnf=hostfile -pathsharename where comm can be either nmpi or vmpi and the remaining options have the same meanings as for the RSHD-based startup described above, with the following differences: • The hostfile specification is required. You can neither spawn nor kill nodes on the cluster using the Network Configuration panel when MPI software is used. • The first computer listed in the hostfile must be the name of the local computer you are working on. As an example, the full command line to start a 3D vendor-MPI-based parallel job on the first 3 computers listed in a hostfile called hosts.txt is as follows: fluent 3d -t3 -pvmpi -cnf=hosts.txt -path\\computer1\fluent.inc

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30.3 Using a Parallel Network of Workstations

30.3

Using a Parallel Network of Workstations

You can create a virtual parallel machine by spawning (and killing) compute node processes on workstations connected by a network. Multiple compute node processes are allowed to exist on the same workstation, even if the workstation contains only a single CPU.

30.3.1

Configuring the Network

If you want to spawn compute nodes on several different machines, or if you want to make any changes to the current network configuration (e.g., if you accidentally spawned too many compute nodes on the host machine when you started the solver), you can use the Network Configuration panel (Figure 30.3.1). Parallel −→ Network −→Configure...

Figure 30.3.1: The Network Configuration Panel

Structure of the Network Compute nodes are labeled sequentially starting at 0. In addition to the compute node processes, there is one host process. The host process is automatically started when FLUENT starts, and it is killed when FLUENT exits. It cannot be killed while running. Compute nodes, however, can be killed at any time, with the exception that compute node 0 can only be killed if it is the last remaining compute node process. The host


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process always spawns compute node 0. Compute node 0 spawns all other compute nodes.

Steps for Spawning Compute Nodes The basic steps for spawning compute nodes are as follows: 1. Choose the host machine(s) on which to spawn compute nodes in the Available Hosts list. If the desired machine is not listed, you can use the Host Entry fields to manually add a host (as described below), or you can copy the desired host from the host database (as described in Section 30.3.2). 2. Set the number of compute node processes to spawn on each selected host machine in the Spawn Count field. 3. Click the Spawn button and the new node(s) will be spawned and added to the Spawned Compute Nodes list. Additional functions related to network configuration are described below. Adding Hosts Manually To add a host to the Available Hosts list in the Network Configuration panel manually, you can enter the internet name of the remote machine in the Hostname field under Host Entry, enter your login name on that machine in the Username field (unless your accounts all have the same login name, in which case you need not specify a username), and then click the Add button. The specified host will be added to the Available Hosts list. Deleting Hosts To delete a host from the Available Hosts list in the Network Configuration panel, select the host and click the Delete button. The host name will be removed from the Available Hosts list (but the hosts database (see Section 30.3.2) will not be affected). Killing Compute Nodes If you spawn an undesired compute node, you can easily remove it by selecting it in the Spawned Compute Nodes list and clicking on the Kill button.

! Remember that compute node 0 can only be killed if it is the last remaining compute node process.

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Saving a Hosts File If you have compiled a group of Available Hosts that you may want to use again in another session, you can save a hosts file containing all entries in the Available Hosts list. Click the Save... button and, in the resulting Select File dialog box, enter the name of the file and save it. In a future session, you can load the contents of this file into the hosts database (see Section 30.3.2) and then copy the hosts over to the Network Configuration panel in order to reproduce the current Available Hosts list.

Common Problems Encountered During Node Spawning The spawning process will try to establish a connection with a new compute node, but if after 50 seconds it receives no response from the new compute node, it will assume the spawn was unsuccessful. The spawn will be unsuccessful, for example, if the remote machine is unable to find the FLUENT executable. To manually test if the spawning machine can start a new compute node, you can type rsh [-l username] hostname fluent -t0 -v from a shell prompt on the spawning machine. hostname should be replaced with the internet name of the machine on which you want to spawn a compute node, and username should be replaced with your login name on the remote machine specified by hostname.

! If all your accounts have the same login name, you do not need to specify a username. (The square brackets around -l username indicate that it is not always required; if you do enter a login name, do not include the square brackets.) Note that on some systems, the remote shell command is remsh instead of rsh. The spawn test could fail for several reasons: Login incorrect. The machine spawning a new compute node must be able to rsh to the machine where the new process will reside, or the spawn will fail. There are several ways to enable this capability. Consult your systems administrator for assistance. fluent: Command not found. The rsh to the remote machine succeeded, but the path to the FLUENT shell script could not be found on that machine. If you are using csh, then the path to the FLUENT shell script should be added to the path variable in your .cshrc file. If that also fails, you can use the parallel/network/ path text command to set the path to the Fluent.Inc installation directory directly before spawning the compute node. parallel −→ network −→path


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30.3.2

The Hosts Database

When you are creating a parallel network of workstations, it is convenient to start with a list of machines that are part of your local network (a “hosts file”). You can load a file containing these names into the hosts database and then select the hosts that are available for creating a parallel configuration (or network) on a cluster of workstations using the Hosts Database panel (Figure 30.3.2). Parallel −→ Network −→Database...

Figure 30.3.2: The Hosts Database Panel (You can also open this panel by clicking on the Database... button in the Network Configuration panel.) If the hosts file fluent.hosts or .fluent.hosts exists in your home directory, its contents are automatically added to the hosts database at startup. Otherwise, the hosts database will be empty until you read in a host file.

Reading Hosts Files If you have a hosts file containing a list of machines on your local network, you can load this file into the Hosts Database panel by clicking on the Load... button and specifying the file name in the resulting Select File dialog box. Once the contents of the file have been read, the host names will appear in the Hosts list. (FLUENT will automatically

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add the IP (Internet Protocol) address for each recognized machine. If a machine is not currently on the local network, it will be labeled unknown.)

Copying Hosts to the Network Configuration Panel If you want to copy one or more of the Hosts in the Hosts Database panel to the Available Hosts list in the Network Configuration panel, select the desired name(s) in the Hosts list and click the Copy button. The selected hosts will be added to the list of Available Hosts on which you can spawn nodes.

30.3.3

Checking Network Connectivity

For any compute node, you can print network connectivity information that includes the hostname, architecture, process ID, and ID of the selected compute node and all machines connected to it. The ID of the selected compute node is marked with an asterisk. The ID for the FLUENT host process is always host. The compute nodes are numbered sequentially starting from node-0. All compute nodes are completely connected. In addition, compute node 0 is connected to the host process. To obtain connectivity information for a compute node, you can use the Parallel Connectivity panel (Figure 30.3.3). Parallel −→Show Connectivity...

Figure 30.3.3: The Parallel Connectivity Panel Indicate the compute node ID for which connectivity information is desired in the Compute Node field, and then click the Print button. Sample output for compute node 0 is shown below:


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-----------------------------------------------------------------------------ID Comm. Hostname O.S. PID Mach ID HW ID Name -----------------------------------------------------------------------------host net balin Linux-32 17272 0 7 Fluent Host n3 smpi balin Linux-32 17307 1 10 Fluent Node n2 smpi filio Linux-32 17306 0 -1 Fluent Node n1 smpi bofur Linux-32 17305 0 1 Fluent Node n0* smpi balin Linux-32 17273 2 11 Fluent Node

O.S is the architecture, Comm. is the communicator, PID is the process ID number, Mach ID is the compute node ID, and HW ID is an identifier specific to the communicator used. You can also check connectivity of a compute node in the Network Configuration panel by selecting it in the Spawned Compute Nodes list and clicking on the Connectivity button. If you click the Connectivity button without selecting any of the Spawned Compute Nodes, the Parallel Connectivity panel will open, and you can specify the node there, as described above. If you select more than one of the Spawned Compute Nodes, clicking on the Connectivity button will print connectivity information for each selected node.

30.4

Partitioning the Grid

Information about grid partitioning is provided in the following sections: • Section 30.4.1: Overview of Grid Partitioning • Section 30.4.2: Partitioning the Grid Automatically • Section 30.4.3: Partitioning the Grid Manually • Section 30.4.4: Grid Partitioning Methods • Section 30.4.5: Checking the Partitions • Section 30.4.6: Load Distribution

30.4.1

Overview of Grid Partitioning

When you use the parallel solver in FLUENT, you need to partition or subdivide the grid into groups of cells that can be solved on separate processors (see Figure 30.4.1). You can either use the automatic partitioning algorithms when reading an unpartitioned grid into the parallel solver (recommended approach, described in Section 30.4.2), or perform the partitioning yourself in the serial solver or after reading a mesh into the parallel solver (as described in Section 30.4.3). In either case, the available partitioning methods are those described in Section 30.4.4. You can partition the grid before or after you set up the problem (by defining models, boundary conditions, etc.), although it is

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30.4 Partitioning the Grid

better to partition after the setup, due to some model dependencies (e.g., adaption on non-conformal interfaces, sliding-mesh and shell-conduction encapsulation).

! If your case file contains sliding meshes, or non-conformal interfaces on which you plan to perform adaption during the calculation, you will have to partition it in the serial solver. See Sections 30.4.2 and 30.4.3 for more information. Note that the relative distribution of cells among compute nodes will be maintained during grid adaption, except if non-conformal interfaces are present, so repartitioning after adaption is not required. See Section 30.4.6 for more information. If you use the serial solver to set up the problem before partitioning, the machine on which you perform this task must have enough memory to read in the grid. If your grid is too large to be read into the serial solver, you can read the unpartitioned grid directly into the parallel solver (using the memory available in all the defined hosts) and have it automatically partitioned. In this case you will set up the problem after an initial partition has been made. You will then be able to manually repartition the case if necessary. See Sections 30.4.2 and 30.4.3 for additional details and limitations, and Section 30.4.5 for details about checking the partitions.

Domain

Before Partitioning

Interface Boundary

After Partitioning

Partition 0

Partition 1

Figure 30.4.1: Partitioning the Grid

30.4.2

Partitioning the Grid Automatically

For automatic grid partitioning, you can select the bisection method and other options for creating the grid partitions before reading a case file into the parallel version of the


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solver. For some of the methods, you can perform pretesting to ensure that the best possible partition is performed. See Section 30.4.4 for information about the partitioning methods available in FLUENT. Note that if your case file contains sliding meshes, or non-conformal interfaces on which you plan to perform adaption during the calculation, you will need to partition it in the serial solver, and then read it into the parallel solver, with the Case File option turned on in the Auto Partition Grid panel (the default setting). The procedure for partitioning automatically in the parallel solver is as follows: 1. (optional) Set the partitioning parameters in the Auto Partition Grid panel (Figure 30.4.2). Parallel −→Auto Partition...

Figure 30.4.2: The Auto Partition Grid Panel If you are reading in a mesh file or a case file for which no partition information is available, and you keep the Case File option turned on, FLUENT will partition the grid using the method displayed in the Method drop-down list. If you want to specify the partitioning method and associated options yourself, the procedure is as follows: (a) Turn off the Case File option. The other options in the panel will become available. (b) Select the bisection method in the Method drop-down list. The choices are the techniques described in Section 30.4.4. (c) You can choose to independently apply partitioning to each cell zone, or you can allow partitions to cross zone boundaries using the Across Zones check button. It is recommended that you not partition cells zones independently (by turning off the Across Zones check button) unless cells in different zones will require significantly different amounts of computation during the solution phase (e.g., if the domain contains both solid and fluid zones).

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(d) If you have chosen the Principal Axes or Cartesian Axes method, you can improve the partitioning by enabling the automatic testing of the different bisection directions before the actual partitioning occurs. To use pretesting, turn on the Pre-Test option. Pretesting is described in Section 30.4.4. (e) Click OK. If you have a case file where you have already partitioned the grid, and the number of partitions divides evenly into the number of compute nodes, you can keep the default selection of Case File in the Auto Partition Grid panel. This instructs FLUENT to use the partitions in the case file. 2. Read the case file. File −→ Read −→Case...

Reporting During Auto Partitioning As the grid is automatically partitioned, some information about the partitioning process will be printed in the text (console) window. If you want additional information, you can print a report from the Partition Grid panel after the partitioning is completed. Parallel −→Partition... When you click the Print Active Partitions or Print Stored Partitions button in the Partition Grid panel, FLUENT will print the partition ID, number of cells, faces, and interfaces, and the ratio of interfaces to faces for each active or stored partition in the console window. In addition, it will print the minimum and maximum cell, face, interface, and face-ratio variations. See Section 30.4.5 for details. You can examine the partitions graphically by following the directions in Section 30.4.5.

30.4.3

Partitioning the Grid Manually

Automatic partitioning in the parallel solver (described in Section 30.4.2) is the recommended approach to grid partitioning, but it is also possible to partition the grid manually in either the serial solver or the parallel solver. After automatic or manual partitioning, you will be able to inspect the partitions created (see Section 30.4.5) and optionally repartition the grid, if necessary. Again, you can do so within the serial or the parallel solver, using the Partition Grid panel. A partitioned grid may also be used in the serial solver without any loss in performance.

Guidelines for Partitioning the Grid The following steps are recommended for partitioning a grid manually: 1. Partition the grid using the default bisection method (Principal Axes) and optimization (Smooth).


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2. Examine the partition statistics, which are described in Section 30.4.5. Your aim is to achieve small values of Interface ratio variation and Global interface ratio while maintaining a balanced load (Cell variation). If the statistics are not acceptable, try one of the other bisection methods. 3. Once you determine the best bisection method for your problem, you can turn on Pre-Test (see Section 30.4.4) to improve it further, if desired. 4. You can also improve the partitioning using the Merge optimization, if desired. Instructions for manual partitioning are provided below.

Using the Partition Grid Panel For grid partitioning, you need to select the bisection method for creating the grid partitions, set the number of partitions, select the zones and/or registers, and choose the optimizations to be used. For some methods, you can also perform pretesting to ensure that the best possible bisection is performed. Once you have set all the parameters in the Partition Grid panel to your satisfaction, click the Partition button to subdivide the grid into the selected number of partitions using the prescribed method and optimization(s). See above for recommended partitioning strategies. You can set the relevant inputs in the Partition Grid panel (Figure 30.4.3 in the parallel solver, or Figure 30.4.4 in the serial solver) in the following manner: Parallel −→Partition...

Figure 30.4.3: The Partition Grid Panel in the Parallel Solver

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Figure 30.4.4: The Partition Grid Panel in the Serial Solver

1. Select the bisection method in the Method drop-down list. The choices are the techniques described in Section 30.4.4. 2. Set the desired number of grid partitions in the Number integer number field. You can use the counter arrows to increase or decrease the value, instead of typing in the box. The number of grid partitions must be an integral multiple of the number of processors available for parallel computing. 3. You can choose to independently apply partitioning to each cell zone, or you can allow partitions to cross zone boundaries using the Across Zones check button. It is recommended that you not partition cells zones independently (by turning off the Across Zones check button) unless cells in different zones will require significantly different amounts of computation during the solution phase (e.g., if the domain contains both solid and fluid zones). 4. You can select Encapsulate Grid Interfaces if you would like the cells surrounding all non-conformal grid interfaces in your mesh to reside in a single partition at all times during the calculation. If your case file contains non-conformal interfaces on which you plan to perform adaption during the calculation, you will have to partition it in the serial solver, with the Encapsulate Grid Interfaces and Encapsulate for Adaption options turned on. 5. If you have enabled the Encapsulate Grid Interfaces option in the serial solver, the Encapsulate for Adaption option will also be available. When you select this option, additional layers of cells are encapsulated such that transfer of cells will be unnecessary during parallel adaption.


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6. You can activate and control the desired optimization methods (described in Section 30.4.4) using the items under Optimizations. You can activate the Merge and Smooth schemes by turning on the Do check button next to each one. For each scheme, you can also set the number of Iterations. Each optimization scheme will be applied until appropriate criteria are met, or the maximum number of iterations has been executed. If the Iterations counter is set to 0, the optimization scheme will be applied until completion, without limit on the maximum number of iterations. 7. If you have chosen the Principal Axes or Cartesian Axes method, you can improve the partitioning by enabling the automatic testing of the different bisection directions before the actual partitioning occurs. To use pretesting, turn on the Pre-Test option. Pretesting is described in Section 30.4.4. 8. In the Zones and/or Registers lists, select the zone(s) and/or register(s) for which you want to partition. For most cases, you will select all Zones (the default) to partition the entire domain. See below for details. 9. Click the Partition button to partition the grid. 10. If you decide that the new partitions are better than the previous ones (if the grid was already partitioned), click the Use Stored Partitions button to make the newly stored cell partitions the active cell partitions. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file. 11. When using the dynamic mesh model in your parallel simulations, the Partition panel includes an Auto Repartition option and a Repartition Interval setting. These parallel partitioning options are provided because FLUENT migrates cells when local remeshing and smoothing is performed. Therefore, the partition interface becomes very wrinkled and the load balance may deteriorate. By default, the Auto Repartition option is selected, where a percentage of interface faces and loads are automatically traced. When this option is selected, FLUENT automatically determines the most appropriate repartition interval based on various simulation parameters. Sometimes, using the Auto Repartition option provides insufficient results, therefore, the Repartition Interval setting can be used. The Repartition Interval setting lets you to specify the interval (in time steps or iterations respectively) when a repartition is enforced. When repartitioning is not desired, then you can set the Repartition Interval to zero.

!

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Note that when dynamic meshes and local remeshing is utilized, updated meshes may be slightly different in parallel FLUENT (when compared to serial FLUENTor when compared to a parallel solution created with a different number of compute nodes), resulting in very small differences in the solutions.



Partitioning Within Zones or Registers The ability to restrict partitioning to cell zones or registers gives you the flexibility to apply different partitioning strategies to subregions of a domain. For example, if your geometry consists of a cylindrical plenum connected to a rectangular duct, you may want to partition the plenum using the Cylindrical Axes method, and the duct using the Cartesian Axes method. If the plenum and the duct are contained in two different cell zones, you can select one at a time and perform the desired partitioning, as described in Section 30.4.3. If they are not in two different cell zones, you can create a cell register (basically a list of cells) for each region using the functions that are used to mark cells for adaption. These functions allow you to mark cells based on physical location, cell volume, gradient or isovalue of a particular variable, and other parameters. See Chapter 25 for information about marking cells for adaption. Section 25.10 provides information about manipulating different registers to create new ones. Once you have created a register, you can partition within it as described above.

! Note that partitioning within zones or registers is not available when the parallel version of FLUENT is used, or when Metis is selected as the partition Method. Reporting During Partitioning As the grid is partitioned, information about the partitioning process will be printed in the text (console) window. By default, the solver will print the number of partitions created, the number of bisections performed, the time required for the partitioning, and the minimum and maximum cell, face, interface, and face-ratio variations. (See Section 30.4.5 for details.) If you increase the Verbosity to 2 from the default value of 1, the partition method used, the partition ID, number of cells, faces, and interfaces, and the ratio of interfaces to faces for each partition will also be printed in the console window. If you decrease the Verbosity to 0, only the number of partitions created and the time required for the partitioning will be reported. You can request a portion of this report to be printed again after the partitioning is completed. When you click the Print Active Partitions or Print Stored Partitions button in the parallel solver, FLUENT will print the partition ID, number of cells, faces, and interfaces, and the ratio of interfaces to faces for each active or stored partition in the console window. In addition, it will print the minimum and maximum cell, face, interface, and face-ratio variations. In the serial solver, you will obtain the same information about the stored partition when you click Print Partitions. See Section 30.4.5 for details.

! Recall that to make the stored cell partitions the active cell partitions you must click the Use Stored Partitions button. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file.


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Resetting the Partition Parameters If you change your mind about your partition parameter settings, you can easily return to the default settings assigned by FLUENT by clicking on the Default button. When you click the Default button, it will become the Reset button. The Reset button allows you to return to the most recently saved settings (i.e., the values that were set before you clicked on Default). After execution, the Reset button will become the Default button again.

30.4.4

Grid Partitioning Methods

Partitioning the grid for parallel processing has three major goals: • Create partitions with equal numbers of cells. • Minimize the number of partition interfaces—i.e., decrease partition boundary surface area. • Minimize the number of partition neighbors. Balancing the partitions (equalizing the number of cells) ensures that each processor has an equal load and that the partitions will be ready to communicate at about the same time. Since communication between partitions can be a relatively time-consuming process, minimizing the number of interfaces can reduce the time associated with this data interchange. Minimizing the number of partition neighbors reduces the chances for network and routing contentions. In addition, minimizing partition neighbors is important on machines where the cost of initiating message passing is expensive compared to the cost of sending longer messages. This is especially true for workstations connected in a network. The partitioning schemes in FLUENT use bisection algorithms to create the partitions, but unlike other schemes which require the number of partitions to be a factor of two, these schemes have no limitations on the number of partitions. For each available processor, you will create the same number of partitions (i.e., the total number of partitions will be an integral multiple of the number of processors).

Bisection Methods The grid is partitioned using a bisection algorithm. The selected algorithm is applied to the parent domain, and then recursively applied to the child subdomains. For example, to divide the grid into four partitions, the solver will bisect the entire (parent) domain into two child domains, and then repeat the bisection for each of the child domains, yielding four partitions in total. To divide the grid into three partitions, the solver will “bisect” the parent domain to create two partitions—one approximately twice as large

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as the other—and then bisect the larger child domain again to create three partitions in total. The grid can be partitioned using one of the algorithms listed below. The most efficient choice is problem-dependent, so you can try different methods until you find the one that is best for your problem. See Section 30.4.3 for recommended partitioning strategies. Cartesian Axes bisects the domain based on the Cartesian coordinates of the cells (see Figure 30.4.5). It bisects the parent domain and all subsequent child subdomains perpendicular to the coordinate direction with the longest extent of the active domain. It is often referred to as coordinate bisection. Cartesian Strip uses coordinate bisection but restricts all bisections to the Cartesian direction of longest extent of the parent domain (see Figure 30.4.6). You can often minimize the number of partition neighbors using this approach. Cartesian X-, Y-, Z-Coordinate bisects the domain based on the selected Cartesian coordinate. It bisects the parent domain and all subsequent child subdomains perpendicular to the specified coordinate direction. (See Figure 30.4.6.) Cartesian R Axes bisects the domain based on the shortest radial distance from the cell centers to that Cartesian axis (x, y, or z) which produces the smallest interface size. This method is available only in 3D. Cartesian RX-, RY-, RZ-Coordinate bisects the domain based on the shortest radial distance from the cell centers to the selected Cartesian axis (x, y, or z). These methods are available only in 3D. Cylindrical Axes bisects the domain based on the cylindrical coordinates of the cells. This method is available only in 3D. Cylindrical R-, Theta-, Z-Coordinate bisects the domain based on the selected cylindrical coordinate. These methods are available only in 3D. Metis uses the METIS software package for partitioning irregular graphs, developed by Karypis and Kumar at the University of Minnesota and the Army HPC Research Center. It uses a multilevel approach in which the vertices and edges on the fine graph are coalesced to form a coarse graph. The coarse graph is partitioned, and then uncoarsened back to the original graph. During coarsening and uncoarsening, algorithms are applied to permit high-quality partitions. Detailed information about METIS can be found in its manual [123].

!

Note that when using the socket version (-pnet), the METIS partitioner is not available. In this case, METIS partitioning can be obtained using the partition filter, as described below.


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Polar Axes bisects the domain based on the polar coordinates of the cells (see Figure 30.4.9). This method is available only in 2D. Polar R-Coordinate, Polar Theta-Coordinate bisects the domain based on the selected polar coordinate (see Figure 30.4.9). These methods are available only in 2D. Principal Axes bisects the domain based on a coordinate frame aligned with the principal axes of the domain (see Figure 30.4.7). This reduces to Cartesian bisection when the principal axes are aligned with the Cartesian axes. The algorithm is also referred to as moment, inertial, or moment-of-inertia partitioning. This is the default bisection method in FLUENT. Principal Strip uses moment bisection but restricts all bisections to the principal axis of longest extent of the parent domain (see Figure 30.4.8). You can often minimize the number of partition neighbors using this approach. Principal X-, Y-, Z-Coordinate bisects the domain based on the selected principal coordinate (see Figure 30.4.8). Spherical Axes bisects the domain based on the spherical coordinates of the cells. This method is available only in 3D. Spherical Rho-, Theta-, Phi-Coordinate bisects the domain based on the selected spherical coordinate. These methods are available only in 3D.

Optimizations Additional optimizations can be applied to improve the quality of the grid partitions. The heuristic of bisecting perpendicular to the direction of longest domain extent is not always the best choice for creating the smallest interface boundary. A “pre-testing” operation (see Section 30.4.4) can be applied to automatically choose the best direction before partitioning. In addition, the following iterative optimization schemes exist: Smooth attempts to minimize the number of partition interfaces by swapping cells between partitions. The scheme traverses the partition boundary and gives cells to the neighboring partition if the interface boundary surface area is decreased. (See Figure 30.4.10.) Merge attempts to eliminate orphan clusters from each partition. An orphan cluster is a group of cells with the common feature that each cell within the group has at least one face which coincides with an interface boundary. (See Figure 30.4.11.) Orphan clusters can degrade multigrid performance and lead to large communication costs. In general, the Smooth and Merge schemes are relatively inexpensive optimization tools.

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3.00e+00

2.25e+00

1.50e+00

7.50e-01

0.00e+00 Contours of Cell Partition

Figure 30.4.5: Partitions Created with the Cartesian Axes Method

3.00e+00

2.25e+00

1.50e+00

7.50e-01


Figure 30.4.6: Partitions Created with the Cartesian Strip or Cartesian X-Coordinate Method


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3.00e+00

2.25e+00

1.50e+00

7.50e-01


Figure 30.4.7: Partitions Created with the Principal Axes Method

3.00e+00

2.25e+00

1.50e+00

7.50e-01


Figure 30.4.8: Partitions Created with the Principal Strip or Principal X-Coordinate Method

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3.00e+00

2.25e+00

1.50e+00

7.50e-01


Figure 30.4.9: Partitions Created with the Polar Axes or Polar Theta-Coordinate Method

Figure 30.4.10: The Smooth Optimization Scheme


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Figure 30.4.11: The Merge Optimization Scheme

Pretesting If you choose the Principal Axes or Cartesian Axes method, you can improve the bisection by testing different directions before performing the actual bisection. If you choose not to use pretesting (the default), FLUENT will perform the bisection perpendicular to the direction of longest domain extent. If pretesting is enabled, it will occur automatically when you click the Partition button in the Partition Grid panel, or when you read in the grid if you are using automatic partitioning. The bisection algorithm will test all coordinate directions and choose the one which yields the fewest partition interfaces for the final bisection. Note that using pretesting will increase the time required for partitioning. For 2D problems partitioning will take 3 times as long as without pretesting, and for 3D problems it will take 4 times as long.

Using the Partition Filter As noted above, you can use the METIS partitioning method through a filter in addition to within the Auto Partition Grid and Partition Grid panels. To perform METIS partitioning on an unpartitioned grid, use the File/Import/Partition/Metis... menu item. File −→ Import −→ Partition −→Metis... FLUENT will use the METIS partitioner to partition the grid, and then read the partitioned grid into the solver. The number of partitions will be equal to the number of processes. You can then proceed with the model definition and solution.

! Direct import to the parallel solver through the partition filter requires that the host machine has enough memory to run the filter for the specified grid. If not, you will need

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to run the filter on a machine that does have enough memory. You can either start the parallel solver on the machine with enough memory and repeat the process described above, or run the filter manually on the new machine and then read the partitioned grid into the parallel solver on the host machine. To manually partition a grid using the partition filter, enter the following command: utility partition input-filename partition-count output-filename where input-filename is the filename for the grid to be partitioned, partition-count is the number of partitions desired, and output-filename is the filename for the partitioned grid. You can then read the partitioned grid into the solver (using the standard File/Read/Case... menu item) and proceed with the model definition and solution. When the File/Import/Partition/Metis... menu item is used to import an unpartitioned grid into the parallel solver, the METIS partitioner partitions the entire grid. You may also partition each cell zone individually, using the File/Import/Partition/Metis Zone... menu item. File −→ Import −→ Partition −→Metis Zone... This method can be useful for balancing the work load. For example, if a case has a fluid zone and a solid zone, the computation in the fluid zone is more expensive than in the solid zone, so partitioning each zone individually will result in a more balanced work load.

30.4.5

Checking the Partitions

After partitioning a grid, you should check the partition information and examine the partitions graphically.

Interpreting Partition Statistics You can request a report to be printed after partitioning (either automatic or manual) is completed. In the parallel solver, click the Print Active Partitions or Print Stored Partitions button in the Partition Grid panel. In the serial solver, click the Print Partitions button. FLUENT distinguishes between two cell partition schemes within a parallel problem: the active cell partition and the stored cell partition. Initially, both are set to the cell partition that was established upon reading the case file. If you re-partition the grid using the Partition Grid panel, the new partition will be referred to as the stored cell partition. To make it the active cell partition, you need to click the Use Stored Partitions button in the Partition Grid panel. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file. This distinction is made mainly to allow you to partition a case on one machine or network


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of machines and solve it on a different one. Thanks to the two separate partitioning schemes, you could use the parallel solver with a certain number of compute nodes to subdivide a grid into an arbitrary different number of partitions, suitable for a different parallel machine, save the case file, and then load it into the designated machine. When you click Print Partitions in the serial solver, you will obtain information about the stored partition. The output generated by the partitioning process includes information about the recursive subdivision and iterative optimization processes. This is followed by information about the final partitioned grid, including the partition ID, number of cells, number of faces, number of interface faces, ratio of interface faces to faces for each partition, number of neighboring partitions, and cell, face, interface, neighbor, mean cell, face ratio, and global face ratio variations. Global face ratio variations are the minimum and maximum values of the respective quantities in the present partitions. For example, in the sample output below, partitions 0 and 3 have the minimum number of interface faces (10), and partitions 1 and 2 have the maximum number of interface faces (19); hence the variation is 10–19. Your aim is to achieve small values of Interface ratio variation and Global interface ratio while maintaining a balanced load (Cell variation). >> Partitions: P Cells I-Cells Cell Ratio 0 134 10 0.075 1 137 19 0.139 2 134 19 0.142 3 137 10 0.073 -----Partition count Cell variation Mean cell variation Intercell variation Intercell ratio variation Global intercell ratio Face variation Interface variation Interface ratio variation Global interface ratio Neighbor variation

Faces I-Faces Face Ratio Neighbors 217 10 0.046 1 222 19 0.086 2 218 19 0.087 2 223 10 0.045 1 = = = = = = = = = = =

4 (134 - 137) ( -1.1% (10 - 19) ( 7.3% 10.7% (217 - 223) (10 - 19) ( 4.5% 3.4% (1 - 2)

1.1%) 14.2%)

8.7%)

Computing connected regions; type ^C to interrupt. Connected region count = 4

Note that partition IDs correspond directly to compute node IDs when a case file is read into the parallel solver. When the number of partitions in a case file is larger than the

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number of compute nodes, but is evenly divisible by the number of compute nodes, then the distribution is such that partitions with IDs 0 to (M − 1) are mapped onto compute node 0, partitions with IDs M to (2M − 1) onto compute node 1, etc., where M is equal to the ratio of the number of partitions to the number of compute nodes.

Examining Partitions Graphically To further aid interpretation of the partition information, you can draw contours of the grid partitions, as illustrated in Figures 30.4.5–30.4.9. Display −→Contours... To display the active cell partition or the stored cell partition (which are described above), select Active Cell Partition or Stored Cell Partition in the Cell Info... category of the Contours Of drop-down list, and turn off the display of Node Values. (See Section 27.1.2 for information about displaying contours.)

! If you have not already done so in the setup of your problem, you will need to perform a solution initialization in order to use the Contours panel.

30.4.6

Load Distribution

If the speeds of the processors that will be used for a parallel calculation differ significantly, you can specify a load distribution for partitioning, using the load-distribution text command. parallel −→ partition −→ set −→load-distribution For example, if you will be solving on three compute nodes, and one machine is twice as fast as the other two, then you may want to assign twice as many cells to the first machine as to the others (i.e., a load vector of (2 1 1)). During subsequent grid partitioning, partition 0 will end up with twice as many cells as partitions 1 and 2. Note that for this example, you would then need to start up FLUENT such that compute node 0 is the fast machine, since partition 0, with twice as many cells as the others, will be mapped onto compute node 0. Alternatively, in this situation, you could enable the load balancing feature (described in Section 30.5.2) to have FLUENT automatically attempt to discern any difference in load among the compute nodes.

! If you adapt a grid that contains non-conformal interfaces, and you want to rebalance the load on the compute nodes, you will have to save your case and data files after adaption, read the case and data files into the serial solver, repartition using the Encapsulate Grid Interfaces and Encapsulate for Adaption options in the Partition Grid panel, and save case and data files again. You will then be able to read the manually repartitioned case and data files into the parallel solver, and continue the solution from where you left it.


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30.5

Checking and Improving Parallel Performance

To determine how well the parallel solver is working, you can measure computation and communication times, and the overall parallel efficiency, using the performance meter. You can also control the amount of communication between compute nodes in order to optimize the parallel solver, and take advantage of the automatic load balancing feature of FLUENT.

30.5.1

Checking Parallel Performance

The performance meter allows you to report the wall clock time elapsed during a computation, as well as message-passing statistics. Since the performance meter is always activated, you can access the statistics by printing them after the computation is completed. To view the current statistics, use the Parallel/Timer/Usage menu item. Parallel −→ Timer −→Usage Performance statistics will be printed in the text window (console). To clear the performance meter so that you can eliminate past statistics from the future report, use the Parallel/Timer/Reset menu item. Parallel −→ Timer −→Reset

30.5.2

Optimizing the Parallel Solver

Increasing the Report Interval In FLUENT, you can reduce communication and improve parallel performance by increasing the report interval for residual printing/plotting or other solution monitoring reports. You can modify the value for Reporting Interval in the Iterate panel. Solve −→Iterate...

! Note that you will be unable to interrupt iterations until the end of each report interval. Load Balancing A dynamic load balancing capability is available in FLUENT. The principal reason for using parallel processing is to reduce the turnaround time of your simulation, ideally by a factor proportional to the collective speed of the computing resources used. If, for example, you were using four CPUs to solve your problem, then you would expect to reduce the turnaround time by a factor of four. This is of course the ideal situation, and assumes that there is very little communication needed among the CPUs, that the CPUs are all of equal speed, and that the CPUs are dedicated to your job. In practice, this is often not the case. For example, CPU speeds can vary if you are solving in parallel on a heterogeneous collection of workstations, other jobs may be competing for use of one or

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30.5 Checking and Improving Parallel Performance

more of the CPUs, and network traffic either from within the parallel solver or generated from external sources may delay some of the necessary communication among the CPUs. If you enable dynamic load balancing in FLUENT, the load across the computational and networking resources will be monitored periodically. If the load balancer determines that performance can be improved by redistributing the cells among the compute nodes, it will automatically do so. There is a time penalty associated with load balancing itself, and so it is disabled by default. If you will be using a dedicated homogeneous resource, or if you are using a heterogeneous resource but have accounted for differences in CPU speeds during partitioning by specifying a load distribution (see Section 30.4.6), then you may not need to use load balancing.

! Note that when the shell conduction model is used, you will not be able to turn on load balancing. To enable and control FLUENT’s automatic load balancing feature, use the Load Balance panel (Figure 30.5.1). Load balancing will automatically detect and analyze parallel performance, and redistribute cells between the existing compute nodes to optimize it. Parallel −→Load Balance...

Figure 30.5.1: The Load Balance Panel The procedure for using load balancing is as follows: 1. Turn on the Load Balancing option. 2. Select the bisection method to create new grid partitions in the Partition Method drop-down list. The choices are the techniques described in Section 30.4.4. As part of the automatic load balancing procedure, the grid will be repartitioned into several small partitions using the specified method. The resulting partitions will then be distributed among the compute nodes to achieve a more balanced load.


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3. Specify the desired Balance Interval. When a value of 0 is specified, FLUENT will internally determine the best value to use, initially using an interval of 25 iterations. You can override this behavior by specifying a non-zero value. FLUENT will then attempt to perform load balancing after every N iterations, where N is the specified Balance Interval. You should be careful to select an interval that is large enough to outweigh the cost of performing the load balancing operations. Note that you can interrupt the calculation at any time, turn the load balancing feature off (or on), and then continue the calculation.

! If problems arise in your computations due to adaption, you can turn off the automatic load balancing, which occurs any time that mesh adaption is performed in parallel. To instruct the solver to skip the load balancing step, issue the following command: (disable-load-balance-after-adaption) To return to the default behavior use the following command: (enable-load-balance-after-adaption)

30.6

Running Parallel FLUENT under SGE

Sun Grid Engine (SGE) software is a distributed computing resource management tool that you can use with either the serial or the parallel version of FLUENT. FLUENT submits a process to the SGE software, then SGE selects the most suitable machine to process the FLUENT simulation. You can configure SGE and select the criteria by which SGE determines the most suitable machine for the FLUENT simulation. Among many other features, running a FLUENT simulation using SGE allows you to: • Save the current status of the job (i.e., in the case of FLUENT saving .case and .data files, also known as checkpointing.) • Migrate the simulation to another machine • Restart the simulation on the same or another machine

30.6.1

Overview of FLUENT and SGE Integration

• Requirements – Sun Grid Engine software version 5.3 or higher, available online at http://www.sun.com/

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30.6 Running Parallel FLUENT under SGE

– Fluent 6.x, available from Fluent Inc. • FLUENT and SGE Communication FLUENT and SGE communicate with each other through checkpointing and migration commands. To checkpoint, or save, FLUENT simulations, SGE uses an executable file called checkpoint command.fluent. To migrate FLUENT simulations to another machine, SGE uses another executable file called migration command.fluent. • Checkpointing Directories FLUENT creates a checkpointing sub-directory, identified by the job ID. The checkpointing directory contains files related only to the submitted job. • Checkpointing Trigger Files When a FLUENT simulation needs to be checkpointed, SGE creates a checkpoint trigger file (.check) in the job subdirectory, which causes FLUENT to checkpoint and continue running. If the job needs to be migrated, because of a machine crash or for some other reason, a different trigger file (.exit) is created which causes FLUENT to checkpoint and exit. • Default File Location By default, the following SGE-related FLUENT files are installed in path/Fluent.Inc /addons/sge1.0, where path is the directory in which you have placed the release directory, Fluent.Inc. – ckpt command.fluent – migr command.fluent – sge request – kill-fluent – sample ckpt obj – sample pe These files are described later in this section.

30.6.2

Configuring SGE for FLUENT

SGE must be installed properly if checkpointing is needed or parallel FLUENT is being run under SGE. The checkpoint queues must be configured first, and they must be configured by someone with manager or root privileges.


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General Configuration Using the SGE graphical interface, the general configuration of SGE and FLUENT requires the following:. 1. The Shell Start Mode must be set to unix behavior. 2. Under Type, the checkpointing option must be marked as true. When running parallel FLUENT simulations, the following options are also important: 1. Under Type, the parallel option must be marked as true. 2. The value of slots should be set to a value greater than 1.

Checkpoint Configuration Checkpointing is configured using the MinCpuTime field. This field specifies the time interval between checkpoints. The value of MinCpuTime should be a reasonable amount of time. Too low a value for MinCpuTime results in frequent checkpointing operations and writing .case and .data files can be computationally expensive. SGE requires checkpointing objects to perform checkpointing operations. FLUENT provides a sample checkpointing object called fluent ckpt obj. Checkpoint configuration also requires root or manager privileges. While creating new checkpointing objects for FLUENT, keep the default values as given in the sample/default object provided by FLUENT and change only the following values: • Queue List The queue list should contain the queues that are able to be used as checkpoint objects. • Checkpointing and Migration Command This value should only be changed when the executable files are not in the default location, in which case, the full path should be specified. All the files (i.e., ckpt command.fluent and migr command.fluent) should be located in a directory that is accessible from all machines where the FLUENT simulation is running. The default place for these files is path/Fluent.Inc/addons/sge1.0, where path is the directory in which you have placed the release directory, Fluent.Inc. • Checkpointing Directory This value dictates where the checkpointing subdirectories are created, and hence users must have the correct permission to this directory. Also this directory should be visible to all machines where the FLUENT simulation is running. The default value is $HOME.

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30.6 Running Parallel FLUENT under SGE

Configuring Parallel Environments For submitting parallel jobs, SGE needs a parallel environment interface, or PE interface. FLUENT provides a sample parallel environment interface, fluent pe. Parallel environment configuration requires root or manager privileges. While creating any new parallel environment for FLUENT, change only the following values: • Queue List This should contain all the queues where qtype has been set to PARALLEL. • User/XUser List This contains the list of users who are allowed or denied access to the parallel environment. • Stop Proc Args This should be changed only if the kill-fluent executable is not in the default directory, in which case, the full path to the file should be given, and the path should be accessible from every machine. • Slots This should be set to a large numerical value indicating the maximum of slots that can be occupied by all the parallel environment jobs that are running. FLUENT uses fluent pe as the default parallel environment, therefore, there must be one parallel environment with this name.

Configuring a Default Request File As an alternative to specifying numerous command line options or arguments when you invoke SGE, you can provide a list of SGE options in a default request file. A default request file should be set up when using SGE with FLUENT. FLUENT provides a sample request file called sge request. All default request options and arguments for SGE that are common to all users can be placed under a default request file, sge request located in the // common/ directory. Individual users can set their own default arguments and options in a private general request file, .sge request, located in their $HOME directory. Private general request files override the options set by the global sge request file in the //common/ directory. Any settings found in either the global or private default request file can be overridden by specifying new options in the command line.


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30.6.3

Running a FLUENT Simulation under SGE

Running FLUENT under SGE requires additional options for the FLUENT command syntax. The command line syntax is as follows: fluent -sge [-sgeckpt ckpt object] [-sgepe parallel env N MIN-N MAX ] The additional parameters are explained below. • -sge Tells FLUENT to run under SGE. • -sgeckpt ckpt obj Specifies the checkpointing object and overrides the checkpointing option specified in the default request file. If this option is not specified in the command line, and the default general request file contains no setting, then the FLUENT simulation is unable to use checkpoints. • sgepe parallel env N MIN-N MA Specifies the parallel environment to be used, when FLUENT is run in parallel. This should be specified only if the -sge option is also specified. N MIN and N MAX represent the minimum and maximum number of requested nodes. This parameter is optional. For parallel FLUENT, if this parameter is not specified, but the command line -sge option is given, FLUENT will take fluent pe as the default parallel environment, 1 as N MIN and the number of nodes requested to FLUENT as N MAX. The following examples demonstrate various command line syntax meanings: • Serial FLUENT simulation running under SGE. fluent 2d -sge • Serial FLUENT simulation with checkpoints. fluent 2d -sge -sgeckpt fluent ckpt • Parallel FLUENT simulation running under SGE. fluent 2d -t -pnet -sge • Parallel FLUENT under SGE with a different parallel environment. fluent 2d -t -pnet -sge -sgepe diff pe -

!

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In this final example, note that the -t option will be ignored and the - option will take precedence.


30.7 Running Parallel FLUENT under LSF

30.7

Running Parallel FLUENT under LSF

Platform Computing Corporation’s LSF software is a distributed computing resource management tool that you can use with either the serial or the parallel versions of FLUENT. Using LSF, FLUENT simulations can take full advantage of LSF checkpointing (i.e., saving FLUENT .case and .data files) and migration features. LSF is also integrated with FLUENT’s vendor-based vmpi and the socket-based net MPI communication libraries for distributed MPI processing, increasing the efficiency of the software and data processing.

! Running FLUENT under LSF is not currently supported on Windows. Platform’s Standard Edition is the foundation for all LSF products, it offers users load sharing and batch scheduling across distributed UNIX, LINUX and Windows NT computing environments. Platform’s LSF Standard Edition provides the following functionality: • Comprehensive Distributed Resource Management – dynamic load sharing services – batch scheduling and resource management policies • Flexible Queues and Sharing Control – priority – load conditions for job scheduling – time windows for job processing – limits on the number of running jobs and job resource consumption • Fair-share Scheduling of Limited Resources – manage shares for users and user groups – ensure fair sharing of limited computing resources • Maximum Fault Tolerance – provides batch service as long as one computer is active – ensures that no job is lost when the entire network goes down – restarts jobs on other compute nodes when a computer goes down

30.7.1

Overview of FLUENT and LSF Integration

• Requirements – LSF Batch 3.2+, available from Platform Computing Corporation http://www.platform.com/ – Fluent 6.x, available from Fluent Inc.


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• Optional Requirements – The echkpnt.fluent and erestart.fluent shell scripts, available from Platform Computing Corporation or Fluent Inc. permit FLUENT checkpointing and restarting from within LSF – Hardware vendor supplied MPI environment for network computing. If available, the vmpi version of FLUENT may perform better than the net version. • Obtaining Distribution Files Distribution files for LSF to be used with FLUENT are available from Platform Computing Corporation. Installation instructions are included. The files are available from your LSF vendor, and from Platform’s corporate web site ( http://www.platform.com/ ) and FTP site ( ftp.platform.com ). The ftp directory location is /lsf/distrib/integra/Fluent. Access to the download area of the Platform web site and the Platform FTP site is controlled by login name and password. If you are unable to access the distribution files, contact Platform at [email protected].

30.7.2

Checkpointing and Restarting

LSF provides utilities to save (i.e., checkpoint), and restart an application. The FLUENT and LSF integration allows FLUENT to take advantage of the checkpoint and restart features of LSF. At the end of each iteration, FLUENT looks for the existence of a checkpoint or checkpoint-exit file. If FLUENT detects the checkpoint file, it writes a case and data file, removes the checkpoint file, and continues iterating. If FLUENT detects the checkpoint-exit file, it writes a case file and data file, then exits. LSF’s bchkpnt utility can be used to create the checkpoint and checkpoint-exit files, thereby forcing FLUENT to checkpoint itself, or checkpoint and terminate itself. In addition to writing a case file and data file, FLUENT also creates a simple journal file with instructions to read the checkpointed case file and data file, and continues iterating. FLUENT uses that journal file when restarted with LSF’s brestart utility. The greatest benefit of the checkpoint facilities occurs when it is used on an automatic basis. By starting jobs with a periodic checkpoint, LSF automatically restarts any jobs that are lost due to host failure from the last checkpoint. This facility can dramatically reduce lost compute time, and also avoids the task of manually restarting failed jobs.

FLUENT Checkpoint Files To checkpoint FLUENT jobs using LSF, LSF supplies special versions of echkpnt and erestart. These FLUENT checkpoint files are called echkpnt.fluent and erestart.fluent.

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Checkpoint Directories When you submit a checkpointing job, you specify a checkpoint directory. Before the job starts running, LSF sets the environment variable LSB CHKPNT DIR. The value of LSB CHKPNT DIR is a subdirectory of the checkpoint directory specified in the command line. This subdirectory is identified by the job ID and only contains files related to the submitted job.

Checkpoint Trigger Files When you checkpoint a FLUENT job, LSF creates a checkpoint trigger file (.check) in the job subdirectory, which causes FLUENT to checkpoint and continue running. A special option is used to create a different trigger file (.exit), to cause FLUENT to checkpoint and exit the job. FLUENT uses the LSB CHKPNT DIR environment variable to determine the location of checkpoint trigger files. It checks the job subdirectory periodically while running the job. FLUENT does not perform any checkpointing unless it finds the LSF trigger file in the job subdirectory. FLUENT removes the trigger file after checkpointing the job.

Restart Jobs If a job is restarted, LSF attempts to restart the job with the -restart option appended to the original fluent command. FLUENT uses the checkpointed data and case files to restart the process from that checkpoint point, rather than repeating the entire process. Each time a job is restarted, it is assigned a new job ID, and a new job subdirectory is created in the checkpoint directory. Files in the checkpoint directory are never deleted by LSF, but you may choose to remove old files once the FLUENT job is finished and the job history is no longer required.

30.7.3

Configuring LSF for FLUENT

LSF provides special versions of echkpnt and erestart called echkpnt.fluent and erestart.fluent to allow checkpointing with FLUENT. You must make sure LSF uses these files instead of the standard versions. 1. To configure LSF (v4.0 or earlier) for FLUENT: • Overwrite the standard versions of echkpnt and erestart with the special FLUENT versions. OR • Complete the following steps: (a) Leave the standard LSF files in the default location and install the FLUENT versions in a different directory.


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(b) In lsf.conf, modify the LSF ECHKPNTDIR environment variable to point to the FLUENT versions. The LSF ECHKPNTDIR environment variable specifies the location of the echkpnt and erestart files that LSF will use. If this variable is not defined, LSF uses the files in the default location, identified by the environment variable LSF SERVERDIR. (c) Save the changes to lsf.conf. (d) Reconfigure the cluster with the commands lsadmin reconfig and badmin reconfig. LSF checks for any configuration errors. If no fatal errors are found, you are asked to confirm reconfiguration. If fatal errors are found, reconfiguration is aborted. 2. To configure LSF (v4.1 or later) for FLUENT: • Copy the echkpnt.fluent and erestart.fluent files to the LSF SERVERDIR for each architecture that is desired. • Submit the job with the method=fluent parameter when specifying the checkpoint information (examples are provided below) .

! Note that LSF includes an email notification utility that sends email notices to users when an LSF job has been completed. If a user submits a batch job to LSF and the email notification utility is enabled, LSF will distribute an email containing the output for the particular LSF job. When a FLUENT job is run under LSF with the -g option, the email will also contain information from the FLUENT console window.

30.7.4

Submitting a FLUENT Job

To submit a FLUENT job using LSF, you need to include certain LSF checkpointing parameters in the standard call to FLUENT. Submitting a batch job requires the bsub command. The syntax for the bsub command to submit a FLUENT job is: bsub [-k checkpoint dir | -k "checkpoint dir[checkpoint period]" [bsub options] FLUENT command [FLUENT options] -lsf The checkpointing feature for FLUENT jobs requires all of the following parameters: • -k checkpoint dir Regular option to bsub that specifies the name of the checkpoint directory. • FLUENT command Regular command used with FLUENT software.

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• -lsf Special option to the FLUENTcommand. Specifies that FLUENT is running under LSF, and causes FLUENT to check for trigger files in the checkpoint directory if the environment variable LSB CHKPNT DIR is set.

30.7.5

Checkpointing FLUENT Jobs

Checkpointing a batch job requires the bchkpnt command. The syntax for the bchkpnt command is: bchkpnt [bsub options][-k]job ID • -k Regular option to the bchkpnt command, specifies checkpoint and exit. The job will be killed immediately after being checkpointed. When the job is restarted, it does not have to repeat any operations. • job ID The job ID of the FLUENT job. Used to specify which job to checkpoint.

30.7.6

Restarting FLUENT Jobs

Restarting a batch job requires the brestart command. The syntax for the brestart command is: brestart [bsub options] checkpoint directory job ID • checkpoint directory Specifies the checkpoint directory, where the job subdirectory is located. • job ID The job ID of the FLUENT job, specifies which job to restart. At this point, the restarted job is assigned a new job ID, and the new job ID is used for checkpointing. The job ID changes each time the job is restarted.

30.7.7

Migrating FLUENT Jobs

Migrating a FLUENT job requires the bmig command. The syntax for the bmig command is: bmig [bsub options] job ID


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• job ID The job ID of the FLUENT job, specifies which job to restart. At this point, the restarted job is assigned a new job ID, and the new job ID is used for checkpointing. The job ID changes each time the job is restarted.

30.7.8

Using FLUENT and LSF

This section describes various examples of running FLUENT and LSF. • Serial FLUENT interactive job under LSF bsub -I fluent 3d -lsf • Serial FLUENT batch job under LSF bsub fluent 3d -g -i journal file -lsf • Parallel FLUENT net version interactive job under LSF, on CPUs bsub -I -n fluent 3d -t0 -pnet -lsf

!

PAM is an extension of LSF that manages parallel processes by choosing the appropriate compute nodes and launching child processes. When using the net version of FLUENT, PAM is not used to launch FLUENT (so the JOB STARTER argument of the LSF queue should not be set). Instead, LSF will set an environment variable that contains a list of hosts, and FLUENT will use this list to launch itself.

!

The integration between PAM and FLUENT is supported on the following platforms: lnx86; Ultra; HPUX; IBM SP (AIX). Of these platforms, all except lnx86 can use the vmpi version of FLUENT. • Parallel FLUENT net version batch job under LSF, using processes bsub -n fluent 3d -t0 -pnet -g -i journal file -lsf The examples below apply to both interactive and batch submissions. For brevity, only batch submissions are described. Usage of the LSF checkpoint and restart capabilities, requiring echkpnt and erestart, are described as follows: • Serial FLUENT batch job under LSF with checkpoint/restart bsub -k " /home/username method=fluent 60" fluent 3d -g -i journal file -lsf – Submits a job that uses /home/username as the checkpoint directory, the LSF 4.1 method= specification for which echkpnt/erestart combination to use, and a 60 minute duration between automatic checkpoints. bjobs

30-48



– Returns the s of the batch jobs in the LSF system bchkpnt – Forces FLUENT to write a case file and a data file as well as a restart journal file at the end of its current iteration – The files are saved in a directory named [chkpnt dir]/ – FLUENT then continues to iterate bchkpnt -k – Forces FLUENT to write a case file and a data file as well as a restart journal file at the end of it’s current iteration – The files are saved in a directory named [chkpnt dir]/ and then FLUENT exits brestart [chkpnt dir] – Starts a FLUENT job using the latest case and data files in the [chkpnt dir]/ directory – The restart journal file [chkpnt dir]//#restart.inp is used to instruct FLUENT to read the latest case and data files in that directory, and continue iterating • Parallel FLUENT VMPI version batch job under LSF with checkpoint/restart, using processes bsub -k [chkpnt dir] -n fluent 3d t -pvmpi -g -i journal file -lsf bjobs – Returns the s of the batch jobs in the LSF system bchkpnt – Forces parallel FLUENT to write a case file and data file as well as a restart journal file at the end of it’s current iteration – The files are saved in a directory named [chkpnt dir]/ – Parallel FLUENT then continues to iterate bchkpnt -k – Forces parallel FLUENT to write a case file and a data file and a restart journal file at the end of it’s current iteration – The files are saved in a directory named [chkpnt dir]/ – Parallel FLUENT then exits


30-49

Parallel Processing

brestart [chkpnt dir] – Starts a FLUENT network parallel job using the latest case and data files in the [chkpnt dir]/ directory – The restart journal file [chkpnt dir]//#restart.inp is used to instruct FLUENT to read the latest case and data files in that directory, and continue iterating – The parallel job will be restarted using same number of processes as that used for the original bsub submission bmig m host 0 – All jobs on host host will be checkpointed and moved to another host.

30-50


Appendix A. A.1

FLUENT Model Compatibility

FLUENT Model Compatibility Chart

The following chart summarizes the compatibility of several FLUENT model categories: • Multiphase Models (see Chapter 20) • Moving Domain Models (See Chapter 9) • Turbulence Models (See Chapter 10) • Combustion Models (See Chapter 12) Note that a y indicates that two models are compatible with each other, while an n indicates that two models are not compatible with each other.


A-1

n y n n n

n n n n n n n n n

Turbulence Models Spalart-Allmaras k-ε * k-ω * * Reynolds Stress LES

Combustion Models Laminar Finite Rate Eddy Dissipation Eddy Dissipation Concept Non-Premixed Premixed Partially Premixed Composition PDF Transport NOx Soot

Figure A.1.1: FLUENT Model Compatibility Chart


n n n n n n n n n

y y y y n

y y n y y

n n n n n n n n n

y y y y n

y n y y y

y y y y y y y y y

y y y y n

y y y y y

* Includes Standard, RNG, and Realizable k-ε models * * Includes Standard, and SST k-ω models

Key: n = not compatibile y = compatible

y n n y y

y y y y y y y y y

y y y y y

y y y y y y y y y

y y y y y

n y n y

y y y y y y y y y

y y y y y

n n y y

y y y y y y y y y

y y y y y

y y y y

y y y y y y y y y

y y y y y

y y y y

n n n n n n n n n

y y y y y

n y y y

y y y y y y y y y

y y y y y

y y y y

y y y y y y y y y

y y y y y

n y y y

y y y y y y y y y

y y y y y

n y y y

y y y y y y y y y

y y y y y

n n n n

M ult iph Eu as l e ria e Mo de VO n ls F Mi xtu re Di scr e t e Ph ase M ov ing Sli D om din ian M gM M i xin esh od g els Pla Dy ne na m i cM Mu esh lt i Sin ple R efe gle r R efe ence ren Fr c Tu e F ame r ram bu len e Sp c e a M lar od t-A els k-ε l lm * ara s k-ω ** Re yn o LE lds S tre S ss

y y y y

y y y y y

n y y y y

y y y y y n n y y y y

n n n y

n y y y y

y y y y y

n n n y

n y y y y

y y y y y

n n n y

n y y y y

y y y y y

n n n y

n y y y y

y y y y y

n n n y

n y y y y

y y y y y

n n n y

n y y y y

y y y y y

n n n y

C o mb ust io La n m M ina od rF els Ed in d i t yD eR ate i s Ed sip dy ati D on i s s No n-P ipatio re n m C P on r ixe e mi cep d xed t Pa rtia lly P Co rem mp ixe o d NO sition x PD n n n y

rt n y y y y

y y y y y

n n n y

t

FT ran spo Soo

A-2

Moving Domain Models Sliding Mesh Mixing Plane Dynamic Mesh Multiple Reference Frame Single Reference Frame

Multiphase Models Eulerian VOF Mixture Discrete Phase

FLUENT Model Compatibility

Nomenclature

A

Area (m2 , ft2 )

~a

Acceleration (m/s2 , ft/s2 )

a

Local speed of sound (m/s, ft/s)

c

Concentration (mass/volume, moles/volume)

CD

Drag coefficient, defined different ways (dimensionless)

cp , cv Heat capacity at constant pressure, volume (J/kg-K, Btu/lbm -◦ F) d

Diameter; dp , Dp , particle diameter (m, ft)

DH

Hydraulic diameter (m, ft)

Dij , D Mass diffusion coefficient (m2 /s, ft2 /s) E

Total energy, activation energy (J, kJ, cal, Btu)

f F~

Mixture fraction (dimensionless)

FD

Drag force (N, lbf )

~g

Gravitational acceleration (m/s2 , ft/s2 ); standard values = 9.80665 m/s2 , 32.1740 ft/s2

Gr

Grashof number ≡ ratio of buoyancy forces to viscous forces (dimensionless)

H

Total enthalpy (energy/mass, energy/mole)

h

Heat transfer coefficient (W/m2 -K, Btu/ft2 -h-◦ F)

h

Species enthalpy; h0 , standard state enthalpy of formation (energy/mass, energy/mole)

I

Radiation intensity (energy per area of emitting surface per unit solid angle)

J

Mass flux; diffusion flux (kg/m2 -s, lbm /ft2 -s)

K

Equilibrium constant = forward rate constant/backward rate constant (units vary)

k

Kinetic energy per unit mass (J/kg, Btu/lbm )

k

Reaction rate constant, e.g., k1 , k−1 ,kf,r , kb,r (units vary)

k

Thermal conductivity (W/m-K, Btu/ft-h-◦ F)

kB

Boltzmann constant (1.38 × 10−23 J/molecule-K)

k,kc

Mass transfer coefficient (units vary); also K, Kc

Force vector (N, lbf )

`, l, L Length scale (m, cm, ft, in)


Nom-1

Nomenclature

Le

Lewis number ≡ ratio of thermal diffusivity to mass diffusivity (dimensionless)

m

Mass (g, kg, lbm )

m ˙

Mass flow rate (kg/s, lbm /s)

Mw

Molecular weight (kg/kgmol, lbm /lbm mol)

M

Mach number ≡ ratio of fluid velocity magnitude to local speed of sound (dimensionless)

Nu

Nusselt number ≡ dimensionless heat transfer or mass transfer coefficient (dimensionless); usually a function of other dimensionless groups

p

Pressure (Pa, atm, mm Hg, lbf /ft2 )

Pe

Peclet number ≡ Re × Pr for heat transfer, and ≡ Re × Sc for mass transfer (dimensionless)

Pr

Prandtl number ≡ ratio of momentum diffusivity to thermal diffusivity (dimensionless)

Q

Flow rate of enthalpy (W, Btu/h)

q

Heat flux (W/m2 , Btu/ft2 -h)

R

Gas-law constant (8.31447 × 103 J/kgmol-K, 1.98588 Btu/lbm mol-◦ F)

r

Radius (m, ft)

R

Reaction rate (units vary)

Ra

Rayleigh number ≡ Gr × Pr; measure of the strength of buoyancy-induced flow in natural (free) convection (dimensionless)

Re

Reynolds number ≡ ratio of inertial forces to viscous forces (dimensionless)

S

Total entropy (J/K, J/kgmol-K, Btu/lbm mol-◦ F)

s

Species entropy; s0 , standard state entropy (J/kgmol-K, Btu/lbm mol-◦ F)

Sc

Schmidt number ≡ ratio of momentum diffusivity to mass diffusivity (dimensionless)

Sij

Mean rate-of-strain tensor (s−1 )

T

Temperature (K, ◦ C, ◦ R, ◦ F)

t

Time (s)

U

Free-stream velocity (m/s, ft/s)

u, v, w Velocity magnitude (m/s, ft/s); also written with directional subscripts (e.g., vx , vy , vz , vr ) V

Volume (m3 , ft3 )

~v

Overall velocity vector (m/s, ft/s)

We

Weber number ≡ ratio of aerodynamic forces to surface tension forces (dimensionless)

Nom-2


Nomenclature

X

Mole fraction (dimensionless)

Y

Mass fraction (dimensionless)

α

Permeability, or flux per unit pressure difference (L/m2 -h-atm, ft3 /ft2 -h-(lbf /ft2 ))

α

Thermal diffusivity (m2 /s, ft2 /s)

α

Volume fraction (dimensionless)

β

Coefficient of thermal expansion (K−1 )

γ

Porosity (dimensionless)

γ

Ratio of specific heats, cp /cv (dimensionless)

∆

Change in variable, final − initial (e.g., ∆p, ∆t, ∆H, ∆S, ∆T )

δ

Delta function (units vary)

Emissivity (dimensionless)

Lennard-Jones energy parameter (J/molecule)

Turbulent dissipation rate (m2 /s3 , ft2 /s3 )

Void fraction (dimensionless)

η

Effectiveness factor (dimensionless)

η 0 , η 00 Rate exponents for reactants, products (dimensionless) θr

Radiation temperature (K)

λ λ

Molecular mean free path (m, nm, ft) ˚, ft) Wavelength (m, nm, A

µ

Dynamic viscosity (cP, Pa-s, lbm /ft-s)

ν

Kinematic viscosity (m2 /s, ft2 /s)

ν 0 , ν 00 Stoichiometric coefficients for reactants, products (dimensionless) ρ

Density (kg/m3 , lbm /ft3 )

σ

Stefan-Boltzmann constant (5.67 ×108 W/m2 -K4 )

σ

Surface tension (kg/m, dyn/cm, lbf /ft)

σs

Scattering coefficient (m−1 )

τ

Stress tensor (Pa, lbf /ft2 )

τ

Shear stress (Pa, lbf /ft2 )

τ

Time scale, e.g., τc , τp , τc (s)

τ

Tortuosity, characteristic of pore structure (dimensionless)

φ

Equivalence ratio (dimensionless)

φ

Thiele modulus (dimensionless)

Ω

Angular velocity; Ωij , Mean rate of rotation tensor (s−1 )


Nom-3

Nomenclature

ω

Specific dissipation rate (s−1 )

Ω, Ω0 Solid angle (degrees, radians, gradians) ΩD

Nom-4

Diffusion collision integral (dimensionless)


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Bib-22


Index

ABAQUS, 3-23 absolute pressure, 7-53, 29-17 absolute velocity, 9-9, 9-12, 9-17, 9-19, 9-26, 9-30, 9-43, 24-56, 24-58 absolute velocity formulation, 9-8, 9-10 absorbed radiation flux, 29-17 absorption coefficient, 7-39, 11-57, 29-17 composition-dependent, 7-39, 11-15, 11-41 effect of particles on, 7-40, 11-44 effect of soot on, 7-40, 11-43, 18-37, 18-40 non-gray radiation, 7-40 WSGGM, 7-39, 11-41 accelerating reference frame, 9-3 accretion, 21-73, 21-105, 29-23 reporting, 21-136 accuracy, 5-12 diffusion terms, 24-8 first-order, 24-8, 24-43 second-order, 24-10, 24-43 Acoustic Signal Computation panel, 19-13 acoustic signals, 19-2 Acoustic Source Specification panel, 19-8 acoustics model, 19-1 computing sound data, 19-13 FW-H formulation, 19-3 limitations, 19-2 quadrupoles, 19-2 receivers, 19-11 source surfaces, 19-8 writing data files, 19-10 Acoustics Models and Parameters panel, 19-6 Activate Cell Zones panel, 5-54 activating zones, 5-52

active cell partition, 29-17, 30-24 Adapt/Boundary..., 25-14 Adapt/Controls..., 25-44 Adapt/Display Options..., 25-42, 25-43 Adapt/Gradient..., 25-18, 25-20 Adapt/Iso-Value..., 25-25 Adapt/Manage..., 25-38 Adapt/Region..., 25-28, 25-30 Adapt/Smooth/Swap..., 25-48 Adapt/Volume..., 25-32, 25-34 Adapt/Y+/Y*..., 25-35 adaption, 5-12, 25-1 y + ,y ∗ , 25-35 boundary, 25-14 choosing the appropriate method, 25-13 coarsening, 25-10, 25-11 conformal, 25-4, 25-6, 25-10 enabling, 25-45 conformal vs. hanging node, 25-13 curvature, 29-18 deleting registers, 25-41 display options, 25-42 displaying registers, 25-42 dynamic gradient, 25-23 example, 25-2 function, 29-17 gradient, 25-18 guidelines, 25-4 hanging node, 25-6, 25-8, 25-45 isovalue, 25-25 limiting, 25-44 manipulating registers, 25-38 marking, 25-6 mask registers, 25-6 modifying registers, 25-41

Index

process, 25-6 refinement, 25-8, 25-10 region, 25-28 registers, 25-6 space gradient, 29-18 volume, 25-32 Adaption Display Options panel, 25-43 adaptive time stepping, 24-65, 24-67 added mass effect, 22-23 adding text, 27-50 Adobe Acrobat Reader, 1-23 aerodynamic noise, 19-1 Airpak, 1-4 algebraic multigrid (AMG), 24-12, 24-30, 24-35 alloys, solidification of, 23-1 alphanumeric reporting, 28-1 angle of internal friction, 22-67 angular coordinate, 29-18 angular discretization, 11-29, 11-55 angular momentum, 8-13 angular velocity, 6-28, 9-8, 9-9, 9-18, 9-25 coordinate-system constraints, 9-8 Animate panel, 27-72 animation, 24-88, 27-62, 27-72 automatic, 24-88 example, 27-67, 27-69 of pathlines, 27-26 playback, 27-74 restrictions, 27-77 saving, 27-75 solution, 24-88 Animation Sequence panel, 24-89, 24-90 Anisotropic Conductivity panel, 7-35 anisotropic thermal conductivity, 7-32, 11-6 Annotate panel, 27-36 annotated text, 27-36, 27-50 ANSYS, 1-3, 3-23 ANSYS file, 3-7, 5-19 architecture, 1-1 ARIES, 1-3, 5-19 Arrhenius reaction rate, 13-4, 13-22, 29-18 ASCII file export, 3-23

Index-2

aspect ratio, 5-10, 5-13 atomizer models, 21-40 Auto Partition Grid panel, 30-20 automatic file saving, 3-11, 9-57, 24-63, 24-97 automatic partitioning, 30-19 Autosave Case/Data panel, 3-11 averaged values, 24-83, 24-87 AVS, 3-23 Axes panel, 27-101 axes, 27-101 attributes, 27-100 axial coordinate, 29-19 axial force, 27-112 axial pull velocity, 29-19 axial velocity, 6-28, 29-19 axis boundary condition, 6-87 axis of rotation, 5-38, 6-90, 6-92, 9-8, 9-9, 9-18, 9-25 axisymmetric cases, 5-11, 5-32, 5-38, 6-87, 8-15, 28-1 axisymmetric flow in multiple reference frames, 9-16 rotation axis, 9-8 axisymmetric swirl, 6-20, 6-21, 6-27, 6-28, 8-12, 8-15 inputs for, 8-17 solution strategies for, 8-17 backflow, 6-44, 6-46 batch execution, 2-37, 24-97 options, 2-39 Batch Options... panel, 2-39 Bernoulli equation, 6-23 Beta-Pdf panel, 14-57 Biaxial Conductivity panel, 7-32 biaxial thermal conductivity, 7-32 binary diffusivity, 21-110 binary files, 3-2, 3-3 Bingham plastics, 7-27 black body temperature, 11-59 Blake-Kozeny equation, 6-104 blowers, 9-31


Index

body forces, 1-14, 24-17, 24-21, 24-44 for multiphase flow, 22-72, 24-21 implicit treatment of, 24-21 boiling, 21-21 point, 21-109 rate equation, 21-24 booleans, 2-24 Boundary Adaption panel, 25-14 boundary adaption, 25-14 boundary cell distance, 25-14, 29-19 Boundary Conditions panel, 6-3 boundary conditions, 6-1 axis, 6-87 centerline, 6-87 compressible flow, 8-24 copying, 6-5 coupling with GT-Power, 6-192 coupling with WAVE, 6-195 discrete phase, 21-11, 21-100 exhaust fan, 6-11, 6-60 fan, 6-112 fixing values in cell zones, 6-183 flow inlets and exits, 6-10 heat exchanger, 6-120 ill-posed, 6-56 inlet, 6-25, 6-187 inlet vent, 6-10, 6-40 intake fan, 6-11, 6-42 listing, 28-18 low-pressure gas slip, 13-39 mass flow inlet, 6-10, 6-32 mixing plane model, 9-26 moving zones, 6-90, 6-92 multiphase flow, 22-75 multiple reference frames, 9-18 non-premixed combustion model, 14-77 non-reflecting, 6-131 non-uniform inputs for, 6-7 outflow, 6-10, 6-54 outlet vent, 6-11, 6-58 overview, 6-2 periodic, 6-84, 11-71 porous jump, 6-129


porous media, 6-93 premixed turbulent combustion, 15-13 pressure far-field, 6-10, 6-50 pressure inlet, 6-10, 6-17 pressure outlet, 6-10, 6-44 radiant, 6-80 radiation, 11-58 discrete ordinates (DO) model, 11-33, 11-34, 11-38 discrete transfer model (DTRM), 11-21, 11-22 flow inlets and exits, 11-58 non-gray discrete ordinates (DO) model, 11-33 P-1 model, 11-25, 11-26 Rosseland model, 11-27 walls, 11-59, 11-60 radiator, 6-120 reading, 3-17 rotating flow, 8-17 rotating reference frame, 9-9 saving, 3-17 setting, 6-4 transient, 6-7 sliding meshes, 9-39 soot, 18-40 source term input, 6-187 species, 6-76, 13-30, 13-37 surface reaction, 6-77, 13-37 swirling flow, 8-17 symmetry, 6-81 thermal, 6-80, 11-7 at walls, 6-63 transient, 6-7 turbulence, 10-41, 10-47, 10-71 input methods, 6-11 velocity inlet, 6-10, 6-25 wall, 6-62 writing, 3-17 boundary grid file, 3-17 boundary layers, 5-12, 8-15, 25-14 boundary normal distance, 25-16, 29-19 Boundary Profiles panel, 6-177

Index-3

Index

boundary profiles, 6-7, 6-174 file format, 6-176 reading and writing files, 3-15 reorienting, 6-180 units of, 4-2 boundary volume distance, 29-19 boundary zones, 6-4 changing name of, 6-6 changing type of, 6-3 bounded plane, 26-13 Bounding Frame panel, 27-71 bounding frame, 27-70 Boussinesq hypothesis, 10-4 Boussinesq model, 7-15, 11-79 limitations, 11-79 branch cuts, 5-49 Brinkman number, 11-4 Brownian force, 21-8, 21-73 browser, 1-17, 2-29 bubble columns, 20-6 bubbles, 21-1 bubbly flow, 20-2, 20-4, 20-6 bulk species, 13-17, 13-18 buoyancy forces, 11-78 buoyancy-driven flows, 11-78 boundary conditions, 6-17, 6-19 inputs for, 11-79 solution procedures, 11-82 theory, 11-78 burnout stoichiometric ratio, 14-89, 21-110 burnt mixture, 15-3 species concentration, 15-10, 15-14 buttons, 2-12

C-type grids, 5-49 Calculate/Flamelet, 14-105 Calculate/PDF Table, 14-53 calculations, 24-59, 24-60 convergence of, 24-101, 24-108 executing commands during, 24-97 in batch mode, 2-37 interrupting, 24-60

Index-4

stability of, 24-100, 24-102 steady-state, 24-59 time-dependent, 24-60 Camera Parameters panel, 27-51, 27-54 cancelling, 2-6 a display operation, 2-16 capabilities, 1-3, 8-2 capillary number, 22-14 captions, 27-35 carpet plot, 27-13 Carreau Model panel, 7-26 Carreau model, 7-26 carrier, 13-41 Cartesian coordinate system for boundary condition inputs, 6-20 Cartesian velocities, 29-3 for boundary condition inputs, 6-27 case files automatic saving of, 3-11, 9-57, 24-63 FLUENT 4, 3-12, 5-21 FLUENT/UNS, 3-12 non-conformal, 5-30 format, 3-34 RAMPANT, 3-12, 5-21 non-conformal, 5-30 reading and writing, 3-9, 3-11 writing, 5-36 cavitation model, 22-45 limitations, 22-45 liquid surface tension, 22-57 non condensable gas, 22-57 non-condensable gases, 22-47 vapor transport, 22-46 vaporization pressure, 22-57 cell aspect ratio, 5-10, 5-13 children, 29-19 element type, 29-19 equiangular skewness, 29-20 equivolume skewness, 29-20 partition, 29-20 refine level, 29-20 Reynolds number, 29-21


Index

skewness, 5-10, 5-13 equiangular, 29-20 equivolume, 29-20 squish index, 29-21 surface area, 29-21 type, 29-22 values, 24-7, 29-1 for contours, 27-15 for pathlines, 27-30 for XY plots, 27-93 volume, 5-13, 29-21 2D, 29-21 change, 5-13, 25-25, 29-21 negative, 5-32 wall distance, 29-21 warpage, 29-21 zones, 29-22 separating, 5-43 centering the display, 27-51 centerline boundary conditions, 6-87 centrifugal impellers, 9-3 CFL condition, 24-27, 24-49 CGNS files, 1-3, 3-8, 3-23 char, 18-18 burnout, 21-34 character strings, 2-24 characteristic length, 7-52 characteristic strain rate, 14-94 check box, 2-12 checking the grid, 5-30 checkpointing, 2-40 using LSF, 2-40, 30-43 using SGE, 2-40, 30-38 chemical database, 14-1, 14-31 chemical mechanism files, 13-35 chemical reaction, 11-4 equilibrium chemistry, 14-8, 14-35, 14-50 mixed is burned, 14-7 non-equilibrium chemistry, 14-8, 14-91 non-premixed combustion model, 14-1 reversible, 13-6, 13-29 chemical vapor deposition, 13-36


CHEMKIN files, 13-35 Chemkin Import panel, 13-35 circumferential average, 9-20, 9-23, 9-43, 27-96 client/server architecture, 1-1 cloud tracking, 21-14, 21-95 clustering, 11-20, 11-40, 11-48 display, 11-69 co-located scheme, 24-16 coal combustion, 14-34, 21-35 carbon conversion, 21-126 char burnout, 21-34, 21-110, 21-111 devolatilization, 21-25, 21-110 discrete phase, 21-79 empirical fuel definition in, 14-36, 14-42 fuel composition, 14-42 heating value, 14-36, 14-86 in non-premixed combustion model, 14-39, 14-84 models for, 21-34, 21-111 particle heating, 21-33 swelling, 21-32 water content, 14-39, 14-86, 14-90, 21-83 coarse grid levels, 24-51, 24-108 coarsening, 25-10, 25-11, 25-13 parameters, 24-107 coefficient of restitution, 22-30 cold flow, 13-31 color scale, 27-35 Colormap panel, 27-39 colormap, 27-39 custom, 27-42 Colormap Editor panel, 27-42 colors, 27-64 contour, 27-10, 27-117, 27-120 for annotation, 27-38 grid, 27-6 pathline, 27-29 vector, 27-22 combustible fraction, 14-89, 21-110

Index-5

Index

combustion, 13-31 coal, 14-19, 14-34, 14-84, 21-25 dissociation in, 14-8 empirical fuel definition, 14-36 equilibrium chemistry, 14-35 finite-rate model, 13-4 flamelet model, 14-91 fuel rich mixtures, 14-50 liquid fuel, 14-19, 14-34, 21-21 model compatibility, A-1 non-equilibrium chemistry, 14-91 non-premixed, 14-1 partially premixed, 16-1 pollutant formation, 14-8, 14-40, 18-1 premixed, 15-1 solution techniques, 24-103 soot formation, 14-39 sulfur in, 14-40 command files, 24-97 command macros, 24-98 communicators, 30-2 LINUX, 30-8 UNIX, 30-5 Windows, 30-10 Composition panel, 14-41 composition PDF transport model, 17-2 IEM model, 17-4 ISAT algorithm, 17-7 model compatibility, A-1 Modified Curl model, 17-4 Monte Carlo method, 17-3 particle tracking, 17-17 reporting options, 17-17 compressed files, 3-3 compressible flows, 1-13, 8-20 boundary conditions for, 8-24 calculations at inlet pressure boundaries, 6-24 floating operating pressure, 8-24 higher-order density interpolation, 24-18, 24-45 inputs for, 7-17, 8-23 physics of, 8-22

Index-6

pressure interpolation, 24-44 solution strategies, 8-26 turbulence modeling, 10-24 computational expense, 5-9, 25-2 compute nodes, 30-1, 30-13 connectivity information for, 30-17 killing, 30-14 spawning, 30-14 troubleshooting, 30-15 computing sound data, 19-13 computing view factors, 11-49 concentration discrete phase, 29-23 concrete, 7-28 Condensed Species Densities panel, 14-38 conduction, 11-1, 11-5 shell, 6-67 conductive heat transfer, 11-1 conformal adaption, 25-4, 25-6, 25-10 enabling, 25-45 conical grid interface, 9-35 conjugate-gradient methods, 24-30 conservation equations, 8-3 discretization of, 24-7 in integral form, 24-16, 24-23 source term additions to, 6-187 consistency factor, 7-28 console, 1-9, 2-1 contact angle, 22-15, 22-86 contact resistance in solidification and melting, 23-7 contact resistivity, 29-22 continuity equation, 8-3, 8-29 continuous casting, 23-1, 23-2, 23-6 inputs for, 23-10 contour plotting, 27-10 for turbomachinery, 27-117, 27-118 Contours panel, 27-10 control volume technique, 24-2 convection in moving solids, 11-5 convective heat transfer, 11-1 conventions used in this guide, UTM-4


Index

convergence, 11-82, 13-31, 24-70, 24-100, 25-25, 25-32 acceleration of, 24-51, 24-55, 24-103, 24-108 criteria, 24-3, 24-4 modifying, 24-74 judging, 24-70, 24-78, 24-101 conversion factors for units, 4-5 coordinate transformation, 9-3 coordinates, 29-31, 29-44 constraints for rotating reference frames, 9-8 Copy BCs panel, 6-5 Coriolis force, 9-8 Cortex, 1-12, 2-23, 2-35 coupled solver, 1-13, 24-4, 24-23 Courant number, 24-49 discretization, 24-27 explicit, 1-13, 24-6 Courant number, 24-49 flux difference splitting, 24-26 implicit, 1-13, 24-6 Courant number, 24-50 memory usage, 1-14 limitations, 1-14 preconditioning, 24-24 residuals, 24-72 temporal discretization, 24-27 coupled walls, 5-49, 6-65 Courant number, 24-27, 24-111 coupled explicit solver, 24-49 coupled implicit solver, 24-50 for VOF calculations, 22-73 setting, 24-49 CPD model, 21-28 CPU time, 1-12 Create Surface panel, 27-32 crevice model, 9-84 output file, 9-93 postprocessing, 9-91 theory, 9-87 critical strain rate, 29-22 Cross Model panel, 7-27


Cross model, 7-27 crystal growth, 23-2 Curves panel, 27-103 Custom Field Function Calculator panel, 29-45 custom field functions, 29-22, 29-45 for solution initialization, 24-58 sample, 29-49 saving, 29-47 units of, 4-2, 29-45 Custom Vectors panel, 27-23 customizing field functions, 29-45 GUI, 2-19 materials database, 7-12 units, 4-4 vectors, 27-23 CVD, 13-36 cvd low-pressure gas slip, 13-39 .cxlayout file, 3-33 cyclic boundary, 6-84 cyclones, 10-9 cylindrical coordinate system for boundary condition inputs, 6-20 Cylindrical Orthotropic Conductivity panel, 7-34 cylindrical orthotropic thermal conductivity, 7-34 cylindrical velocities, 29-3 for boundary condition inputs, 6-27 Damkohler number, 29-22 Darcy’s Law, 6-94, 6-95, 6-129 data export, 3-23 data files automatic saving of, 3-11, 9-57, 24-63 FLUENT/UNS, 3-12 format, 3-34 postprocessing time-sequence data, 27-123 RAMPANT, 3-12 reading and writing, 3-9–3-11 writing, 5-36

Index-7

Index

data resetting, 24-60 database materials, 7-3 materials, 21-106 customizing, 7-12 data sources, 7-5 thermodynamic, 14-31, 14-113 transport, 14-113 Database Materials panel, 7-5, 13-18 Data Explorer, 3-23 Deactivate Cell Zones panel, 5-52 deactivating zones, 5-52 Define Case panel, 14-33 Define Event panel, 9-70 Define Macro panel, 24-99 Define Species panel, 14-37 Define Surface Monitor panel, 24-82, 24-83 Define Unit panel, 4-5 Define Volume Monitor panel, 24-85, 24-86 Define/Boundary Conditions..., 6-3 define/boundary-conditions/non-reflecting, 6-140 define/boundary-conditions/target-mass-flow-ratesettings, 6-49

Define/Custom Field Functions..., 29-45 Define/Dynamic Mesh/Events..., 9-68, 9-69 Define/Dynamic Mesh/Parameters..., 9-57 Define/Dynamic Mesh/Zones..., 9-62, 9-63 Define/Grid Interfaces..., 5-28, 9-39 define/grid-interfaces/make-periodic, 5-47 define/grid-interfaces/recreate, 5-30 Define/Injections..., 21-79 Define/Materials..., 7-3, 13-15, 14-79 Define/Mixing Planes..., 9-27 define/mixing-planes/set/conserve-swirl, 9-29, 9-30 define/mixing-planes/set/fix-pressure-level, 9-29 Define/Models/Acoustics/Models and Parameters..., 19-6 Define/Models/Acoustics/Receivers..., 19-11 Define/Models/Acoustics/Sources..., 19-8 Define/Models/Discrete Phase..., 21-71, 21-113

Index-8

define/models/dpm/tracking/track-in-absoluteframe, 21-3 define/models/dpm/tracking/track-in-absoluteframe, 9-15 define/models/dpm/velocity-gradient-correction,

21-116 Define/Models/Energy..., 8-23, 11-6, 11-79 define/models/energy?, 11-3, 11-6 Define/Models/Multiphase..., 22-53 Define/Models/Pollutants/NOx..., 18-26, 18-27 Define/Models/Pollutants/Soot..., 18-36, 18-37 Define/Models/Radiation..., 11-46, 11-49, 11-56, 11-64 define/models/radiation/s2s-parameters/split-angle, 11-53 Define/Models/Solidification and Melting..., 23-8 Define/Models/Solver..., 1-15, 8-17, 24-62 define/models/species-transport/inlet-diffusion?, 13-30, 14-77 Define/Models/Species..., 13-41, 14-73, 15-10 Define/Models/Viscous..., 8-30, 10-64 define/models/viscous/turbulence-expert/detachededdy-simulation?, 10-66 define/models/viscous/turbulence-expert/rke-cmurotation-term?, 10-22 define/models/viscous/turbulence-expert/turb-nonnewtonian?, 10-71

Define/Operating Conditions..., 7-16, 7-17, 7-54, 8-23, 11-80 Define/Periodic Conditions..., 8-8 Define/Phases..., 22-58 Define/Profiles..., 6-177 Define/Ray Tracing..., 11-47 Define/Turbo Topology..., 27-106 Define/Units..., 4-3 Define/User-Defined/1D Coupling..., 6-193, 6-195, 6-196 define/user-defined/compiled-functions, 7-64 Define/User-Defined/Fan Model..., 6-143


Index

Exchanger diffusion coefficient, 13-3, 13-12, 13-28 species, 29-25, 29-28 thermal, 7-44 Exchanger..., user-defined scalar, 29-22 define/user-defined/heat-exchanger/heat-exchanger- diffusion flames, 14-1 diffusivity report, 6-174 binary, 21-110 define/user-defined/real-gas, 7-60 direct numerical simulation, 10-43 definitions discrete ordinates (DO) radiation model, for field functions, 29-1 11-14 for flow variables, 29-1 advantages, 11-18 deforming zones, 9-62, 9-65 angular discretization, 11-29, 11-55 degrees of freedom, 7-52 boundary conditions Delaunay triangulation, 25-11 flow inlets and exits, 11-38 Delete Zones panel, 5-52 gray-diffuse walls, 11-33 deleting zones, 5-52 opaque walls, 11-60 Delta-Eddington scattering phase function, periodic boundaries, 11-38 7-41, 11-31 semi-transparent walls, 11-34, 11-61 density, 7-14, 13-28, 29-22 specular walls, 11-38 Boussinesq model, 7-14 symmetry boundaries, 11-38 composition-dependent, 7-17 two-sided walls, 11-63 constant, 7-14, 7-15 limitations, 11-18 discrete phase, 21-109 non-gray, 11-28 for premixed turbulent combustion, inputs for, 11-56 15-9 limitations, 11-18 ideal gas law, 7-14, 7-16 particulate effects, 11-33 incompressible ideal gas law, 7-14, 7-16 particulate effects, 11-32 interpolation schemes, 24-18, 24-44 pixelation, 11-29, 11-55 restrictions, 7-14 properties, 7-38 temperature-dependent, 7-14, 7-15 residuals, 11-66 derivative evaluation, 24-15 solution parameters, 11-65 derivatives, 29-22 theory, 11-28 detached eddy simulation (DES) model, discrete phase, 21-1 10-6, 10-13, 10-68 aborted trajectories, 21-113 devolatilization, 29-24 absorption coefficient, 29-23 models, 21-25, 21-111 accretion, 21-73, 21-105, 29-23 dialog box, 2-5 reporting, 21-136 diesel engines, 9-84 air-blast atomizer, 21-52 diffusion, 5-10 injections, 21-92 preferential, 15-7 atomizer models, 21-40 species, 11-9, 13-3 boiling, 21-21 thermal, 29-39 Define/User-Defined/Heat Group..., 6-167 Define/User-Defined/Heat 6-158


Index-9

Index

boundary conditions, 21-11, 21-100 escape, 21-101 interior, 21-103 reflect, 21-100 trap, 21-101 wall jet, 21-101 Brownian force, 21-8, 21-73 burnout, 29-23 cloud tracking, 21-9, 21-14, 21-95 coefficient of restitution, 21-100, 21-104 combusting, 21-79, 21-106 concentration, 21-131, 29-23 cone injections, 21-77, 21-88 coupled calculations, 21-4, 21-68, 21-70, 21-118, 21-120, 24-3, 24-4 coupled heat-mass solution, 21-73 customized particle laws, 21-83, 21-96 devolatilization, 21-25, 29-24 display, 21-121 drag coefficient, 21-5, 21-73 drag force, 21-5 droplet, 21-79, 21-105 collision model, 21-55 dynamic drag model, 21-66 effervescent atomizer, 21-54 injections, 21-93 emission, 29-23 erosion, 21-73, 21-105, 29-23 reporting, 21-136 evaporation, 29-24 flat-fan atomizer, 21-53 injections, 21-93 group injections, 21-77, 21-84 heat transfer, 21-4, 21-18, 21-19, 21-68, 21-69, 21-125 in multiple reference frames, 9-15, 21-3 inert, 21-79, 21-105 initial conditions, 21-76 read from a file, 21-77, 21-78 injections, 21-77 copying, 21-80 creating, 21-79 deleting, 21-80

Index-10

listing, 21-81 read from a file, 21-77, 21-78 setting properties, 21-81 setting properties for multiple, 21-97 inputs, 21-71 for boundary conditions, 21-100 for initial conditions, 21-76 for material properties, 21-105 for optional models, 21-71 for particle tracking, 21-74 for spray modeling, 21-75 lift force, 21-9, 21-73 limitations of, 9-15, 21-2, 21-3, 22-6 mass flow rate, 21-84, 21-88, 21-89 mass transfer, 21-4, 21-18, 21-23, 21-68, 21-70, 21-101, 21-110, 21-125 materials, 7-3, 21-83, 21-105 model compatibility, A-1 options, 21-71 overview, 21-4 parallel processing, 21-120 message passing, 21-120 shared memory, 21-120 workpile, 21-120 particle cloud tracking, 21-9, 21-14, 21-95 particle stream, 21-81 particle summary reporting, 21-134 particle tracking, 21-74 plain-orifice atomizer, 21-41 injections, 21-91 point properties, 21-84 postprocessing, 21-121 pressure-swirl atomizer, 21-47 injections, 21-91 properties, 21-105 radiation heat transfer to, 21-20, 21-23, 21-39, 21-71, 21-112 residence time, 21-126 restitution coefficient, 21-100, 21-104 rotating reference frames, 21-7 scattering, 29-24


Index

solution parameters, 11-64 setup, 21-79 theory, 11-19 for steady-state problem, 21-4 discrete values for unsteady problem, 21-4 storage points, 24-7 size distribution, 21-10, 21-85 discretization, 5-10, 24-7, 24-16 solution procedures, 21-113 first-order scheme, 24-8, 24-43 sources, 29-23, 29-24 frozen flux formulation, 24-23 spray breakup models, 21-58 inputs for, 24-43 spray modeling, 21-40 node vs cell, 24-15 atomizers, 21-40 power-law scheme, 24-8, 24-44 breakup, 21-58 QUICK scheme, 24-10, 24-44 droplet collision, 21-55 second-order scheme, 24-10, 24-43 dynamic drag, 21-66 temporal, 24-12, 24-22, 24-27, 24-29 stochastic tracking, 21-9, 21-12, 21-94, display, 27-1 21-119 animation, 27-72 summary report, 21-124 restrictions, 27-77 surface injections, 21-77, 21-90 annotation, 27-36 thermophoretic coefficient, 21-109 bounding frame, 27-70 thermophoretic force, 21-7, 21-71 captions, 27-35 time step, 21-69, 21-113 centering, 27-51 trajectory calculations, 21-5, 21-116 choosing surfaces for, 26-1 trajectory reporting, 21-124, 21-128 colormap, 27-39 at boundaries, 21-132 colors, 27-6, 27-22, 27-29, 27-64 unsteady tracking, 21-129 composing, 27-61 turbulent dispersion, 21-2, 21-9, 21-12, contours, 27-10 21-14 for turbomachinery, 27-117, 27-118 uncoupled calculations, 21-116 deleting objects, 27-70 under-relaxation, 21-119 grid, 27-2 user-defined functions, 21-74, 21-96 in multiple graphics windows, 27-34 using, 21-71 lights, 27-43 vapor pressure, 21-23 magnifying, 27-49, 27-54 vaporization, 21-21, 21-101 mirroring, 27-58 wet combustion, 21-83 on surfaces with uniform distribution, Discrete Phase Model panel, 21-71, 21-79, 26-9, 26-13 21-113, 21-122 outline, 27-2, 27-7 Discrete Random Walk model, 21-12, 21-13, overlaying, 27-33 21-95 pathlines, 27-25 discrete transfer radiation model (DTRM), 11-14 periodic repeats, 27-58 advantages, 11-17 profiles, 27-10 boundary conditions, 11-21, 11-22 properties, 27-62 limitations, 11-17 rendering options, 27-46 properties, 7-38 rotating, 27-49, 27-52 scaling, 27-51 residuals, 11-66


Index-11

Index

sweep surface, 27-31 symmetry, 27-58 title, 27-36, 27-95 translating, 27-49, 27-53 transparency, 27-64 turbomachinery 2D contours, 27-118 turbomachinery averaged contours, 27-117 vectors, 27-17 view modification, 27-51 visibility, 27-63 zooming, 27-54 Display Options panel, 27-34, 27-35, 27-44, 27-46 Display Properties panel, 27-63 Display/Annotate..., 27-36 Display/Beta PDF..., 14-57 Display/Colormaps..., 27-39 Display/Contours..., 27-10 Display/DTRM Graphics..., 11-69 Display/Flamelet PDF Table..., 14-107 Display/Grid..., 27-2 Display/IC Zone Motion..., 9-67, 9-68 Display/Lights..., 27-43, 27-44 Display/Mouse Buttons..., 27-49, 27-50 Display/Nonadiabatic-Table..., 14-65 Display/Options..., 27-33–27-35, 27-44, 27-46 Display/Partially Premixed Properties..., 16-6 Display/Particle Tracks..., 17-17, 21-121 Display/Path Lines..., 27-25 Display/PDF Table..., 14-62 Display/Property Curves..., 14-58, 14-60 Display/Scalar Dissipation, 14-107 Display/Scene Animation..., 27-72 Display/Scene..., 27-33, 27-61 display/set/title, 27-36 display/set/windows/scale, 27-35 display/set/windows/text, 27-35 Display/Sweep Surface..., 27-31 Display/Vectors..., 27-17, 27-18 Display/Video Control..., 27-78 Display/Views..., 27-51, 27-56, 27-58

Index-12

dissipation, 24-113 divergence, 24-48 troubleshooting, 24-53 DNS, 10-43 DO radiation model, 11-28 documentation, 1-17 donor-acceptor scheme, 22-11, 22-54 double buffering, 27-47 double-precision solvers, 1-7, 24-70 double-sided face zones, 6-4 dough, 7-28 drag coefficient, 24-78 discrete phase, 21-5, 21-73 in Eulerian multiphase model, 20-6 drift flux model, 22-18 drift velocity, 22-18 drop-down list, 2-14 droplet, 21-1, 21-79, 21-105 boiling, 21-24 devolatilization, 21-25 inert heating or cooling, 21-19 initial conditions, 21-71, 21-76 size distribution, 21-10 surface combustion, 21-34 trajectories alphanumeric reporting, 21-131 display of, 21-121 vaporization, 21-21 droplet flow, 20-2, 20-4, 20-6 DTRM, 11-14, 11-19 DTRM Graphics panel, 11-69 dual time stepping, 24-13, 24-29 dynamic head, 6-120 Dynamic Mesh panel, 9-57 Dynamic Mesh Events panel, 9-69 dynamic meshes, 9-44 in-cylinder model parameters, 9-62 constraints, 9-47, 9-50, 9-52 dynamic layering, 9-48, 9-60 grid requirements dynamic layering, 9-50 local remeshing, 9-52 spring-based smoothing, 9-47


Index

in-cylinder motion, 9-58, 9-62, 9-68, 9-75 local remeshing, 9-50, 9-60 mesh motion, 9-46 model compatibility, A-1 partitioning in parallel, 30-24 setup, 9-56 solid-body kinematics, 9-54 spring-based smoothing, 9-46, 9-58 theory, 9-45 dynamic pressure, 29-24 Dynamic Zones panel, 9-63

equilibrium chemistry, 14-1, 14-8, 14-35, 14-50 condensed phase species, 14-38 empirical fuels, 14-36, 14-43 partial equilibrium, 14-8 equivalence ratio, 14-6, 14-8, 14-51 Ergun equation, 6-104 erosion, 21-73, 21-105, 29-23 reporting, 21-136 Error dialog box, 2-6 error messages, 2-6 in prePDF, 14-68 error reduction, 24-43 EDC model, 13-10 rate, 24-38 model compatibility, A-1 using multigrid, 24-30, 24-31 eddy dissipation model Euler equations, 8-28 model compatibility, A-1 Euler explicit interpolation scheme, 22-12, eddy-dissipation model, 13-8 22-54 effective density, 22-21 Euler-Euler multiphase modeling, 20-5 effective Prandtl number, 29-25 Euler-Lagrange multiphase modeling, 20-4 effective thermal conductivity, 29-25 Eulerian multiphase model, 20-5, 22-5 effective viscosity, 29-25 added mass effect, 22-23 effectiveness, 6-163 bulk viscosity, 22-32 heat exchangers, 6-154 conservation equations, 22-21 effectiveness factor, 13-45 convergence of, 22-6 efficiencies for pumps and compressors, dispersed turbulence model, 22-37 27-113 drag function, 22-69 efficiencies for turbines, 27-115 exchange coefficients, 22-25 elastic collision, 21-101 frictional viscosity, 22-33 emissivity, 11-16, 11-58–11-60 granular temperature, 22-33 empirical fuel, 14-36, 14-42 heat exchange coefficient, 22-35 Energy panel, 8-23, 11-6, 11-79 heat transfer, 22-34 energy, 29-28, 29-39 kinetic viscosity, 22-32 equation, 8-30, 11-2 lift forces, 22-22, 22-70 in solid regions, 11-5 limitations of, 22-5 parameter, 7-52 mass transfer, 22-44 sources, 6-189, 11-4 mixture turbulence model, 22-36 enhanced wall functions, 10-59 model compatibility, A-1 EnSight, 3-23 overview, 22-5 enthalpy, 29-25 per-phase turbulence model, 22-41 equation, 11-3 restitution coefficients, 22-70 standard-state, 13-28 solids pressure, 22-30 enthalpy-porosity method, 23-3 entropy, 13-29, 28-16, 29-26 solids shear stresses, 22-32


Index-13

Index

solution strategies, 22-52, 22-92 theory, 22-20 turbulence in, 22-6, 22-35 virtual mass force, 22-23, 22-71 volume fraction, 22-20 evaporation, 21-21, 29-24 Events Preview panel, 9-70 Execute Commands panel, 24-97 Exhaust Fan panel, 6-60 exhaust fan boundary, 6-11, 6-60 existing value, 29-26 exiting, 2-41 explicit time stepping, 24-14, 24-29 restrictions, 24-51 exploded views, 27-67 Export panel, 3-23 exporting data, 3-23 heat flux, 11-12 external flows, 6-50 boundary conditions, 6-17 external heat transfer boundary conditions, 6-80 external radiation, 11-16 extruding face zones, 5-50 F-cycle multigrid, 24-37 face flux, 24-18 face handedness, 5-32, 29-26 face squish index, 29-27 face swapping, 25-51 face zones fusing, 5-48 separating, 5-41 slitting, 5-49 Fan panel, 6-113 fan model, 6-112 user-defined, 6-112, 6-141 fans, 9-2 postprocessing for, 27-15, 27-31, 27-93 far-field boundary, 6-10, 6-29, 6-50 FAS multigrid, 24-39 FAST, 3-23

Index-14

Fast Fourier Transform(FFT) customizing the input, 27-127 customizing the output, 27-128 limitations, 27-124 loading a data file, 27-126 postprocessing, 27-123 using, 27-126 windowing, 27-124 fe2ram, 5-20 feature outline, 27-7 Fick’s law, 7-42 FIDAP, 1-4 FIDAP neutral files, 3-13, 5-21 Field Function Definitions panel, 29-47 field functions custom, 29-45 sample, 29-49 saving, 29-47 units of, 4-2, 29-45 definitions, 29-1 for solution initialization, 24-58 Fieldview, 3-23 file format, 3-3 file suffixes, 3-2, 3-10 File XY Plot panel, 27-94 File/Batch Options..., 2-39 file/confirm-overwrite?, 3-6 File/Exit, 2-41 File/Export..., 3-23 file/export/custom-heat-flux, 11-12 File/Hardcopy..., 3-18 File/Import/ANSYS..., 3-7 File/Import/CGNS/Mesh and Data..., 3-8 File/Import/CGNS/Mesh..., 3-8 File/Import/Chemkin..., 13-35 File/Import/FIDAP..., 3-13, 5-21 File/Import/FLUENT 4 Case..., 3-12, 5-21 File/Import/GAMBIT..., 3-6 File/Import/IDEAS Universal..., 3-7, 5-16 File/Import/NASTRAN..., 3-8, 5-17 File/Import/Oppdif Flamelets..., 14-112


Index

files, 3-1 File/Import/Partition/Metis Zone..., 30-33 automatic saving of, 3-11, 9-57, 24-63, File/Import/Partition/Metis..., 30-32 24-97 File/Import/PATRAN..., 3-8, 5-18 binary, 3-2, 3-3, 3-9 File/Import/preBFC Structured Mesh..., 3-7, boundary grid, 3-17 5-15 case and data, 3-9 File/Import/Standard Flamelets..., 14-112 CGNS, 3-8 File/Interpolate..., 3-30 chemical mechanism, 13-35 file/read-bc, 3-17 compressed file/read-macros, 24-100 reading, 3-3 file/read-transient-table, 6-9 writing, 3-4 File/Read/Case and Data..., 1-10, 3-9, 3-11 flamelet, 14-113 File/Read/Case..., 1-10, 3-6, 3-7, 3-9, 3-10 format, 3-34 File/Read/Data..., 3-9, 3-10 formatted, 3-3, 3-9 File/Read/Journal..., 3-13, 3-14 grid, 3-6 File/Read/Pdf..., 14-74 hardcopy, 3-18 File/Read/Profile..., 3-15, 6-177 interpolation, 3-31 File/Read/Rays..., 11-49 journal, 3-13 File/Read/Scheme..., 3-33 log, 3-13 File/Read/View Factors..., 11-52 MPEG, 24-96, 27-76 File/Run..., 1-8, 30-4, 30-7 naming conventions for, 3-2 File/Save Layout, 3-33 numbering, 3-5, 24-100 file/set-batch-options, 2-40 overwriting, 3-6 file/write-bc, 3-17 profile, 3-15 file/write-macros, 24-100 ray, 11-47, 11-48 file/write-surface-clusters/split-angle, 11-53 reading and writing, 3-1 File/Write/Autosave..., 3-11, 9-57, 24-63 compressed, 3-3 File/Write/Boundary Grid..., 3-17 shortcuts, 3-2 File/Write/Case and Data..., 3-9, 3-11 reading multiple, 2-9 File/Write/Case..., 3-9, 3-10 recently read, 3-3 File/Write/Data..., 3-9, 3-10 searching for, 2-8 File/Write/Input..., 14-53 selecting, 2-7 File/Write/Pdf..., 14-57 shortcuts for reading and writing, 3-2 File/Write/Profile..., 3-15 surface grid, 3-17 File/Write/Start Journal..., 3-13, 3-14 text, 3-3, 3-9 File/Write/Start Particle History..., 21-75 transcript, 3-14 File/Write/Start Transcript..., 3-14 unformatted, 3-2, 3-3, 3-9 File/Write/Stop Journal, 3-13, 3-14 filled File/Write/Stop Particle History, 21-75 contours, 27-13 File/Write/Stop Transcript, 3-14, 3-15 grids, 27-6, 27-64 File/Write/Surface Clusters..., 11-51, 11-52 profiles, 27-13 filenames, 2-25


Index-15

Index

filter papers, 6-93, 6-106 fine scale mass fraction, 29-27 fine scale temperature, 29-27 fine scale transfer rate, 29-27 finite-rate reactions, 13-4 particle surface, 13-43 volumetric, 13-2 wall surface, 13-36 finite-volume scheme, 24-7 first-order accuracy, 24-8, 24-43 first-order time stepping, 24-13 fixing variable values in cell zones, 6-183 fl42seg, 5-15, 5-21 flame front, 15-3 thickening, 15-4 flame sheet chemistry, 14-7 flame speed, 15-4 flame stretching, 15-6 Flamelet Generation panel, 14-101 flamelet model, 14-8, 14-91 approaches generation, 14-95 import, 14-98 assumptions, 14-92 chemistry files, 14-101, 14-116 files, 14-113 chemistry, 14-116 standard, 14-114 flamelet generation approach, 14-95 inputs for, 14-100 flamelet import approach, 14-98 inputs for, 14-110 importing a flamelet file, 14-112 inputs for, 14-100 look-up tables, 14-107 merging flamelet files, 14-113 multiple-flamelet import approach OPPDIF files, 14-99 standard format files, 14-99 non-adiabatic, 14-97 look-up tables, 14-109 OPPDIF files, 14-99 parameters, 14-102

Index-16

PDF table parameters, 14-104 prePDF setup, 14-100, 14-110 restrictions, 14-92 scalar dissipation, 14-94, 14-107 single-flamelet import approach OPPDIF files, 14-98 standard format files, 14-98 standard format files, 14-99, 14-114 strain rate, 14-94 theory, 14-92 Flamelet Model Parameters panel, 14-111 FLAMELET-MODEL/MERGE-FLAMELETS, 14-113 Flamelet-PDF-Table panel, 14-107 flex-cycle multigrid, 24-38, 24-105 floating operating pressure, 8-24 flow direction at mass flow inlets, 6-35 at pressure far-field boundaries, 6-51 at pressure inlets, 6-20 flow distributors, 6-93 flow rate, 28-7 for multiphase calculations, 22-95 flow variable definitions, 29-1 flue gas recycle in non-premixed combustion model, 14-16, 14-19 FLUENT model compatibility, A-1 .fluent file, 3-33 fluent -help, 1-11 FLUENT 4, 1-13 FLUENT 4 case files, 3-12, 5-21 FLUENT/UNS, 1-13 FLUENT/UNS case and data files, 3-12 non-conformal, 5-30 FLUENT/UNS case files, 5-21 Fluid panel, 6-88, 6-98 fluid materials, 6-88, 7-3, 13-18 fluid phase reactions, 12-1 fluid zone, 6-88 fluid-fluid multiphase flows, 22-24 fluidized beds, 20-2, 20-4, 20-6, 20-7


Index

flux difference splitting, 24-26 Flux Reports panel, 28-2 flux through a surface, 28-8 fluxes through boundaries, 28-2 Force Monitors panel, 24-79 Force Reports panel, 28-5 forces coefficients of, 28-16 monitoring, 24-78 on boundaries, 28-4 formation enthalpy, 7-50, 13-28 formation rate, 29-31 formats of case and data files, 3-34 Fourier Transform (Spectral Analysis) panel, 27-126 free stream, 6-50 free vortex, 8-13 free-surface flow, 20-2, 20-4, 20-6 freezing, 23-2 frictional viscosity, 22-67 frozen flux formulation, 24-23, 24-62 fuel rich flames, 14-8, 14-50 full multicomponent diffusion, 7-43 full-approximation storage (FAS) multigrid, 24-30, 24-39 fully-developed flow, 8-5 Fuse Face Zones panel, 5-48 fusing face zones, 5-48

governing equations, 8-3 discretization of, 24-7 in integral form, 24-16, 24-23 source term additions to, 6-187 gradient dynamic adaption, 25-23 Gradient Adaption panel, 25-20 gradient adaption, 25-18 gradient option, 24-15 setting, 24-42 granular bulk viscosity, 22-67 granular conductivity, 22-67, 29-27 granular flows, 20-5, 20-6, 22-24 stresses in, 22-24 granular temperature, 22-33 granular viscosity, 22-67 graphical user interface (GUI), 2-1 customizing the, 2-19 graphics, 27-1 captions, 27-35 display windows, 2-16 active, 27-34 closing, 27-34 multiple, 27-34 opening, 27-34 Windows features, 2-16 hardcopy files, 3-18 overlay of, 27-33 title, 27-36 GAMBIT, 1-2 window dumps, 3-21 GAMBIT grid file, 3-6, 5-14 Graphics Hardcopy panel, 3-18 gas constant, 29-27 Graphics Periodicity panel, 27-59 gas law, 7-14, 7-16, 7-18, 7-53, 8-23 Grashof number, 11-78 gaseous solid catalyzed reactions, 13-47 gravitational acceleration, 11-80, 21-6 gauge pressure, 7-53 gray-band model, 11-28 Gauss-Seidel method, 24-30 grid, 1-2, 5-1, 29-28 GeoMesh, 1-3 activating zones, 5-52 GeoMesh grid file, 3-6, 5-14 adaption, 5-12, 25-1 geometric reconstruction scheme, 22-9, aspect ratio, 5-10, 5-13 22-54 C-type, 5-49 getting started, 1-1 checking the, 5-30 Gidaspow model, 22-29 coarse levels, 24-51 global time stepping, 24-14 gnuplot, 9-93 coarsening, 25-10, 25-11, 25-13


Index-17

Index

based on gradient, 25-22 near walls, 25-35 colors in display, 27-6 deactivating zones, 5-52 deleting zones, 5-52 display, 27-2 extrusion, 5-50 files, 3-6 new, 3-9 reading multiple, 5-22, 5-48 filters fe2ram, 5-20 fl42seg, 5-15 partition, 30-33 tmerge, 5-22 importing, 5-14 ANSYS files, 5-19 CGNS, 3-8 FIDAP files, 5-21 FLUENT 4 files, 5-21 FLUENT/UNS files, 5-21 GAMBIT files, 5-14 GeoMesh files, 5-14 I-DEAS files, 5-16 ICEMCFD files, 5-15 NASTRAN files, 5-17 PATRAN files, 5-18 preBFC files, 5-14 RAMPANT files, 5-21 TGrid files, 5-14 interfaces, 5-24, 9-33, 9-35 creating, 5-28, 9-39 deleting, 5-29, 9-40 recreating, 5-30 shapes of, 9-33 memory usage, 5-34 motion of, 9-1, 9-31, 9-44 multiblock, 5-22, 5-48 non-conformal, 5-24 requirements, 5-26 O-type, 5-49

Index-18

partitioning, 30-18 automatic, 30-19 check, 30-33 filter, 30-32 guidelines, 30-21 inputs for, 30-19, 30-22 interpreting statistics, 30-34 manual, 30-21 methods, 30-26 METIS, 30-32 optimizations, 30-28 report, 5-36, 30-25 statistics, 5-36, 30-25 within registers, 30-25 within zones, 30-25 periodicity, 5-46 quality, 5-12 reading, 5-14 refinement, 6-187, 25-2, 25-5, 25-8, 25-10, 25-13 at boundaries, 25-14 based on cell volume, 25-32 based on gradient, 25-18 based on isovalue, 25-25 dynamic, 25-23 in a region, 25-28 near walls, 25-35 reordering, 5-52 requirements, 5-11 axisymmetric, 5-11 dynamic meshes, 9-47, 9-50, 9-52 multiple reference frames, 9-17 non-conformal, 5-26 periodic, 5-11 rotating flow, 8-15 rotating reference frame, 9-8 sliding meshes, 9-38 swirling flow, 8-15 turbulence, 10-61 volume of fluid (VOF) model, 22-55


Index

resolution, 5-10, 5-12, 10-61, 25-2, 25-5 rotation of, 9-1 scaling, 5-37 setup constraints, 5-11 axisymmetric, 5-11 dynamic meshes, 9-47, 9-50, 9-52 multiple reference frames, 9-17 non-conformal, 5-26 periodic, 5-11 rotating flow, 8-15 rotating reference frame, 9-8 sliding meshes, 9-38 swirling flow, 8-15 turbulence, 10-61 volume of fluid (VOF) model, 22-55 setup time, 5-9, 25-2 size, 5-33 skewness, 5-10, 5-13 smoothing, 25-48 spacing at walls, 5-12 in laminar flows, 6-78 in turbulent flows, 10-61, 25-35 storage points, 24-7 topologies, 1-5, 5-2 translation, 5-38 type, 5-2 units of, 4-2 velocity, 29-28 zone information, 5-35 Grid Adaption Controls panel, 25-44 Grid Display panel, 27-2 Grid Interfaces panel, 5-28, 9-39 Grid/Check, 5-30 Grid/Fuse..., 5-48 Grid/Info/Memory Usage, 5-34 Grid/Info/Partitions, 5-36 Grid/Info/Size, 5-33 Grid/Info/Zones, 5-35 Grid/Merge..., 5-39 grid/modify-zones/extrude-face-zone-delta, 5-51 grid/modify-zones/extrude-face-zone-para, 5-51 grid/modify-zones/fuse-face-zones, 5-49 grid/modify-zones/make-periodic, 5-46


grid/modify-zones/matching-tolerance, 5-46, 5-49 grid/modify-zones/repair-periodic, 5-32 grid/modify-zones/slit-face-zone, 5-50 grid/modify-zones/slit-periodic, 5-47

Grid/Reorder/Domain, 5-51 Grid/Reorder/Print Bandwidth, 5-51 Grid/Reorder/Zones, 5-51 Grid/Scale..., 5-37 Grid/Separate/Cells..., 5-41, 5-44 Grid/Separate/Faces..., 5-41, 5-42 Grid/Smooth/Swap..., 25-48 Grid/Translate..., 5-38, 5-39 Grid/Zone/Activate..., 5-52, 5-54 Grid/Zone/Deactivate..., 5-52 Grid/Zone/Delete..., 5-52 GT-Power, 6-192 GUI, 2-1 customizing the, 2-19 hanging node adaption, 25-6, 25-8, 25-45 hanging nodes, 5-2, 25-8 hardcopy files for animation, 24-96, 27-76 options, 3-18 saving files, 3-18 automatically, 24-100 using gray-scale colormap, 27-39 HCN density, 29-28 heat capacity, 7-36 Heat Exchanger panel, 6-158 heat exchanger default core model, 6-163 reading parameters from an external file, 6-165 heat exchanger groups, 6-150, 6-157 Heat Exchanger Model panel, 6-164 heat exchanger models, 6-120, 6-150, 6-162 defining, 6-162 effectiveness, 6-154, 6-163 group connectivity, 6-157 heat rejection, 6-155 inputs, 6-158 macros, 6-151, 6-160

Index-19

Index

NTU model, 6-150 features, 6-152 restrictions, 6-151 reports, 6-174 restrictions, 6-151 simple effectiveness model, 6-150 features, 6-152 restrictions, 6-151 heat flux, 6-80, 28-2, 29-40 exporting data, 11-12 wall, 6-79 heat of formation, 7-50 heat of reaction, 13-25 surface reaction, 13-39 heat rejection, 6-155 heat exchangers, 6-155 heat sources, 6-92, 6-120, 6-187, 6-189, 11-5 heat transfer, 11-1 boundary conditions, 6-80 at walls, 6-63 convective and conductive, 11-1 theory, 11-2 inputs for, 11-6 overview of models, 11-1 periodic, 11-71 radiation, 6-80, 11-13 rate, 28-3 reporting, 11-10 for radiation, 11-67 solution procedures, 11-9 to the wall, 6-79 volume sources, 6-92, 6-187 heat transfer coefficient, 5-12, 28-16, 29-38 calculations of, 6-80 helicity, 29-28 help, 1-17, 2-29 text interface, 2-34 Help/Context-Sensitive Help, 2-30 Help/More Documentation..., 2-32 Help/User’s Guide Contents..., 2-30 Help/User’s Guide Index..., 2-32 Help/Using Help..., 2-32 Help/Version..., 2-34

Index-20

Herschel-Bulkley panel, 7-28 Herschel-Bulkley model, 7-27 hidden line removal, 27-47 hidden surface removal, 27-48 histograms, 27-88, 27-99, 28-15 Hosts Database panel, 30-16 hosts for parallel processing, 30-16 HTML files, 1-17 hydraulic diameter, 6-13 hydrostatic head, 6-19 hydrotransport, 20-2, 20-4, 20-7 I-DEAS, 1-3, 3-23 I-DEAS Universal file, 3-7, 5-16 IC Zone Motion panel, 9-68 ICEMCFD grid file, 5-15 Icepak, 1-4 ideal gas law, 6-50, 7-16, 7-18, 7-53, 8-23, 21-79 ignition source, 13-32 impeller-baffle interaction, 9-13 impellers, 9-2 multiple, 9-14 implicit interpolation scheme, 22-12, 22-55 implicit time stepping, 24-13, 24-29 in-cylinder model parameters, 9-62 in-cylinder models, 9-74 crevice model, 9-84 output file, 9-93 postprocessing, 9-91 theory, 9-87 incident radiation, 29-28, 29-38 incomplete particle trajectories, 21-115 incompressible flow calculations at inlet pressure boundaries, 6-23 inertial reference frame, 9-2 Information dialog box, 2-5 initial conditions, 24-55 discrete phase, 21-76 initializing the solution, 24-55 using average values, 24-55 Injections panel, 21-79 inlet boundaries, 6-25


Index

Inlet Operating Conditions panel, 14-103 Inlet Vent panel, 6-40 inlet vent boundary, 6-10, 6-40 Intake Fan panel, 6-42 intake fan boundary, 6-11, 6-42 integer entry, 2-13 integral reporting, 24-83, 24-87, 28-7, 28-12 integral time scale, 21-12 Integration Parameters panel, 17-10 interface zone, 9-33, 9-39 contour display, 9-43 Interior Cell Zone Selection panel, 19-9 interior zone, 6-2, 6-113, 6-123, 9-35 internal energy, 29-28 interphase exchange coefficients, 22-25 Interpolate Data panel, 3-30 interpolation, 3-30, 24-8, 24-16 file format, 3-31 grid-to-grid, 3-30 interrupt, 2-27 of calculations, 24-60 Intrinsic Combustion Model panel, 21-111 inviscid flow, 8-28 equations, 8-28 inputs for, 8-30 solution, 8-30 ISAT algorithm, 17-7 Iso-Clip panel, 26-22 Iso-Surface panel, 26-20 Iso-Value Adaption panel, 25-25 isosurfaces, 26-2, 26-20 isotropic scattering phase function, 7-41 IsoValue panel, 27-67 isovalue, 26-21, 26-22 adaption, 25-25 modification, 27-67 Iterate panel, 24-59, 24-64 iteration, 24-59 control during, 24-97 interrupt of, 24-60 iterative procedure, 24-2, 24-4, 24-59


jet breakup, 20-5, 22-2, 22-56 journal files, 3-13 k- model, 10-15 model compatibility, A-1 realizable, 10-7, 10-19 RNG, 10-6, 10-16 standard, 10-6, 10-15 k-ω model model compatibility, A-1 SST, 10-8 standard, 10-8 key frame, 27-72 kinetic theory, 7-22, 7-23, 7-30, 7-37, 7-48 in granular flows, 20-5 parameters, 7-51 Kinetics/Diffusion Limited Combustion Model panel, 21-111 Knudsen number, 13-39, 21-8 Kobayashi model, 21-27 Lagrangian discrete phase model, 21-1 laminar finite rate model model compatibility, A-1 laminar finite-rate model, 13-4 laminar flow shear stress, 6-78 laminar viscosity, 29-30 laminar zone, 6-89, 6-109 Laplacian smoothing, 25-48 large eddy simulation (LES), 10-43 boundary conditions, 10-47 model compatibility, A-1 reporting mean flow quantities, 10-82 solution strategies, 10-77 subgrid-scale models, 10-45 RNG-based model, 10-46 Smagorinsky-Lilly model, 10-45 latent heat, 23-9 of vaporization, 14-89, 21-109 legend, 27-35, 27-95 length scale, 6-13 Lennard-Jones parameters, 7-22, 7-48, 7-51

Index-21

Index

LES, 10-2, 10-43 model compatibility, A-1 lever rule, 23-2, 23-3 Lewis number, 13-3, 13-39 lift coefficient, 24-78 lift force, 21-9, 21-73 lift forces in multiphase flow, 22-22 Lights panel, 27-44 lights, 27-43, 27-63 line solvers, 24-30 line surfaces, 26-2, 26-9 using the line tool, 26-10 line tool, 26-10 Line/Rake Surface panel, 26-9 linear pressure-strain model, 10-37 linear-anisotropic scattering phase function, 7-41, 11-23, 11-27, 11-31 linearization, 24-4 liquid fraction, 23-3, 29-29 liquid fuel combustion, 14-34, 21-21 in non-premixed combustion model, 14-42, 14-84 liquid surface tension, 22-57 liquidus temperature, 23-9 list drop-down, 2-14 multiple selection, 2-14 single selection, 2-13 Load Balance panel, 30-37 load balancing, 25-2, 25-24 local cylindrical coordinate system for boundary condition inputs, 6-21 local cylindrical velocities for boundary condition inputs, 6-27 log files, 3-13 logarithmic plots, 27-102 Lookup Points panel, 14-66 loss coefficient, 6-120 heat exchanger, 6-165 inlet vent, 6-41 outlet vent, 6-58 radiator, 6-123 low-Reynolds-number flows, 10-17

Index-22

LSF checkpointing, 2-40, 30-43 checkpointing a FLUENT job, 30-47 checkpointing and restarting, 30-44 configuration, 30-45 migrating FLUENT jobs, 30-47 overview, 30-43 parallel processing, 2-40, 30-43 restarting a FLUENT job, 30-47 serial processing, 2-40, 30-43 submitting a FLUENT job, 30-46 using with FLUENT, 30-48 lumped parameter models, 6-112 Mach number, 6-51, 8-21, 8-27, 29-29 macros, 6-151, 6-160, 24-98 magnifying the display, 27-49, 27-54 Manage Adaption Registers panel, 25-38 manuals, 1-17 using the, UTM-1 Marangoni stress, 6-71, 6-72 mass diffusion, 13-3 to surfaces, 13-38 Mass Diffusion Coefficients panel, 7-46, 7-47 mass diffusion coefficients, 7-42, 7-50, 13-28, 29-25, 29-28 kinetic theory, 7-48 mass flow inlet boundary, 6-10, 6-32 mass flow rate, 6-33, 28-3, 28-7 through a surface, 28-9 mass flow split, 6-56 mass flux, 6-33, 28-2 mass fraction, 29-29 mass sources, 6-189 mass transfer, 22-44 mass-averaged quantities, 28-9, 28-13 Mass-Flow Inlet panel, 6-33 massively parallel machines, 30-4, 30-7 Materials panel, 7-3, 13-15, 14-79 materials, 7-3 copying from the database, 7-5 creating new, 7-7


Index

database, 7-3, 13-12, 13-18 customizing, 7-12 data sources, 7-5 deleting, 7-7 discrete phase, 7-3, 21-83, 21-105 mixture, 7-3, 13-12 modifying, 7-3 PDF mixture, 14-79 renaming, 7-5 reordering, 7-8 saving, 7-7 Maxwell-Stefan equations, 7-43 mean beam length, 7-39 mean flow quantities, 24-69 mean free path, 13-39, 21-8 memory usage, 5-34 in multigrid, 24-52, 24-107 in the coupled implicit solver, 1-14 menu bar, 2-4 Merge Zones panel, 5-39 merging zones, 5-39 meridional view, 27-67 mesh, 1-2 Mesh Motion panel, 9-67 message passing library, 30-2 metallurgy, 23-1 METIS, 30-32 Mirror Planes panel, 27-60 mixed convection, 11-78, 24-48 inputs for, 11-79 mixed-is-burned chemistry, 14-7, 14-45 mixing, 12-1 mixing plane model, 9-16, 9-20 boundary conditions, 9-26 enthalpy conservation, 9-29 fixing the pressure level, 9-29 mass conservation, 9-24 model compatibility, A-1 patching values, 24-58 postprocessing, 9-30 pressure boundary conditions in, 9-26 setup, 9-25 solution initialization, 24-56


solution procedures, 9-30 swirl conservation, 9-24, 9-29 theory, 9-21 total enthalpy conservation, 9-25 velocity formulation in, 9-25 with non-reflecting boundary conditions, 6-141 Mixing Planes panel, 9-27 mixing rate, 13-14, 13-24 mixing tanks, 9-2, 9-3, 9-14 MixSim, 1-4 mixture fraction, 14-2 boundary conditions, 14-77 conservation of, 14-4 limitations on, 14-18 secondary, 29-35 variance, 14-5, 29-29 secondary, 29-35 mixture materials, 7-3, 13-12 creating, 13-17 PDF, 14-79 mixture model, 20-5 body forces, 22-72 drift flux model, 22-18 drift velocity, 22-18 droplet diameter, 22-63 limitations, 22-4 model compatibility, A-1 momentum equation, 22-17 overview, 22-3 patching initial volume fraction, 22-89 properties, 22-62 relative velocity, 22-18 slip velocity, 22-18 solution strategies, 22-91 theory, 22-16 volume fraction, 22-19 mixture multiphase model cavitation model, 22-45 mass transfer, 22-44 mixture properties, 13-15, 13-28 modified turbulent viscosity, 29-29

Index-23

Index

molar concentration species, 29-30 mole fraction, 29-30 soot, 29-30 molecular heat transfer coefficient, 7-51, 15-12 molecular viscosity, 29-30 molecular weight, 7-16, 7-17, 13-28 moment coefficient, 24-78, 28-16 moments, 28-4 momentum accommodation coefficient, 13-29 momentum equation, 8-3, 8-29 momentum sources, 6-189 monitoring forces and moments, 24-63, 24-78 residuals, 24-70 solution convergence, 24-70 statistics, 24-77 surfaces, 24-63, 24-82 volume integrals, 24-85 Monte Carlo method, 17-3 Morsi and Alexander model, 22-26 mouse functions, 27-49 GAMBIT-style, 27-49 manipulation, 27-47, 27-49 probe, 27-49 Mouse Buttons panel, 27-50 moving domains model compatibility, A-1 moving grid, 9-1 moving reference frames, 9-1 patching values, 24-58 postprocessing, 27-19 solution initialization, 24-56 moving walls, 6-68 MPEG file, 24-96, 27-76 MPGS, 3-23 mud, 7-28 Multi-Stage Parameters panel, 24-112

Index-24

multi-stage scheme, 24-27 controls for, 24-111 modifying, 24-112 stability, 24-49 multiblock grids, 5-22, 5-48 multicomponent diffusion, 7-43 Multigrid Controls panel, 24-52, 24-104–24106, 24-109, 24-111 multigrid solver, 24-30 algebraic (AMG), 24-35 inputs for, 24-103 coarsening parameters, 24-107 cycles, 24-32 default parameters, 24-108 F cycle, 24-37 flex cycle, 24-38, 24-105 full-approximation storage (FAS), 24-39 creating coarse grid levels for, 24-51 inputs for, 24-51, 24-108 levels, 24-51 inputs for algebraic (AMG), 24-103 full-approximation storage (FAS), 24-51, 24-108 limitations, 24-51 memory usage, 24-52, 24-107 performance monitoring, 24-104 prolongation, 24-32 residual reduction rate, 24-38 residual reduction tolerance, 24-107 restriction, 24-32 termination criteria, 24-39, 24-107 turning off, 24-107, 24-108 V cycle, 24-33, 24-105 W cycle, 24-33, 24-105 with parallel solver, 24-105 multiphase flow, 20-1 body forces, 22-72, 24-21 boundary conditions, 22-75 cavitation model, 22-45


Index

choosing a model for, 20-6, 22-2 compressible, 22-89 Euler-Euler approach, 20-5 Euler-Lagrange approach, 20-4 Eulerian model, 20-5, 22-5, 22-20 examples, 20-4 fluid-fluid, 22-24 fluid-solid, 22-24 gas-liquid, 20-2 gas-solid, 20-2 granular, 22-24 homogeneous, 22-19 inputs for, 22-50 cavitation model, 22-57 heat transfer in Eulerian model, 22-71 mass transfer, 22-56 interphase exchange coefficients, 22-25 introduction, 20-1 liquid-liquid, 20-2 liquid-solid, 20-2 mixture model, 20-5, 22-3, 22-16 model compatibility, A-1 overview, 20-1 particulate loading, 20-7 postprocessing, 22-93 regimes, 20-2 reporting flow rates, 22-95 solution strategies, 22-90 Stokes number, 20-8 volume of fluid (VOF) model, 20-5, 22-2, 22-7 Multiphase Model panel, 22-53 multiple graphics windows, 27-34 multiple reference frame model compatibility, A-1 multiple reference frames, 9-3, 9-13 boundary conditions, 9-18 discrete phase in, 9-15, 21-3 for axisymmetric flow, 9-16 grid setup, 9-17, 9-18 patching values, 24-58 pathlines, 9-15 postprocessing, 9-19, 27-19, 28-17


pressure boundary conditions in, 9-19 restrictions of, 9-14 setup, 9-18 solution initialization, 24-56 solution strategies, 9-19 steady flow approximation, 9-13 theory of, 9-16 velocity formulation in, 9-16, 9-18 multiple selection list, 2-14 multiple surface reactions model, 13-48, 21-38 multiprocessor workstations, 30-4, 30-7 mushy zone, 23-3, 23-4 NASTRAN, 1-3, 3-23 NASTRAN file, 3-8, 5-17 natural convection, 11-78, 24-17, 24-48 boundary conditions, 6-19 high-Rayleigh-number flows, 11-82 in a closed domain, 11-78 inputs for, 11-79 natural time, 7-27 Navier-Stokes equations, 8-3 filtered, 10-44 near-wall flows, 10-17 near-wall treatments, 10-47 neighbor correction, 24-21 Network Configuration panel, 30-13 NH3 density, 29-30 NIST real gas model, 7-55 limitations, 7-56 NO density, 29-30 no-slip condition, 6-62, 6-71 node values, 24-7, 29-2 for contours, 27-15 for pathlines, 27-30 for XY plots, 27-93 nodes display of, 27-6, 27-46 original, 25-11, 25-47 refinement, 25-11, 25-47 removing, 25-47 noise, 19-2 non condensable gas, 22-57

Index-25

Index

non-conformal grids, 5-24 requirements for, 5-26 non-equilibrium chemistry, 14-8 non-equilibrium wall functions, 10-54, 10-55 non-gray radiation, 11-16, 11-28 boundary conditions, 11-33 inputs for, 11-56 limitations, 11-18 particulate effects, 11-33 non-inertial reference frame, 9-2 non-isotropic thermal conductivity user-defined, 6-108 non-Newtonian fluids, 7-24 Non-Newtonian Power Law panel, 7-26 non-Newtonian power law, 7-25 non-Newtonian viscosity, 7-24 Carreau model, 7-26 Cross model, 7-27 Herschel-Bulkley model, 7-27 power law, 7-25 non-premixed combustion model, 14-1 adding species to the prePDF database, 14-118 boundary conditions, 14-77 condensed phase species, 14-38 empirical fuels, 14-36, 14-42 equilibrium chemistry, 14-8, 14-35, 14-43, 14-50 flamelet model, 14-91 flue gas recycle, 14-16, 14-19 FLUENT setup, 14-72 FLUENT solution, 14-79 secondary mixture fraction parameters, 14-80 for coal combustion, 14-34, 14-39, 14-84 for liquid fuels, 14-34 fuel inlet temperature, 14-44, 14-51, 14-78 limitations of, 14-2, 14-18 look-up tables, 14-13, 14-16, 14-25, 14-47, 14-56, 14-62, 14-64 flamelet model, 14-107

Index-26

model compatibility, A-1 multiple fuel inlets, 14-16, 14-18 non-adiabatic look-up tables, 14-109 non-adiabatic form, 14-13, 14-34 non-equilibrium chemistry, 14-8, 14-91 partial equilibrium, 14-8, 14-47 PDF functions in, 14-12, 14-35, 14-57 postprocessing, 14-82 prePDF errors, 14-68 prePDF setup, 14-29, 14-100, 14-110 secondary stream, 14-33 solution parameters, 14-80 solution parameters, 14-47 solution procedure, 14-22 species selection, 14-39 stability issues, 14-56, 14-68 using old PDF files, 14-74 non-reacting species transport, 13-49 non-reflecting boundary conditions, 6-131 limitations of, 6-131 overview of, 6-131 parallel processing with, 6-141 theory, 6-132 using, 6-140 with mixing plane model, 6-141 Nonadiabatic-Table panel, 14-65 normalization, 28-16 of residuals, 24-71, 24-72, 24-75 NOx Model panel, 18-27 NOx model, 14-8, 14-40, 18-1 coal, 18-16, 18-29 fuel, 18-11, 18-28 gaseous fuel, 18-29 inputs for, 18-26 liquid fuel, 18-12, 18-29 model compatibility, A-1 PDF functions in, 18-23 prompt, 18-8, 18-27 reburn, 18-22, 18-28 restrictions, 18-2 thermal, 18-3, 18-27


Index

solution parameters, 11-65 turbulence-chemistry interaction, 18-23 under-relaxation for, 18-26 theory, 11-22 user-defined functions for, 18-31 packed beds, 6-93, 6-104 NTU model, 6-150 packing limit, 22-68 features, 6-152 Page Setup panel, 2-17 restrictions, 6-151 panel layout, 3-33 nuclei formation, 18-35 panels, 2-9 numerical diffusion, 5-10, 24-43 Parallel Connectivity panel, 30-17 numerical scheme, 24-2 parallel processing, 30-1 Nusselt number, 29-38 efficiency, 30-1 active cell partition, 29-17 O-type grids, 5-49 architecture, 30-1 oil-flow pathlines, 27-30 automatic partitioning, 30-19 on-line help, 2-29 cell partition, 29-20 Operating Conditions panel, 7-16, 7-17, 7-54, checkpointing, 2-40 8-23, 11-80, 14-43, 21-6 communication, 30-36 operating density, 11-81 hosts database, 30-16 operating pressure, 7-16–7-19, 7-53, 8-23, introduction, 30-1 11-80 floating, 8-24 load balancing, 30-36 operating temperature, 11-81 load distribution, 30-35 OPPDIF, 14-95, 14-111 manual partitioning, 30-21 opposed-flow diffusion flamelet, 14-92 multigrid settings for, 24-105 optical thickness, 11-16 network configuration, 30-13 Orient Profile panel, 6-180 network connectivity, 30-17 orienting boundary profiles, 6-180 on a multiprocessor workstation, original nodes, 25-11, 25-47 30-4, orthographic, 27-54 30-7, 30-10 Orthotropic Conductivity panel, 7-33 on a workstation cluster, 30-6, orthotropic thermal conductivity, 7-33, 7-34 30-9, 30-10, 30-13 outflow boundary, 6-10, 6-54 partition surfaces, 26-4 outflow gauge pressure, 6-29 partitioning, 30-1, 30-18 Outlet Vent panel, 6-58 performance, 30-36 outlet vent boundary, 6-11, 6-58 recommended procedure, 30-1 outline display, 27-2, 27-7 starting the solver, 30-4 overlay of graphics, 27-33 on a LINUX workstation cluster, 30-9 on a multiprocessor LINUX machine, P-1 radiation model, 11-14 30-7 advantages, 11-17 on a multiprocessor UNIX machine, boundary conditions, 11-25, 11-26 30-4 limitations, 11-17 on a multiprocessor Windows maparticulate effects in, 11-23 chine, 30-10 properties, 7-38 residuals, 11-66 on a UNIX workstation cluster, 30-6


Index-27

Index

on a Windows workstation cluster, 30-10 stored cell partition, 29-36 troubleshooting, 30-15 using LSF, 2-40, 30-43 using SGE, 2-40, 30-38 Parallel/Auto Partition..., 30-20 Parallel/Load Balance..., 30-37 Parallel/Network/Configure..., 30-13 Parallel/Network/Database..., 30-16 parallel/network/path, 30-15 Parallel/Partition..., 30-22 parallel/partition/set/load-distribution, 30-35 Parallel/Show Connectivity..., 30-17 Parallel/Timer/Reset, 30-36 Parallel/Timer/Usage, 30-36 partial equilibrium model, 14-8, 14-47, 14-50 partially premixed combustion model, 16-1 limitations of, 16-1 model compatibility, A-1 overview, 16-1 theory, 16-2 using, 16-4 partially premixed flames, 15-2, 16-1 Partially Premixed Model Properties panel, 16-6 particle, 21-1 accretion, 21-73, 21-105 boiling, 21-24 cloud tracking, 21-14, 21-95 devolatilization, 21-25 erosion, 21-73, 21-105 heat/mass transfer calculations, 21-18 incomplete, 21-115 inert heating or cooling, 21-19 initial conditions, 21-71, 21-76 laws, 21-18 custom, 21-83, 21-96 radiation, 11-16, 11-23, 11-32, 11-44, 21-20, 21-23, 21-112 size distribution, 21-10, 21-85 sub-micron, 21-6, 21-8

Index-28

surface combustion, 21-34 trajectory calculations, 21-5, 21-74 trajectory reports, 21-124, 21-128 alphanumeric reporting, 21-131 display of, 21-121 PDF tracking, 17-17 step-by-step track report, 21-128 unsteady, 21-129 turbulent dispersion, 21-12 vaporization, 21-21 Particle Summary panel, 21-134 particle summary reporting, 21-134 particle surface reactions, 13-16, 13-20, 13-43 catalyst species, 13-48 gaseous solid catalyzed reactions, 13-47 inputs for, 13-47 solid decomposition reactions, 13-46 solid deposition reactions, 13-46 solid-solid reactions, 13-46 theory, 13-43 particle tracking, 21-74 Particle Tracks panel, 21-121 particle-laden flow, 20-2, 20-4, 20-6 particulate loading, 20-7 particulate reactions, 12-1 partition boundary cell distance, 29-30 Partition Grid panel, 30-22 partition neighbors, 29-30, 30-26 Partition Surface panel, 26-4 partition surfaces, 26-2, 26-4 partitioning, 29-20, 29-30, 30-1, 30-18 automatic, 30-19 check, 30-33 filter, 30-32 guidelines, 30-21 inputs for, 30-19, 30-22 manual, 30-21 methods, 30-26 METIS, 30-32 optimizations, 30-28 report, 5-36, 30-25


Index

statistics, 5-36, 30-25 interpreting, 30-34 using dynamic mesh model, 30-24 within registers, 30-25 within zones, 30-25 passage loss coefficient, 27-112 Patch panel, 24-57 patching field functions, 24-57 initial values, 24-55, 24-57 Path Lines panel, 27-25 Path Style Attributes panel, 27-28 Pathline Attributes panel, 27-69 pathlines, 26-2, 27-25 animation of, 27-69 in multiple reference frames, 9-15 oil-flow, 27-30 reversing, 27-29 twisting, 27-28 XY plots along trajectories, 27-30 PATRAN, 1-3, 3-23 PATRAN Neutral file, 3-8, 5-18 PDF files, 1-23 PDF reaction, 17-5 Pdf-Table panel, 14-62 Peclet number, 24-9 perforated plates, 6-93, 6-105 Periodic panel, 6-84, 8-10 periodic boundaries, 5-11, 5-32, 5-49, 6-84, 9-35, 27-58 creating, 5-46 slitting, 5-47 periodic flow, 8-5 constraints, 8-6 inputs for the coupled solvers, 8-9 inputs for the segregated solver, 8-8 pressure, 8-7 theory, 8-6 periodic heat transfer, 11-71 constant flux, 11-72 constant temperature, 11-72 constraints, 11-71 inputs for, 11-74


postprocessing, 11-76 restrictions, 11-71 solution strategies, 11-75 theory, 11-72 Periodicity Conditions panel, 8-8 permeability, 6-94 perspective, 27-54 phase, 20-1 defining, 22-58 for Eulerian model, 22-64 for mixture model, 22-62 for VOF model, 22-58 granular, 22-66 diameter, 22-63, 22-66, 29-22 drag (mixture), 22-63 interaction, 22-68 Phase Interaction panel, 22-60, 22-63, 22-64, 22-68 Phases panel, 22-58 Piecewise Polynomial Profile panel, 7-11 Piecewise-Linear Profile panel, 7-10 PISO algorithm, 24-20, 24-47 neighbor correction, 24-21 skewness correction, 24-21 skewness-neighbor coupling, 24-21 under-relaxation, 24-47 pixelation, 11-29, 11-55 planar sector, 9-35 Plane Surface panel, 26-13 plane surfaces, 26-2, 26-13 using the plane tool, 26-15 plane tool, 26-15 planning the analysis, 1-5 Playback panel, 24-92 plot axes, 27-101 plot types, 27-87 plot/circum-avg-axial, 27-96 plot/circum-avg-radial, 27-96 plot/fft, 27-126 Plot/FFT..., 27-126 Plot/File..., 27-94 Plot/Histogram..., 27-99 Plot/Prune Input Signal panel, 27-127

Index-29

Index

Plot/Residuals..., 24-73, 27-99 Plot/XY Plot..., 27-89 plots external data, 27-94 histogram, 27-88, 27-99 logarithmic, 27-102 residual, 27-99 solution, 27-89, 27-99 title for, 27-95 XY, 27-88, 27-89, 27-94, 27-99 along pathline trajectories, 27-30 axis attributes, 27-100 circumferential average, 27-96 curve attributes, 27-103 file format, 27-98 turbomachinery, 27-121 pneumatic transport, 20-2, 20-4, 20-6 Point Surface panel, 26-6 point surfaces, 26-2, 26-6 using the point tool, 26-7 point tool, 26-6, 26-7 pollutant formation, 14-40, 18-1 NOx, 14-8, 14-40, 18-1 soot, 18-32 POLYFLOW, 1-4 Polynomial Profile panel, 7-9 porosity user-defined, 6-108 Porous Jump panel, 6-129 porous jump, 6-129 porous media, 6-93 1D, 6-129 enabling reactions, 6-100 heat transfer in, 6-96 inputs for, 6-98 limitations of, 6-94 physical velocity formulation, 6-109 postprocessing for, 27-15, 27-31, 27-93 power-law model, 6-95, 6-107 solution strategies, 6-110 turbulence in, 6-97 velocity formulation, 6-94, 6-99 velocity formulation setting, 24-42

Index-30

positivity rate limit, 24-54 postprocessing, 27-1 Fast Fourier Transform (FFT), 27-123 reports, 27-108, 28-1 turbomachinery, 27-105 Power Law panel, 7-22 power law, 7-21 index, 7-28 non-Newtonian, 7-25 power-law scheme, 24-8 Prandtl number, 29-25, 29-30 pre-exponential factor, 13-22 preBFC, 1-3 preBFC structured grid file, 3-7, 5-14 preBFC unstructured grid file, 3-7, 5-15 precision, 1-7, 24-70 preconditioning, 24-24, 29-30 matrix, 24-24 preferential diffusion, 15-7 premixed flames, 15-2 premixed turbulent combustion, 15-1 adiabatic, 15-8 boundary conditions, 15-13 density, 15-9 flame front, 15-3 wrinkling, 15-4 flame speed, 15-4 flame stretching, 15-6 FLUENT 5 case files, 15-15 inputs for, 15-10 model compatibility, A-1 non-adiabatic, 15-8 physical properties, 15-12 postprocessing, 15-13 preferential diffusion, 15-7 product formation, 15-3 progress variable, 15-3, 15-13 restrictions, 15-2 species concentrations, 15-10, 15-14 stretch factor, 15-6 theory, 15-3


Index

prePDF, 1-2, 14-23 error messages, 14-68 setup procedures, 14-30 pressure, 29-31 absolute, 7-53 coefficient, 28-16, 29-31 drop, 6-120 heat exchanger, 6-153, 6-163 dynamic, 29-24 gauge, 7-53 interpolation schemes, 24-16, 24-44 jump exhaust fan, 6-60 fan, 6-115 intake fan, 6-43 operating, 7-53 reference, 7-55, 22-90 relative total, 29-33 static, 29-36 total, 29-40 pressure boundary conditions, 6-17 in mixing plane model, 9-26 in multiple reference frames, 9-19 in rotating reference frames, 9-10 Pressure Far-Field panel, 6-51 pressure far-field boundary, 6-10, 6-50 Pressure Inlet panel, 6-18 pressure inlet boundary, 6-10, 6-17 Pressure Outlet panel, 6-45 pressure outlet boundary, 6-10, 6-44 pressure work, 11-3 pressure-correction equation, 24-19 Pressure-Dependent Reaction panel, 13-23 pressure-velocity coupling, 24-19 inputs for, 24-46 PRESTO, 8-17, 9-11, 11-81, 24-17, 24-44 Primary Phase panel, 22-59 Print panel, 2-17 probability density function, 14-9 problem setup, 1-5 product formation, 15-3 production of k, 29-31 Profile Options panel, 27-11


profile plotting, 27-10 scaling factor, 27-12 profiles boundary, 6-174 reading and writing, 3-15 units of, 4-2 program structure, 1-2 progress variable, 15-3, 15-13, 29-31 projected surface area, 28-6 prolongation, 24-32 properties, 7-1 composition-dependent, 13-12 database, 7-3, 13-12, 13-18, 14-1 customizing, 7-12 data sources, 7-5 discrete phase, 21-105 for solid materials, 7-2 listing, 28-18 mixture, 13-15, 13-28 modifying, 7-3 saving, 7-7 species, 13-28 temperature-dependent, 7-8 solution techniques for, 24-103 units for, 4-2, 7-8 Property Curves panel, 14-58, 14-60 pseudo-plastics, 7-26 pull velocity, 23-5, 23-6 inputs for, 23-10 pull-down menu, 2-4 pyrolysis, 21-110 quadratic pressure-strain model, 10-38 Quadric Surface panel, 26-18 quadric surfaces, 26-2, 26-18 quadrupoles, 19-2 Question dialog box, 2-7 QUICK scheme, 24-10

Index-31

Index

radial equilibrium pressure distribution, 6-46 radial pull velocity, 29-31 radial velocity, 6-28, 29-31 radiation boundary temperature correction, 11-59 radiation heat flux, 28-2, 28-3, 29-32 Radiation Model panel, 11-46, 11-49, 11-56, 11-64 radiation temperature, 29-32 radiative heat transfer, 11-13 applications, 11-15 black body temperature, 11-59 boundary conditions, 11-58 flow inlets and exits, 11-58 walls, 11-59, 11-60 choosing a model, 11-16 discrete ordinates (DO) model, 11-28 non-gray, 11-28 discrete phase, 21-71, 21-112 discrete transfer radiation model (DTRM), 11-19 clustering, 11-20, 11-48, 11-69 ray tracing, 11-20, 11-48, 11-69 emissivity, 11-16, 11-58 external, 11-16 inputs for, 11-44 non-gray, 11-16, 11-28 non-gray discrete ordinates (DO) model, 11-28 inputs for, 11-56 limitations, 11-18 optical thickness, 11-16 overview of, 11-14 P-1 model, 11-22 participation in radiation, 11-62 particulate effects, 11-16, 11-44 properties, 7-38, 11-57 reporting, 11-67 Rosseland model, 11-26 scattering, 11-16 semi-transparent media, 11-16, 11-34 inputs for, 11-45

Index-32

solution, 11-63, 11-66 soot effects on, 11-43 surface-to-surface (S2S) radiation model, 11-38 clustering, 11-40 smoothing, 11-41 turning on, 11-46 Radiator panel, 6-122 radiators, 6-120 radio buttons, 2-12 RadTherm, 3-23 rake surfaces, 26-2, 26-9 using the line tool, 26-10 RAMPANT, 1-13 RAMPANT case and data files, 3-12 non-conformal, 5-30 RAMPANT case files, 5-21 raster file, 3-20 ray file, 11-48 Ray Tracing panel, 11-47 ray tracing, 11-20, 11-47, 11-48 Rayleigh number, 11-78, 24-60 reacting flows, 13-1 choosing a model for, 12-3 diffusion reactions, 14-2 eddy-dissipation model, 13-14, 13-15 equilibrium chemistry, 14-1 finite-rate model, 13-14 inputs for, 13-13 overview of inputs for, 13-11 heterogeneous reactions, 21-35 models for, 12-1 non-premixed combustion model, 14-1 overview of, 12-1 partially premixed combustion, 16-1 pollutant formation in, 18-1 premixed combustion, 15-1 solution techniques, 24-103 Reaction Mechanisms panel, 13-26 Reaction Parameters panel, 13-22 reaction progress variable, 15-3, 15-13 reaction rate, 29-32, 29-41 surface reactions, 13-36


Index

reactions defining, 13-19 for fuel mixtures, 13-25 zone-based mechanisms, 13-25 pressure-dependent, 13-7 reversible, 13-6, 13-29 read-case, 1-10 read-case-data, 1-10 real gas models NIST, 7-55 limitations, 7-56 UDRGM, 7-55 example, 7-65, 7-70 limitations, 7-60 using the NIST model, 7-57 using the UDRGM model, 7-59 real number entry, 2-13 realizable k- model, 10-7, 10-19 model compatibility, A-1 reburning, 18-22 reference frames multiple, 9-13, 9-14 rotating, 9-1 translating, 9-2 reference pressure, 28-4 location, 7-55, 22-90 reference temperature, 13-28 Reference Values panel, 9-20, 9-31, 9-43, 28-16 reference values, 28-16 for force reports, 24-79, 28-4 reference zone, 9-20, 9-31, 9-43, 27-19, 28-17 refinement, 25-8, 25-10, 25-13 refinement nodes, 25-11, 25-47 reflected radiation flux, 29-32 refractive index, 7-41, 11-14, 29-32 refrigerant, 7-55 Region Adaption panel, 25-30 region adaption, 25-28 registers, 25-6 adaption, 25-6 combining, 25-39


deleting, 25-39, 25-41 displaying, 25-42 manipulating, 25-38 mask, 25-6 modifying, 25-41 patching with, 24-55, 24-58 relative humidity, 29-32 relative Mach number, 29-33 relative total pressure, 29-33 relative total temperature, 29-33 relative velocity, 9-9, 9-12, 9-17, 9-19, 9-26, 9-31, 9-43, 24-56, 24-58, 27-19, 29-3, 29-32, 29-34 angle, 29-33 for mixture model, 22-18 relative velocity formulation, 9-8, 9-10 in multiple reference frames, 9-16 relaxation scheme, 24-30, 24-35 relaxation sweeps, 24-33, 24-35 remote execution, 2-35 limitations on Windows systems, 2-35 rendering options, 27-46 renormalization group (RNG) theory, 10-16 reordering, 5-51 grid, 5-52 zones, 5-52 reorienting boundary profiles, 6-180 Report/Acoustics/Read and Compute Sound..., 19-13 Report/Acoustics/Write Sound Pressure..., 19-13, 19-14 Report/Discrete Phase/Histogram..., 21-133 Report/Discrete Phase/Sample..., 21-132 Report/Discrete Phase/Summary..., 21-134 Report/Fluxes..., 28-2 Report/Forces..., 28-4, 28-5 Report/Histogram..., 28-15 report/mass-flow, 22-95 Report/Projected Areas..., 28-6 Report/Reference Values..., 28-16 Report/Summary..., 28-18 Report/Surface Integrals..., 28-7, 28-10 Report/Volume Integrals..., 28-12, 28-14

Index-33

Index

reporting case settings, 28-18 conventions, 28-1 fluxes through boundaries, 28-2 forces on boundaries, 28-4 heat flux, 28-2 histograms, 28-15 mass flux, 28-2 moments, 28-4 options for velocity, 29-3 projected surface areas, 28-6 radiation heat flux, 28-2 surface integrals, 28-7 turbomachinery quantities, 27-108 volume integrals, 28-12 resetting data, 24-60 residence time, 21-125 Residual Monitors panel, 24-73 residual reduction rate criteria, 24-38, 24-107 residual smoothing, 24-28, 24-111 residuals, 29-34 definition of coupled solver, 24-72 segregated solver, 24-70 display controls, 24-74 display of, 24-73 divergence of, 24-48 for the discrete ordinates (DO) radiation model, 11-66 for the discrete transfer radiation model (DTRM), 11-66 for the P-1 radiation model, 11-66 for the surface-to-surface (S2S) radiation model, 11-67 monitoring, 24-70 normalization of, 24-71, 24-72, 24-75 plotting, 27-99 reduction of, 24-101 reduction rate, 24-39 renormalization of, 24-76 scaling of, 24-70, 24-72 XY plots, 27-99

Index-34

resistance coefficients, 6-100 user-defined, 6-100 restriction, 24-32 reversible reactions, 13-6, 13-29 Reynolds averaging, 10-2, 10-3 Reynolds number, 11-78, 28-2, 28-16, 29-21 Reynolds stress model (RSM), 10-9, 10-35 boundary conditions, 10-41 linear pressure-strain model, 10-37 model compatibility, A-1 pressure-strain term in, 10-37 quadratic pressure-strain model, 10-38 solution strategies, 10-76 Reynolds stresses, 10-4, 29-42 Ribbon Attributes panel, 27-28 rich limit, 14-6, 14-8, 14-47, 14-50, 14-51 Riemann invariants, 6-52 RIF, 14-95 risers, 20-6 RMS flow quantities, 24-69, 29-34 RNG k- model, 10-6, 10-16 model compatibility, A-1 swirl modification, 10-18 RNG-based subgrid-scale model, 10-46 root-mean-square flow quantities, 24-69 Rosin-Rammler size distribution, 21-10, 21-85 Rosseland radiation model, 11-14 advantages, 11-17 boundary conditions, 11-27 limitations, 11-17 properties, 7-38 theory, 11-26 rotating equipment, 9-3 rotating flow, 8-11, 9-1, 9-10 grid sensitivity in, 8-15 multiple reference frames, 9-14 physics of, 8-13 pressure interpolation, 24-44 turbulence modeling in, 10-7, 10-9 rotating objects in a scene, 27-66 rotating passages, 9-3


Index

rotating reference frame, 9-1, 9-13 boundary conditions, 9-9 constraints, 9-10 coordinate-system constraints, 9-8 discrete phase, 21-7 mathematical equations, 9-3 patching values, 24-58 postprocessing, 9-12, 27-19, 28-17 pressure boundary conditions, 9-10 setup, 9-9 solution initialization, 24-56 solution procedures, 9-10 velocity formulation, 9-9, 9-10 rotating the display, 27-49, 27-52 rotation axis, 6-90, 6-92, 9-8, 9-9, 9-18, 9-25 rotation vector, 9-8 rothalpy, 29-34 rotor-stator interaction, 9-2, 9-3, 9-13 round-off error, 24-70 RSM, 10-35 RUN-1DL, 14-95 Saffman’s lift force, 21-9, 21-73 sample session, 1-24 Sample Trajectories panel, 21-132 saving boundaty condtions, 3-17 case and data files, 3-11, 5-36 case files, 3-9 data files, 3-10 hardcopy files, 3-18 model settings, 3-17 panel layout, 3-33 solver settings, 3-17 scalar dissipation, 14-94, 14-107 scale (in a GUI panel), 2-15 Scale Grid panel, 5-37 scaling objects in a scene, 27-67 the display, 27-51 the grid, 5-37 vectors, 27-19


scattering, 11-16 coefficient, 7-40, 11-57, 29-35 phase function, 7-41 Delta-Eddington, 7-41, 11-31 isotropic, 7-41 linear-anisotropic, 7-41, 11-23, 11-27, 11-31 user-defined, 7-41, 11-31 Scene Description panel, 27-33, 27-61 scene description, 27-61 Scheme, 2-21, 2-23, 2-24, 2-28 loading source files, 3-33 Schiller and Naumann model, 22-26 Schmidt number, 7-42, 7-50, 13-3, 13-28 search pattern, 2-8 second-order accuracy, 24-10, 24-43 second-order time stepping, 9-42, 24-14 secondary mixture fraction, 14-3, 14-4, 29-35 variance, 29-35 Secondary Phase panel, 22-60, 22-62, 22-65, 22-66 secondary stream, 14-33 solution parameters, 14-80 sedimentation, 20-2, 20-4, 20-5, 20-7 segregated solver, 1-13, 24-2, 24-5, 24-16 density interpolation schemes, 24-18, 24-44 discretization, 24-16 frozen flux formulation, 24-23, 24-62 limitations, 1-15 porous media velocity formulation, 24-42 pressure interpolation schemes, 24-16, 24-44 pressure-velocity coupling, 24-19, 24-46 residuals, 24-70 steady-state flows, 24-22 time-dependent flows, 24-22 Select File dialog box, 2-7 Select Solver panel, 1-9, 30-4, 30-7 selecting files, 2-7

Index-35

Index

semi-transparent media, 7-41, 11-16, 11-34 inputs for, 11-45 sensible enthalpy, 11-2 Separate Cell Zones panel, 5-44 Separate Face Zones panel, 5-42 separated flows, 5-12 separating cell zones, 5-43 face zones, 5-41 sequential solution, 24-2 serial processing checkpointing, 2-40 using LSF, 2-40, 30-43 using SGE, 2-40, 30-38 Set Injection Properties panel, 14-89, 21-79, 21-81 Set Multiple Injection Properties panel, 21-97 Set Units panel, 4-3 setting up a problem, 1-5 Setup/Case..., 14-33 Setup/Flamelet Generation..., 14-101 Setup/Flamelet Parameters..., 14-111 Setup/Operating Conditions..., 14-43, 14-103 Setup/Solution Parameters..., 14-47 Setup/Species/Composition..., 14-41 Setup/Species/Define..., 14-37 Setup/Species/Density..., 14-38 Setup/Species/Stoichiometry..., 14-46 SGE checkpointing, 2-40, 30-38, 30-40 configuration, 30-39 overview, 30-38 parallel processing, 2-40, 30-38 running a parallel FLUENT job, 30-42 serial processing, 2-40, 30-38 shear layers, 5-12 shear stress, 5-12, 6-78, 29-19, 29-43, 29-45 laminar flow, 6-78 shear thinning, 7-28 shell conduction, 6-67 shock waves, 5-12, 25-5, 25-20, 25-39 postprocessing for, 27-15, 27-31, 27-93

Index-36

SIMPLE algorithm, 24-19, 24-46 comparison to SIMPLEC, 24-46 simple effectiveness model, 6-150 features, 6-152 restrictions, 6-151 SIMPLEC algorithm, 24-20, 24-46 under-relaxation, 24-46 Single Rate Devolatilization Model panel, 21-111 single reference frame model compatibility, A-1 single selection list, 2-13 single-precision solvers, 1-7 Site Parameters panel, 13-27 site species, 13-26, 13-37 skewness, 5-10, 5-13 correction, 24-21 equiangular, 29-20 equivolume, 29-20 skewness-neighbor coupling, 24-21 skin friction coefficient, 28-16, 29-35 Slice panel, 14-66 slider, 2-15 sliding meshes, 9-31 boundary conditions, 9-39 constraints, 9-33, 9-38, 9-41 contour display, 9-43 file saving, 9-40, 9-41 grid interface shapes, 9-33 grid requirements, 9-38 grid setup, 9-31 initial conditions for, 9-14 model compatibility, A-1 patching values, 24-58 postprocessing, 9-42, 27-19, 28-17 rotation speed, 9-39 setup, 9-38 solution initialization, 24-56 solution procedure, 9-40 theory, 9-35 time step, 9-40, 9-42 translational, 9-39 slip velocity, 22-18


Index

slip wall, 6-62, 6-71, 6-72, 6-81 slitting face zones, 5-49 sloshing, 20-5 slug flow, 20-2, 20-4, 20-6 slurry flow, 20-2, 20-4, 20-7 Smagorinsky-Lilly subgrid-scale model, 10-45 Smooth/Swap Grid panel, 25-48 smoothing, 11-41, 25-48 Laplacian, 25-48 residuals, 24-28 skewness-based, 25-50 Solid panel, 6-91 solid decomposition reactions, 13-46 solid deposition reactions, 13-46 solid materials, 6-91, 7-2, 13-41, 13-47 solid species, 13-16, 13-26, 13-37 solid suspension, 21-3 solid zone, 6-91 convection in a moving, 11-5 solid-solid reactions, 13-46 Solidification and Melting panel, 23-8 solidification and melting, 23-1 in a VOF calculation, 22-90 inputs for, 23-8 limitations, 23-2 overview, 23-1 postprocessing, 23-11 solution procedure, 23-11 theory, 23-3 solids pressure, 22-30 radial distribution function, 22-31 solidus temperature, 23-9 solution, 24-1 accuracy, 24-8, 24-43 animating, 24-88 calculations, 24-59 convergence, 24-70 convergence and stability, 24-100 executing commands during, 24-97 histograms, 27-99 initialization, 24-55, 24-57, 24-60 inputs, 24-42


interpolation, 3-30 interrupt of, 24-60 limits, 24-53 pressure, 8-26 temperature, 8-26, 11-8 monitoring, 24-77 in time-dependent flows, 24-79 numerical scheme overview, 24-2 parameters listing, 28-18 under-relaxation, 24-48 procedure, 24-42 process, 24-1 stability, 24-48 techniques compressible flow, 8-26 discrete phase, 21-113 for convergence monitoring, 24-77 for heat transfer, 11-9 for periodic heat transfer, 11-75 for porous media, 6-110 for radiation, 11-63 for reacting flows, 13-30, 24-103 for swirling or rotating flow, 8-17 for turbulence, 10-75 step-by-step, 24-102 turning equations on/off, 24-102 under-relaxation, 24-12, 24-48 XY plots, 27-89 Solution Animation panel, 24-89 Solution Controls panel, 9-11, 24-45, 24-47, 24-49, 24-50, 24-52, 24-102, 24-111 Solution Histogram panel, 27-99, 28-15 Solution Initialization panel, 24-55 Solution Limits panel, 24-53 Solution Parameters panel, 14-47 Solution XY Plot panel, 27-89 Solve/Animate/Define..., 24-89 Solve/Animate/Playback..., 24-92 Solve/Controls/Limits..., 24-53 Solve/Controls/Multi-Stage..., 24-112

Index-37

Index

Solve/Controls/Multigrid..., 24-52, 24-104– 24-106, 24-109, 24-111 Solve/Controls/Solution..., 24-45, 24-47, 24-49, 24-50, 24-52, 24-102 solve/dpm-update, 21-119 Solve/Execute Commands..., 24-97 solve/initialize/init-flow-statistics, 10-78 Solve/Initialize/Initialize..., 24-55 Solve/Initialize/Patch..., 24-55, 24-57 Solve/Initialize/Reset DPM Sources, 21-120 Solve/Initialize/Reset Statistics, 24-62, 24-64 Solve/Iterate..., 24-59, 24-64 Solve/Mesh Motion..., 9-67 Solve/Monitors/Force..., 24-78, 24-79 Solve/Monitors/Residual..., 24-70, 24-73 Solve/Monitors/Statistic..., 24-77 Solve/Monitors/Surface..., 24-82 Solve/Monitors/Volume..., 24-85, 24-86 solve/set/expert, 24-77 solve/set/multi-stage, 24-112 solve/set/stiff-chemistry, 13-33 Solver panel, 1-15, 8-17, 24-62 solver, 24-1 coupled, 24-4, 24-23 explicit, 1-13, 24-6 implicit, 1-13, 24-6 limitations, 1-14 discretization, 24-7 double-precision, 1-7 formulation choosing, 1-13 inputs for, 24-42 linearization, 24-4 explicit, 24-5 implicit, 24-4 multi-stage scheme, 24-27 multigrid, 24-12, 24-30 algebraic (AMG), 24-30, 24-35 full-approximation storage (FAS), 24-30, 24-39 node vs. cell discretization, 24-15 numerical scheme, 24-2 overview of, 24-2

Index-38

parallel, 30-1 saving settings to a file, 3-17 segregated, 1-13, 24-2, 24-5, 24-16 limitations, 1-15 selection, 2-35 single-precision, 1-7 using, 24-42 soot mole fraction, 29-30 soot density, 29-35 soot formation, 14-39 Soot Model panel, 18-37 soot model, 18-32 boundary conditions, 18-40 combustion process parameters, 18-37 inputs for, 18-36 model compatibility, A-1 radiation effects, 11-43 restrictions, 18-33 single-step, 18-33 model parameters, 18-39 theory, 18-33 two-step, 18-34 model parameters, 18-39 Soret diffusion, 7-44 sound data, 19-13 sound pressure level, 19-7 sound speed, 29-35 source terms in conservation equations, 6-187 units for, 4-2 Spalart-Allmaras model, 10-5, 10-10 DES model, 10-6 model compatibility, A-1 spawning compute nodes, 30-14 Species panel, 13-16, 13-18 species, 7-3, 13-12 adding, 13-17 to the prePDF database, 14-118 boundary conditions, 6-76, 13-30 bulk, 13-17, 13-18 defining, 13-16 for fuel mixtures, 13-25


Index

deleting, 13-18 diffusion, 11-4, 11-9, 13-3 mass fractions, 13-30 mixing, 12-1 molar concentration, 29-30 order of, 13-17–13-19, 13-41 properties, 13-28 removing, 13-18 reordering, 13-18 sources, 13-30, 13-36 transport, 13-1 inputs for, 13-13 overview, 12-1 without reactions, 13-49 Species Model panel, 13-41, 14-73, 15-10 specific dissipation rate, 29-36 specific heat capacity, 7-36, 13-28, 13-29, 29-36 composition-dependent, 7-37 constant, 7-36 discrete phase, 21-109 kinetic theory, 7-37 temperature-dependent, 7-37 specific heat ratio, 29-36 specular boundaries, 11-16 speed of sound, 29-35 split mass flow, 6-56 spray modeling, 21-40 atomizers, 21-40 breakup, 21-58 droplet collision, 21-55 dynamic drag, 21-66 inputs for, 21-75 spread parameter, 21-86 SST k-ω model, 10-8 model compatibility, A-1 stability, 24-12, 24-46, 24-100, 24-102 under-relaxation and, 24-48 stagnation pressure, 8-22 stagnation temperature, 8-22 standard k- model, 10-6, 10-15 model compatibility, A-1


standard k-ω model, 10-8 model compatibility, A-1 standard state enthalpy, 7-50 standard state entropy, 7-51 Stanton number, 29-38 starting FLUENT, 1-7, 30-4 on a LINUX workstation cluster, 30-9 on a multiprocessor LINUX machine, 30-7 on a multiprocessor UNIX machine, 304 on a multiprocessor Windows machine, 30-10 on a UNIX system, 1-8 on a UNIX workstation cluster, 30-6 on a Windows system, 1-10 on a Windows workstation cluster, 3010 starting prePDF on a UNIX system, 14-30 on a Windows system, 14-30 static pressure, 6-22, 6-35, 6-45, 6-51, 29-36 static temperature, 6-29, 6-51, 29-36 Statistic Monitors panel, 24-77 step-by-step solution techniques, 24-102 stiff chemistry, 13-32 stirred tank reactors, 9-2 stochastic particle tracking, 21-12, 21-94 in coupled calculations, 21-119 Stoichiometric Coefficients panel, 14-46 stoichiometric ratio, 14-6, 14-51 stoichiometry, 13-12 in non-premixed combustion model, 14-45 Stokes number, 20-8 Stokes-Cunningham law, 21-6, 21-74 stored cell partition, 29-36, 30-24 strain rate, 14-94, 29-37 stratified flow, 20-2, 20-4–20-6 stream function, 29-37 streamwise-periodic flow, 8-5 stretch factor, 15-6, 29-37 strings, 2-24

Index-39

Index

sub-micron particles, 21-6, 21-8 subgrid turbulent kinetic energy, 29-37 subgrid turbulent viscosity, 29-38 ratio, 29-38 subgrid-scale models, 10-45 RNG-based model, 10-46 Smagorinsky-Lilly model, 10-45 subsonic, 6-22, 8-21 Summary panel, 28-18 supersonic, 6-22, 8-21 surface area (projected), 28-6 surface coverage, 29-38 surface deposition, 13-37, 13-38 rate, 29-38 surface grid file, 3-17 Surface Integrals panel, 28-10 surface integration, 28-7 Surface Monitors panel, 24-82 surface tension, 6-72, 22-13 inputs for, 22-60 surface-to-surface (S2S) radiation model, 11-14 advantages, 11-18 boundary conditions, 11-59 limitations, 11-18 residuals, 11-67 solution parameters, 11-64 theory, 11-38 Surface/Iso-Clip..., 26-22 Surface/Iso-Surface..., 26-20 Surface/Line/Rake..., 26-9 Surface/Manage..., 26-26 Surface/Partition..., 26-4 Surface/Plane..., 26-13 Surface/Point..., 26-6 Surface/Quadric..., 26-18 Surface/Transform..., 26-24 Surface/Zone..., 26-3 Surfaces panel, 26-26 surfaces, 26-1 clipping, 26-22 deleting, 26-26 grouping, 26-26

Index-40

isodistancing, 26-25 isosurfaces, 26-2, 26-20 line, 26-2, 26-9 monitoring, 24-82 partition, 26-2, 26-4 plane, 26-2, 26-13 point, 26-2, 26-6 quadric, 26-2, 26-18 rake, 26-2, 26-9 renaming, 26-26 rotating, 26-24 transforming, 26-24 translating, 26-25 using, 26-2 zone, 26-2, 26-3 Sutherland Law panel, 7-21 swapping, 25-48, 25-51 Sweep Surface panel, 27-31 sweep surface, 27-31 sweeps, for radiation, 11-64, 11-65 swelling, 21-110 coefficient, 21-32 swirl number, 8-14 swirl pull velocity, 29-39 swirl velocity, 6-28, 8-12, 29-39 for fans, 6-113, 6-118 swirling flow, 8-11, 24-17 grid sensitivity in, 8-15 physics of, 8-13 pressure interpolation, 24-44 solution strategies for, 8-17 turbulence modeling in, 10-6, 10-7, 10-9, 10-18 Syamlal-O’Brien model, 22-28 symbols, 2-25 symmetric model, 22-27 symmetry boundary, 6-81, 27-58 symmetry in the display, 27-58

8-14,

tab (in a GUI panel), 2-11 TAB model, 21-59 tangential velocity, 6-28, 29-39 Taylor analogy breakup model, 21-59 Taylor-Foster approximation, 11-44


Index

Tecplot, 3-23 temperature, 29-33, 29-36, 29-39, 29-40, 29-43 temperature-dependent properties, 7-8, 11-9 density, 7-15 specific heat capacity, 7-37 thermal conductivity, 7-29 viscosity, 7-19 temporal discretization, 24-22, 24-27, 24-29 solver, 24-12 terminal emulator, 2-3 termination criteria, 24-39, 24-107 text annotation, 27-50 entry, 2-12 prompts, 2-23 user interface, 2-21 TGrid, 1-2 TGrid grid file, 3-6, 5-14 thermal accommodation coefficient, 13-29 thermal boundary conditions external heat transfer coefficient, 6-79 heat flux, 6-79 thermal conductivity, 7-29, 13-28, 13-29, 29-25, 29-39 anisotropic, 7-32, 11-6 composition-dependent, 7-30 constant, 7-29 cylindrical orthotropic, 7-34 discrete phase, 21-109 kinetic theory, 7-30 temperature-dependent, 7-29 user-defined, 7-35 thermal diffusion coefficients, 7-44, 29-39 thermal diffusivity, 15-12 thermal expansion coefficient, 7-15 thermal mixing, 11-1 thermal resistance, 6-65 thermodynamic database, 14-31, 14-113 thermophoretic coefficient, 21-109 thermophoretic force, 21-7, 21-71 thin walls, 6-65


third-body efficiency, 13-6, 13-22 tilde expansion, 3-5 time step, 24-30, 24-64, 29-39 discrete phase, 21-10, 21-69, 21-113 scale, 29-39 time stepping adaptive, 24-67 dual, 24-13, 24-29 explicit, 24-14, 24-29 restrictions, 24-51 first-order, 24-13 global, 24-14 implicit, 24-13, 24-29 second-order, 24-14 time-dependent problems, 24-60 adaptive time stepping, 24-67 animations of, 24-88 boundary conditions for, 6-7 inputs for, 24-62 mean flow quantities, 24-69 postprocessing, 24-69, 24-88 root-mean-square quantities, 24-69 solution monitoring, 24-79 solution parameters for, 24-64 statistical analysis, 24-64, 24-69 time-periodic, 9-41, 9-42 time-periodic flows, 9-41, 9-42 title, 27-36, 27-95 tmerge, 5-22 toothpaste, 7-28 topology global setting, 27-122 torque, 27-113 torque converters, 9-29 total energy, 29-39 total enthalpy, 29-39 total pressure, 6-19, 8-22, 8-27, 29-40 total temperature, 6-19, 6-35, 8-22, 8-27, 29-40 trajectory calculations, 21-5 transcript files, 3-14 Transform Surface panel, 26-24 Transformations panel, 27-66

Index-41

Index

transforming objects in a scene, 27-65 transient boundary conditions, 6-7 Translate Grid panel, 5-39 translating objects in a scene, 27-66 reference frames, 9-2, 9-13 the display, 27-49, 27-53 the grid, 5-38 translation velocity, 9-18, 9-26 transmitted radiation flux, 29-40 transonic, 8-21 transparency, 27-64 transport database, 14-113 troubleshooting of calculations, 24-53 tube banks, 6-93 TUI, 2-21 turbines, 9-2 Turbo 2D Contours panel, 27-119 Turbo Averaged Contours panel, 27-117 Turbo Averaged XY Plot panel, 27-121 Turbo Options panel, 27-122 Turbo Report panel, 27-108 Turbo Topology panel, 27-106 Turbo/2D Contours..., 27-119 Turbo/Averaged Contours..., 27-117 Turbo/Averaged XY Plot..., 27-121 Turbo/Options..., 27-122 Turbo/Report..., 27-108 turbomachinery, 9-2, 26-24 2D contours, 27-118 average flow angles, 27-111 average total pressure, 27-110 average total temperature, 27-111 averaged contours, 27-117 axial force, 27-112 coordinates, 27-123 defining topology, 27-105 efficiency, 27-113, 27-115, 28-16 mass flow, 27-110 passage loss coefficient, 27-112 postprocessing, 27-105 quantities, 27-110 report, 27-108

Index-42

setting global topology, 27-122 swirl number, 27-110 topology, 27-105 torque, 27-113 XY plots, 27-121 turbulence, 10-1 boundary conditions, 10-71 computing, 6-14 input methods, 6-11 relationships for deriving, 6-14 buoyancy effects, 10-23, 10-39 choosing a model, 10-2 compressibility effects, 10-24 computational expense, 10-9 DES model, 10-6, 10-13, 10-68 discrete phase interaction, 21-2 dissipation rate, 29-41 enhanced wall functions, 10-59 grid considerations for, 10-61, 10-75, 25-35 inputs for, 10-64 intensity, 6-12, 29-40 k- model, 10-15 realizable, 10-7, 10-19 RNG, 10-6, 10-16 standard, 10-6, 10-15 k-ω model SST, 10-8 standard, 10-8 kinetic energy, 29-41 large eddy simulation (LES), 10-43 length scale, 6-13 model compatibility, A-1 modeling, 10-1, 10-4 in multiphase flows, 22-6 near-wall treatments, 10-47 options, 10-65 production, 10-11, 10-23 realizable k- model, 10-7, 10-19 reporting, 10-79 Reynolds stress model (RSM), 10-35 RNG k- model, 10-6, 10-16 solution strategies, 10-75


Index

sources, 6-190 Spalart-Allmaras model, 10-5, 10-10 SST k-ω model, 10-8 standard k- model, 10-6, 10-15 standard k-ω model, 10-8 transition, 6-89, 6-109 troubleshooting, 10-82 two-layer model, 10-48, 10-57 user-defined functions, 10-70 v 2 -f model, 10-8 wall functions, 10-48, 10-49 limitations of, 10-55 non-equilibrium, 10-54 standard, 10-50 wall roughness, 6-73, 10-71, 10-72 turbulence-chemistry interaction, 13-8, 14-1, 14-9, 18-23 turbulent reaction rate, 29-41 turbulent Reynolds number, 29-41 turbulent viscosity, 29-41 in the k- model, 10-16 modified, 29-29 ratio, 6-14, 29-41 subgrid, 29-38 subgrid, 29-38 tutorial, 1-24 twisting pathlines, 27-28 Two Competing Rates Model panel, 21-111 two-layer model, 10-48, 10-57 two-sided wall, 6-63, 6-65, 6-71 unburnt mixture, 15-3 physical properties, 15-12 species concentration, 15-10, 15-14 under-relaxation, 24-12 default values, 24-49 discrete phase, 21-70, 21-119 inputs for, 24-48 of body forces, 24-22 of density, 13-32 of energy, 11-9 of temperature, 11-9 with PISO, 24-47 with SIMPLEC, 24-46


uniform distribution for display, 26-9, 26-13 units, 4-1, 29-17 conversion factors, 4-5 custom systems, 4-4 for custom field functions, 29-45 for length, 5-38 restrictions, 4-2 unsteady flows, 24-60 in multiple reference frames, 9-15 upwind schemes, 24-8 first-order, 24-8 second-order, 24-10 user interface graphical, 2-1 text, 2-21 User-Defined Fan Model panel, 6-143 user-defined fan model, 6-141 user-defined functions (UDFs), 6-7 discrete phase, 21-74, 21-96 in multiphase models, 20-6 turbulence, 10-70 units in, 4-2 update of, 24-59 user-defined quantities non-isotropic thermal conductivity, 6-108 porosity, 6-108 resistance coefficients, 6-100 user-defined real gas model (UDRGM), 7-55 ideal gas equation example, 7-65 limitations, 7-60 Redlich-Kwong equation example, 7-70 using the manual, UTM-1 v 2 -f model, 10-8 V-cycle multigrid, 24-33, 24-105 vapor pressure, 21-110 vaporization, 21-19, 21-21, 21-25 pressure, 22-57 temperature, 14-89, 21-19, 21-109 variable definitions, 29-1 Vector Definitions panel, 27-24

Index-43

Index

vector file, 3-20 Vector Options panel, 27-19 Vectors panel, 27-18 vectors, 27-17 custom, 27-23 velocity, 29-34, 29-42 angle, 29-42 relative, 29-33 axial, 6-28, 29-19 boundary conditions, 6-26 Cartesian, 29-3 for boundary condition inputs, 6-27 components, 29-45 cylindrical, 29-3 for boundary condition inputs, 6-27 fixed values of, 6-183 local cylindrical for boundary condition inputs, 6-27 magnitude, 29-43 radial, 6-28, 29-31 reporting options, 29-3 swirl, 8-12, 29-39 tangential, 6-28, 29-39 velocity far-field boundary, 6-29 velocity formulation in rotating reference frames, 9-9 porous media, 6-94, 6-99 Velocity Inlet panel, 6-26 velocity inlet boundary, 6-10, 6-25 velocity vectors, 27-17 video, 27-78 View Factor and Cluster Parameters panel, 11-52 view factors, 11-39 computing, 11-49 adaptive method, 11-54 for large meshes or complex models, 11-50, 11-51 hemicube method, 11-54 inside FLUENT, 11-51 outside FLUENT, 11-51 reading, 11-52 setting parameters, 11-52

Index-44

view last, 27-51

view modification in graphics, 27-51 Views panel, 27-51, 27-56, 27-58 views restoring, 27-58 saving, 27-57 virtual mass force, 21-7, 22-23 viscosity, 7-19, 13-28, 13-29, 29-25, 29-30, 29-41 Carreau model, 7-26 composition-dependent, 7-22 constant, 7-19 Cross model, 7-27 kinetic theory, 7-22 non-Newtonian, 7-24 Carreau model, 7-26 Cross model, 7-27 Herschel-Bulkley model, 7-27 power law, 7-25 power law, 7-21 non-Newtonian, 7-25 Sutherland’s law, 7-20, 7-21 temperature-dependent, 7-19 zero-shear-rate, 7-27 viscous dissipation, 8-23, 11-4, 11-6 Viscous Model panel, 7-50, 8-30, 10-64 viscous stresses, 24-113 visibility, 27-62 visualizing results, 27-1 volatile fraction, 14-89, 21-19, 21-109 volatiles, 18-19, 18-21 Volume Adaption panel, 25-34 volume adaption, 25-32 volume fraction, 20-5, 22-20, 29-43 in Eulerian multiphase model, 22-20 in Lagrangian discrete phase model, 21-3 in mixture model, 22-19 in VOF model, 22-7 Volume Integrals panel, 28-14 volume integrals, monitoring, 24-85 volume integration, 28-12 Volume Monitors panel, 24-85, 24-86


Index

volume of fluid (VOF) model, 20-5 donor-acceptor scheme, 22-11, 22-54 Euler explicit scheme, 22-12, 22-54 geometric reconstruction scheme, 22-9, 22-54 implicit scheme, 22-12, 22-55 interpolation, 22-9 donor-acceptor scheme, 22-11, 22-54 Euler explicit scheme, 22-12, 22-54 geometric reconstruction scheme, 22-9, 22-54 implicit scheme, 22-12, 22-55 limitations, 22-3 mass transfer, 22-44 model compatibility, A-1 momentum equation, 22-8 overview, 22-2 properties, 22-8, 22-59, 22-60 reporting flow rates, 22-95 solidification and melting in, 22-90 solution strategies, 22-90 steady-state calculations, 22-3, 22-55 surface tension, 22-13 inputs for, 22-60 theory, 22-7 time-dependent calculations, 22-3, 22-54, 22-55 inputs for, 22-72 volume fraction, 22-7 wall adhesion, 22-15 inputs for, 22-61, 22-86 volumetric heat sources, 11-5 volumetric species, 13-13 vortex shedding, 24-60 vorticity, 29-28, 29-43 components, 29-45 magnitude, 29-43 W-cycle multigrid, 24-33, 24-105 Wall panel, 6-63, 6-68, 6-71, 6-75 wall adhesion, 22-15 inputs for, 22-61, 22-86 boundary conditions, 6-62


motion, 6-68 shear, 6-71 thermal, 6-63 coupled, 5-49, 6-65 fluxes, 29-43 functions, 10-48, 10-49 limitations of, 10-53, 10-55 non-equilibrium, 10-54 standard, 10-50 heat flux, 6-79 Marangoni stress, 6-71, 6-72 motion, 6-68, 9-39 no-slip, 6-71 rotation, 8-14, 9-9, 9-18, 9-26 roughness, 6-73, 10-71, 10-72 shear stress, 6-78, 29-19, 29-43 components, 29-45 shell conduction, 6-67 slip, 6-71, 6-72 specified shear, 6-71, 6-72 temperature, 29-43 thickness, 6-65 translation, 9-18, 9-26 two-sided, 6-63, 6-65, 6-71 wall surface reactions, 12-1, 13-16, 13-36 boundary conditions, 6-77, 13-37 heat transfer, 13-39 inputs for, 13-41 reaction rate, 13-36 site species, 13-26, 13-37 solid species, 13-26, 13-37 Warning dialog box, 2-6 WAVE, 6-195 wave breakup model, 21-64 wavelength bands, 11-28 web browser, 1-17, 2-29 Weber number, 21-46, 22-14 weighted-sum-of-gray-gases model (WSGGM), 7-39, 11-15, 11-41 Wen and Yu model, 22-29 window dumps, 3-21 windows, 2-16

Index-45

Index

Windows systems graphics display window features, 2-16 starting FLUENT on, 1-10, 30-10 starting prePDF on, 14-30 wireframe animations, 27-47 Working dialog box, 2-6 workpile, 21-120 workstation clusters, 30-6, 30-9 Write Profile panel, 3-15 Write Sound Signals panel, 19-14 Write Views panel, 27-57 WSGGM User Specified panel, 7-40 XY plot files units in, 4-2 XY plots, 27-88, 27-89, 27-94, 27-101 along pathline trajectories, 27-30 axis attributes, 27-100 circumferential average, 27-96 curve attributes, 27-103 file format, 27-98 residuals, 27-99 turbomachinery, 27-121 y ∗ , 10-50, 10-61, 29-44 adaption, 25-35 y + , 10-51, 10-61, 29-43 adaption, 25-35 Y+/Y* Adaption panel, 25-35 yield stress, 7-28 zero-shear-rate viscosity, 7-27 Zone Surface panel, 26-3 zone surfaces, 26-2, 26-3 zones changing name of, 6-6 changing type of, 6-3 deforming, 9-44, 9-62, 9-65 double-sided, 6-4 moving, 9-1, 9-31 reordering, 5-52 zooming, 27-49, 27-54

Index-46
