FLUENT 6.1 Tutorial Guide

FLUENT 6.1

February 2003

Tutorial 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 8 9 10 11

Introduction to Using Fluent Modeling Periodic Flow and Heat Transfer Modeling External Compressible Flow Modeling Unsteady Compressible Flow Modeling Radiation and Natural Convection Using a Non-Conformal Mesh Using a Single Rotating Reference Frame Using Multiple Rotating Reference Frames Using the Mixing Plane Model Using Sliding Meshes Using Dynamic Meshes

Volume 2 12 13 14 15 16 17 18 19 20 21 22 23 24

Modeling Species Transport and Gaseous Combustion Using the Non-Premixed Combustion Model Modeling Surface Chemistry Modeling Evaporating Liquid Spray Using the VOF Model Modeling Cavitation Using the Mixture and Eulerian Multiphase Models Using the Eulerian Multiphase Model for Granular Flow Modeling Solidification Using the Eulerian Granular Multiphase Model with Heat Transfer Postprocessing Turbo Postprocessing Parallel Processing

Using This Manual

What’s In This Manual The FLUENT Tutorial Guide contains a number of tutorials that teach you how to use FLUENT to solve different types of problems. In each tutorial, features related to problem setup and postprocessing are demonstrated. Tutorial 1 is a detailed tutorial designed to introduce the beginner to FLUENT. This tutorial provides explicit instructions for all steps in the problem setup, solution, and postprocessing. The remaining tutorials assume that you have read or solved Tutorial 1, or that you are already familiar with FLUENT and its interface. In these tutorials, some steps will not be shown explicitly. All of the tutorials include some postprocessing instructions, but Tutorial 22 is devoted entirely to standard postprocessing, and Tutorial 23 is devoted to turbomachinery-specific postprocessing.

Where to Find the Files Used in the Tutorials Each of the tutorials uses an existing mesh file. (Tutorials for mesh generation are provided with the mesh generator documentation.) You will find the appropriate mesh file (and any other relevant files used in the tutorial) on the FLUENT documentation CD. The “Preparation” step of each tutorial will tell you where to find the necessary files. (Note that Tutorials 22, 23, and 24 use existing case and data files.) Some of the more complex tutorials may require a significant amount of computational time. If you want to look at the results immediately, without waiting for the calculation to finish, you can find the case and data files associated with the tutorial on the documentation CD (in the same directory where you found the mesh file).

How To Use This Manual Depending on your familiarity with computational fluid dynamics and Fluent Inc. software, you can use this tutorial guide in a variety of ways.

For the Beginner If you are a beginning user of FLUENT you should first read and solve Tutorial 1, in order to familiarize yourself with the interface and with basic setup and solution procedures.

c Fluent Inc. January 28, 2003

i

Using This Manual

You may then want to try a tutorial that demonstrates features that you are going to use in your application. For example, if you are planning to solve a problem using the non-premixed combustion model, you should look at Tutorial 13. You may want to refer to other tutorials for instructions on using specific features, such as custom field functions, grid scaling, and so on, even if the problem solved in the tutorial is not of particular interest to you. To learn about postprocessing, you can look at Tutorial 22, which is devoted entirely to postprocessing (although the other tutorials all contain some postprocessing as well). For turbomachinery-specific postprocessing, see Tutorial 23.

For the Experienced User If you are an experienced FLUENT user, you can read and/or solve the tutorial(s) that demonstrate features that you are going to use in your application. For example, if you are planning to solve a problem using the non-premixed combustion model, you should look at Tutorial 13. You may want to refer to other tutorials for instructions on using specific features, such as custom field functions, grid scaling, and so on, even if the problem solved in the tutorial is not of particular interest to you. To learn about postprocessing, you can look at Tutorial 22, which is devoted entirely to postprocessing (although the other tutorials all contain some postprocessing as well). For turbomachinery-specific postprocessing, see Tutorial 23.

Typographical Conventions Used In This Manual Several typographical conventions are used in the text of the tutorials to facilitate your learning process. • An exclamation point (!) to the left of a paragraph 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., Zone Surface panel, surface/zone-surface command). • The text interface type style is also used when illustrating exactly what appears on the screen or exactly what you must type in the text window or in a panel. • Instructions for performing each step in a tutorial will appear in standard type. Additional information about a step in a tutorial appears in italicized type. • A mini flow chart is used to indicate the menu selections that lead you to a specific command or panel. For example,

ii


Using This Manual

Define −→Boundary Conditions... indicates that the Boundary Conditions... menu item can be selected from the Define pull-down menu. The words surrounded by boxes invoke menus (or submenus) and the arrows point from a specific menu toward the item you should select from that menu.


iii

Using This Manual

iv


Contents

1 Introduction to Using FLUENT

1-1

2 Modeling Periodic Flow and Heat Transfer

2-1

3 Modeling External Compressible Flow

3-1

4 Modeling Unsteady Compressible Flow

4-1

5 Modeling Radiation and Natural Convection

5-1

6 Using a Non-Conformal Mesh

6-1

7 Using a Single Rotating Reference Frame

7-1

8 Using Multiple Rotating Reference Frames

8-1

9 Using the Mixing Plane Model

9-1

10 Using Sliding Meshes

10-1

11 Using Dynamic Meshes

11-1

12 Modeling Species Transport and Gaseous Combustion

12-1

13 Using the Non-Premixed Combustion Model

13-1

14 Modeling Surface Chemistry

14-1

15 Modeling Evaporating Liquid Spray

15-1

16 Using the VOF Model

16-1


i

CONTENTS

17 Modeling Cavitation

17-1

18 Using the Mixture and Eulerian Multiphase Models

18-1

19 Using the Eulerian Multiphase Model for Granular Flow

19-1

20 Modeling Solidification

20-1

21 Using the Eulerian Granular Multiphase Model with Heat Transfer 21-1

ii

22 Postprocessing

22-1

23 Turbo Postprocessing

23-1

24 Parallel Processing

24-1


Tutorial 1.

Introduction to Using FLUENT

Introduction: This tutorial illustrates the setup and solution of the two-dimensional turbulent fluid flow and heat transfer in a mixing junction. The mixing elbow configuration is encountered in piping systems in power plants and process industries. It is often important to predict the flow field and temperature field in the neighborhood of the mixing region in order to properly design the location of inlet pipes. In this tutorial you will learn how to: • Read an existing grid file into FLUENT • Use mixed units to define the geometry and fluid properties • Set material properties and boundary conditions for a turbulent forced convection problem • Initiate the calculation with residual plotting • Calculate a solution using the segregated solver • Examine the flow and temperature fields using graphics • Enable the second-order discretization scheme for improved prediction of temperature • Adapt the grid based on the temperature gradient to further improve the prediction of temperature Prerequisites: This tutorial assumes that you have little experience with FLUENT, but that you are generally familiar with the interface. If you are not, please review the sample session in Chapter 1 of the User’s Guide.


1-1


Problem Description: The problem to be considered is shown schematically in Figure 1.1. A cold fluid at 26◦ C enters through the large pipe and mixes with a warmer fluid at 40◦ C in the elbow. The pipe dimensions are in inches, and the fluid properties and boundary conditions are given in SI units. The Reynolds number at the main inlet is 2.03 × 105 , so that a turbulent model will be necessary.

Density:

ρ= 1000 kg/m

Viscosity:

µ = 8 x 10

-4

3

Pa-s 32 ″

Conductivity: k = 0.677 W/m-K Specific Heat: C p = 4216 J/kg-K

39.9 3°

Ux= 0.2 m/s T = 26°C I = 5%

39.9

16 ″

3°

16 ″ 12 ″ 32 ″

4″ Uy= 1 m/s T = 40° C I = 5%

Figure 1.1: Problem Specification

1-2



Preparation 1. Copy the file elbow/elbow.msh from the FLUENT documentation CD to your working directory. For UNIX systems, you can find the file by inserting the CD into your CD-ROM drive and going to the following directory: /cdrom/fluent6.1/help/tutfiles/ where cdrom must be replaced by the name of your CD-ROM drive. For Windows systems, you can find the file by inserting the CD into your CD-ROM drive and going to the following directory: cdrom:\fluent6.1\help\tutfiles\ where cdrom must be replaced by the name of your CD-ROM drive (e.g., E). 2. Start the 2D version of FLUENT.


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Step 1: Grid 1. Read the grid file elbow.msh. File −→ Read −→Case...

(a) Select the file elbow.msh by clicking on it under Files and then clicking on OK. Note: As this grid is read by FLUENT, messages will appear in the console window reporting the progress of the conversion. After reading the grid file, FLUENT will report that 918 triangular fluid cells have been read, along with a number of boundary faces with different zone identifiers. 2. Check the grid. Grid −→Check

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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): 2.782193e-01 maximum volume (m3): 3.926232e+00 total volume (m3): 1.682930e+03 Face area statistics: minimum face area (m2): 8.015718e-01 maximum face area (m2): 4.118252e+00 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.

Note: The grid check lists the minimum and maximum x and y values from the grid, in the default SI units of meters, and reports on a number of other grid features that are checked. Any errors in the grid would be reported at this time. In particular, you should always make sure that the minimum volume is not negative, since FLUENT cannot begin a calculation if this is the case. To scale the grid to the correct units of inches, the Scale Grid panel will be used.


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3. Smooth (and swap) the grid. Grid −→ Smooth/Swap...

To ensure the best possible grid quality for the calculation, it is good practice to smooth a triangular or tetrahedral grid after you read it into FLUENT. (a) Click the Smooth button and then click Swap repeatedly until FLUENT reports that zero faces were swapped. If FLUENT cannot improve the grid by swapping, no faces will be swapped. (b) Close the panel. 4. Scale the grid. Grid −→Scale... (a) Under Units Conversion, select in from the drop-down list to complete the phrase Grid Was Created In in (inches). (b) Click Scale to scale the grid. The reported values of the Domain Extents will be reported in the default SI units of meters. (c) Click Change Length Units to set inches as the working units for length. Confirm that the maximum x and y values are 64 inches (see Figure 1.1).

1-6



(d) The grid is now sized correctly, and the working units for length have been set to inches. Close the panel. Note: Because the default SI units will be used for everything but the length, there will be no need to change any other units in this problem. The choice of inches for the unit of length has been made by the actions you have just taken. If you want to change the working units for length to something other than inches, say, mm, you would have to visit the Set Units panel in the Define pull-down menu. 5. Display the grid (Figure 1.2). Display −→Grid...

(a) Make sure that all of the surfaces are selected and click Display.


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Grid

Nov 13, 2002 FLUENT 6.1 (2d, segregated, lam)

Figure 1.2: The Triangular Grid for the Mixing Elbow

Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.

1-8



Step 2: Models 1. Keep the default solver settings. Define −→ Models −→Solver...

2. Turn on the standard k- turbulence model. Define −→ Models −→Viscous... (a) Select k-epsilon in the Model list. The original Viscous Model panel will expand when you do so. (b) Accept the default Standard model by clicking OK.


1-9


3. Enable heat transfer by activating the energy equation. Define −→ Models −→Energy...

1-10



Step 3: Materials 1. Create a new material called water. Define −→Materials...

(a) Type the name water in the Name text-entry box. (b) Enter the values shown in the table below under Properties: Property Value density 1000 kg/m3 cp 4216 J/kg-K thermal conductivity 0.677 W/m-K viscosity 8 ×10−4 kg/m-s (c) Click Change/Create. (d) Click No when FLUENT asks if you want to overwrite air. The material water will be added to the list of materials which originally contained only air. You can confirm that there are now two materials defined by examining the drop-down list under Fluid Materials.


1-11


Extra: You could have copied the material water from the materials database (accessed by clicking on the Database... button). If the properties in the database are different from those you wish to use, you can still edit the values under Properties and click the Change/Create button to update your local copy. (The database will not be affected.) (e) Close the Materials panel.

1-12



Step 4: Boundary Conditions Define −→Boundary Conditions...

1. Set the conditions for the fluid. (a) Select fluid-9 under Zone. The Type will be reported as fluid. (b) Click Set... to open the Fluid panel. (c) Specify water as the fluid material by selecting water in the Material Name drop-down list. Click on OK.


1-13


2. Set the boundary conditions at the main inlet. (a) Select velocity-inlet-5 under Zone and click Set.... Hint: If you are unsure of which inlet zone corresponds to the main inlet, you can probe the grid display with the right mouse button and the zone ID will be displayed in the FLUENT console window. In the Boundary Conditions panel, the zone that you probed will automatically be selected in the Zone list. In 2D simulations, it may be helpful to return to the Grid Display panel and deselect the display of the fluid and interior zones (in this case, fluid-9 and internal-3) before probing with the mouse button for zone names.

1-14



(b) Choose Components as the Velocity Specification Method. (c) Set an X-Velocity of 0.2 m/s. (d) Set a Temperature of 293 K. (e) Select Intensity and Hydraulic Diameter as the Turbulence Specification Method. (f) Enter a Turbulence Intensity of 5%, and a Hydraulic Diameter of 32 in. 3. Repeat this operation for velocity-inlet-6, using the values in the following table: velocity specification method y velocity temperature turbulence specification method turbulence intensity hydraulic diameter


components 1.0 m/s 313 K intensity & hydraulic diameter 5% 8 in

1-15


4. Set the boundary conditions for pressure-outlet-7, as shown in the panel below.

These values will be used in the event that flow enters the domain through this boundary. 5. For wall-4, keep the default settings for a Heat Flux of 0.

1-16



6. For wall-8, you will also keep the default settings. Note: If you probe your display of the grid (without the interior cells) you will see that wall-8 is the wall on the outside of the bend just after the junction. This separate wall zone has been created for the purpose of doing certain postprocessing tasks, to be discussed later in this tutorial.


1-17


Step 5: Solution 1. Initialize the flow field using the boundary conditions set at velocity-inlet-5. Solve −→ Initialize −→Initialize... (a) Choose velocity-inlet-5 from the Compute From list. (b) Add a Y Velocity value of 0.2 m/sec throughout the domain. Note: While an initial X Velocity is an appropriate guess for the horizontal section, the addition of a Y Velocity will give rise to a better initial guess throughout the entire elbow. (c) Click Init and Close the panel.

1-18



2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual...

(a) Select Plot under Options, and click OK. Note: By default, all variables will be monitored and checked for determining the convergence of the solution.


1-19


3. Save the case file (elbow1.cas). File −→ Write −→Case...

Keep the Write Binary Files (default) option on so that a binary file will be written. 4. Start the calculation by requesting 100 iterations. Solve −→Iterate... (a) Input 100 for the Number of Iterations and click Iterate.

The solution reaches convergence after approximately 60 iterations. The residual plot is shown in Figure 1.3. Note that since the residual values are different for different computers, the plot that appears on your screen may not be exactly the same as the one shown here.

1-20



Residuals continuity x-velocity y-velocity energy k epsilon

1e+03 1e+02 1e+01 1e+00 1e-01 1e-02 1e-03 1e-04 1e-05 1e-06 1e-07 0

10

20

30

40

50

60

Iterations

Scaled Residuals

Nov 12, 2002 FLUENT 6.1 (2d, segregated, ske)

Figure 1.3: Residuals for the First 60 Iterations

5. Check for 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 and checking for mass and energy balances. The three methods to check for convergence are: • Monitoring the residuals. Convergence will occur when the Convergence Criterion for each variable has been reached. The default criterion is that each residual will be reduced to a value of less than 10−3 , except the energy residual, for which the default criterion is 10−6 . • Solution no longer changes with more iterations. Sometimes the residuals may not fall below the convergence criterion set in the case setup. However, monitoring the representative flow variables through iterations may show that the residuals have stagnated and do not change with further iterations. This could also be considered as convergence.


1-21


• Overall mass, momentum, energy and scalar balances are obtained. Check the overall mass, momentum, energy and scalar balances in the Flux Reports panel. The net imbalance should be less than 0.1% of the net flux through the domain. Report −→Fluxes

6. Save the data file (elbow1.dat). Use the same prefix (elbow1) that you used when you saved the case file earlier. Note that additional case and data files will be written later in this session. File −→ Write −→Data...

1-22



Step 6: Displaying the Preliminary Solution 1. Display filled contours of velocity magnitude (Figure 1.4). Display −→ Contours...

(a) Select Velocity... and then Velocity Magnitude from the drop-down lists under Contours Of. (b) Select Filled under Options. (c) Click Display. Note: Right-clicking on a point in the domain will cause the value of the corresponding contour to be displayed in the console window.


1-23


1.24e+00 1.18e+00 1.12e+00 1.05e+00 9.93e-01 9.31e-01 8.69e-01 8.07e-01 7.45e-01 6.82e-01 6.20e-01 5.58e-01 4.96e-01 4.34e-01 3.72e-01 3.10e-01 2.48e-01 1.86e-01 1.24e-01 6.20e-02 0.00e+00

Contours of Velocity Magnitude (m/s)


Figure 1.4: Predicted Velocity Distribution After the Initial Calculation

1-24



2. Display filled contours of temperature (Figure 1.5).

(a) Select Temperature... and Static Temperature in the drop-down lists under Contours Of. (b) Click Display.


1-25


3.13e+02 3.12e+02 3.11e+02 3.10e+02 3.09e+02 3.08e+02 3.07e+02 3.06e+02 3.05e+02 3.04e+02 3.03e+02 3.02e+02 3.01e+02 3.00e+02 2.99e+02 2.98e+02 2.97e+02 2.96e+02 2.95e+02 2.94e+02 2.93e+02

Contours of Static Temperature (k)


Figure 1.5: Predicted Temperature Distribution After the Initial Calculation

1-26



3. Display velocity vectors (Figure 1.6). Display −→ Vectors... (a) Click Display to plot the velocity vectors. Note: The Auto Scale button is on by default under Options. This scaling sometimes creates vectors that are too small or too large in the majority of the domain. (b) Resize the vectors by increasing the Scale factor to 3.

(c) Display the vectors once again. (d) Use the middle mouse button to zoom the view. To do this, hold down the button and drag your mouse to the right and either up or down to construct a rectangle on the screen. The rectangle should be a frame around the region that you wish to enlarge. Let go of the mouse button and the image will be redisplayed (Figure 1.7). (e) Un-zoom the view by holding down the middle mouse button and dragging it to the left to create a rectangle. When you let go, the image will be redrawn. If the resulting image is not centered, you can use the left mouse button to translate it on your screen.


1-27


1.40e+00 1.33e+00 1.27e+00 1.20e+00 1.13e+00 1.06e+00 9.96e-01 9.28e-01 8.61e-01 7.93e-01 7.26e-01 6.59e-01 5.91e-01 5.24e-01 4.56e-01 3.89e-01 3.21e-01 2.54e-01 1.86e-01 1.19e-01 5.16e-02

Velocity Vectors Colored By Velocity Magnitude (m/s)


Figure 1.6: Resized Velocity Vectors




Figure 1.7: Magnified View of Velocity Vectors

1-28



4. Create an XY plot of temperature across the exit (Figure 1.8). Plot −→ XY Plot...

(a) Select Temperature... and Static Temperature in the drop-down lists under the Y Axis Function. (b) Select pressure-outlet-7 from the Surfaces list. (c) Click Plot.


1-29


pressure-outlet-7 3.10e+02

3.08e+02

3.06e+02

3.04e+02

Static Temperature (k)

3.02e+02

3.00e+02

2.98e+02

2.96e+02 48

50

52

54

56

58

60

62

64

Position (in)

Static Temperature


Figure 1.8: Temperature Distribution at the Outlet

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5. Make an XY plot of the static pressure on the outer wall of the large pipe, wall-8 (Figure 1.9).

(a) Choose Pressure... and Static Pressure from the Y Axis Function drop-down lists. (b) Deselect pressure-outlet-7 and select wall-8 from the Surfaces list. (c) Change the Plot Direction for X to 0, and the Plot Direction for Y to 1. With a Plot Direction vector of (0,1), FLUENT will plot static pressure at the cells of wall-8 as a function of y. (d) Click Plot.


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wall-8 1.00e+02

0.00e+00

-1.00e+02

-2.00e+02

Static Pressure (pascal)

-3.00e+02

-4.00e+02

-5.00e+02

-6.00e+02 10

20

30

40

50

60

70

Position (in)

Static Pressure


Figure 1.9: Pressure Distribution along the Outside Wall of the Bend

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6. Define a custom field function for the dynamic head formula (ρ|V |2 /2). Define −→ Custom Field Functions...

(a) In the Field Functions drop-down list, select Density and click the Select button. (b) Click the multiplication button, X. (c) In the Field Functions drop-down list, select Velocity and Velocity Magnitude and click Select. (d) Click y^x to raise the last entry to a power, and click 2 for the power. (e) Click the divide button, /, and then click 2. (f) Enter the name dynam-head in the New Function Name text entry box. (g) Click Define, and then Close the panel.


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7. Display filled contours of the custom field function (Figure 1.10). Display −→ Contours...

(a) Select Custom Field Functions... in the drop-down list under Contours Of. The function you created, dynam-head, will be shown in the lower drop-down list. (b) Click Display, and then Close the panel. Note: You may need to un-zoom your view after the last vector display, if you have not already done so.

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Contours of dynam-head


Figure 1.10: Contours of the Custom Field Function, Dynamic Head


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Step 7: Enabling Second-Order Discretization The elbow solution computed in the first part of this tutorial uses first-order discretization. The resulting solution is very diffusive; mixing is overpredicted, as can be seen in the contour plots of temperature and velocity distribution. You will now change to second-order discretization for the energy equation in order to improve the accuracy of the solution. With the second-order discretization, you will need to use a less aggressive (lower) value for the energy under-relaxation to ensure convergence. 1. Enable the second-order scheme for the calculation of energy and decrease the energy under-relaxation factor. Solve −→ Controls −→ Solution...

(a) Under Discretization, select Second Order Upwind for Energy. (b) Under Under-Relaxation Factors, set the Energy under-relaxation factor to 0.8. Note: You will have to scroll down both the Discretization and Under-Relaxation Factors lists to see the Energy options.

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2. Continue the calculation by requesting 100 more iterations. Solve −→ Iterate...

The solution converges in approximately 35 additional iterations. Residuals continuity x-velocity y-velocity energy k epsilon

1e+03 1e+02 1e+01 1e+00 1e-01 1e-02 1e-03 1e-04 1e-05 1e-06 1e-07 0

10

20

30

40

50

60

70

80

90

Iterations

Scaled Residuals


Figure 1.11: Residuals for the Second-Order Energy Calculation

Note: Whenever you change the solution control parameters, it is natural to see the residuals jump.


1-37


3. Write the case and data files for the second-order solution (elbow2.cas and elbow2.dat). File −→ Write −→ Case & Data... (a) Enter the name elbow2 in the Case/Data File box. (b) Click OK. The files elbow2.cas and elbow2.dat will be created in your directory. 4. Examine the revised temperature distribution (Figure 1.12). Display −→ Contours...

The thermal spreading after the elbow has been reduced from the earlier prediction (Figure 1.5).

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Figure 1.12: Temperature Contours for the Second-Order Solution


1-39


Step 8: Adapting the Grid The elbow solution can be improved further by refining the grid to better resolve the flow details. In this step, you will adapt the grid based on the temperature gradients in the current solution. Before adapting the grid, you will first determine an acceptable range of temperature gradients over which to adapt. Once the grid has been refined, you will continue the calculation. 1. Plot filled contours of temperature on a cell-by-cell basis (Figure 1.13). Display −→ Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-down lists. (b) Deselect Node Values under Options and click Display. Note: When the contours are displayed you will see the cell values of temperature instead of the smooth-looking node values. Node values are obtained by averaging the values at all of the cells that share the node. Cell values are the values that are stored at each cell center and are displayed throughout the cell. Examining the cell-by-cell values is helpful when you are preparing to do an adaption of the grid because it indicates the region(s) where the adaption will take place.

1-40



2. Plot the temperature gradients that will be used for adaption (Figure 1.14).

(a) Select Adaption... and Adaption Function in the Contours Of drop-down lists. (b) Click Display to see the gradients of temperature, displayed on a cell-by-cell basis.




Figure 1.13: Temperature Contours for the Second-Order Solution: Cell Values


1-41


1.30e-01 1.23e-01 1.17e-01 1.10e-01 1.04e-01 9.74e-02 9.09e-02 8.44e-02 7.79e-02 7.14e-02 6.49e-02 5.84e-02 5.20e-02 4.55e-02 3.90e-02 3.25e-02 2.60e-02 1.95e-02 1.30e-02 6.49e-03 1.42e-14

Contours of Adaption Function


Figure 1.14: Contours of Adaption Function: Temperature Gradient Note: The quantity Adaption Function defaults to the gradient of the variable whose Max and Min were most recently computed in the Contours panel. In this example, the static temperature is the most recent variable to have its Max and Min computed, since this occurs when the Display button is pushed. Note that for other applications, gradients of another variable might be more appropriate for performing the adaption. 3. Plot temperature gradients over a limited range in order to mark cells for adaption (Figure 1.15). (a) Under Options, deselect Auto Range so that you can change the minimum temperature gradient value to be plotted. The Min temperature gradient is 0 K/m, as shown in the Contours panel. (b) Enter a new Min value of 0.02. (c) Click Display. The colored cells in the figure are in the “high gradient” range, so they will be the ones targeted for adaption. 4. Adapt the grid in the regions of high temperature gradient. Adapt −→ Gradient... (a) Select Temperature... and Static Temperature in the Gradients Of drop-down lists. (b) Deselect Coarsen under Options, so that only a refinement of the grid will be performed.

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Contours of Adaption Function


Figure 1.15: Contours of Temperature Gradient Over a Limited Range

(c) Click Compute. FLUENT will update the Min and Max values. (d) Enter the value of 0.02 for the Refine Threshold.


1-43


(e) Click Mark. FLUENT will report the number of cells marked for adaption in the console window. (f) Click Manage... to display the marked cells. This will open the Manage Adaption Registers panel.

(g) Click Display. FLUENT will display the cells marked for adaption (Figure 1.16). (h) Click Adapt. Click Yes when you are asked for confirmation.

Note: There are two different ways to adapt. You can click on Adapt in the Manage Adaption Registers panel as was just done, or Close this panel and do the adaption in the Gradient Adaption panel. If you use the Adapt button in the Gradient Adaption panel, FLUENT will recreate an adaption register. Therefore, once you have the Manage Adaption Registers panel open, it saves time to use the Adapt button there. (i) Close the Manage Adaption Registers and Gradient Adaption panels.

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Adaption Markings (gradient-r0)


Figure 1.16: Cells Marked for Adaption


1-45


5. Display the adapted grid (Figure 1.17). Display −→ Grid...

Grid


Figure 1.17: The Adapted Grid

6. Request an additional 100 iterations. Solve −→ Iterate...

The solution converges after approximately 40 additional iterations. 7. Write the final case and data files (elbow3.cas and elbow3.dat) using the prefix elbow3. File −→ Write −→ Case & Data...

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Residuals continuity x-velocity y-velocity energy k epsilon

1e+03 1e+02 1e+01 1e+00 1e-01 1e-02 1e-03 1e-04 1e-05 1e-06 1e-07 0

20

40

60

80

100

120

140

Iterations

Scaled Residuals


Figure 1.18: The Complete Residual History

8. Examine the filled temperature distribution (using node values) on the revised grid (Figure 1.19). Display −→ Contours... Summary: Comparison of the filled temperature contours for the first solution (using the original grid and first-order discretization) and the last solution (using an adapted grid and second-order discretization) clearly indicate that the latter is much less diffusive. While first-order discretization is the default scheme in FLUENT, it is good practice to use your first-order solution as a starting guess for a calculation that uses a higher-order discretization scheme and, optionally, an adapted grid. Note that in this problem, the flow field is decoupled from temperature since all properties are constant. For such cases, it is more efficient to compute the flow-field solution first (i.e., without solving the energy equation) and then solve for energy (i.e., without solving the flow equations). You will use the Solution Controls panel to turn solution of the equations on and off during this procedure.


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Figure 1.19: Filled Contours of Temperature Using the Adapted Grid

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Tutorial 2. Modeling Periodic Flow and Heat Transfer Introduction: Many industrial applications, such as steam generation in a boiler or air cooling in the coil of an air conditioner, can be modeled as two-dimensional periodic heat flow. This tutorial illustrates how to set up and solve a periodic heat transfer problem, given a pregenerated mesh. The system that is modeled is a bank of tubes containing a flowing fluid at one temperature that is immersed in a second fluid in cross-flow at a different temperature. Both fluids are water, and the flow is classified as laminar and steady, with a Reynolds number of approximately 100. The mass flow rate of the cross-flow is known, and the model is used to predict the flow and temperature fields that result from convective heat transfer. Due to symmetry of the tube bank, and the periodicity of the flow inherent in the tube bank geometry, only a portion of the geometry will be modeled in FLUENT, with symmetry applied to the outer boundaries. The resulting mesh consists of a periodic module with symmetry. In the tutorial, the inflow boundary will be redefined as a periodic zone, and the outflow boundary defined as its shadow. In this tutorial you will learn how to: • Create periodic zones • Define a specified periodic mass flow rate • Model periodic heat transfer with specified temperature boundary conditions • Calculate a solution using the segregated solver • Plot temperature profiles on specified isosurfaces Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps will not be shown explicitly.


2-1

Modeling Periodic Flow and Heat Transfer

Problem Description: This problem considers a 2D section of a tube bank. A schematic of the problem is shown in Figure 2.1. The bank consists of uniformly spaced tubes with a diameter of 1 cm, that are staggered in the direction of cross-fluid flow. Their centers are separated by a distance of 2 cm in the x direction, and 1 cm in the y direction. The bank has a depth of 1 m. Because of the symmetry of the tube bank geometry, only a portion of the domain needs to be modeled. The computational domain is shown in outline in Figure 2.1. A mass flow rate of 0.05 kg/s is applied to the inflow boundary of the periodic module. The temperature of the tube wall (Twall ) is 400 K and the bulk temperature of the cross-flow water (T∞ ) is 300 K. The properties of water that are used in the model are shown in Figure 2.1.

Preparation 1. Copy the file tubebank/tubebank.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

Step 1: Grid 1. Read in the mesh file tubebank.msh. File −→ Read −→Case... 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Scale the grid. Grid −→Scale...

2-2



4 cm

Τ

∞ = 300 K

⋅

m = 0.05 kg/s

{

1 cm

Τ wall = 400 K 0.5 cm

3 ρ = 998.2 kg/m µ = 0.001003 kg/m-s

c p = 4182 J/kg-K k = 0.6 W/m-K

Figure 2.1: Schematic of the Problem


2-3


(a) In the Units Conversion drop-down list, select cm to complete the phrase Grid Was Created In cm (centimeters). (b) Click on Scale to scale the grid. The final Domain Extents should appear as in the panel above. 4. Display the mesh (Figure 2.2). Display −→Grid...

In Figure 2.2 you can see that quadrilateral cells are used in the regions surrounding the tube walls, and triangular cells are used for the rest of the domain, resulting in a “hybrid” mesh. The quadrilateral cells provide better resolution of the viscous gradients near the tube walls. The remainder of the computational domain is conveniently filled with triangular cells.

2-4



Grid


Figure 2.2: Mesh for the Periodic Tube Bank

Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly. 5. Create the periodic zone. wall-9 and wall-12, the inflow and outflow boundaries, respectively, are currently defined as wall zones and need to be redefined as periodic. wall-9 will be made into a translationally periodic zone, and wall-12 will be deleted and redefined as wall-9’s periodic shadow. (a) In the console window, type the commands shown in boxes in the dialog below. Hint: You may need to enter press the key to get the > prompt.


2-5


grid/modify-zones/make-periodic Periodic zone [()] 9 Shadow zone [()] 12 Rotational periodic? (if no, translational) [yes] no Create periodic zones? [yes] yes Auto detect translation vector? [yes] yes computed translation deltas: 0.040000 0.000000 all 26 faces matched for zones 9 and 12. zone 12 deleted created periodic zones.

2-6






2-7


3. Set the periodic flow conditions. Define −→Periodic Conditions...

(a) Select Specify Mass Flow under Type. This will allow you to specify the Mass Flow Rate. (b) Enter a Mass Flow Rate of 0.05 kg/s. (c) Click OK.

2-8



Step 3: Materials You will need to add liquid water to the list of fluid materials by copying it from the materials database. 1. Copy the properties of liquid water from the database. Define −→Materials... (a) Click on the Database... button. This will open the Database Materials panel.


2-9


(b) Scroll down the Fluid Materials list to the bottom, and select water-liquid (h2o). This will display the default settings for water-liquid as shown in the panel above. (c) Click Copy, and Close the Database Materials panel. The Materials panel will now display the copied information for water.

2-10



Step 4: Boundary Conditions Define −→Boundary Conditions... 1. Set the conditions for fluid-16.

(a) Select water-liquid in the Material Name drop-down list.


2-11


2. Set the boundary conditions for wall-21. wall-21 is the bottom wall of the left tube in the periodic module shown in Figure 2.1.

(a) Change the Zone Name from wall-21 to wall-bottom. (b) Select Temperature under Thermal Conditions. (c) Change the Temperature to 400 K.

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3. Set the boundary conditions for wall-3. wall-3 is the top wall of the right tube in the periodic module shown in Figure 2.1.

(a) Change the Zone Name from wall-3 to wall-top. (b) Select Temperature under Thermal Conditions. (c) Change the Temperature to 400 K.


2-13


Step 5: Solution 1. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Change the Under-Relaxation Factor for Energy to 0.9. Hint: You will need to scroll down the Under-Relaxation Factors list to see Energy. (b) Under Discretization, select Second Order Upwind for Momentum and Energy.

2-14



2. Enable the plotting of residuals. Solve −→ Monitors −→Residual...

(a) Under Options, select Plot. (b) Click the OK button.


2-15


3. Initialize the solution. Solve −→ Initialize −→Initialize...

(a) Under Initial Values, check that the value for Temperature is set to 300 K. (b) Click Init, and Close the panel. 4. Save the case file (tubebank.cas). File −→ Write −→Case... 5. Start the calculation by requesting 350 iterations. Solve −→Iterate...

(a) Set the Number of Iterations to 350. (b) Click Iterate.

2-16



The energy residual curve begins to flatten out after about 350 iterations. In order for the solution to converge, the relaxation factor for energy will have to be further reduced. 6. Change the Under-Relaxation Factor for Energy to 0.6. Solve −→ Controls −→Solution... 7. Continue the calculation by requesting another 300 iterations. Solve −→Iterate... After restarting the calculation, you will see an initial dip in the plot of the energy residual, resulting from a reduction in the under-relaxation factor. The solution will converge in a total of approximately 580 iterations. 8. Save the case and data files (tubebank.cas and tubebank.dat). File −→ Write −→Case & Data...


2-17


Step 6: Postprocessing 1. Display filled contours of static pressure (Figure 2.3). Display −→Contours...

(a) Select Filled under Options. (b) Select Pressure... and Static Pressure in the Contours Of drop-down list. (c) Click Display.

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8.20e-02 7.56e-02 6.93e-02 6.29e-02 5.66e-02 5.02e-02 4.39e-02 3.75e-02 3.12e-02 2.48e-02 1.85e-02 1.21e-02 5.78e-03 -5.66e-04 -6.91e-03 -1.33e-02 -1.96e-02 -2.60e-02 -3.23e-02 -3.87e-02 -4.50e-02

Contours of Static Pressure (pascal)

Dec 17, 2002 FLUENT 6.1 (2d, segregated, lam)

Figure 2.3: Contours of Static Pressure

2. Change the view to mirror the display across the symmetry planes (Figure 2.4). Display −→Views...

(a) Select all of the symmetry zones by clicking the shaded icon to the right of Mirror Planes. Note: There are four symmetry zones in the Mirror Planes list because the top and bottom symmetry planes in the domain are each comprised of two symmetry zones, one on each side of the tube. It is also possible to generate the same display shown in Figure 2.4 by selecting just one of the symmetry zones on the top symmetry plane, and one on the bottom.


2-19


(b) Click Apply, and Close the panel. (c) Using the left button of your mouse, translate the view so that it is centered in the window.

8.20e-02 7.56e-02 6.93e-02 6.29e-02 5.66e-02 5.02e-02 4.39e-02 3.75e-02 3.12e-02 2.48e-02 1.85e-02 1.21e-02 5.78e-03 -5.66e-04 -6.91e-03 -1.33e-02 -1.96e-02 -2.60e-02 -3.23e-02 -3.87e-02 -4.50e-02



Figure 2.4: Contours of Static Pressure with Symmetry

Note: The pressure contours displayed in Figure 2.4 do not include the linear pressure gradient computed by the solver; thus the contours are periodic at the inflow and outflow boundaries.

2-20



3. Display filled contours of static temperature (Figure 2.5). Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-down list. (b) Click Display.


2-21





Figure 2.5: Contours of Static Temperature

The contours reveal the temperature increase in the fluid due to heat transfer from the tubes. The hotter fluid is confined to the near-wall and wake regions, while a narrow stream of cooler fluid is convected through the tube bank.

2-22



4. Display the velocity vectors (Figure 2.6). Display −→Vectors...

(a) Select Velocity... and Velocity Magnitude in the Color By drop-down list. (b) Change the Scale to 2. This will enlarge the vectors that are displayed, making it easier to view the flow patterns. (c) Click Display. (d) Zoom in on the upper right portion of the left tube using your middle mouse button, to get the display shown in Figure 2.6. This zoomed-in view of the velocity vector plot clearly shows the recirculating flow behind the tube and the boundary layer development along the tube surface.


2-23





Figure 2.6: Velocity Vectors

2-24



5. Plot the temperature profiles at three cross-sections of the tube bank. (a) Create an isosurface on the periodic tube bank at x = 0.01 m (through the first tube). You will first need to create a surface of constant x coordinate for each crosssection: x = 0.01, 0.02, and 0.03 m. These isosurfaces correspond to the vertical cross-sections through the first tube, halfway between the two tubes, and through the second tube. Surface −→Iso-Surface...

i. In the Surface of Constant drop-down lists, select Grid... and X-Coordinate. ii. Enter x=0.01m under New Surface Name. iii. Enter 0.01 for Iso-Values. iv. Click Create. (b) Follow the same procedure to create surfaces at: • x = 0.02 m (halfway between the two tubes) • x = 0.03 m (through the middle of the second tube)


2-25


(c) Create an XY plot of static temperature on the three isosurfaces. Plot −→XY Plot...

i. Change the Plot Direction for X to 0, and the Plot Direction for Y to 1. With a Plot Direction vector of (0,1), FLUENT will plot the selected variable as a function of y. Since you are plotting the temperature profile on cross-sections of constant x, the y direction is the one in which the temperature varies. ii. Select Temperature... and Static Temperature in the Y-Axis Function dropdown lists. iii. Scroll down the Surfaces list and select x=0.01m, x=0.02m, and x=0.03m. iv. Click Curves... to define different styles for the different plot curves. This will open the Curves - Solution XY Plot panel.

2-26



v. Select + in the Symbol drop-down list. vi. Click Apply. This assigns the + symbol to the x = 0.01 m curve. vii. Increase the Curve # to 1 to define the style for the x = 0.02 m curve. viii. Select x in the Symbol drop-down list. ix. Change the Size to 0.5. x. Click Apply, and Close the panel. Since you did not change the curve style for the x = 0.03 m curve, the default symbol will be used. xi. In the Solution XY Plot panel, click Plot. Summary: In this tutorial, periodic flow and heat transfer in a staggered tube bank were modeled in FLUENT. The model was set up assuming a known mass flow through the tube bank and constant wall temperatures. Due to the periodic nature of the flow and symmetry of the geometry, only a small piece of the full geometry was modeled. In addition, the tube bank configuration lent itself to the use of a hybrid mesh with quadrilateral cells around the tubes and triangles elsewhere. The Periodicity Conditions panel makes it easy to run this type of model over a variety of operating conditions. For example, different flow rates (and hence different Reynolds numbers) can be studied, or a different inlet bulk temperature can be imposed. The resulting solution can then be examined to extract the pressure drop per tube row and overall Nusselt number for a range of Reynolds numbers.


2-27


x=0.01m x=0.02m x=0.03m

4.00e+02

3.80e+02

3.60e+02

3.40e+02


3.20e+02

3.00e+02

2.80e+02

2.60e+02 0

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

0.01

Position (m)

Static Temperature


Figure 2.7: Static Temperature at x=0.01, 0.02, and 0.03 m

2-28


Tutorial 3. Flow

Modeling External Compressible

Introduction: The purpose of this tutorial is to compute the turbulent flow past a transonic airfoil at a non-zero angle of attack. You will use the Spalart-Allmaras turbulence model. In this tutorial you will learn how to: • Model compressible flow (using the ideal gas law for density) • Set boundary conditions for external aerodynamics • Use the Spalart-Allmaras turbulence model • Calculate a solution using the coupled implicit solver • Use force and surface monitors to check solution convergence • Check the grid by plotting the distribution of y + Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly.


3-1

Modeling External Compressible Flow

Problem Description: The problem considers the flow around an airfoil at an incidence angle of α = 4◦ and a free stream Mach number of 0.8 (M∞ = 0.8). This flow is transonic, and has a fairly strong shock near the mid-chord (x/c = 0.45) on the upper (suction) side. The chord length is 1 m. The geometry of the airfoil is shown in Figure 3.1. α = 4°

M∞= 0.8 1m


Preparation 1. Copy the file airfoil/airfoil.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

3-2



Step 1: Grid 1. Read the grid file airfoil.msh. File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...

(a) Display the grid with the default settings (Figure 3.2). (b) Use the middle mouse button to zoom in on the image so you can see the mesh near the airfoil (Figure 3.3). Quadrilateral cells were used for this simple geometry because they can be stretched easily to account for different size gradients in different directions. In the present case, the gradients normal to the airfoil wall are much greater than those tangent to the airfoil, except near the leading and trailing edges and in the vicinity of the shock expected on the upper surface. Consequently, the cells nearest the surface have very high aspect ratios. For geometries that are


3-3


Grid


Figure 3.2: The Grid Around the Airfoil

Grid


Figure 3.3: The Grid After Zooming In on the Airfoil

3-4



more difficult to mesh, it may be easier to create a hybrid mesh comprised of quadrilateral and triangular cells. A parabola was chosen to represent the far-field boundary because it has no discontinuities in slope, enabling the construction of a smooth mesh in the interior of the domain. Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.


3-5


Step 2: Models 1. Select the Coupled, Implicit solver. Define −→ Models −→Solver... The coupled solver is recommended when dealing with applications involving highspeed aerodynamics. The implicit solver will generally converge much faster than the explicit solver, but will use more memory. For this 2D case, memory is not an issue.

2. Enable heat transfer by turning on the energy equation. Define −→ Models −→Energy...

3-6



3. Turn on the Spalart-Allmaras turbulence model. Define −→ Models −→Viscous...

(a) Select the Spalart-Allmaras model and retain the default options and constants. 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.


3-7


Step 3: Materials The default Fluid Material is air, which is the working fluid in this problem. The default settings need to be modified to account for compressibility and variations of the thermophysical properties with temperature. Define −→Materials...

1. Select ideal-gas in the Density drop-down list. 2. Select sutherland in the drop-down list for Viscosity. This will open the Sutherland Law panel.

3-8



(a) Click OK to accept the default Three Coefficient Method and parameters. The Sutherland law for viscosity is well suited for high-speed compressible flows. 3. Click Change/Create in the Materials panel to save these settings, and then close the panel. Note: While Density and Viscosity have been made temperature-dependent, Cp and Thermal Conductivity have been left constant. For high-speed compressible flows, thermal dependency of the physical properties is generally recommended. In this case, however, the temperature gradients are sufficiently small that the model is accurate with Cp and Thermal Conductivity constant.


3-9


Step 4: Operating Conditions Set the operating pressure to 0 Pa. Define −→Operating Conditions...

For flows with Mach numbers greater than 0.1, an operating pressure of 0 is recommended. For more information on how to set the operating pressure, see the FLUENT User’s Guide.

3-10



Step 5: Boundary Conditions Set the boundary conditions for pressure-far-field-1 as shown in the panel. Define −→Boundary Conditions...

For external flows, you should choose a viscosity ratio between 1 and 10. Note: The X- and Y-Component of Flow Direction are set as above because of the 4◦ angle of attack: cos 4◦ ≈ 0.997564 and sin 4◦ ≈ 0.069756.


3-11


Step 6: Solution 1. Set the solution controls. Solve −→ Controls −→Solution...

(a) Set the Under-Relaxation Factor for Modified Turbulent Viscosity to 0.9. Larger (i.e., closer to 1) under-relaxation factors will generally result in faster convergence. However, instability can arise that may need to be eliminated by decreasing the under-relaxation factors. (b) Under Solver Parameters, set the Courant Number to 5. (c) Under Discretization, select Second Order Upwind for Modified Turbulent Viscosity. The second-order scheme will resolve the boundary layer and shock more accurately than the first-order scheme.

3-12



2. Turn on residual plotting during the calculation. Solve −→ Monitors −→Residual... 3. Initialize the solution. Solve −→ Initialize −→Initialize...

(a) Select pressure-far-field-1 in the Compute From drop-down list. (b) Click Init to initialize the solution. To monitor the convergence of the solution, you are going to enable the plotting of the drag, lift, and moment coefficients. You will need to iterate until all of these forces have converged in order to be certain that the overall solution has converged. For the first few iterations of the calculation, when the solution is fluctuating, the values of these coefficients will behave erratically. This can cause the scale of the y axis for the plot to be set too wide, and this will make variations in the value of the coefficients less evident. To avoid this problem, you will have FLUENT perform a small number of iterations, and then you will set up the monitors. Since the drag, lift, and moment coefficients are global variables, indicating certain overall conditions, they may converge while conditions at specific points are still varying from one iteration to the next. To monitor this, you will create a point monitor at a point where there is likely to be significant variation, just upstream of the shock wave, and monitor the value of the skin friction coefficient. A small number of iterations will be sufficient to roughly determine the location of the shock. After setting up the monitors, you will continue the calculation. 4. Request 100 iterations. Solve −→Iterate...


3-13


This will be sufficient to see where the shock wave is, and the fluctuations of the solution will have diminished significantly. 5. Increase the Courant number. Solve −→ Controls −→Solution... Under Solver Parameters, set the Courant Number to 20. The solution will generally converge faster for larger Courant numbers, unless the integration scheme becomes unstable. Since you have performed some initial iterations, and the solution is stable, you can try increasing the Courant number to speed up convergence. If the residuals increase without bound, or you get a floating point exception, you will need to decrease the Courant number, read in the previous data file, and try again. 6. Turn on monitors for lift, drag, and moment coefficients. Solve −→ Monitors −→Force...

(a) In the drop-down list under Coefficient, select Drag. (b) Select wall-bottom and wall-top in the Wall Zones list. (c) Under Force Vector, enter 0.9976 for X and 0.06976 for Y. These magnitudes ensure that the drag and lift coefficients are calculated normal and parallel to the flow, which is 4◦ off of the global coordinates. (d) Select Plot under Options to enable plotting of the drag coefficient. (e) Select Write under Options to save the monitor history to a file, and specify cd-history as the file name. If you do not select the Write option, the history information will be lost when you exit FLUENT.

3-14



(f) Click Apply. (g) Repeat the above steps for Lift, using values of 0.06976 for X and 0.9976 for Y under Force Vector. (h) Repeat the above steps for Moment, using values of 0.25 m for X and 0 m for Y under Moment Center. 7. Set the reference values that are used to compute the lift, drag, and moment coefficients. The reference values are used to non-dimensionalize the forces and moments acting on the airfoil. The dimensionless forces and moments are the lift, drag, and moment coefficients. Report −→Reference Values... (a) In the Compute From drop-down list, select pressure-far-field-1. FLUENT will update the Reference Values based on the boundary conditions at the far-field boundary.


3-15


8. Define a monitor for tracking the skin friction coefficient value just upstream of the shock wave. (a) Display filled contours of pressure overlaid with the grid. Display −→Contours... i. Turn on Filled. ii. Select Draw Grid. This will open the Grid Display panel. iii. Close the Grid Display panel, since there are no changes to be made here. iv. Click Display in the Contours panel. v. Zoom in on the airfoil (Figure 3.4).



Nov 14, 2002 FLUENT 6.1 (2d, coupled imp, S-A)

Figure 3.4: Pressure Contours After 100 Iterations The shock wave is clearly visible on the upper surface of the airfoil, where the pressure first jumps to a higher value. vi. Zoom in on the shock wave, until individual cells adjacent to the upper surface (wall-top boundary) are visible (Figure 3.5).

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Figure 3.5: Magnified View of Pressure Contours Showing Wall-Adjacent Cells The zoomed-in region contains cells just upstream of the shock wave that are adjacent to the upper surface of the airfoil. In the following step, you will create a point surface inside a wall-adjacent cell, to be used for the skin friction coefficient monitor. (b) Create a point surface just upstream of the shock wave. Surface −→Point...

i. Under Coordinates, enter 0.53 for x0, and 0.051 for y0. ii. Click on Create to create the point surface (point-4).


3-17





Figure 3.6: Pressure Contours With Point Surface Note: Here, you have entered the exact coordinates of the point surface so that your convergence history will match the plots and description in this tutorial. In general, however, you will not know the exact coordinates in advance, so you will need to select the desired location in the graphics window as follows: i. Click Select Point With Mouse. ii. Move the mouse to a point located anywhere inside one of the cells adjacent to the upper surface (wall-top boundary), in the vicinity of the shock wave. (See Figure 3.6.) iii. Click the right mouse button. iv. Click Create to create the point surface.

3-18



(c) Create a surface monitor for the point surface. Solve −→ Monitors −→Surface...

i. Increase Surface Monitors to 1. ii. To the right of monitor-1, turn on the Plot and Write options and click Define.... This will open the Define Surface Monitor panel.

iii. Select Wall Fluxes... and Skin Friction Coefficient under Report Of. iv. Select point-4 in the Surfaces list. v. In the Report Type drop-down list, select Vertex Average.


3-19


vi. Increase the Plot Window to 4. vii. Specify monitor-1.out as the File Name, and click OK in the Define Surface Monitor panel. viii. Click OK in the Surface Monitors panel. 9. Save the case file (airfoil.cas). File −→ Write −→Case... 10. Continue the calculation by requesting 200 iterations. Solve −→Iterate...

2.00e-03 1.80e-03 1.60e-03 1.40e-03 1.20e-03

Vertex Average Skin Friction Coefficient

1.00e-03 8.00e-04 6.00e-04 4.00e-04 2.00e-04 100

110

120

130

140

150

160

170

180

190

200

Iteration

Convergence history of Skin Friction Coefficient on point-4 (in SI units) Nov 14, 2002 FLUENT 6.1 (2d, coupled imp, S-A)

Figure 3.7: Skin Friction Convergence History for the Initial Calculation

Note: After about 90 iterations, the residual criteria are satisfied and FLUENT stops iterating. Since the skin friction monitor indicates that the skin friction coefficient at point-4 has not converged (Figure 3.7), you will need to decrease the convergence criterion for the modified turbulent viscosity and continue iterating.

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11. Reduce the convergence criterion for the modified turbulent viscosity equation. Solve −→ Monitors −→Residual...

(a) Set the Convergence Criterion for nut to 1e-7 and click OK. nut stands for νt . This is the residual for the modified turbulent viscosity that the Spalart-Allmaras model solves for. 12. Continue the calculation for another 600 iterations. After 600 additional iterations, the force monitors and the skin friction coefficient monitor (Figures 3.8–3.11), indicate that the solution has converged. 13. Save the data file (airfoil.dat). File −→ Write −→Data...


3-21


2.00e-03 1.80e-03 1.60e-03 1.40e-03 1.20e-03

Vertex Average Skin Friction Coefficient

1.00e-03 8.00e-04 6.00e-04 4.00e-04 2.00e-04 100

200

300

400

500

600

700

800

Iteration

Convergence history of Skin Friction Coefficient on point-4 (in SI units) Nov 14, 2002 FLUENT 6.1 (2d, coupled imp, S-A)

Figure 3.8: Skin Friction Coefficient History

8.00e-02

7.50e-02

7.00e-02

Cd

6.50e-02

6.00e-02

5.50e-02

5.00e-02 100

200

300

400

500

600

700

800

Iterations

Drag Convergence


Figure 3.9: Drag Coefficient Convergence History

3-22



6.00e-01 5.75e-01 5.50e-01 5.25e-01 5.00e-01 4.75e-01

Cl

4.50e-01 4.25e-01 4.00e-01 3.75e-01 3.50e-01 3.25e-01 100

200

300

400

500

600

700

800

Iterations

Lift Convergence


Figure 3.10: Lift Coefficient Convergence History

7.00e-02 6.00e-02 5.00e-02 4.00e-02 3.00e-02

Cm 2.00e-02 1.00e-02 0.00e+00 -1.00e-02 -2.00e-02 100

200

300

400

500

600

700

800

Iterations

Moment Convergence


Figure 3.11: Moment Coefficient Convergence History


3-23


Step 7: Postprocessing 1. Plot the y + distribution on the airfoil. Plot −→XY Plot...

(a) Under Y Axis Function, select Turbulence... and Wall Yplus. (b) In the Surfaces list, select wall-bottom and wall-top. (c) Deselect Node Values and click Plot. Wall Yplus is available only for cell values. The values of y + are dependent on the resolution of the grid and the Reynolds number of the flow, and are meaningful only in boundary layers. The value of y + in the wall-adjacent cells dictates how wall shear stress is calculated. When you use the Spalart-Allmaras model, you should check that y + of the wall-adjacent cells is either very small (on the order of y + = 1), or approximately 30 or greater. Otherwise, you will need to modify your grid. The equation for y + is y+ =

y√ ρτw µ

where y is the distance from the wall to the cell center, µ is the molecular viscosity, ρ is the density of the air, and τw is the wall shear stress. Figure 3.12 indicates that, except for a few small regions (notably at the shock and the trailing edge), y + > 30 and for much of these regions it does not drop significantly below 30. Therefore, you can conclude that the grid resolution is acceptable.

3-24



wall-bottom wall-top 8.00e+01 7.00e+01 6.00e+01 5.00e+01

Wall Yplus

4.00e+01 3.00e+01 2.00e+01 1.00e+01 0.00e+00 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Wall Yplus


Figure 3.12: XY Plot of y + Distribution

2. Display filled contours of Mach number (Figure 3.13). Display −→Contours... (a) Select Velocity... and Mach Number under Contours Of. (b) Turn off the Draw Grid option. (c) Click Display. Note the discontinuity, in this case a shock, on the upper surface at about x/c ≈ 0.45. 3. Plot the pressure distribution on the airfoil (Figure 3.14). Plot −→XY Plot... (a) Under Y Axis Function, choose Pressure... and Pressure Coefficient from the drop-down lists. (b) Click Plot. Notice the effect of the shock wave on the upper surface. 4. Plot the x component of wall shear stress on the airfoil surface (Figure 3.15). Plot −→XY Plot... (a) Under Y Axis Function, choose Wall Fluxes... and X-Wall Shear Stress from the drop-down lists. (b) Click Plot.


3-25


1.44e+00 1.37e+00 1.30e+00 1.22e+00 1.15e+00 1.08e+00 1.01e+00 9.39e-01 8.68e-01 7.96e-01 7.25e-01 6.53e-01 5.82e-01 5.10e-01 4.39e-01 3.67e-01 2.96e-01 2.25e-01 1.53e-01 8.17e-02 1.02e-02

Contours of Mach Number


Figure 3.13: Contour Plot of Mach Number

wall-bottom wall-top 1.25e+00 1.00e+00 7.50e-01 5.00e-01 2.50e-01

Pressure Coefficient

0.00e+00 -2.50e-01 -5.00e-01 -7.50e-01 -1.00e+00 -1.25e+00 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)



Figure 3.14: XY Plot of Pressure

3-26



wall-bottom wall-top 2.25e+02 2.00e+02 1.75e+02 1.50e+02 1.25e+02

X-Wall Shear Stress (pascal)

1.00e+02 7.50e+01 5.00e+01 2.50e+01 0.00e+00 -2.50e+01 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

X-Wall Shear Stress


Figure 3.15: XY Plot of x Wall Shear Stress

The large, adverse pressure gradient induced by the shock causes the boundary layer to separate. The point of separation is where the wall shear stress vanishes. Flow reversal is indicated here by negative values of the x component of the wall shear stress. 5. Display filled contours of the x component of velocity (Figure 3.16). Display −→Contours... (a) Select Velocity... and X Velocity under Contours Of. (b) Click Display. Note the flow reversal behind the shock. 6. Plot velocity vectors (Figure 3.17). Display −→Vectors... (a) Increase Scale to 15, and click Display. Zooming in on the upper surface, behind the shock, will produce a display similar to Figure 3.17. Flow reversal is clearly visible. Summary: This tutorial demonstrated how to set up and solve an external aerodynamics problem using the Spalart-Allmaras turbulence model. It showed how to monitor convergence using residual, force, and surface monitors, and demonstrated the use of several postprocessing tools to examine the flow phenomena associated with a shock wave.


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4.46e+02 4.20e+02 3.94e+02 3.68e+02 3.42e+02 3.16e+02 2.90e+02 2.64e+02 2.38e+02 2.12e+02 1.86e+02 1.60e+02 1.34e+02 1.08e+02 8.17e+01 5.56e+01 2.96e+01 3.60e+00 -2.24e+01 -4.85e+01 -7.45e+01

Contours of X Velocity (m/s)


Figure 3.16: Contour Plot of x Component of Velocity




Figure 3.17: Plot of Velocity Vectors Near Upper Wall, Behind Shock

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Tutorial 4. Modeling Unsteady Compressible Flow Introduction: In this tutorial, FLUENT’s coupled implicit solver is used to predict the time-dependent flow through a two-dimensional nozzle. As an initial condition for the transient problem, a steady-state solution is generated to provide the initial values for the mass flow rate at the nozzle exit. In this tutorial you will learn how to: • Calculate a steady-state solution (using the coupled implicit solver) as an initial condition for a transient flow prediction • Define an unsteady boundary condition using a user-defined function (UDF) • Use dynamic mesh adaption for both steady-state and transient flows • Calculate a transient solution using the second-order implicit unsteady formulation and the coupled implicit solver • Create an animation of the unsteady flow using FLUENT’s unsteady solution animation feature Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The geometry to be considered in this tutorial is shown in Figure 4.1. Flow through a simple nozzle is simulated as a 2D planar model. The nozzle has an inlet height of 0.2 m, and the nozzle contours have a sinusoidal shape that produces a 10% reduction in flow area. Due to symmetry, only half of the nozzle is modeled.

Preparation 1. Copy the files nozzle/nozzle.msh and nozzle/pexit.c from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.


4-1

Modeling Unsteady Compressible Flow

plane of symmetry

p (t )

0.2 m

exit

p = 0.9 atm inlet

p = 0.7369 atm exit


4-2



Step 1: Grid 1. Read in the mesh file nozzle.msh. File −→ Read −→Case... 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...

To make the view more realistic, you will need to mirror it across the centerline.


4-3


4. Mirror the view across the centerline. Display −→Views...

(a) Select symmetry under Mirror Planes. (b) Click Apply. The grid for the nozzle is shown in Figure 4.2.

Grid


Figure 4.2: 2D Nozzle Mesh Display

4-4



Step 2: Units 1. For convenience, define new units for pressure. The pressure for this problem is specified in atm, which is not the default unit. You will need to redefine the pressure unit as atm. Define −→Units...

(a) Select pressure under Quantities, and atm under Units. Hint: Use the scroll bar to access pressure, which is not initially visible in the list. (b) Close the panel.


4-5


Step 3: Models 1. Select the coupled implicit solver. The coupled implicit solver is the solver of choice for compressible, transonic flows. Define −→ Models −→Solver...

Note: Initially, you will solve for the steady flow through the nozzle. Later, after obtaining the steady flow as a starting point, you will revisit this panel to enable an unsteady calculation.

4-6



2. Enable the Spalart-Allmaras turbulence model. Define −→ Models −→Viscous...

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 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.


4-7


Step 4: Materials 1. Set the properties for air, the default fluid material. Define −→Materials...

(a) Select the ideal-gas law to compute Density. Note: FLUENT will automatically enable solution of the energy equation when the ideal gas law is used. You do not need to visit the Energy panel to turn it on. (b) Retain the default values for all other properties. !

4-8

Don’t forget to click the Change/Create button to save your change.



Step 5: Operating Conditions 1. Set the operating pressure to 0 atm. Define −→Operating Conditions...

Here, the operating pressure is set to zero and boundary condition inputs for pressure will be defined in terms of absolute pressures. Boundary condition inputs should always be relative to the value used for operating pressure.


4-9


Step 6: Boundary Conditions Define −→Boundary Conditions... 1. Set the conditions for the nozzle inlet (inlet).

(a) Set the Gauge Total Pressure to 0.9 atm. (b) Set the Supersonic/Initial Gauge Pressure to 0.7369 atm. The inlet static pressure estimate is the mean pressure at the nozzle exit. This value will be used during the solution initialization phase to provide a guess for the nozzle velocity. (c) In the Turbulence Specification Method drop-down list, select Turbulent Viscosity Ratio. (d) Set the Turbulent Viscosity Ratio to 1. For low to moderate inlet turbulence, a viscosity ratio of 1 is recommended.

4-10



2. Set the conditions for the nozzle exit (outlet).

(a) Set the Gauge Pressure to 0.7369 atm. (b) In the Turbulence Specification Method drop-down list, select Turbulent Viscosity Ratio. (c) Accept the default value of 10 for Backflow Turbulent Viscosity Ratio. If substantial backflow occurs at the outlet, you may need to adjust the backflow values to levels close to the actual exit conditions.


4-11


Step 7: Solution: Steady Flow 1. Initialize the solution. Solve −→ Initialize −→Initialize...

(a) Select inlet in the Compute From drop-down list. (b) Click Init, and Close the panel.

4-12



2. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Under Discretization, select Second Order Upwind for Modified Turbulent Viscosity. Second-order discretization provides optimum accuracy.


4-13


3. Perform gradient adaption to refine the mesh. Adapt −→Gradient

(a) Under Method, select Gradient. The mesh adaption criterion can either be the gradient or the curvature (second gradient). Because strong shocks occur inside the nozzle, the gradient is used as the adaption criterion. (b) Under Gradients Of, make sure that Pressure... and Static Pressure are selected. (c) Under Normalization, select Scale. Mesh adaption can be controlled by the raw (or standard) value of the gradient, the scaled value (by its average in the domain), or the normalized value (by its maximum in the domain). For dynamic mesh adaption, it is recommended to use either the scaled or normalized value because the raw values will probably change strongly during the computation, which would necessitate a readjustment of the coarsen and refine thresholds. In this case, the scaled gradient is used. (d) Set the Coarsen Threshold to 0.3. (e) Set Refine Threshold to 0.7. As the refined regions of the mesh get larger, the coarsen and refine thresholds should get smaller. A coarsen threshold of 0.3 and a refine threshold of 0.7 result in a “medium” to “strong” mesh refinement in combination with the scaled gradient.

4-14



(f) Turn on the Dynamic option under Dynamic and set the Interval to 100. For steady-state flows, it is sufficient to only seldomly adapt the mesh—in this case an interval of 100 iterations is chosen. For time-dependent flows, a considerably smaller interval must be used. (g) Click Compute and then click Mark to store the information. (h) Click on Controls... to modify the adaption controls.

i. In the Grid Adaption Controls panel, turn on the Dynamic option under Dynamic and set the Interval to 100. For steady-state flows, it is sufficient to only seldomly adapt the mesh— in this case an interval of 100 iterations is chosen. For time-dependent flows, a considerably smaller interval must be used. ii. Make sure that fluid is selected under Zones. iii. Set the Max # of Cells to 20000. To restrict the mesh adaption, the maximum number of cells can be limited. If this limit is violated during the adaption, the corsen and refine thresholds are adjusted to respect the maximum number of cells. Additional restrictions can be placed on the minimum cell volume, minimum number of cells, and maximum level of refinement. iv. Click OK.


4-15



(a) Under Options, select Plot. (b) Click OK. 5. Enable the plotting of mass flow rate at the flow exit. Solve −→ Monitors −→Surface...

4-16



(a) Increase the number of Surface Monitors to 1. (b) Turn on the Plot and Write options for monitor-1. Note: When the Write option is selected in the Surface Monitors panel, the mass flow rate history will be written to a file. If you do not select the write option, the history information will be lost when you exit FLUENT. (c) Click on Define... to specify the surface monitor parameters in the Define Surface Monitor panel.

i. Select Mass Flow Rate in the Report Type drop-down list. ii. Select outlet in the Surfaces list. iii. In the File Name field, enter the name noz ss.out. iv. Click on OK to define the monitor. (d) Click on OK in the Surface Monitors panel to enable the monitor. 6. Save the case file (noz ss.cas). File −→ Write −→Case...


4-17


7. Start the calculation by requesting 2000 iterations. Solve −→Iterate...

The solution will converge after about 1800 iterations. The mass flow rate history is shown in Figure 4.3.

-14.0000

-14.5000

-15.0000

Mass Flow Rate (kg/s)

-15.5000

-16.0000

-16.5000

-17.0000 0

200

400

600

800

1000

1200

1400

1600

1800

Iteration

Convergence history of Mass Flow Rate on outlet


Figure 4.3: Mass Flow Rate History

8. Save the data file (noz ss.dat). File −→ Write −→Data...

4-18



9. Check the mass flux balance. Report −→Fluxes... !

Although the mass flow rate history indicates that the solution is converged, you should also check the mass fluxes through the domain to ensure that mass is being conserved.

(a) Keep the default Mass Flow Rate option. (b) Select inlet and outlet in the Boundaries list. (c) Click Compute. !

The net mass imbalance should be a small fraction (say, 0.5%) of the total flux through the system. If a significant imbalance occurs, you should decrease your residual tolerances by at least an order of magnitude and continue iterating.


4-19


10. Display the steady-flow velocity vectors (Figure 4.4). Display −→Vectors...

(a) Change the Scale to 10. (b) In the Surfaces list, select all of the surfaces. (c) Click Display. The steady flow prediction shows the expected form, with peak velocity of about 335 m/s through the nozzle.

4-20



3.35e+02 3.19e+02 3.02e+02 2.85e+02 2.69e+02 2.52e+02 2.35e+02 2.18e+02 2.02e+02 1.85e+02 1.68e+02 1.51e+02 1.35e+02 1.18e+02 1.01e+02 8.46e+01 6.78e+01 5.11e+01 3.44e+01 1.77e+01 9.40e-01


Dec 17, 2002 FLUENT 6.1 (2d, coupled imp, S-A)

Figure 4.4: Velocity Vectors (Steady Flow)


4-21


11. Display the steady flow contours of static pressure (Figure 4.5). Display −→Contours...

(a) Under Options, select Filled. (b) In the Surfaces list, select all of the surfaces. (c) Click Display. The steady flow prediction shows the expected pressure distribution, with low pressure near the nozzle throat.

4-22




Contours of Static Pressure (atm)

Dec 17, 2002 FLUENT 6.1 (2d, coupled imp, S-A)

Figure 4.5: Contours of Static Pressure (Steady Flow)


4-23


Step 8: Enable Time Dependence and Set Unsteady Conditions In this step you will define a transient flow by specifying an unsteady pressure condition for the nozzle. 1. Enable a time-dependent flow calculation. Define −→ Models −→Solver...

(a) Under Time, select Unsteady. (b) Under Unsteady Formulation, select 2nd-Order Implicit. Implicit (dual) time-stepping allows you to set the physical time step used for the transient flow prediction (while FLUENT continues to determine the time step used for inner iterations based on a Courant condition). Here, second-order implicit time-stepping is enabled: this provides higher accuracy in time than the first-order option.

4-24



2. Define the unsteady condition for the nozzle exit (outlet). The pressure at the outlet is defined as a wave-shaped profile, and is described by the following equation: pexit (t) = 0.12 sin(ωt) + pexit where ω = pexit =

(4.1)

circular frequency of unsteady pressure (rad/s) mean exit pressure (atm)

In this case, ω = 2200 rad/s, and pexit = 0.7369 atm. A user-defined function (pexit.c) has been written to define the equation (Equation 4.1) required for the pressure profile. Note: To input the value of Equation 4.1 in the correct units, the function pexit.c has been multiplied by a factor of 101325 to convert from the chosen pressure unit (atm) to the SI unit required by FLUENT (Pa). This will not affect the displayed results. See the separate UDF Manual for details about user-defined functions. (a) Read in the user-defined function. Define −→ User-Defined −→ Functions −→Interpreted...

i. Enter pexit.c as the Source File Name. ii. Click Interpret. The user-defined function has already been defined, but it needs to be compiled within FLUENT before it can be used in the solver. iii. Close the Interpreted UDFs panel.


4-25


(b) Set the unsteady boundary conditions at the exit.

i. Select udf unsteady pressure (the user-defined function) in the Gauge Pressure drop-down list. 3. Update the gradient adaption parameters for the transient case. Adapt −→Gradient (a) Reset the Coarsen Threshold to 0.3. (b) Reset the Refine Threshold to 0.7. The refine and coarsen thresholds have been changed during the steady-state computation to meet the limit of 20000 cells. Therefore, you need to reset these parameters to their original values. (c) Under Dynamic, set the Interval to 1. For the transient case, the mesh adaption will be done every time step. (d) Click Compute and then Mark to store the values. The console window will print statistics on the cells that are to be refined and coarsened. (e) Click on Controls... to modify the adaption controls. i. In the Grid Adaption Controls panel, set the Min # of Cells to 8000. ii. Set the Max # of Cells to 30000. The maximum number of cells is increased to try to avoid readjustment of the coarsen and refine thresholds. Additionally, the minimum number of cells has been limited to 8000 because it is not desired to have a coarse mesh during the computation (the current mesh has about 10000 cells). iii. Click OK.

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Step 9: Solution: Unsteady Flow 1. Set the time step parameters. The selection of the time step is critical for accurate time-dependent flow predictions. Using a time step of 2.85596 × 10−5 seconds, 100 time steps are required for one pressure cycle. The pressure cycle begins and ends with the initial pressure at the nozzle exit. Solve −→Iterate...

(a) Set the Time Step Size to 2.85596e-5 s. (b) Set the Number of Time Steps to 600. (c) Set the Max Iterations per Time Step to 30. (d) Click Apply.


4-27


2. Modify the plotting of the mass flow rate at the nozzle exit. Because each time step requires 30 iterations, a smoother plot will be generated by plotting at every time step. Solve −→ Monitors −→Surface...

(a) For monitor-1, select Time Step in the drop-down list under Every. (b) Click Define... to modify the surface monitor parameters. i. In the Define Surface Monitor panel, change the File Name to noz uns.out. ii. In the X Axis drop-down list, select Time Step. iii. Click OK. (c) Click OK in the Surface Monitors panel. 3. Save the transient solution case file (noz uns.cas). File −→ Write −→Case...

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4. Start the transient calculation. Solve −→Iterate... !

Calculation of 600 time steps will require significant CPU resources. Instead of calculating, you can read the data file saved after the iterations have been completed: noz uns.dat (The data file is available in the same directory where you found the mesh and UDF files.)

By requesting 600 time steps, you are asking FLUENT to compute six pressure cycles. The mass flow rate history is shown in Figure 4.6.

-4.00e+00 -6.00e+00 -8.00e+00 -1.00e+01

Mass Flow Rate Mass Flow Rate

-1.20e+01 -1.40e+01 -1.60e+01 -1.80e+01 -2.00e+01 0

100

200

300

400

500

600

Time Step

Convergence history of Mass Flow Rate on outlet (in SI units) (Time=1.7136e-02) Dec 09, 2002 FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

Figure 4.6: Mass Flow Rate History (Unsteady Flow)

5. Save the transient solution data file (noz uns.dat). File −→ Write −→Data...


4-29


Step 10: Saving and Postprocessing Time-Dependent Data Sets The solution has reached a time-periodic state. To study how the flow changes within a single pressure cycle, you will now continue the solution for 100 more time steps. You will use FLUENT’s solution animation feature to save contour plots of pressure and Mach number at each time step, and the autosave feature to save case and data files every 10 time steps. After the calculation is complete, you will use the solution animation playback feature to view the animated pressure and Mach number plots over time. 1. Request saving of case and data files every 10 time steps. File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 10. (b) In the Filename field, enter noz anim. (c) Click OK. When FLUENT saves a file, it will append the time step value to the file name prefix (noz anim). The standard extensions (.cas and .dat) will also be appended. This will yield file names of the form noz anim0640.cas and noz anim0640.dat, where 0640 is the time step number. Optionally, you can add the extension .gz to the end of the file name (e.g., noz anim.gz), which will instruct FLUENT to save the case and data files in compressed format, yielding file names of the form noz anim0640.cas.gz.

4-30



2. Create animation sequences for the nozzle pressure and Mach number contour plots. Solve −→ Animate −→Define...

(a) Increase the number of Animation Sequences to 2. (b) Under Name, enter pressure for the first sequence and mach-number for the second sequence. (c) In the When drop-down lists, select Time Step. With the default value of 1 for Every, this instructs FLUENT to update the animation sequence at every time step.


4-31


3. Define the animation sequence for pressure. (a) Click Define... on the line for pressure to set the parameters for the pressure sequence. The Animation Sequence panel will open.

(b) Under Storage Type, select In Memory. The Memory option is acceptable for a small 2D case such as this. For larger 2D or 3D cases, saving animation files with either the Metafile or PPM Image option is preferable to avoid using too much of your machine’s memory. (c) Increase the Window number to 2 and click Set. Graphics window number 2 will open. (d) Under Display Type, select Contours. The Contours panel will open.

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i. In the Contours panel, keep the default selections of Pressure... and Static Pressure. ii. Make sure that Filled is selected under Options, and deselect Auto Range. iii. Enter 0.25 under Min and 1.25 under Max. This will set a fixed range for the contour plot and subsequent animation. iv. In the Surfaces list, select all of the surfaces. v. Click Display. Figure 4.7 shows the contours of static pressure in the nozzle after 600 time steps. (e) Click OK in the Animation Sequence panel.


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Contours of Static Pressure (atm) (Time=1.7136e-02)

Dec 17, 2002 FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

Figure 4.7: Pressure Contours at t = 0.01714 s

4-34



4. Define the animation sequence for Mach number. (a) In the Solution Animation panel, click Define... on the line for mach-number to set the parameters for the Mach number sequence. (b) Under Storage Type in the Animation Sequence panel, select In Memory. (c) Increase the Window number to 3 and click Set. Graphics window number 3 will open. (d) Under Display Type, select Contours. i. In the Contours panel, select Velocity... and Mach Number. ii. Make sure that Filled is selected under Options, and deselect Auto Range. iii. Enter 0.00 under Min and 1.30 under Max. iv. In the Surfaces list, make sure that all of the surfaces are selected. v. Click Display. Figure 4.8 shows the Mach number contours in the nozzle after 600 time steps.

1.30e+00 1.23e+00 1.17e+00 1.11e+00 1.04e+00 9.75e-01 9.10e-01 8.45e-01 7.80e-01 7.15e-01 6.50e-01 5.85e-01 5.20e-01 4.55e-01 3.90e-01 3.25e-01 2.60e-01 1.95e-01 1.30e-01 6.50e-02 0.00e+00

Contours of Mach Number (Time=1.7136e-02)


Figure 4.8: Mach Number Contours at t = 0.01714 s (e) Click OK in the Animation Sequence panel. (f) Click OK in the Solution Animation panel.


4-35


5. Continue the calculation by requesting 100 time steps. Requesting 100 time steps will march the solution through an additional 0.0028 seconds, or roughly one pressure cycle. With the autosave and animation features active (as defined above), the case and data files will be saved approximately every 0.00028 seconds; animation files will be saved every 0.000028 seconds. Solve −→Iterate...

When the calculation finishes, you will have ten pairs of case and data files and there will be 100 pairs of contour plots stored in memory. In the next few steps, you will play back the animation sequences and examine the results at several time steps after reading in pairs of newly-saved case and data files.

4-36



6. Change the display options to include double buffering. Double buffering will allow for a smoother transition between the frames of the animations. Display −→Options...

(a) Under Rendering Options, select Double Buffering. (b) Click Apply.


4-37


7. Play back the animation of the pressure contours. Solve −→ Animate −→Playback...

(a) Under Sequences, select pressure. The playback control buttons now become active. (b) Keep the default settings in the rest of the panel and click the play button (the second from the right in the group of buttons under Playback). Examples of pressure contours at t = 0.01799 s (630th time step) and t = 0.0191 s (670th time step) are shown in Figures 4.9 and 4.10. 8. Repeat steps 6 and 7, selecting the appropriate active window and sequence name for the Mach number contours. Examples of Mach number contours at t = 0.01799 s and t = 0.0191 s are shown in Figures 4.11 and 4.12.

4-38












4-39





Figure 4.11: Mach Number Contours at t = 0.01799 s




Figure 4.12: Mach Number Contours at t = 0.0191 s

4-40



Extra: FLUENT gives you the option of exporting an animation as an MPEG file or as a series of files in any of the hardcopy formats available in the Graphics Hardcopy panel (including TIFF and PostScript). To save an MPEG file, select MPEG from the Write/Record Format drop-down list in the Playback panel and then click the Write button. The MPEG file will be saved in your working directory. You can view the MPEG movie using an MPEG player (e.g., Windows Media Player or another MPEG movie player). To save a series of TIFF, PostScript, or other hardcopy files, select Hardcopy Frames in the Write/Record Format drop-down list in the Playback panel. Click on the Hardcopy Options... button to open the Graphics Hardcopy panel and set the appropriate parameters for saving the hardcopy files. Click Apply in the Graphics Hardcopy panel to save your modified settings. In the Playback panel, click the Write button. FLUENT will replay the animation, saving each frame to a separate file in your working directory. If you want to view the solution animation in a later FLUENT session, you can select Animation Frames as the Write/Record Format and click Write. !

Since the solution animation was stored in memory, it will be lost if you exit FLUENT without saving it to one of the formats described above. Note that only the animation-frame format can be read back into the Playback panel for display in a later FLUENT session.

9. Display velocity vectors after 60 time steps (Figure 4.13). (a) Read case and data files for the 660th time step (noz anim0660.cas and noz anim0660.dat) into FLUENT. File −→ Read −→Case & Data... (b) Plot vectors at t = 0.01885 s. Display −→Vectors...


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i. Change the Scale to 10. ii. Click Display. The unsteady flow prediction shows the expected form, with peak velocity of about 241 m/s through the nozzle at t = 0.01885 seconds. 10. Repeat step 9 using case and data files saved for other time steps of interest.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=1.8849e-02) Dec 17, 2002 FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

Figure 4.13: Velocity Vectors at t = 0.01885 s

Summary: In this tutorial, you modeled the transient flow of air through a nozzle. You learned how to generate a steady-state solution as an initial condition for the unsteady case, and how to set solution parameters for implicit time-stepping. You also learned how to manage the file saving and graphical postprocessing for time-dependent flows, using file autosaving to automatically save solution information as the transient calculation proceeds. Finally, you learned how to use FLUENT’s solution animation tool to create animations of transient data, and how to view the animations using the playback feature.


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Tutorial 5. Modeling Radiation and Natural Convection Introduction: In this tutorial, combined radiation and natural convection are solved in a two-dimensional square box on a mesh consisting of quadrilateral elements. In this tutorial you will learn how to: • Use the radiation models in FLUENT (Rosseland, P-1, DTRM, discrete ordinates (DO), and surface-to-surface (S2S)) and understand their ranges of application • Use the Boussinesq model for density • Set the boundary conditions for a heat transfer problem involving natural convection and radiation • Separate a single wall zone into multiple wall zones • Change the properties of an existing fluid material • Calculate a solution using the segregated solver • Display velocity vectors and contours of stream function and temperature for flow visualization Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem to be considered is shown schematically in Figure 5.1. A square box of side L has a hot right wall at T = 2000 K, a cold left wall at T = 1000 K, and adiabatic top and bottom walls. Gravity points downwards. A buoyant flow develops because of thermally-induced density gradients. The medium contained in the box is assumed to be absorbing and emitting, so that the radiant exchange between the walls is attenuated by absorption and augmented by emission in the medium. All walls are black. The objective is to compute the flow and temperature patterns in the box, as well as the wall heat flux, using the radiation models available in FLUENT, and to compare their performance for different values of the optical thickness aL. The working fluid has a Prandtl number of approximately 0.71, and the Rayleigh number based on L is 5 × 105 . This means the flow is inherently laminar. The


5-1

Modeling Radiation and Natural Convection

Boussinesq assumption is used to model buoyancy. The Planck number k/(4σLT03 ) is 0.02, and measures the relative importance of conduction to radiation; here T0 = (Th + Tc )/2. Three values for the optical thickness are considered: aL = 0, aL = 0.2, and aL = 5. Note that the values of physical properties and operating conditions (e.g., gravitational acceleration) have been adjusted to yield the desired Prandtl, Rayleigh, and Planck numbers. Adiabatic

ρ = 1000 kg/m3

y

➢

h

T = 2000 K

g

➢

Tc= 1000 K

cp= 1.1030x10

L

J/kgK

k = 15.309 W/mK -3 µ = 10 kg/ms -5 1/K β = 10 -5 g = -6.96 x 10 m/s2 a = 0, 0.2, 5 1/m L=1m Ra = 5 x 10 Pr = 0.71 Pl = 0.02

x

4

5

τ = 0.2, 5


Preparation 1. Copy the file rad/rad.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

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Step 1: Grid 1. Read the mesh file rad.msh. File −→ Read −→Case... As the mesh is read in, messages will appear in the console window reporting the progress of the reading. The mesh size will be reported as 2500 cells. 2. Check the grid. Grid −→Check FLUENT performs various checks on the mesh and reports the progress in the console window. Pay particular attention to the minimum volume. Make sure this is a positive number. 3. Display the grid (Figure 5.2). Display −→ Grid...

Note: All the walls are currently contained in a single wall zone, wall-4. You will need to separate them out into four different walls so that you can specify different boundary conditions for each wall.


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Grid


Figure 5.2: Graphics Display of Grid

4. Separate the single wall zone into four wall zones. Grid −→ Separate −→Faces...

(a) Select the Angle separation method (the default) under Options. (b) Select wall-4 in the Zones list. (c) Specify 89◦ as the significant Angle. (d) Click on the Separate button. Faces with normal vectors that differ by more than 89◦ will be placed in separate zones. Since the four wall zones are perpendicular (angle = 90◦ ), wall-4 will be separated into four zones.

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5. Display the grid again. (a) Select all Surfaces and click on Display. Notice that you now have four different wall zones instead of only one. Extra: You can use the right mouse button to check which wall zone number corresponds to each wall boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly. In some cases, you may want to disable the display of the interior grid so as to more accurately select the boundaries for identification.


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Step 2: Models As discussed earlier, in this tutorial you will enable each radiation model in turn, obtain a solution, and postprocess the results. You will start with the Rosseland model, then use the P-1 model, the discrete transfer radiation model (DTRM), and the discrete ordinates (DO) model. At the end of the tutorial, you will use the surface-to-surface (S2S) model. 1. Keep the default solver settings. Define −→ Models −→Solver...

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2. Turn on the Rosseland radiation model. Define −→ Models −→Radiation...

When you click OK in the Radiation Model panel, FLUENT will present an Information dialog box telling you that new material properties have been added for the radiation model. You will be setting properties later, so you can simply click OK in the dialog box to acknowledge this information. Note: FLUENT will automatically enable the energy calculation when you enable a radiation model, so you need not visit the Energy panel. 3. Add the effect of gravity on the model. Define −→Operating Conditions...


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(a) Turn on Gravity. The panel will expand to show additional inputs. (b) Set the Gravitational Acceleration in the Y direction to -6.94e-5 m/s2 . As mentioned earlier, the gravitational acceleration has been adjusted to yield the correct dimensionless quantities (Prandtl, Rayleigh, and Planck numbers). See Figure 5.1 and the associated comments. (c) Set the Operating Temperature to 1000 K. The operating temperature will be used by the Boussinesq model, which you will enable in the next step.

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Step 3: Materials The default fluid material is air, which is the working fluid in this problem. However, since you are working with a fictitious fluid whose properties have been adjusted to give the desired values of the dimensionless parameters, you must change the default properties for air. You will use an optical thickness aL of 0.2 for this calculation. (Since L = 1, the absorption coefficient a will be set to 0.2.) Later in the tutorial, results for an optically thick medium with aL = 5 and non-participating medium with aL = 0 are computed to show how the different radiation models behave for different optical thicknesses. Define −→Materials...

1. Select boussinesq in the drop-down list next to Density, and then set the Density to 1000 kg/m3 . For details about the Boussinesq model, see the User’s Guide. 2. Set the specific heat, Cp, to 1.103e4 J/kg-K. 3. Set the Thermal Conductivity to 15.309 W/m-K. 4. Set the Viscosity to 0.001 kg/m-s.


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5. Set the Absorption Coefficient to 0.2 m−1 . Hint: Use the scroll bar to access the properties that are not initially visible in the panel. 6. Keep the default settings for the Scattering Coefficient and the Scattering Phase Function, since there is no scattering in this problem. 7. Set the Thermal Expansion Coefficient (used by the Boussinesq model) to 1e-5 K−1 . 8. Click on Change/Create and close the Materials panel.

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Step 4: Boundary Conditions Define −→Boundary Conditions... 1. Set the boundary conditions for the bottom wall (wall-4.006). Note: The bottom wall should be called wall-4.006, but to be sure that you have the correct wall, use your right mouse button to click on the bottom wall in the graphics window. When you do this, the corresponding zone will be selected automatically in the Zone list in the Boundary Conditions panel. You can do this when you set boundary conditions for the other walls as well, to be sure that you are defining the correct conditions.

(a) Change the Zone Name to bottom. (b) Retain the default thermal conditions (heat flux of 0) to specify an adiabatic wall. Note: The Rosseland model does not require you to set a wall emissivity. Later in the tutorial, you will need to define the wall emissivity for the other radiation models. 2. Set the boundary conditions for the left wall, wall-4. (a) Change the Zone Name to left. (b) Select Temperature under Thermal Conditions and set the Temperature to 1000 K.


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3. Set the boundary conditions for the right wall, wall-4:007. (a) Change the Zone Name to right. (b) Select Temperature under Thermal Conditions and set the Temperature to 2000 K. 4. Set the boundary conditions for the top wall, wall-4:005. (a) Change the Zone Name to top. (b) Retain the default thermal conditions (heat flux of 0) to specify an adiabatic wall.

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Step 5: Solution for the Rosseland Model 1. Set the parameters that control the solution. Solve −→ Controls −→Solution...

(a) Retain the default selected Equations (all of them) and Under-Relaxation Factors. (b) Under Discretization, select PRESTO! for Pressure, and Second Order Upwind for Momentum and Energy.


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2. Initialize the flow field. Solve −→ Initialize −→Initialize...

(a) Set the Temperature to 1500 K and click on Init. 3. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual...

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(a) Under Options, select Plot. (b) Click OK. Note: There is no extra residual for the radiation heat transfer because the Rosseland model does not solve extra transport equations for radiation; instead, it augments the thermal conductivity in the energy equation. When you use the P-1 and DO radiation models, which both solve additional transport equations, you will see additional residuals for radiation. 4. Save the case file (rad ross.cas). File −→ Write −→Case... 5. Start the calculation by requesting 200 iterations. Solve −→Iterate... The solution will converge in about 180 iterations. 6. Save the data file (rad ross.dat). File −→ Write −→Data...


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Step 6: Postprocessing for the Rosseland Model 1. Display velocity vectors (Figure 5.3). Display −→Vectors...

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Figure 5.3: Velocity Vectors for the Rosseland Model

2. Display contours of stream function (Figure 5.4). Display −→Contours...


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The recirculatory patterns observed are due to the natural convection in the box. At a low optical thickness (0.2), radiation should not have a large influence on the flow. The flow pattern is expected to be similar to that obtained with no radiation (Figure 5.5). However, the Rosseland model predicts a flow pattern that is very symmetric (Figure 5.4), and quite different from the pure natural convection case. This discrepancy occurs because the Rosseland model is not appropriate for small optical thickness.

6.96e-02 6.62e-02 6.27e-02 5.92e-02 5.57e-02 5.22e-02 4.88e-02 4.53e-02 4.18e-02 3.83e-02 3.48e-02 3.13e-02 2.79e-02 2.44e-02 2.09e-02 1.74e-02 1.39e-02 1.04e-02 6.96e-03 3.48e-03 0.00e+00

Contours of Stream Function (kg/s)


Figure 5.4: Contours of Stream Function for the Rosseland Model

Extra: If you want to compute the results the radiation models in the Radiation factor for energy to 0.8, and calculate the under-relaxation factor to 1 before

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without radiation yourself, turn off all Model panel, set the under-relaxation until convergence. (Remember to reset continuing with the tutorial).






Figure 5.5: Contours of Stream Function with No Radiation

3. Display filled contours of temperature (Figure 5.6). Display −→Contours...


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Figure 5.6: Contours of Temperature for the Rosseland Model

The Rosseland model predicts a temperature field (Figure 5.6) very different from that obtained without radiation (Figure 5.7). For the low optical thickness in this problem, the temperature field predicted by the Rosseland model is not physical. 4. Plot the y velocity along the horizontal centerline of the box. (a) Create an isosurface at y = 0.5, the horizontal line through the center of the box. Surface −→Iso-Surface...

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Figure 5.7: Contours of Temperature with No Radiation

i. Select Grid... in the Surface of Constant drop-down list and select YCoordinate from the list below. ii. Click on Compute to see the extents of the domain. iii. Set a value of 0.5 in the Iso-Values field, and change the New Surface Name to y=0.5. iv. Click on Create to create a surface at y = 0.5.


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(b) Create an XY plot of y velocity on the isosurface. Plot −→XY Plot...

i. Make sure that Node Values is turned on under Options. By default, the Node Values option is turned on, and the values that have been interpolated to the nodes are displayed. If you prefer to display the cell values, turn the Node Values option off. Note that you will need to ensure that the selected option for Node Values is used throughout the tutorial for displaying and saving XY plots. This will enable you to correctly compare the XY plots for different radiation models in a later step, as they will use identical options. ii. Check that the Plot Direction for X is 1, and the Plot Direction for Y is 0. With a Plot Direction vector of (1,0), FLUENT will plot the selected variable as a function of x. Since you are plotting the velocity profile on a cross-section of constant y, the x direction is the one in which the velocity varies. iii. Select Velocity... and Y Velocity under Y Axis Function. iv. Select y=0.5 in the Surfaces list. v. Click on Plot. The velocity profile reflects the rising plume at the hot right wall, and the falling plume at the cold left wall. Compared to the case with no radiation,

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y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity (m/s)

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.8: XY Plot of Centerline y Velocity for the Rosseland Model the profile predicted by the Rosseland model exhibits thicker wall layers. As discussed before, the expected profile for aL = 0.2 is similar to the case with no radiation. (c) Save the plot data to a file. i. Select the Write to File option, and click the Write... push button. ii. In the resulting Select File dialog box, specify rad ross.xy in the XY File text entry box and click OK.


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5. Compute the total wall heat flux on each lateral wall. Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options. (b) Select right and left under Boundaries. (c) Click the Compute button. The total wall heat transfer rate is reported for the hot and cold walls as approximately 7.43 × 105 W. The sum of the heat fluxes on the lateral walls is a negligible imbalance. 6. Save the case and data files (rad ross.cas and rad ross.dat). File −→ Write −→Case & Data... Thus far in this tutorial, you have learned how to set up a natural convection problem using the Rosseland model to compute radiation. You have also learned to postprocess the results. You will now turn on the P-1 model and compare the results so computed with those of the Rosseland model.

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Step 7: P-1 Model Definition, Solution, and Postprocessing You will now repeat the above calculation using the P-1 radiation model. The main steps are identical to the procedure described above for the Rosseland model. 1. Enable the P-1 model. Define −→ Models −→Radiation... 2. Confirm that the wall emissivity is 1 for all walls. Define −→Boundary Conditions... For each wall boundary, there will be a new entry, Internal Emissivity, in the Thermal section of the Wall panel. Retain the default value of 1. 3. Modify the under-relaxation parameters. Solve −→ Controls −→Solution... (a) Under Under-Relaxation Factors, set the factor for P1 to 1.0, and retain the default factors for Pressure, Momentum, and Energy (0.3, 0.7, and 1.0). Note that an additional equation, P1, appears because the P-1 model solves an additional radiation transport equation. This problem is relatively easy to converge for the P-1 model since there is not much coupling between the radiation and temperature equations at low optical thicknesses. Consequently a high under-relaxation factor can be used for P-1. 4. Save the case file (rad p1.cas). File −→ Write −→Case... 5. Continue the calculation by requesting another 200 iterations. Solve −→Iterate... The P-1 model reaches convergence after about 115 additional iterations. 6. Save the data file (rad p1.dat). File −→ Write −→Data...


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7. Examine the results of the P-1 model calculation. Note: The steps below do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more detailed instructions. (a) Display velocity vectors (Figure 5.9). Display −→Vectors...




Figure 5.9: Velocity Vectors for the P-1 Model (b) Plot the y velocity along the horizontal centerline (Figure 5.10), and save the plot data to a file called rad p1.xy. Plot −→XY Plot... !

You will need to reselect Y Velocity under Y Axis Function. Also, remember to turn off the Write to File option so that you can access the Plot button to generate the plot.

(c) Compute the total wall heat transfer rate. Report −→Fluxes ... The total heat transfer rate reported on the right wall is 8.47 × 105 W. The heat imbalance at the lateral walls is negligibly small. You will see later that the Rosseland and P-1 wall heat transfer rates are substantially different from those obtained by the DTRM and the DO model.

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y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05 -1.36e-20

Y Velocity (m/s)

-5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 -3.00e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.10: XY Plot of Centerline y Velocity for the P-1 Model Notice how different the velocity vectors and y-velocity profile are from those obtained using the Rosseland model. The P-1 velocity profiles show a clear momentum boundary layer along the hot and cold walls. These profiles are much closer to those obtained from the non-radiating case (Figures 5.11 and 5.12). Though the P-1 model is not appropriate for this optically thin limit, it yields the correct velocity profiles since the radiation source in the energy equation, which is proportional to the absorption coefficient, is small. The Rosseland model uses an effective conductivity to account for radiation, and yields the wrong temperature field, which in turn results in an erroneous velocity field.


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Figure 5.11: Velocity Vectors with No Radiation

y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity (m/s)

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.12: XY Plot of Centerline y Velocity with No Radiation

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Step 8: DTRM Definition, Solution, and Postprocessing 1. Turn on the discrete transfer radiation model (DTRM) and define the ray tracing. Define −→ Models −→Radiation...

(a) Select Discrete Transfer under Model. The panel will expand to show additional inputs. (b) Accept the defaults by clicking OK. The Ray Tracing panel will open automatically.

(c) Accept the default settings for Clustering and Angular Discretization by clicking OK. When you click OK, FLUENT will open a Select File dialog box so you can specify a name for the ray file used by the DTRM. A detailed description of the ray tracing procedure can be found in the User’s Guide. In brief, the number of Cells Per Volume Cluster and Faces Per Surface Cluster control the total number of radiating surfaces and absorbing cells. For a small 2D problem, the default


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number of 1 is acceptable. For a large problem, however, you will want to increase these numbers to reduce the ray tracing expense. The Theta Divisions and Phi Divisions control the number of rays being created from each surface cluster. For most practical problems, the default settings will suffice. (d) In the Ray File text entry box in the Select File dialog box, enter rad dtrm.ray for the name of the ray file. Then click OK. FLUENT will print an informational message describing the progress of the ray tracing procedure. 2. Retain the current under-relaxation factors for pressure, momentum, and energy (0.3, 0.7, and 1.0). Solve −→ Controls −→Solution... 3. Save the case file (rad dtrm.cas). File −→ Write −→Case... 4. Continue the calculation by requesting another 100 iterations. Solve −→Iterate... The solution will converge after about 80 additional iterations. 5. Save the data file (rad dtrm.dat). File −→ Write −→Data... 6. Examine the results of the DTRM calculation. Note: The steps below do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more detailed instructions. (a) Display velocity vectors (Figure 5.13). Display −→Vectors... (b) Plot the y velocity along the horizontal centerline (Figure 5.14), and save the plot data to a file called rad dtrm.xy. Plot −→XY Plot... !

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Figure 5.13: Velocity Vectors for the DTRM

y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05 -1.36e-20

Y Velocity (m/s)

-5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 -3.00e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.14: XY Plot of Centerline y Velocity for the DTRM


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(c) Compute the total wall heat transfer rate. Report −→Fluxes ... The total heat transfer rate reported on the right wall is 6.06 × 105 W. Note that this is substantially lower than the values predicted by the Rosseland and P-1 models.

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Step 9: DO Model Definition, Solution, and Postprocessing 1. Turn on the discrete ordinates (DO) radiation model and define the angular discretization. Define −→ Models −→Radiation...

(a) Select Discrete Ordinates under Model. The panel will expand to show additional inputs for the DO model. (b) Set the number of Flow Iterations Per Radiation Iteration to 1. This is a relatively simple flow problem, and will converge easily. Consequently it is useful to do the DO calculation every iteration of the flow solution. For problems that are difficult to converge, it is sometimes useful to allow the flow solution to establish itself between radiation calculations. In such cases, it may be useful to set Flow Iterations Per Radiation Iteration to a higher value, such as 10. (c) Retain the default settings for Angular Discretization and Non-Gray Model. For details about the angular discretization used by the DO model, see the User’s Guide. The Number of Bands for the Non-Gray Model is zero because only gray radiation is being modeled in this tutorial.


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Note: When you click OK in the Radiation Model panel, FLUENT will present an Information dialog box telling you that new material properties have been added for the radiation model. The property that is new for the DO model is the refractive index, which is relevant only when you are modeling semi-transparent media. Since you are not modeling semi-transparent media here, you can simply click OK in the dialog box to acknowledge this information. 2. Retain the current under-relaxation factors for pressure, momentum, and energy (0.3, 0.7, and 1.0), as well as the default under-relaxation of 1 for the discrete ordinates transport equation. Solve −→ Controls −→Solution... 3. Save the case file (rad do.cas). File −→ Write −→Case... 4. Continue the calculation by requesting another 100 iterations. Solve −→Iterate... The solution will converge after about 25 additional iterations. 5. Save the data file (rad do.dat). File −→ Write −→Data... 6. Examine the results of the DO calculation. Note: The steps below do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more detailed instructions. (a) Display velocity vectors (Figure 5.15). Display −→Vectors... (b) Plot the y velocity along the horizontal centerline (Figure 5.16), and save the plot data to a file called rad do.xy. Plot −→XY Plot... !


(c) Compute the total wall heat transfer rate. Report −→Fluxes ...

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Figure 5.15: Velocity Vectors for the DO Model

y=0.5 3.00e-04

2.00e-04

1.00e-04

Y Velocity (m/s)

-1.36e-20

-1.00e-04

-2.00e-04

-3.00e-04 0

0.1

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0.3

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0.9

1

Position (m)

Y Velocity


Figure 5.16: XY Plot of Centerline y Velocity for the DO Model


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The total heat transfer rate reported on the right wall is 6.12 × 105 W. Note that this is about 1.5% higher than that predicted by the DTRM. The DO and DTRM values are comparable to each other, while the Rosseland and P-1 values are both substantially different. The DTRM and DO models are valid across the range of optical thickness, and the heat transfer rates computed using them are expected to be closer to the correct heat transfer rate.

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Step 10: Comparison of y-Velocity Plots In this step, you will read the plot files you saved for all the solutions and compare them in a single plot. Plot −→File...

1. Read in all the XY plot files. (a) Click on the Add... button. (b) In the resulting Select File dialog box, select rad do.xy, rad dtrm.xy, rad p1.xy, and rad ross.xy in the Files list. They will be added to the XY File(s) list. If you accidentally add an incorrect file, you can select it in this list and click Remove. (c) Click OK to load the 4 files. 2. Click on Plot. Extra: You can click Curves... in the File XY Plot panel to open the Curves panel, where you can define different styles for different plot curves. In Figure 5.17, different symbols have been selected for each curve. 3. Resize and move the legend box so that you can read the information inside it. (a) To resize the box, press any mouse button on a corner and drag the mouse to the desired position. (b) To move the legend box, press any mouse button anywhere else on the box and drag it to the desired location.


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Y Velocity Y Velocity Y Velocity (rad_dtrm.xy) Y Velocity (rad_p1.xy) Y Velocity (rad_ross.xy)

3.00e-04

2.00e-04

1.00e-04

Y Velocity

-1.36e-20

-1.00e-04

-2.00e-04

-3.00e-04 0

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1

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Y Velocity


Figure 5.17: Comparison of Computed y Velocities for aL = 0.2

Notice in Figure 5.17 that the velocity profiles for the P-1 model, DTRM, and DO model are nearly identical even though the reported wall heat transfer rates are different. This is because in an optically thin problem, the velocity field is essentially independent of the radiation field, and all three models give a flow solution very close to the non-radiating case. The Rosseland model gives substantially erroneous solutions for an optically thin case.

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Step 11: Comparison of Radiation Models for an Optically Thick Medium In the previous steps, you compared the results of four radiation models for an optically thin (aL = 0.2) medium. It was found that, as a result of the low optical thickness, the velocity fields predicted by the P-1, DTRM, and DO models were very similar and close to that obtained in the non-radiating case. The wall heat transfer rates for DO and DTRM were very close to each other, and substantially different from those obtained with the Rosseland and P-1 models. In this step, you will recalculate a solution (using each radiation model) for an optically thick (aL = 5) medium. This is accomplished by increasing the value of the absorption coefficient from 0.2 to 5. You will repeat the process outlined below for each set of case and data files that you saved earlier in the tutorial. 1. For each radiation model, calculate a new solution for aL = 5. (a) Read in the case and data file saved earlier (e.g., rad ross.cas and rad ross.dat). File −→ Read −→Case & Data... (b) Set the absorption coefficient to 5. This will result in an optical thickness aL of 5, since L = 1. Define −→Materials... (c) Calculate until the new solution converges. Solve −→Iterate... !

For the DTRM calculation, you may need to click the Iterate button repeatedly until the radiation field is updated. Since the number of Flow Iterations Per Radiation Iteration in the Radiation Model panel is 10, it is possible that the radiation field will not be updated for as many as 9 iterations, although FLUENT will report that the solution is converged. If this happens, keep clicking the Iterate button until the radiation field is updated and the solution proceeds for multiple iterations.

(d) Save the new case and data files using a different file name (e.g., rad ros5.cas and rad ros5.dat). File −→ Write −→Case & Data... (e) Compute the total wall heat transfer rate. Report −→Fluxes... (f) Plot the y velocity along the horizontal centerline, and save the plot data to a file (e.g., rad ros5.xy). Plot −→XY Plot...


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2. Compare the computed heat transfer rates for the four models. The wall heat transfer rates predicted by the four radiation models range from 3.50× 105 to 3.97 × 105 W. 3. Compare the y-velocity profiles in a single plot (Figure 5.18). Plot −→File... Note: Use the Delete button in the File XY Plot panel to remove the old XY plot data files.

Y Velocity Y Velocity Y Velocity (rad_dtr5.xy) Y Velocity (rad_p15.xy) Y Velocity (rad_ros5.xy)

5.00e-04 4.00e-04 3.00e-04 2.00e-04 1.00e-04

Y Velocity

1.36e-20 -1.00e-04 -2.00e-04 -3.00e-04 -4.00e-04 -5.00e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position

Y Velocity


Figure 5.18: Comparison of Computed y Velocities for aL = 5

The XY plots of y velocity are nearly identical for the P-1 model, DO model, and DTRM. The Rosseland model gives somewhat different velocities, but is still within 10% of the other results. The Rosseland and P-1 models are suitable for the optically thick limit; the DTRM and DO models are valid across the range of optical thicknesses. Consequently, they yield similar answers at aL = 5. For many applications with large optical thicknesses, the Rosseland and P-1 models provide a simple low-cost alternative.

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Step 12: S2S Model Definition, Solution and Postprocessing for a Non-Participating Medium In the previous steps, you compared the results of four radiation models for optically thin (aL = 0.2) and optically thick (aL = 5) media. The surface-to-surface (S2S) 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 S2S model assumes that all surfaces are gray and diffuse. Thus, according to the gray-body model, if a certain amount of radiation is incident on a surface, a fraction is reflected, a fraction is absorbed, and a fraction is transmitted. 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. For most applications the surfaces in question are opaque to thermal radiation (in the infrared spectrum), so the surfaces can be considered opaque. The transmissivity, therefore, can be neglected. Effectively, for the S2S model the absorption coefficient can be considered to be zero. 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 radiative heat transfer calculation. In this step, you will calculate a solution for aL = 0 using the S2S radiation model without partial enclosure. In the next step, you will use the DTRM and DO models for aL = 0, and compare the results of the three models. The Rosseland and P-1 models are not considered here as they have been shown (earlier in the tutorial) to be inappropriate for optically thin media. Later in the tutorial, you will calculate a solution for S2S model with partial enclosure and compare the results with the solution for S2S model for a non-participating medium calculated here. 1. Turn on the surface-to-surface (S2S) radiation model and define the view factor and cluster parameters. Define −→ Models −→Radiation... (a) Select Surface to Surface under Model. The panel will expand to show additional inputs for the S2S model.


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(b) Set the view factor and cluster parameters. i. Click Set... under Parameters. The View Factor and Cluster Parameters panel will open automatically.

ii. Click OK to accept the default settings. The S2S radiation model is computationally very expensive when there are a large number of radiating surfaces. The number of radiating surfaces is

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reduced by clustering surfaces into 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. For a small 2D problem, the default value of 1 for Faces Per Surface Cluster is acceptable. For a large problem, you can increase this number to reduce the memory requirement for the view factor file that is saved in a later step. This may also lead to some reduction in the computational expense. However, this is at the cost of some accuracy. Using the Blocking option ensures that any additional surface that is blocking the view between two opposite surfaces is considered in the view factor calculation. In this case, there is no obstructing surface between the opposite walls, so selecting either the Blocking or the Nonblocking option will produce the same result. The default setting for Smoothing is None, which is appropriate for small problems. The Least Square option is more accurate, but also more computationally expensive. See the User’s Guide for details about view factors and clusters for the S2S model. (c) Compute the view factors for the S2S model. This step is required only if the problem is being solved for the first time. For subsequent calculations, you can read the view factor and cluster information from an existing file (by clicking Read... instead of Compute/Write...). i. Click Compute/Write... under Methods in the Radiation Model panel. FLUENT will open a Select File dialog box so you can specify a name for the file where the cluster and view factor parameters are stored. ii. In the S2S File text entry box in the Select File dialog box, enter rad s2s.s2s for the name of the S2S file. Then click OK. FLUENT will print an informational message describing the progress of the view factor calculation. 2. Retain the current under-relaxation factors for pressure, momentum, and energy (0.3, 0.7, and 1.0). Solve −→ Controls −→Solution... 3. Save the case file (rad s2s.cas). File −→ Write −→Case... 4. Continue the calculation by requesting another 100 iterations. Solve −→Iterate... The solution will converge after about 80 additional iterations. 5. Save the data file (rad s2s.dat). File −→ Write −→Data...


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6. Examine the results of the S2S calculation. Note: The steps below do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more detailed instructions. (a) Display velocity vectors (Figure 5.19). Display −→Vectors...




Figure 5.19: Velocity Vectors for the S2S Model (b) Plot the y velocity along the horizontal centerline (Figure 5.20), and save the plot data to a file called rad s2s.xy. Plot −→XY Plot... !

You will have to reselect Y Velocity under Y Axis Function. Also, remember to turn off the Write to File option to access the Plot button to generate the plot.

(c) Compute the total wall heat transfer rate. Report −→Fluxes ... The total heat transfer rate on the right wall is 6.77 × 105 W.

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y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity (m/s)

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.20: XY Plot of Centerline y Velocity for the S2S Model


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Step 13: Comparison of Radiation Models for a NonParticipating Medium In this step, you will calculate a solution for the aL = 0 case, using the DTRM and DO models, and then compare the results with the S2S results. 1. For the DTRM and DO models, calculate a new solution for aL = 0. (a) Read in the case and data files saved earlier (e.g., rad dtrm.cas and rad dtrm.dat). File −→ Read −→Case & Data... (b) Set the absorption coefficient to 0. This will result in an optical thickness aL of 0. Define −→Materials... (c) Calculate until the new solution converges. Solve −→Iterate... !

For the DTRM calculation, you may need to click the Iterate button repeatedly until the radiation field is updated. Since the number of Flow Iterations Per Radiation Iteration in the Radiation Model panel is 10, it is possible that the radiation field will not be updated for as many as 9 iterations, although FLUENT will report that the solution is converged. If this happens, keep clicking the Iterate button until the radiation field is updated and the solution proceeds for multiple iterations.

(d) Save the new case and data files using a different file name (e.g., rad dtr0.cas and rad dtr0.dat). File −→ Write −→Case & Data... (e) Compute the total wall heat transfer rate. Report −→Fluxes... (f) Plot the y velocity along the horizontal centerline, and save the plot data to a file (e.g., rad dtr0.xy) Plot −→XY Plot... 2. Compare the computed heat transfer rates for the three models. For the S2S model, the total heat transfer rate on the right wall was 6.77 × 105 W. This is about 5% higher than that predicted by the DTRM and 1.5% higher than DO. Although the S2S, DO, and DTRM values are comparable to each other, this problem involves enclosure radiative transfer without participating media. Therefore, the S2S model provides the most accurate solution.

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3. Compare the y-velocity profiles in a single plot (Figure 5.21) Plot −→File... (a) Use the Delete button in the File XY Plot panel to remove the old XY plot data files. (b) Read in all the XY plot files you saved for the S2S, DTRM, and DO models. (c) Click on Plot.

Y Velocity Y Velocity Y Velocity (rad_dtr0.xy) Y Velocity (rad_s2s.xy)

2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position

Y Velocity


Figure 5.21: Comparison of Computed y Velocities for aL = 0

In Figure 5.21, the velocity profiles for the DTRM, DO, and S2S models are almost identical even though the wall heat transfer rates are different.


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Step 14: S2S Model Definition, Solution and Postprocessing with Partial Enclosure As mentioned earlier, 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 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. For this problem, you will specify the left wall boundary as the non-participating wall in S2S radiation. Consequently, you will need to specify the partial enclosure temperature for the wall boundary that is not participating in S2S radiation. Note that if multiple wall boundaries are not participating in S2S radiation and each has a different temperature, then the partial enclosure option may not yield accurate results, as the same partial enclosure temperature is specified for each of the non-participating walls. 1. Read in the case and data files for the S2S model (rad s2s.cas and rad s2s.dat). 2. In the Radiation Model panel, retain Surface to Surface (S2S) as the radiation model. Define −→ Models −→Radiation... 3. Under Partial Enclosure, set the Temperature to 1000 k. In previous radiation model setups for this problem, the left wall temperature was specified as 1000 k. Therefore, you will set the partial enclosure temperature to this temperature. 4. Click OK to close the Radiation Model panel.

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5. Set the boundary conditions for the left wall. Define −→Boundary Conditions

(a) Turn off the Participates in S2S Radiation option. You will now revisit the Radiation Model panel to recompute the view factors. 6. Compute the view factors for the S2S model. Define −→ Models −→Radiation... The view factor file will store the view factors for the radiating surfaces only. This may help you to control the size of the view factor file as well as the memory required to store view factors in FLUENT. Furthermore, the time required to compute the view factors will reduce as only the view factors for radiating surfaces will be calculated. !

You should compute the view factors only when you have specified the boundaries that will participate in the radiation model using the Boundary Conditions panel. If you first compute the view factors and then make a change to the boundary conditions, FLUENT will use the view factor file stored earlier for calculating a solution, in which case, the changes that you made to the model will not be used for the calculation. Therefore, you should recompute the view factors and save the case file whenever you modify the number of objects that will participate in radiation.


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(a) Click Compute/Write... under Methods in the Radiation Model panel. FLUENT will open a Select File dialog box so you can specify a name for the file where the cluster and view factor parameters are stored. (b) In the S2S File text entry box in the Select File dialog box, enter rad s2sp.s2s for the name of the S2S file. Then click OK. FLUENT will print an informational message describing the progress of the view factor calculation. 7. Retain the current under-relaxation factors for pressure, momentum, and energy (0.3, 0.7, and 1.0). Solve −→ Controls −→Solution... 8. Save the case file (rad s2sp.cas). File −→ Write −→Case... 9. Continue the calculation by requesting another 100 iterations. Solve −→Iterate... The solution will converge after about 80 additional iterations. 10. Save the data file (rad s2sp.dat). File −→ Write −→Data... 11. Examine the results of the S2S calculation. Note: The steps below do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more detailed instructions. (a) Display velocity vectors (Figure 5.22). Display −→Vectors... (b) Plot the y velocity along the horizontal centerline (Figure 5.20), and save the plot data to a file called rad s2s.xy. Plot −→XY Plot... !

You will have to reselect Y Velocity under Y Axis Function. Also, remember to turn off the Write to File option to access the Plot button to generate the plot.

(c) Compute the total wall heat transfer rate. Report −→Fluxes ... The total heat transfer rate on the right wall is 6.77 × 105 W. Note that the total heat transfer rate on left wall is zero as it is not participating in S2S radiation.

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Figure 5.22: Velocity Vectors for the S2S Model with Partial Enclosure

y=0.5 2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity (m/s)

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Y Velocity


Figure 5.23: XY Plot of Centerline y Velocity for the S2S Model with Partial Enclosure


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Step 15: Comparison of S2S Models with and without Partial Enclosure 1. Compare the computed heat transfer rates for the two S2S models. 2. Compare the y-velocity profiles in a single plot (Figure 5.24) Plot −→File... (a) Use the Delete button in the File XY Plot panel to remove the old XY plot data files. (b) Read in all the XY plot files you saved for the S2S models. (c) Click on Plot.

Y Velocity Y Velocity Y Velocity (rad_s2sp.xy)

2.50e-04 2.00e-04 1.50e-04 1.00e-04 5.00e-05

Y Velocity

6.78e-21 -5.00e-05 -1.00e-04 -1.50e-04 -2.00e-04 -2.50e-04 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position

Y Velocity


Figure 5.24: Comparison of Computed y Velocities for S2S models

In Figure 5.24, the velocity profiles for the S2S model without partial enclosure and the S2S model with partial enclosure are almost identical.

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Summary: In this tutorial, you studied combined natural convection and radiation in a square box and compared the performance of four radiation models in FLUENT for optically thin and optically thick cases, and the performance of three radiation models for a non-participating medium. • For the optically thin case, the Rosseland and P-1 models are not appropriate; the DTRM and the DO model are applicable, and yield similar results. • In the optically thick limit, all four models are appropriate and yield similar results. In this limit, the less computationally-expensive Rosseland and P-1 models may be adequate for many engineering applications. • The S2S radiation model is appropriate for modeling the enclosure radiative transfer without participating media, where the methods for participating radiation may not always be efficient. For more information about the applicability of the different radiation models, see the User’s Guide.


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Tutorial 6.

Using a Non-Conformal Mesh

Introduction: Film cooling is a process that is used to protect turbine vanes in a gas turbine engine from exposure to hot combustion gases. This tutorial illustrates how to set up and solve a film cooling problem using a non-conformal mesh. The system that is modeled consists of three parts: a duct, a hole array, and a plenum. The duct is modeled with a hexahedral mesh, and the plenum and hole regions are modeled using a tetrahedral mesh. These two meshes are merged together to form a “hybrid” mesh, with a non-conformal interface boundary between them. Due to symmetry of the hole array, only a portion of the geometry is modeled in FLUENT, with symmetry applied to the outer boundaries. The duct contains a high-velocity, hot fluid in streamwise flow (Figure 6.1). An array of holes intersects the duct at an inclined angle, and a cooler fluid is injected into the holes from a plenum. The coolant that moves through the holes acts to cool the surface of the duct, downstream of the injection. Both fluids are air, and the flow is classified as turbulent. The velocity and temperature of the streamwise and cross-flow fluids are known, and FLUENT is used to predict the flow and temperature fields that result from convective heat transfer. In this tutorial you will learn how to: • Merge hexahedral and tetrahedral meshes to form a hybrid mesh • Create a non-conformal grid interface • Model heat transfer across a non-conformal interface with specified temperature and velocity boundary conditions • Calculate a solution using the segregated solver • Plot temperature profiles on specified isosurfaces Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps will not be shown explicitly. Problem Description: This problem considers a model of a 3D section of a film cooling test rig. A schematic is shown in Figures 6.1 and 6.2. The problem consists of a duct, 24.5 in long, with cross-sectional dimensions of 0.75 in × 5 in. An array of uniformly spaced holes is located at the bottom of the duct. Each hole has a diameter of 0.5 inches, is inclined at 35 degrees, and is spaced 1.5 inches apart


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laterally. Cooler injected air enters the system through the plenum, with crosssectional dimensions of 3.3 in × 1.25 in. Because of the symmetry of the geometry, only a portion of the domain needs to be modeled. The computational domain is shown in outline in Figure 6.2. The bulk temperature of the streamwise air (T∞ ) is 273 K, and the velocity of the air stream is 20 m/s. The bottom wall of the duct that intersects the hole array is assumed to be a completely insulated (adiabatic) wall. The secondary (injected) air enters the plenum at a uniform velocity of 0.4559 m/s. The temperature of the injected air (Tinject ) is 136.6 K. The properties of air that are used in the model are shown in Figure 6.2. 9.5 in v = 20 m/s Τ ∞ = 273 K

0.5 in

14.5 in

Duct 5 in

y

1.25 in

Hole

1.25 in

x 35° Plenum

3.3 in

v = 0.4559 m/s T = 136.6 K inject

Figure 6.1: Schematic of the Problem, Front View

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Using a Non-Conformal Mesh z x Τ

∞ = 273 K

0.75 in

0.25 in

µ = 0.000017894 kg/m-s

c p = 1006.43 J/kg-K Figure 6.2: Schematic of the Problem, Top View

Preparation 1. Copy the files filmcool/film_hex.msh and filmcool/film_tet.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1).


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Step 1: Merging the Mesh Files 1. Start the 3D version of tmerge by typing utility tmerge -3d at the system prompt. 2. Provide the mesh file names film tet.msh and film hex.msh as prompted. Provide scaling of 1 and translations and rotations of zero for each mesh file. Save the new merged mesh file as filmcool.msh.

Append 3D grid files. tmerge3D Fluent Inc, Version 2.1.8 Enter name of grid file (ENTER to continue) : film_tet.msh x,y,z scaling factor, eg. 1 1 1

: 1 1 1

x,y,z translation, eg. 0 1 0

: 0 0 0

rot axis (0,1,2), angle (deg), eg. 1 45 : 0 0 Enter name of grid file (ENTER to continue) : film_hex.msh x,y,z scaling factor, eg. 1 1 1

: 1 1 1

x,y,z translation, eg. 0 1 0

: 0 0 0

rot axis (0,1,2), angle (deg), eg. 1 45 : 0 0 Enter name of grid file (ENTER to continue) : Enter name of output file

!

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: filmcool.msh

The mesh files must be read into tmerge in this order for the tutorial to run as written. Otherwise, zone names and numbers will be assigned differently when the files are merged together. In general, however, you can specify files to be read into tmerge in any order.



Step 2: Grid 1. Start the 3D version of FLUENT. 2. Read in the mesh file filmcool.msh. File −→ Read −→Case... 3. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 4. Scale the grid and change the unit of length to inches. Grid −→Scale...

(a) In the Units Conversion drop-down list, select in to complete the phrase Grid Was Created In in (inches). (b) Click Scale to scale the grid. (c) Click Change Length Units to set inches as the working units for length. The final Domain Extents should appear as in the panel above.


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5. Display an outline of the 3D grid (Figure 6.3). Display −→Grid...

(a) In the Surfaces list, deselect symmetry-3, symmetry-5 and symmetry-tet. (b) Click Display.

Y Z

Grid

X


Figure 6.3: Hybrid Mesh for Film Cooling Problem

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(c) Zoom in using your middle mouse button to get the view displayed in Figure 6.4.

Y Z

Grid

X


Figure 6.4: Hybrid Mesh (Zoomed-In View)

In Figure 6.4 you can see the quadrilateral faces of the hexahedral cells that are used to model the duct region, and the triangular faces of the tetrahedral cells that are used to model the plenum and hole regions, resulting in a hybrid mesh. Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.


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3. Enable the standard k- turbulence model. Define −→ Models −→Viscous...


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Step 4: Materials Define −→Materials... 1. Select air (the default material) as the fluid material, and use the incompressibleideal-gas law to compute density. Retain the default values for all other properties.

!

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Don’t forget to click the Change/Create button after selecting incompressibleideal-gas in the drop-down list for Density.



Step 5: Operating Conditions 1. Keep the default operating conditions. Define −→Operating Conditions...


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Step 6: Boundary Conditions Define −→Boundary Conditions... 1. Set the boundary conditions for the streamwise flow inlet (velocity-inlet-1).

(a) Change the Zone Name from velocity-inlet-1 to velocity-inlet-duct. (b) Set the Velocity Magnitude to 20 m/s. (c) Set the Temperature to 273 K. (d) In the Turbulence Specification Method drop-down list, select Intensity and Hydraulic Diameter. (e) Set the Turbulence Intensity to 1% and the Hydraulic Diameter to 5 in. The Intensity and Hydraulic Diameter specification method is convenient in this case since the hydraulic diameter of the duct at the inlet is known. 2. Set the boundary conditions for the injected stream inlet (velocity-inlet-14). (a) Change the Zone Name from velocity-inlet-14 to velocity-inlet-plenum. (b) Set the Velocity Magnitude to 0.4559 m/s. (c) Set the Temperature to 136.6 K. (d) In the Turbulence Specification Method drop-down list, select Intensity and Viscosity Ratio.

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(e) Set the Turbulence Intensity to 1% and keep the Turbulent Viscosity Ratio default of 10. In the absence of any identifiable length scale for turbulence, the Intensity and Viscosity Ratio method should be used. See the User’s Guide for more information on how to set the boundary conditions for turbulence. 3. Set the boundary conditions for the flow exit (pressure-outlet-1).

(a) Change the Zone Name from pressure-outlet-1 to pressure-outlet-duct.


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(b) Keep the default setting of 0 Pa for Gauge Pressure. (c) Set the Backflow Total Temperature to 273 K. (d) In the Turbulence Specification Method drop-down list, select Intensity and Viscosity Ratio. (e) Set the Backflow Turbulence Intensity to 1% and keep the Backflow Turbulent Viscosity Ratio default of 10. 4. Set the conditions for the fluid in the duct (fluid-9).

(a) Change the Zone Name from fluid-9 to fluid-duct. (b) Keep the default selection of air as the Material Name. 5. Set the conditions for the fluid in the plenum and hole (fluid-17). (a) Change the Zone Name from fluid-17 to fluid-plenum. (b) Keep the default selection of air as the Material Name.

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6. Keep the default boundary conditions for the plenum and hole wall (wall-15).


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7. Define the zones on the non-conformal boundary as interface zones. The non-conformal grid interface contains two boundary zones: wall-1 and wall-12. wall-1 is the bottom surface of the duct, and wall-12 represents the hole through which the cool air is injected from the plenum (Figure 6.5). These boundaries were defined as walls in the original mesh files, film hex.msh and film tet.msh, and must be redefined as interface boundary types.

X

Y Z

Grid

Aug 02, 2002 FLUENT 6.1 (3d, segregated, lam)

Figure 6.5: Grid for the wall-1 and wall-12 Boundaries

(a) Select wall-1 in the Zone list and choose interface as the new Type.

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(b) Confirm that it is OK to change the boundary type. (c) Change the Zone Name to interface-duct.

(d) Repeat this procedure to convert wall-12 to an interface boundary zone named interface-hole.


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Step 7: Grid Interfaces In this step, you will create a non-conformal grid interface between the hexahedral and tetrahedral meshes. Define −→Grid Interfaces...

1. Select interface-hole in the Interface Zone 1 list. !

When one interface zone is smaller than the other, it is recommended that you choose the smaller zone as Interface Zone 1.

2. Select interface-duct in the Interface Zone 2 list. 3. Enter the name junction under Grid Interface. 4. Click Create. Note: In the process of creating the grid interface, FLUENT creates two new wall boundary zones: wall-11 and wall-18. You will not be able to display these walls. wall-11 is the non-overlapping region of the interface-hole zone that results from the intersection of the interface-hole and interface-duct boundary zones, and is listed under Boundary Zone 1 in the Grid Interfaces panel. wall-11 is empty, since interface-hole is completely contained within the interface-duct boundary. wall-18 is the non-overlapping region of the interface-duct zone that results from the intersection of the two interface zones, and is listed under Boundary Zone 2 in the Grid Interfaces panel.

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!

In general, you will need to set boundary conditions for wall-18 (since it is not empty). In this case, default settings are used.


(a) Under Discretization, select Second Order Upwind for Momentum and Turbulence Kinetic Energy. (b) Scroll down the list and select Second Order Upwind for Turbulence Dissipation Rate and Energy. 2. Enable the plotting of residuals. Solve −→ Monitors −→Residual... (a) Under Options, select Plot. (b) Click the OK button.


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(a) Select velocity-inlet-duct in the Compute From drop-down list. (b) Click Init, and Close the panel.

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4. Save the case file (filmcool.cas). File −→ Write −→Case... 5. Start the calculation by requesting 250 iterations. Solve −→Iterate...

(a) Set the Number of Iterations to 250. (b) Click Iterate. Note: During the first few iterations, the console window will report that turbulent viscosity is limited in a couple of cells. This message should go away as the solution converges and the turbulent viscosity approaches more reasonable levels. The solution will converge after about 190 iterations. 6. Save the case and data files (filmcool.cas and filmcool.dat). File −→ Write −→Case & Data... Note: If you choose a file name that already exists in the current directory, FLUENT will prompt you for confirmation to overwrite the file.


6-21


Step 9: Postprocessing 1. Display filled contours of static pressure (Figure 6.6). Display −→Contours...

(a) Select Filled under Options. (b) Select Pressure... and Static Pressure in the Contours Of drop-down lists. (c) In the Surfaces list, select interface-duct and interface-hole. (d) Scroll down the Surfaces list and select symmetry-1, symmetry-tet, and wall-15.

6-22



(e) Reset the view to the default view. Display −→Views... i. Click Default under Actions.

ii. Close the panel. (f) In the Contours panel, click Display. (g) Zoom in on the view to get the display shown in Figure 6.6.

3.43e+02 3.17e+02 2.91e+02 2.65e+02 2.39e+02 2.14e+02 1.88e+02 1.62e+02 1.36e+02 1.10e+02 8.45e+01 5.87e+01 3.28e+01 7.03e+00 -1.88e+01 -4.46e+01 -7.04e+01 -9.62e+01 -1.22e+02 -1.48e+02 -1.74e+02

Y Z

X



Figure 6.6: Contours of Static Pressure Note the high/low pressure zones on the upstream/downstream sides of the coolant hole, where the jet first penetrates the primary flow in the duct.


6-23


2. Display filled contours of static temperature (Figures 6.7 and 6.8). Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-down lists. (b) Under Options, deselect Auto Range so that you can change the maximum and minimum temperature gradient values to be plotted. (c) Keep the default Min value of 0. (d) Enter a new Max value of 273.096. (e) Under Options, deselect Clip to Range. (f) Reset the view to the default view. Display −→Views... (g) In the Contours panel, click Display. (h) Zoom in on the view to get the display shown in Figure 6.8. Figures 6.7 and 6.8 clearly show how the coolant flow insulates the bottom of the duct from the higher-temperature primary flow.

6-24




Y Z

X



Figure 6.7: Contours of Static Temperature


Y Z

X



Figure 6.8: Contours of Static Temperature (Zoomed-In View)


6-25


3. Display the velocity vectors (Figure 6.9). Display −→Vectors...

(a) Select Velocity... and Velocity Magnitude in the Color By drop-down lists. (b) Change the Scale to 2. This will enlarge the vectors that are displayed, making it easier to view the flow patterns. (c) In the Surfaces list, select interface-duct and interface-hole. (d) Scroll down the Surfaces list and select symmetry-1, symmetry-tet, and wall-15. (e) Reset the view to the default view. Display −→Views... (f) In the Vectors panel, click Display. (g) Zoom in on the view to get the display shown in Figure 6.9. The flow pattern in the vicinity of the coolant hole shows the level of penetration of the coolant jet into the main flow. Notice that the velocity field varies smoothly across the non-conformal interface.

6-26




Y Z

X




4. Plot the temperature profile along a horizontal cross-section of the duct, 0.1 inches above the bottom. (a) Create an isosurface on the duct surface at y = 0.1 in. Surface −→Iso-Surface...

i. Select Grid... and Y-Coordinate in the Surface of Constant drop-down lists. ii. Enter y=0.1in under New Surface Name. iii. Enter 0.1 for Iso-Values.


6-27


iv. Click Create. (b) Create an XY plot of static temperature on the isosurface. Plot −→XY Plot... i. Keep the default Plot Direction. ii. Select Temperature... and Static Temperature in the Y-Axis Function dropdown lists. iii. Scroll down the Surfaces list and select y=0.1in.

iv. Click Plot.

6-28



y=0.1in 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 -10

Y Z

-7.5

-5

-2.5

X

Static Temperature

0

2.5

5

7.5

10

12.5

15

17.5

Position (in)


Figure 6.10: Static Temperature at y=0.1 in In this plot you can see how the temperature of the fluid changes as the cool air from the injection hole mixes with the primary flow. As expected, the temperature is coolest just downstream of the hole. Note that you could also make a similar plot on the lower wall itself, to examine the wall surface temperature. Summary: This tutorial demonstrates how FLUENT’s non-conformal grid interface capability can be used to handle hybrid meshes for complex geometries, such as the film cooling hole configuration examined here. One of the principal advantages of this approach is that it allows you to merge existing component meshes together to create a larger, more complex mesh system, without requiring that the different components have the same node locations on their shared boundaries. Thus, you can perform parametric studies by merging the desired meshes, creating the nonconformal interface(s), and solving the model. For example, in the present case, you can • Use a different hole/plenum mesh • Reposition the existing hole/plenum mesh • Add additional hole/plenum meshes to create aligned or staggered multiple hole arrays


6-29


6-30


Tutorial 7. Using a Single Rotating Reference Frame Introduction: This tutorial considers the flow within a 2D, axisymmetric, co-rotating disk cavity system. Understanding the behavior of such flows is important in the design of secondary air passages for turbine disk cooling. In this tutorial you will learn how to: • Set up a 2D axisymmetric model with swirl, using a rotating reference frame • Use the standard k- and RNG k- turbulence models with the enhanced nearwall treatment • Calculate a solution using the segregated solver • Display velocity vectors and contours of pressure • Set up and display XY plots of radial velocity • Restart the solver from an existing solution Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem to be considered is shown schematically in Figure 7.1. This case is similar to a disk cavity configuration that was extensively studied by Pincombe [1]. Air enters the cavity between two co-rotating disks. The disks are 88.6 cm in diameter and the air enters at 1.146 m/s through a circular bore 8.86 cm in diameter. The disks, which are 6.2 cm apart, are spinning at 71.08 rpm, and the air enters with no swirl. As the flow is diverted radially, the rotation of the disk has a significant effect on the viscous flow developing along the surface of the disk.


7-1

Using a Single Rotating Reference Frame Outflow

44.3 cm

Rotating Disk

Rotating Disk

6.2 cm

71.08 rpm Inflow

4.43 cm


As noted by Pincombe [1], there are two nondimensional parameters that characterize this type of disk cavity flow: the volume flow rate coefficient, Cw , and the rotational Reynolds number, Reφ . These parameters are defined as follows: Cw =

Reφ =

Q ν rout

(7.1)

2 Ωrout ν

(7.2)

where Q is the volumetric flow rate, Ω is the rotational speed, ν is the kinematic viscosity, and rout is the outer radius of the disks. Here, you will consider a case for which Cw = 1092 and Reφ = 105 .

7-2


Using a Single Rotating Reference Frame

Preparation 1. Copy the file disk/disk.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

Step 1: Grid 1. Read the grid file (disk.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid (Figure 7.2). Display −→Grid...


7-3


Grid

Aug 02, 2002 FLUENT 6.1 (axi, swirl, segregated, ske)

Figure 7.2: Grid Display for the Disk Cavity

Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.

7-4



Step 2: Units 1. For convenience, define new units for angular velocity and length. In the problem description, angular velocity and length are specified in rpm and cm, respectively. These are not the default units for these quantities. Define −→Units...

(a) Select angular-velocity under Quantities, and rpm under Units. (b) Select length under Quantities, and cm under Units. (c) Close the panel.


7-5


Step 3: Models 1. Specify the solver formulation to be used for the model calculation, and enable the modeling of axisymmetric swirl. Define −→ Models −→Solver...

(a) Retain the default Segregated solver. (b) Select Axisymmetric Swirl under Space. (c) Retain the default selection of Absolute under Velocity Formulation. For a rotating reference frame, the absolute velocity formulation has some numerical advantages. (d) Retain the default selection of Cell-Based under Gradient Option. (e) Retain the default selection of Superficial Velocity under Porous Formulation.

7-6



2. Turn on the standard k- turbulence model with the enhanced near-wall treatment. Define −→ Models −→Viscous...

(a) Under Model, select k-epsilon. The panel will expand. (b) Keep the Standard setting under k-epsilon Model. (c) Under Near-Wall Treatment, select Enhanced Wall Treatment and keep the default settings. The ability to calculate a swirl velocity permits the use of a 2D mesh, so the calculation is simpler and more economical to run. This is especially important for problems where the enhanced wall treatment is used, and the near-wall flow field is resolved through the viscous sublayer and buffer zones (that is, the first grid point away from the wall is placed at a y+ on the order of 1). See the User’s Guide for details.


7-7


Step 4: Materials 1. Accept the default properties for air. Define −→Materials...

For the present analysis, you will model air as an incompressible fluid with a density of 1.225 kg/m3 and a dynamic viscosity of 1.7894×10−5 kg/m-s. Since these are the default values, no change is required in the Materials panel. Extra: You can modify the fluid properties for air at any time or copy another material from the database. See the “Physical Properties” chapter of the User’s Guide for details.

7-8



Step 5: Boundary Conditions You will set up the present problem using a rotating reference frame for the fluid. The disk walls will then be defined to rotate with the moving frame. Define −→Boundary Conditions... 1. Define the rotating reference frame for the fluid zone (fluid-7).

(a) Select Moving Reference Frame in the Motion Type drop-down list. (b) Scroll down below Motion Type and set the Speed (under Rotational Velocity) to 71.08 rpm.


7-9


2. Set the following conditions at the flow inlet (velocity-inlet-2).

3. Set the following conditions at the flow outlet (pressure-outlet-3).

Note: FLUENT will use the backflow conditions only if the fluid is flowing into the computational domain through the outlet. Since backflow might occur at some point during the solution procedure, you should set reasonable backflow conditions to prevent convergence from being adversely affected.

7-10



4. Accept the default settings for the disk walls (wall-6).

Note: For a rotating reference frame, FLUENT assumes by default that all walls rotate at the speed of the moving reference frame, and hence are moving with respect to the stationary (absolute) reference frame. To specify a non-rotating wall, you must specify a rotational speed of 0 in the absolute frame.


7-11


Step 6: Solution Using the Standard k- Model 1. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Under Discretization, select PRESTO! from the drop-down list to the right of Pressure. The PRESTO! scheme is well suited for steep pressure gradients involved in rotating flows. It provides improved pressure interpolation in situations where large body forces or strong pressure variations are present as in swirling flows. (b) Select Second Order Upwind from the adjacent drop-down list for Momentum, Swirl Velocity, Turbulence Kinetic Energy, and Turbulence Dissipation Rate. !

Use the scroll bar to access the turbulence discretization schemes.

(c) Retain the default Under-Relaxation Factors. Note: For this problem, the default under-relaxation factors are satisfactory. However, if the solution diverges or the residuals display large oscillations, you may need to reduce the under-relaxation factors from their default values. See the User’s Guide for tips on how to adjust the under-relaxation parameters for different situations.

7-12




(a) Under Options, select Plot. (b) Click the OK button. Note: For this calculation, the convergence tolerance on the continuity equation is kept at 0.001. You can reduce this value if necessary, depending on the behavior of the solution. 3. Enable the plotting of mass flow rate at the flow exit. Solve −→ Monitors −→Surface... (a) Increase the number of Surface Monitors to 1. (b) Turn on the Plot and Write options for monitor-1. Note: When the Write option is selected in the Surface Monitors panel, the mass flow rate history will be written to a file. If you do not select the Write option, the history information will be lost when you exit FLUENT.


7-13


(c) Click Define... to specify the surface monitor parameters. This will open the Define Surface Monitor panel.

i. Select Mass Flow Rate from the Report Type drop-down list. ii. Select pressure-outlet-3 in the Surfaces list. iii. Click OK to define the monitor. (d) Click OK in the Surface Monitors panel to enable the monitor.

7-14



4. Initialize the flow field using the boundary conditions set at velocity-inlet-2. Solve −→ Initialize −→Initialize...

(a) Choose velocity-inlet-2 from the Compute From list. (b) Click Init and close the panel. 5. Save the case file (disk ke.cas). File −→ Write −→Case... 6. Start the calculation by requesting 500 iterations. Solve −→Iterate...

Throughout the calculation, FLUENT will report reversed flow at the exit. This is reasonable for the current case. The solution should be sufficiently converged after about 230 iterations. The mass flow rate history is shown in Figure 7.3.


7-15


0.0300

0.0200

0.0100

Mass Flow Rate

0.0000

-0.0100

-0.0200

-0.0300 0

25

50

75

100

125

150

175

200

225

250

Iteration

Convergence history of Mass Flow Rate on pressure-outlet-3


Figure 7.3: Mass Flow Rate History (k- Turbulence Model)

7. Check the mass flux balance. Report −→Fluxes... !

7-16

Although the mass flow rate history indicates that the solution is converged, you should also check the net mass fluxes through the domain to ensure that mass is being conserved.



(a) Select velocity-inlet-2 and pressure-outlet-3 under Boundaries. (b) Keep the default Mass Flow Rate option. (c) Click Compute. !


8. Save the data file (disk ke.dat). File −→ Write −→Data...


7-17


Step 7: Postprocessing for the Standard k- Solution 1. Display the velocity vectors. Display −→Vectors...

(a) Increase the Scale value to 50. (b) Increase the Skip value to 1.

7-18



(c) Click Vector Options... to open the Vector Options panel.

i. Turn off the Z Component. This allows you to examine the non-swirling components only. ii. Click Apply and close the panel. (d) Click Display in the Vectors panel to plot the velocity vectors. A magnified view of the velocity field displaying a counter-clockwise circulation of the flow is shown in Figure 7.4.

3.27e+00 3.10e+00 2.94e+00 2.78e+00 2.62e+00 2.45e+00 2.29e+00 2.13e+00 1.97e+00 1.80e+00 1.64e+00 1.48e+00 1.32e+00 1.15e+00 9.91e-01 8.29e-01 6.66e-01 5.04e-01 3.41e-01 1.79e-01 1.64e-02



Figure 7.4: Magnified View of Velocity Vectors within the Disk Cavity


7-19


2. Display filled contours of static pressure. Display −→Contours...

(a) Select Pressure... and Static Pressure in the Contours Of drop-down list. (b) Turn on the Filled option. (c) Click Display. The pressure contours are displayed in Figure 7.5. Notice the high pressure that occurs on the right disk near the hub due to the stagnation of the flow entering from the bore.

7-20



6.56e-01 5.92e-01 5.27e-01 4.63e-01 3.98e-01 3.34e-01 2.69e-01 2.04e-01 1.40e-01 7.53e-02 1.07e-02 -5.39e-02 -1.18e-01 -1.83e-01 -2.48e-01 -3.12e-01 -3.77e-01 -4.41e-01 -5.06e-01 -5.70e-01 -6.35e-01



Figure 7.5: Contours of Static Pressure for Entire Disk Cavity

3. Create a constant y-coordinate line for postprocessing. Surface −→Iso-Surface...

(a) Select Grid... and Y-Coordinate in the Surface of Constant drop-down lists. (b) Click Compute to update the minimum and maximum values. (c) Enter 37 in the Iso-Values field. This is the radial position along which you will plot the radial velocity profile.


7-21


(d) Enter y=37cm for the New Surface Name. (e) Click Create to create the isosurface. Note: The name you use for an iso-surface can be any continuous string of characters (without spaces). 4. Plot the radial velocity distribution on the surface y=37cm. Plot −→XY Plot...

(a) Enable Node Values under Options. (b) Select Velocity... and Radial Velocity from the Y Axis Function drop-down lists. (c) Select the y-coordinate line y=37cm under Surfaces. (d) Click Plot. Figure 7.6 shows a plot of the radial velocity distribution along y = 37 cm. (e) Save the radial velocity profile. i. Select Write to File under Options. ii. Click the Write... button. iii. In the resulting Select File dialog box, specify ke-data.xy in the XY File text entry box and click OK.

7-22



y=37cm 3.50e-01 3.00e-01 2.50e-01 2.00e-01

Radial Velocity (m/s)

1.50e-01 1.00e-01 5.00e-02 0.00e+00 -5.00e-02 0

1

2

3

4

5

6

7

Position (cm)

Radial Velocity


Figure 7.6: Radial Velocity Distribution: Standard k- Solution


7-23


Step 8: Solution Using the RNG k- Model You will now recalculate the solution using the RNG k- turbulence model. 1. Turn on the RNG k- turbulence model with the enhanced near-wall treatment. Define −→ Models −→Viscous...

(a) Select RNG under k-epsilon Model. (b) Enable the Differential Viscosity Model and Swirl Dominated Flow under RNG Options. The differential viscosity model and swirl modification can provide better accuracy for swirling flows such as the disk cavity. See the User’s Guide for more information. (c) Keep the Enhanced Wall Treatment as the Near-Wall Treatment.

7-24



2. Continue the calculation by requesting 200 iterations. Solve −→Iterate... The solution should converge after about 160 additional iterations. 3. Save the case and data files (disk rng.cas and disk rng.dat). File −→ Write −→Case & Data...


7-25


Step 9: Postprocessing for the RNG k- Solution 1. Plot the radial velocity distribution for the RNG solution and compare it with the distribution for the standard k- solution. Plot −→XY Plot...

(a) Load the k- data. i. Click the Load File... button. This will open the Select File dialog box. ii. In the Select File dialog box, select the file ke-data.xy in the Files list. iii. Click OK. (b) In the Solution XY Plot panel, select Velocity... and Radial Velocity in the Y Axis Function drop-down lists. (c) In the Surfaces list, select y=37cm. (d) Turn off the Write to File option.

7-26



(e) Click the Curves... button to define a different curve symbol for the RNG k- data. This will open the Curves - Solution XY Plot panel.

i. Set the Curve # to 0. ii. Select x in the Symbol drop-down list. iii. Click Apply and Close the panel. (f) Click Plot in the Solution XY Plot panel. y=37cm y=37cm 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01


1.50e-01 1.00e-01 5.00e-02 0.00e+00 -5.00e-02 -1.00e-01 0

1

2

3

4

5

6

7

Position (cm)

Radial Velocity

Aug 02, 2002 FLUENT 6.1 (axi, swirl, segregated, rngke)

Figure 7.7: Radial Velocity Distribution: RNG and Standard k- Solutions The plot should be similar to the one shown in Figure 7.7. The peak velocity predicted by the RNG solution is higher than that predicted by the k- solution. This is due to the less diffusive character of the RNG k- model.


7-27


(g) Adjust the range of the x axis to magnify the region of the peaks. i. In the Solution XY Plot panel, click the Axes... button to specify the x-axis range. This will open the Axes - Solution XY panel.

ii. Deselect Auto Range under Options. iii. Under Range, enter 0 for the Minimum and 1 for the Maximum. iv. Click Apply and Close the panel. v. Click Plot in the Solution XY Plot panel. The difference between the peak values calculated by the two models is now more apparent.

7-28



y=37cm y=37cm 4.00e-01 3.50e-01 3.00e-01 2.50e-01


2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (cm)

Radial Velocity

Aug 02, 2002 FLUENT 6.1 (axi, swirl, segregated, rngke)

Figure 7.8: Radial Velocity Distribution: RNG and Standard k- Solutions (x = 0 cm to x = 1 cm)

Summary: This tutorial has demonstrated how to set up an axisymmetric disk cavity problem in FLUENT. The ability to calculate a swirl velocity permits the use of a 2D mesh, so the calculation is simpler and more economical to run. This is especially important for problems where the enhanced wall treatment is used, and the near-wall flow field is resolved through the viscous sublayer and buffer zones (that is, the first grid point away from the wall is placed at a y + on the order of 1). See the User’s Guide for more information about grid considerations for turbulence modeling.


7-29


Further Improvements: The case modeled in this tutorial lends itself to parametric study due to its relatively small size. Here are some things you may wish to try: • Separate wall-6 into two walls. Grid −→ Separate −→Faces... Specify one wall to be stationary, and rerun the calculation. • Use adaption to see if resolving the high velocity and pressure-gradient region of the flow has a significant effect on the solution. • Introduce a non-zero swirl at the inlet or use a velocity profile for fullydeveloped pipe flow. This is probably more realistic than the constant axial velocity used here, since the flow at the inlet is typically being supplied by a pipe. • Model compressible flow (using the ideal gas law for density) rather than assuming incompressible flow. References: 1. Pincombe, J.R., “Velocity Measurements in the Mk II - Rotating Cavity Rig with a Radial Outflow”, Thermo-Fluid Mechanics Research Centre, University of Sussex, Brighton, UK, 1981.

7-30


Tutorial 8. Using Multiple Rotating Reference Frames Introduction: Many engineering problems involve rotating flow domains. One example is the centrifugal blower unit that is typically used in automotive climate control systems. For problems where all the moving parts (fan blades, hub and shaft surfaces, etc.) are rotating at a prescribed angular velocity, and the stationary walls (e.g., shrouds, duct walls) are surfaces of revolution with respect to the axis of rotation, the entire domain can be referred to as a single rotating frame of reference. However, when each of several parts is rotating about a different axis of rotation, or about the same axis at different speeds, or when the stationary walls are not surfaces of revolution (such as the volute around a centrifugal blower wheel), a single rotating coordinate system is not sufficient to “immobilize” the computational domain so as to predict a steady-state flow field. In FLUENT, the flow features associated with multiple rotating parts can be analyzed using the multiple reference frame (MRF) capability. This model is powerful in that multiple rotating reference frames can be included in a single domain. The resulting flow field is representative of a snapshot of the transient flow field in which the rotating parts are moving. However, in many cases the interface can be chosen in such a way that the flow field at this location is independent of the orientation of the moving parts. In other words, if an interface can be drawn on which there is little or no angular dependence, the model can be a reliable tool for simulating time-averaged flow fields. It is therefore very useful in complicated situations where one or more rotating parts are present. This tutorial illustrates the procedure for setting up and solving a problem using the MRF capability. As an example, the flow field on a 2D section of a centrifugal blower will be calculated. The example will be limited to a single rotating reference frame. The following FLUENT features will be demonstrated in this tutorial: • Specifying different frames of reference for different fluid zones. • Setting the relative velocity of each wall. • Calculating a solution using the segregated solver Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps will not be shown explicitly. In general, to solve problems using the MRF feature, you should be familiar with the concept of creating multiple fluid zones in your grid generator.


8-1

Using Multiple Rotating Reference Frames

Problem Description: This problem considers a 2D section of a generic centrifugal blower. A schematic of the problem is shown in Figure 8.1. The blower consists of 32 blades, each with a chord length of 13.5 mm. The blades are located approximately 56.5 mm (measured from the leading edge) from the center of rotation. The radius of the outer wall varies logarithmically from 80 mm to 146.5 mm. The total pressure at the inlet is defined to be 200 Pa and the flow discharges to ambient conditions (static pressure = 0 Pa). The blades are rotating with an angular velocity of 261 rad/s. The flow is assumed to be turbulent.

Pressure-inlet-5

261 rad/s

35 mm

▼

56.5 mm

blower blades (13.5 mm chord length)

Pressure-Outlet-9

145 mm


Preparation 1. Copy the file blower/blower.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

8-2



Step 1: Grid 1. Read in the mesh file (blower.msh). File −→ Read −→Case... 2. Check the grid. Grid −→Check Note: FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Smooth and swap the grid. Grid −→Smooth/Swap... Node smoothing and face swapping will improve the mesh quality. This step is recommended for triangular and tetrahedral meshes.

(a) Retain the default smoothing parameters and click Smooth. (b) Click Swap repeatedly until the Number Swapped under Swap Info is zero. 4. Display the mesh (Figure 8.2). Display −→Grid... The mesh consists of three fluid zones, fluid-13, fluid-14, and fluid-18. These are reported in the console window when the grid is read. In the Grid Display panel, the fluid zones are reported as interior zones interior-61, interior-62 and interior-66. In a later step, you will learn how to associate a fluid zone with an interior zone. The fluid zone containing the blades will be solved in a rotational reference frame.


8-3


Grid

Jul 09, 2002 FLUENT 6.1 (2d, segregated, ske)

Figure 8.2: Mesh of the 2D Centrifugal Blower

The fluid zones are separated by wall boundaries. These boundaries were used in the grid generator to separate the fluid zones, and will be converted to interior zones when the boundary conditions are set later in this tutorial. Each of these wall zones also has an associated “shadow wall” which was created by FLUENT when it read the grid. Shadow walls are created whenever a wall has fluid zones on both sides.

8-4





8-5


2. Turn on the standard k- turbulence model. Define −→ Models −→Viscous...

8-6



Step 3: Materials You will use the default material, air, with its predefined properties, for all fluid zones. No action is required in the panel. Define −→Materials...

Extra: If needed, you could modify the fluid properties for air or copy another material from the database. See Chapter 7 of the User’s Guide for details.


8-7


Step 4: Boundary Conditions Define −→Boundary Conditions... 1. Change wall-2 and wall-3 to type interior. The zones wall-2 and wall-3 are the interfaces between the three fluid zones. They need to be changed to type interior, as discussed earlier. The resulting interior faces are those that have fluid cells on both sides but do not require any boundary conditions to be set.

(a) Select wall-2 in the Zone list and then select interior in the Type list. FLUENT will prompt for confirmation before changing the zone type.

(b) Click Yes and FLUENT will fuse wall-2 and wall-shadow-2 together to form interior-2.

8-8



(c) Click OK to keep the default Zone Name. (d) Repeat the previous steps to change wall-3 to an interior zone named interior-3. 2. Identify the rotating fluid zone (i.e., the zone containing the blades) by displaying the mesh for each zone. Display −→Grid... It is unclear when you read the grid which fluid zone corresponds to which interior zone. While the interior zones can be selected individually in the Grid Display panel, the fluid zones cannot. Commands in the text interface, however, can be used to make this association. (a) Deselect all surfaces by clicking on the unshaded icon to the right of Surfaces. (b) Click the Outline button at the bottom of the panel to select only the outline surfaces of the domain. (c) Click Display. Only the domain boundaries and interior walls will be displayed. (d) In the console window, type the commands shown in boxes in the dialog below. Hint: You may need to press the key to get the > prompt.

> display /display> zone-grid () zone id/name(1) [()] 13 zone id/name(2) [()]

The resulting display (Figure 8.3) shows that zone fluid-13 corresponds to the rotating region.


8-9


Thread Grid: (13)


Figure 8.3: Mesh in fluid-13

3. Define a rotational reference frame for fluid-13. Define −→Boundary Conditions... (a) Keep the Rotation-Axis Origin default setting of (0,0). This is the center of curvature for the circular boundaries of the rotating zone. (b) Select Moving Reference Frame from the Motion Type drop-down list. Hint: Use the scroll bar to access the Motion Type list. (c) Scroll down further, and set the Speed under Rotational Velocity to 261 rad/s.

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Note: Since the other fluid zones are stationary, you do not need to set any boundary conditions for them. If one of the remaining fluid zones was also rotating, you would need to set the appropriate rotational speed for it. 4. Set the following conditions (see Figure 8.1) for the flow inlet (pressure-inlet-5).

Note: All pressures that you specify in FLUENT are gauge pressures, relative to the operating pressure specified in the Operating Conditions panel. By default, the operating pressure is 101325 Pa. See the User’s Guide for details.


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5. Set the backflow turbulence parameters for the flow outlet (pressure-outlet-9) to the same values used for pressure-inlet-5.

Note: The backflow values are used only if reversed flow occurs at the outlet, but it is a good idea to use reasonable values, even if you do not expect any backflow to occur. 6. Define the velocity of the wall zone representing the blades (wall-7) relative to the moving fluid zone. With fluid-13 set to a rotating reference frame, wall-7 becomes a moving wall. (a) In the Momentum section of the Wall panel, enable the Moving Wall option. The panel will expand to show the wall motion parameters. (b) Under Motion, select Relative to Adjacent Cell Zone and Rotational. (c) Set the (relative) Speed to 0 rad/s. The Rotation-Axis Origin should be located at x = 0 m and y = 0 m. With these settings, the blades will move at the same speed as the surrounding fluid.

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Step 5: Solution 1. Choose the second-order discretization scheme for the governing equations. Solve −→ Controls −→Solution...

(a) In the drop-down lists next to Momentum, Turbulence Kinetic Energy, and Turbulence Dissipation Rate, select Second Order Upwind. The second-order scheme will provide a more accurate solution. (b) Keep the default parameters for all other solution controls. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual... (a) Select Plot under Options, and click OK.

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3. Initialize the solution using the boundary conditions set at pressure-inlet-5. Solve −→ Initialize −→Initialize...

(a) Select pressure-inlet-5 in the Compute From drop-down list. (b) Select Absolute under Reference Frame. (c) Click Init to initialize the solution.


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Note: In this tutorial, you chose an Absolute reference frame for initializing the solution. In certain cases, Relative to Cell Zone may help the solution converge faster. See the User’s Guide for guidelines. 4. Save the case file (blower.cas). File −→ Write −→Case... 5. Start the calculation by requesting 400 iterations. Solve −→Iterate...

During the calculation, FLUENT will report that there is reversed flow occurring at the exit. This is due to the sudden expansion, which results in a recirculating flow near the exit. The solution will converge in around 160 iterations (when all residuals have dropped below 0.001). 6. Save the case and data files (blower2.cas and blower2.dat). File −→ Write −→Case & Data... Note: It is good practice to save the case file whenever you are saving the data. This will ensure that the relevant parameters corresponding to the current solution data are saved accordingly.

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Step 6: Postprocessing 1. Display filled contours of total pressure (Figure 8.4). Display −→Contours...

(a) Select Pressure... and Total Pressure in the Contours Of drop-down lists. (b) Select Filled under Options. (c) Click Display. Total pressure contours show the expected pressure jump across the blower blades.


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1.13e+03 1.03e+03 9.26e+02 8.25e+02 7.24e+02 6.23e+02 5.21e+02 4.20e+02 3.19e+02 2.17e+02 1.16e+02 1.47e+01 -8.66e+01 -1.88e+02 -2.89e+02 -3.91e+02 -4.92e+02 -5.93e+02 -6.94e+02 -7.96e+02 -8.97e+02

Contours of Total Pressure (pascal)


Figure 8.4: Contours of Total Pressure

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2. Display velocity vectors (Figure 8.5). Display −→Vectors...

(a) Set the Scale factor to 5. (b) Click Display to view the vectors. By default, Auto Scale is chosen. This will automatically scale the length of velocity vectors relative to the size of the smallest cell in the mesh. To increase the length of the “scaled” vectors, set the Scale factor to a value greater than 1.


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3. Report the mass flux at pressure-inlet-5 and pressure-outlet-9. Report −→Fluxes...

(a) Keep the Mass Flow Rate setting under Options. (b) Select pressure-inlet-5 and pressure-outlet-9 in the Boundaries list. (c) Click Compute. The net mass imbalance should be no more than a small fraction (say, 0.5%) of the total flux through the system. If a significant imbalance occurs, you should decrease your residual tolerances by at least an order of magnitude and continue iterating. The flux report will compute fluxes only for boundary zones. To report fluxes on surfaces or planes, use the Surface Integrals... option in the Report menu. Summary: This tutorial illustrates the procedure for setting up and solving problems with multiple reference frames using FLUENT. Although this tutorial considers only one rotating fluid zone, extension to multiple rotating fluid zones is straightforward as long as you delineate each fluid zone. Note that this tutorial was solved using the default absolute velocity formulation. For some problems involving rotating reference frames, you may wish to use the relative velocity formulation. See the User’s Guide for details.


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Tutorial 9.

Using the Mixing Plane Model

Introduction: This tutorial considers the flow in an axial fan with a rotor in front and stators (vanes) in the rear. This configuration is typical of a single-stage axial flow turbomachine. By considering the rotor and stator together in a single calculation, you can determine the interaction between these components. In this tutorial you will learn how to: • Use the standard k- model with standard wall functions • Use a mixing plane to model the rotor-stator interface • Calculate a solution using the segregated solver • Compute and display circumferential averages of total pressure on a surface Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem to be considered is shown schematically in Figure 9.1. The rotor and stator consist of 9 and 12 blades, respectively. A steady-state solution for this configuration using only one rotor blade and one stator blade is desired. Since the periodic angles for the rotor and stator are different, a mixing plane must be used at the interface. The mixing plane is defined at the rotor outlet/stator inlet. The grid is set up with periodic boundaries on either side of the rotor and stator blades. A pressure inlet is used at the upstream boundary and a pressure outlet at the downstream boundary. Ambient air is drawn into the fan (at 0 Pa gauge total pressure) and is exhausted back out to the ambient environment (0 Pa static pressure). The hub and blade of the rotor are assumed to be rotating at 1800 rpm.

Preparation 1. Copy the file mstage/fanstage.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 3D version of FLUENT.


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rotor

stator outlet

inlet

y z

x

ω = 1800 rpm


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Step 1: Grid 1. Read the grid file (fanstage.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the grid and will report the progress in the console window. Pay particular attention to the minimum volume. Make sure that this is a positive number. 3. Display the grid (Figure 9.2). Display −→Grid...

(a) Select rotor-blade, rotor-hub, rotor-inlet-hub, stator-blade, and stator-hub in the Surfaces list. (b) Click Display. (c) Rotate the view to get the display shown in Figure 9.2. Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.


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Y Z

Grid

X


Figure 9.2: Grid Display for the Multistage Fan

Step 2: Units 1. For convenience, define new units for angular velocity. The angular velocity for this problem is known in rpm, which is not the default unit for angular velocity. You will need to redefine the angular velocity units as rpm. Define −→Units...

(a) Select angular-velocity under Quantities, and rpm under Units. (b) Close the panel.

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2. Turn on the standard k- turbulence model with standard wall functions. Define −→ Models −→Viscous...

(a) Under Model, select k-epsilon. The panel will expand. (b) Under k-epsilon Model, keep the default Standard option. (c) Under Near-Wall Treatment, keep the default Standard Wall Functions option.

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Step 4: Mixing Plane In this step, you will create the mixing plane between the pressure outlet of the rotor and the pressure inlet of the stator. Define −→Mixing Planes...

1. Select pressure-outlet-rotor in the Upstream Zone list. 2. Select pressure-inlet-stator in the Downstream Zone list. 3. Click Create. FLUENT will name the mixing plane by combining the names of the zones selected as the Upstream Zone and Downstream Zone. This new name will be displayed in the Mixing Plane list. The essential idea behind the mixing plane concept is that each fluid zone (stator and rotor) 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 rotor outlet and the stator inlet boundaries. FLUENT uses these circumferential averages to define “profiles” of flow properties. These profiles are then used to update boundary conditions along the two zones of the mixing plane interface. In this example, profiles of averaged total pressure (p0 ), static pressure (ps ), 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, the same profiles, except for that of total pressure are computed at the stator inlet and used as a boundary condition on the


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rotor exit. You can view the profiles computed at the rotor exit and stator inlet in the Boundary Profiles panel. Define −→Profiles... You will also see that these profiles appear in the boundary conditions panels for the rotor exit and stator inlet. See the User’s Guide for more information on mixing planes.

Step 5: Materials 1. Accept the default properties for air. Define −→Materials...

For the present analysis, you will model air as an incompressible fluid with a density of 1.225 kg/m3 and a dynamic viscosity of 1.7894× 10−5 kg/m-s. Since these are the default values, no change is required in the materials panel.

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Step 6: Boundary Conditions Define −→Boundary Conditions... 1. Set the conditions for the rotor fluid (fluid-rotor).

(a) Under Rotation-Axis Direction, enter -1 next to Z . According to the right-hand rule and Figure 9.1, the axis of rotation is the −Z axis. You specify this by entering the vector (0, 0, −1) for the Rotation-Axis Direction. (b) Select Moving Reference Frame in the Motion Type drop-down list. Hint: Use the scroll bar to access Motion Type. (c) Set the Speed (under Rotational Velocity) to 1800 rpm. Hint: Use the scroll bar to access Rotational Velocity.


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2. Set the conditions for the stator fluid (fluid-stator).

(a) Under Rotation-Axis Direction, enter -1 next to Z. 3. Specify rotational periodicity for the periodic boundary of the rotor (periodic-11).

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4. Specify rotational periodicity for the periodic boundary of the stator (periodic-22).

5. Set the following conditions for the pressure inlet of the rotor (pressure-inlet-rotor).

To model ambient conditions, you use P0 = 0 gauge. The turbulence level is assumed to be low (1% ) and the hydraulic diameter is used as the length scale.


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6. Examine the conditions for the pressure inlet of the stator (pressure-inlet-stator). The profiles computed at the rotor outlet are used to update the boundary conditions at the stator inlet. These profiles were set for you automatically when the mixing plane was created. Therefore, you do not need to set any parameters in this panel.

7. Examine the conditions for the pressure outlet of the rotor (pressure-outlet-rotor). The Backflow Direction Specification Method was set to Direction Vector when you created the mixing plane, and the Coordinate System to Cylindrical (like for the stator inlet ). The values for the direction cosines are taken from the profiles at the stator.

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8. Set the conditions for the pressure outlet of the stator (pressure-outlet-stator).

(a) Select Radial Equilibrium Pressure Distribution. Radial equilibrium is used to simulate the pressure distribution which exists due to rotation according to ∂p ρv 2 = θ ∂r r


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where vθ is the tangential velocity. This is a good approximation for axial flow configurations with 0 straight flow paths (i.e., little change in radius from inlet to exit). (b) Retain the default Backflow Direction Specification Method. In problems where a backflow exists at the pressure outlet boundary (e.g., torque-converter), you can use this option to specify the direction of the backflow. (c) Select Intensity and Viscosity Ratio for the Turbulence Specification Method. (d) Set the Backflow Turbulence Intensity to 1%. (e) Set the Backflow Turbulent Viscosity Ratio to 1. 9. Set the conditions for the inlet hub of the rotor (rotor-inlet-hub).

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(a) Select Moving Wall. The panel will expand to show the wall motion inputs. (b) Select Absolute and Rotational under Motion. (c) Set the Rotation-Axis Direction by entering -1 next to Z. These conditions set the rotor-inlet-hub to be a stationary wall in the absolute frame. 10. Set the conditions for the shroud of the rotor inlet (rotor-inlet-shroud).

(a) Select Moving Wall. (b) Select Absolute and Rotational under Motion. (c) Set the Rotation-Axis Direction by entering -1 next to Z. These conditions set the rotor-inlet-shroud to be a stationary wall in the absolute frame.


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11. Set the following conditions for the rotor shroud (rotor-shroud).

(a) Select Moving Wall. (b) Select Absolute and Rotational under Motion. (c) Set the Rotation-Axis Direction by entering -1 next to Z. These conditions set the rotor-shroud to be a stationary wall in the absolute frame.

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12. Accept the default conditions for the rotor-hub. For a rotating reference frame, FLUENT assumes by default that walls rotate with the grid, and hence are moving with respect to the stationary (absolute) reference frame. Since the rotor-hub is rotating, you should keep the default settings.


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(a) Under Discretization, select Second Order Upwind for Momentum. (b) Select Power Law for Turbulence Kinetic Energy and Turbulence Dissipation Rate. (c) Set the Under-Relaxation Factors for Pressure to 0.2, Momentum to 0.5, Turbulence Kinetic Energy to 0.5, and Turbulence Dissipation Rate to 0.5. Note: For this problem, it was found that these under-relaxation factors worked well. See the User’s Guide for tips on how to adjust the under-relaxation parameters for different situations.

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(a) Under Options, select Plot. (b) Click OK. 3. Enable the plotting of mass flow rate at the flow exit. Solve −→ Monitors −→Surface...


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(a) Increase the Surface Monitors value to 1. (b) Turn on the Plot and Write options for monitor-1. Note: When the Write option is selected in the Surface Monitors panel, the mass flow rate history will be written to a file. If you do not select the write option, the history information will be lost when you exit FLUENT. (c) Click on Define... to specify the surface monitor parameters in the Define Surface Monitor panel.

i. Select Mass Flow Rate from the Report Type drop-down list. ii. Select pressure-outlet-stator in the Surfaces list. iii. Click on OK to define the monitor. (d) Click on OK in the Surface Monitors panel to enable the monitor.

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4. Initialize the flow field. Solve −→ Initialize −→Initialize...

(a) Select Absolute under Reference Frame. For rotor-stator problems, the absolute velocity formulation is superior to the relative velocity formulation, since, at the inlet/outlet boundaries, the absolute velocity and total pressure are uniform, whereas the corresponding relative conditions are non-uniform. (b) Set the initial value for Z Velocity to -1. (c) Click on Init and close the panel. 5. Save the case file (fanstage.cas). File −→ Write −→Case... 6. Start the calculation by requesting 800 iterations. Solve −→Iterate...


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!

Calculating until the mass flow rate converges will require significant CPU resources. Instead of calculating the solution, you can read the data file (fanstage.dat) with the pre-calculated solution, and proceed to the postprocessing section of the tutorial (Step 8). This data file can be found in the directory where you found the mesh file.

The solution will converge after about 640 iterations. However, the residual history plot is only one indication of solution convergence. Notice that the mass flow rate has not reached a constant value. To remedy this, you will reduce the convergence criterion for the continuity equation and iterate until the mass flow rate reaches a constant value. 7. Reduce the convergence criterion for the continuity equation. Solve −→ Monitors −→Residual... (a) Set the Convergence Criterion for continuity to 1e-05.

(b) Click OK. Note: In this case, the reason for continuing the calculation is to obtain better global mass conservation; thus, only the convergence tolerance for the continuity equation is adjusted. In general, the convergence behavior of the continuity equation is a good indicator of the overall convergence of the solution.

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8. Request 2000 more iterations. Solve −→Iterate... After about 1400 iterations, the mass flow rate has leveled off and the solution has converged. The mass flow rate history is shown in Figure 9.3.

-0.0020 -0.0040 -0.0060 -0.0080 -0.0100

Mass Flow Rate (kg/s)

-0.0120 -0.0140 -0.0160 -0.0180 -0.0200 -0.0220 0

Y Z

200

400

X

600

800

1000

1200

1400

1600

1800

2000

Iteration

Convergence history of Mass Flow Rate on pressure-outlet-stator


Figure 9.3: Mass Flow Rate History

9. Save the data file (fanstage.dat). File −→ Write −→Data... 10. Check the mass flux balance. Report −→Fluxes... !

Although the mass flow rate history indicates that the solution is converged, you should also check the mass fluxes through the domain to ensure that mass is being conserved.


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(a) Select pressure-outlet-stator, pressure-inlet-stator, pressure-inlet-rotor, and pressureoutlet-rotor under Boundaries. (b) Keep the default Mass Flow Rate option and click on Compute. !


Note: The fluxes for the portions of the rotor and stator that have been modeled are different. However, the flux for the whole rotor and the whole stator are very nearly equal: approximately 0.23274 kg/s (0.02586 × 9 rotor blades), versus approximately 0.23328 kg/s (0.01944 × 12 stator blades).

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Step 8: Postprocessing 1. Create two surfaces for postprocessing, one at y = 0.12 m and one at z = −0.1 m. Surface −→Iso-Surface... The surface y = 0.12 m is a midspan slice through the grid. This view is good for looking at the blade-to-blade flow field. The surface z = −0.1 m is an axial plane downstream of the stator. This will be used to plot circumferentially-averaged profiles.

(a) Select Grid... and Y-Coordinate in the Surface of Constant lists. (b) Click on Compute to update the minimum and maximum values. (c) Enter 0.12 in the Iso-Values field. (d) Enter y=0.12 for the New Surface Name. (e) Click on Create to create the isosurface. (f) Select Grid... and Z-Coordinate in the Surface of Constant lists. (g) Click on Compute to update the minimum and maximum values. (h) Enter -0.1 in the Iso-Values field. (i) Enter z=-0.1 for the New Surface Name. Note: The default name that FLUENT gave the surface, z-coordinate-17, indicates that this is surface number 17. This fact will be used later in the tutorial when you plot circumferential averages. (j) Click on Create to create the isosurface.


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2. Display velocity vectors on the midspan surface y = 0.12. Display −→Vectors...

(a) Select y=0.12 in the Surfaces list. (b) Increase the Scale value to 10. (c) Increase the Skip value to 2. (d) Select arrow from the Style drop-down list. (e) Click on Display to plot the velocity vectors. (f) Rotate and zoom the view to get the display shown in Figure 9.4.

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Y X Z



Figure 9.4: Velocity Vectors on y = 0.12 Near the Stator Blade Plotting the velocity field in this manner gives a good indication of the midspan flow over the stator. For the rotor, it is instructive to similarly plot the relative velocity field. 3. Plot a circumferential average of the total pressure on the plane z = −0.1. (a) In the console window, type the commands shown in boxes in the dialog below. Note: Surface 17 is the surface z = −0.1 you created earlier. For increased resolution, 15 bands are used instead of the default 5.

> plot /plot> circum-avg-radial averages of> total-pressure on surface [] 17 number of bands [5] 15

The radial variation in the total pressure can be seen to be very non-uniform in this plot (Figure 9.5). This implies that losses are largest near the hub.


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3.75e+01 3.50e+01 3.25e+01 3.00e+01 2.75e+01

Total Pressure (kg/s)

2.50e+01 2.25e+01 2.00e+01 1.75e+01 1.50e+01 0.1

0.105

0.11

0.115

Y X

0.12

0.125

0.13

0.135

0.14

Radius

Z Circumferential Averages


Figure 9.5: Plot of Circumferential Average of the Total Pressure on the Plane z = −0.1.

4. Display filled contours of total pressure. Display −→Contours...

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(a) Select rotor-blade and rotor-hub in the Surfaces list. (b) Select Pressure... and Total Pressure in the Contours Of drop-down lists. (c) Turn on the Filled option. (d) Click Display. The pressure contours are displayed in Figure 9.6. Notice the high pressure that occurs on the leading edge of the rotor blade due to the motion of the blade.

5.38e+02 4.98e+02 4.59e+02 4.20e+02 3.81e+02 3.41e+02 3.02e+02 2.63e+02 2.24e+02 1.84e+02 1.45e+02 1.06e+02 6.65e+01 2.73e+01 -1.20e+01 -5.12e+01 -9.05e+01 -1.30e+02 -1.69e+02 -2.08e+02 Z -2.48e+02

Y X

Contours of Total Pressure (pascal)


Figure 9.6: Contours of Total Pressure for the Rotor Blade and Hub

Summary: This tutorial has demonstrated the use of the mixing plane model for a typical axial flow turbomachine configuration. The mixing plane model is useful for predicting steady-state flow in a turbomachine stage, where local interaction effects (such as wake and shock waves) are secondary. If local effects are important, then an unsteady, sliding mesh calculation is required.


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Tutorial 10.

Using Sliding Meshes

Introduction: In this tutorial, the sliding mesh capability of FLUENT is used to predict the time-dependent flow through a two-dimensional rotor-stator blade row. The time-varying rotor-stator interaction is modeled by allowing the mesh associated with the moving rotor to translate (slide) relative to the stationary mesh associated with the stator blade. In this tutorial you will learn how to: • Merge two meshes into a single mesh, using tmerge • Define boundary conditions and create grid-interface planes for sliding mesh simulations • Calculate a steady-state solution (using the coupled explicit solver) as an initial guess for a transient flow prediction • Calculate a transient solution using the second-order implicit unsteady formulation and the coupled explicit solver • Monitor solution history for time-dependent parameters • Postprocess and store transient data sets, using the automatic procedures available in FLUENT Prerequisites: This tutorial assumes that you are familiar with the basic menu structure and solution procedure used by FLUENT and that you have solved Tutorial 1. Problem Description: The rotor-stator geometry considered in this tutorial is shown in Figure 10.1. The geometry consists of a planar slice through the rotor and stator blades, extracted by unrolling a plane of constant radius (R = 0.686 m) in an axial flow turbomachine. The speed of rotation, 410 RPM, yields a linear velocity of the rotor, RΩ, equal to 29.4 m/s, as indicated in the figure. The fluid, assumed to be air, enters the stator row at the specified total pressure and temperature and exits the rotor at the specified exit static pressure. The inlet Mach number is 0.07 and the flow will be treated as compressible.


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Stator Vanes

Rotor Blades

(stationary)

(moving) Cx = 0.1524 m

P01 = 101325 Pa

blade pitch = 0.1959 m

T01 = 300 K M = 0.07

P2 = 97576 Pa

sliding interface

direction of motion (V = 29.445 m/s)

Figure 10.1: Rotor-Stator Problem Description

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Preparation 1. Copy the files slide/rotor.msh and slide/stator.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). Note: The geometries of the rotor and stator flow domains have been meshed separately. This is the usual procedure when the sliding mesh capability is used: separate mesh files are created for the sliding and stationary mesh regions. This ensures that the sliding interface between the two regions is defined by two separate boundary zones which share no common nodes. The two separate mesh files must be merged prior to reading them into FLUENT, as detailed in Step 1, below.


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Step 1: Merging the Mesh Files 1. Start tmerge by typing utility tmerge -2d at the system prompt. 2. Provide the mesh file names, rotor.msh and stator.msh, as prompted. Provide scaling factors of 1 and translations and rotations of zero for each mesh file. Save the new merged mesh file as slide.msh.

Append 2D grid files. tmerge2D Fluent Inc, Version 2.1.8 Enter name of grid file (ENTER to continue) : rotor.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) : stator.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

!

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: slide.msh

The mesh files must be read into tmerge in this order for the tutorial to run as written. Otherwise, zone names and numbers will be assigned differently when the files are merged together. In general, however, you can specify files to be read into tmerge in any order.



Step 2: Grid 1. Start the 2D version of FLUENT. 2. Read in the mesh file slide.msh. File −→ Read −→Case... 3. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 4. Scale the grid. Grid −→Scale...

(a) Select in in the Units Conversion drop-down list to complete the phrase Grid Was Created In in (inches). (b) Click on Scale to scale the grid. The final domain extents should appear as in the panel above.


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5. Display the grid (Figure 10.2). Display −→Grid...

Note: You can use the mouse probe button (right button, by default) to find out the boundary zone labels. As annotated in Figure 10.3, the upstream boundary is a pressure inlet, the downstream boundary is a pressure outlet, and the lateral top and bottom boundaries are periodic. The stator blade and stator-side fluid are identified as wall-7 and fluid-9. The rotor blade and rotor-side fluid are wall-16 and fluid-18. (Your mouse probe will report the fluid regions as interior-8 and interior-17 zones, for the stator and rotor sides, respectively. These are the face zones associated with the fluid regions.) To determine which fluid zone is the stator-side fluid, you can create the fluid9 and fluid-18 display surfaces using the Zone Surface panel. Then, display the zones (one at a time) using the Grid Display panel. If you wish to annotate your own graphics display, you can use the Annotate panel. Display −→Annotate...

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Grid


Figure 10.2: Rotor-Stator Mesh Display

Rotor

Stator

periodic-15

periodic-8

fluid-18

pressure-outlet-14 pressure-inlet-3 wall-7

Grid

wall-16


Figure 10.3: Annotated Mesh


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Step 3: Models 1. Select the coupled explicit solver. Define −→ Models −→Solver...

Note: Initially, you will solve for the steady flow through the blade passage. Later, after obtaining the steady flow as the starting point for the transient calculation, you will revisit this panel to turn on time-dependent flow.

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2. Enable the standard k- turbulence model. Define −→ Models −→Viscous...

Note: The Reynolds number of the flow is about 105 , and the flow will be treated as fully turbulent.


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Step 4: Materials 1. Select air (the default material) as the fluid material, and use the ideal-gas law to compute density. Retain the default values for all other properties. Define −→Materials...

!

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Don’t forget to click the Change/Create button after selecting ideal-gas in the drop-down list for Density.



Step 5: Operating Conditions 1. Set the operating pressure to 0 Pa. Define −→Operating Conditions...

Here, the operating pressure is set to zero and boundary condition inputs for pressure will be defined in terms of absolute pressures. Boundary condition inputs should always be relative to the value used for operating pressure.


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Step 6: Boundary Conditions Define −→Boundary Conditions... 1. Set the conditions for the upstream boundary (pressure-inlet-3).

(a) Change the Zone Name from pressure-inlet-3 to pressure-inlet. (b) Set the Gauge Total Pressure to 101325 Pa. (c) Set the Supersonic/Initial Gauge Pressure to 100978.2 Pa. The inlet static pressure estimate is computed from the assumed inlet total pressure and Mach number (see Figure 10.1). (d) Set the Total Temperature to 300 K. (e) In the Direction Specification Method drop-down list, select Direction Vector. (f) In the Turbulence Specification Method drop-down list, select Intensity and Hydraulic Diameter. (g) Set the Turbulence Intensity to 5%, and the Hydraulic Diameter to 0.1959 m. The inlet turbulence length scale will be computed using the blade pitch as an equivalent “hydraulic diameter”.

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2. Set the conditions for the exit plane boundary (pressure-outlet-14).

(a) Change the Zone Name from pressure-outlet-14 to pressure-outlet. (b) Set the Gauge Pressure to 97576 Pa. (c) Set the Backflow Total Temperature to 300 K. (d) In the Turbulence Specification Method drop-down list, select Intensity and Hydraulic Diameter. (e) Set the Turbulence Intensity to 5%, and the Hydraulic Diameter to 0.1959 m. Note: The temperature and turbulence conditions you input at the pressure outlet will be used only if flow enters the domain through this boundary. You can set them equal to the inlet values, as no flow reversal is expected at the domain exit in this problem. In general, however, it is important to set reasonable values for these downstream scalar values, in case flow reversal occurs at some point during the calculation.


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3. Keep the default Momentum boundary conditions for the stator blades (wall-7) and the rotor blades (wall-16).

The velocity of a “non-moving” wall is assumed to match that of the adjacent mesh region, yielding a no-slip condition in the reference frame of the mesh. Thus, FLUENT will assume that the stator blade is stationary in the non-moving reference frame of the stator mesh. Similarly, FLUENT will assume that the rotor blade is moving at the grid speed in the sliding rotor region. Therefore, you will not modify the wall velocity of the rotor (wall-16), even though the rotor is moving. The default setting of a non-moving wall is correct and implies zero velocity in the moving reference frame of the sliding region. (The motion of the mesh region will be defined as a boundary condition for the fluid zone, below.) 4. Set the conditions for the stator-side fluid (fluid-9).

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(a) Change the Zone Name from fluid-9 to fluid-stator. (b) Keep the default selection of air as the Material Name, and the Motion Type as Stationary. Hint: Use the scroll bar to access the Motion Type field. 5. Set the conditions for the rotor-side fluid (fluid-18).


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(a) Change the Zone Name from fluid-18 to fluid-rotor. (b) Keep the default selection of air as the Material Name, and the Motion Type as Stationary. Later, after solving the steady flow through the non-moving rotor passage, you will return to this panel to specify that the rotor zone is sliding, as illustrated in Figure 10.1. 6. Define the zones on the sliding boundary as interface zones. The sliding grid interface contains two boundary zones: pressure-inlet-12 and pressureoutlet-5. pressure-inlet-12 is the upstream boundary of the rotor-side fluid region, and pressure-outlet-5 is the downstream boundary of the stator-side fluid region. These boundaries were defined as the upstream and downstream boundaries of the original mesh files, rotor.msh and stator.msh, and must be redefined as interface boundary types for the merged mesh. (a) Select pressure-inlet-12 in the Zone list and choose interface as the new Type.

(b) Confirm that it is OK to change the boundary type.

(c) Change the Zone Name to interface-rotor.

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(d) Repeat this procedure to convert pressure-outlet-5 to an interface boundary named interface-stator.


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Step 7: Grid Interfaces In this step, you will create a periodic grid interface between the rotor and stator mesh regions. Define −→Grid Interfaces...

1. Select interface-rotor in the Interface Zone 1 list. Note: In general, when one interface zone is smaller than the other, it is recommended that you choose the smaller zone as Interface Zone 1. In this case, however, since both zones are the same size, the order is not significant. 2. Select interface-stator in the Interface Zone 2 list. 3. Enter the name interface-rotor-stator under Grid Interface. 4. Select Periodic under Interface Type, and click Create. The interface between the sliding and non-sliding zones will be treated as periodic where the two zones are non-overlapping.

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Step 8: Solution: Steady Flow with Non-Moving Rotor 1. Initialize the solution for steady flow. Solve −→ Initialize −→Initialize...

(a) Select pressure-inlet in the Compute From drop-down list. (b) Click Init, and Close the panel.


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2. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Set the Courant Number to 2. Setting the Courant number to 2.0 promotes rapid convergence for the steady flow simulation. (For more information on the Courant number, see Step 9: Enable Time Dependence and Sliding Rotor Motion). (b) Change Multigrid Levels to 5. Five levels of multigrid enable boundary condition information to propagate rapidly across the solution domain. (c) Under Discretization, select Second Order Upwind for Turbulence Kinetic Energy and Turbulence Dissipation Rate. Second-order discretization provides optimum accuracy.

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(a) Select Plot under Options, and click OK.


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4. Enable the monitoring of the lift force on the rotor blade (wall-16). Note: Monitoring forces on the rotor blade provides a good measure of convergence during the initial steady-state flow prediction. Here, you will request dynamic plotting of lift as the solution proceeds. In addition, you will write the lift information to a file, cl-hist.ss. You could choose to monitor any other variable (e.g., mass flow rate), including a custom field function. Solve −→ Monitors −→Force...

(a) Select Lift in the Coefficient drop-down list. (b) In the Wall Zones list, select wall-16 (the rotor). (c) Enable the Plot and Write options. (d) In the File Name field, enter cl-hist.ss. (e) Keep the Plot Window set to 1. (f) Click Apply, and Close the panel.

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5. Set the reference values to be used in the lift coefficient calculation. Report −→Reference Values...

(a) Select pressure-inlet in the Compute From drop-down list. (b) Change the Area to 0.1524 m2 . (c) Change the Length to 0.1524 m (the axial chord length). 6. Save the steady flow case file (slide ss.cas). File −→ Write −→Case... 7. Start the calculation by requesting 500 iterations. Solve −→Iterate... The residual history and lift force history will be displayed as the calculation proceeds. The lift history should be similar to Figure 10.4. Note: After 500 iterations, the steady flow calculation may not be fully converged. Here, this is not of concern, as the steady-state prediction will be used only as a starting solution for the transient sliding-mesh calculation.


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-2.00e+00

-4.00e+00

-6.00e+00

-8.00e+00

Cl -1.00e+01

-1.20e+01

-1.40e+01

-1.60e+01 0

50

100

150

200

250

300

350

400

450

500

Iterations

Lift Convergence

Nov 15, 2002 FLUENT 6.1 (2d, coupled exp, ske)

Figure 10.4: Lift Coefficient History: Steady Flow, Non-Moving Rotor

8. Save the case and data files (slide ss.cas and slide ss.dat). File −→ Write −→Case & Data... Note: If you choose a file name that already exists in the current directory, FLUENT will prompt you for confirmation to overwrite the file.

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9. Display the steady flow velocity vectors (Figure 10.5). Display −→Vectors...

(a) Change the Scale to 10. (b) Click Display. The steady flow prediction shows the expected form, with peak velocity of about 140 m/s through the passage.


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10. Enable the display of three periodic repeats of the solution domain (Figure 10.5). Display −→Views...

(a) Set the number of Periodic Repeats to 3. (b) Under Periodic Repeats, click the Define... button. This will open the Graphics Periodicity panel.

(c) Click Reset. This will reset Y Translation to the value shown above. (d) Click OK in the Graphics Periodicity panel. (e) In the Views panel, click Apply. The grid display will be updated to show three periodic repeats. You may need to translate the display using your mouse to get the view shown in Figure 10.5.

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Dec 17, 2002 FLUENT 6.1 (2d, coupled exp, ske)

Figure 10.5: Velocity Vectors: Steady Flow, Non-Moving Rotor


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11. Display the steady flow contours of static pressure (Figure 10.6). Display −→Contours...

The steady flow prediction shows the expected pressure distribution through the passage, with low pressure on the suction surfaces and stagnation around the impingement point on the rotor.

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Dec 17, 2002 FLUENT 6.1 (2d, coupled exp, ske)

Figure 10.6: Contours of Static Pressure: Steady Flow, Non-Moving Rotor


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Step 9: Enable Time Dependence and Sliding Rotor Motion In this step you will enable the rotor motion by turning on time dependence and setting the sliding velocity of the rotor fluid zone. 1. Enable a time-dependent flow calculation. Define −→ Models −→Solver...

(a) Under Time, select Unsteady. (b) Under Unsteady Formulation, select 2nd-Order Implicit. Implicit (dual) time-stepping allows you to set the physical time step used for the transient flow prediction (while FLUENT continues to determine the time step used for inner iterations based on a Courant condition). Here, second-order implicit time-stepping is enabled: this provides higher accuracy in time than the first-order option. In explicit (global) time-stepping, FLUENT uses a single time step for the transient calculation. This time step is based on the Courant condition: ∆t =

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CFL∆x λmax



where CFL is the Courant number. Explicit time-stepping might be the optimum solution strategy if you are modeling a traveling shock wave, where the Courant condition is ideal for determination of the time step value. 2. Define the sliding motion of the rotor-side fluid zone (fluid-rotor). Define −→Boundary Conditions...

(a) Scroll down and select Moving Mesh in the Motion Type drop-down list. (b) Change the Translational Velocity in the Y direction to -29.445. 3. Save the case file. (slide un.cas). File −→ Write −→Case... The mesh changes during the preview so be sure to save the case before mesh preview.


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4. Preview the sliding motion of the rotor-side fluid zone. Solve −→Mesh Motion...

(a) Under Number of Time Steps, enter 50. (b) Click Preview. The graphics display will preview the sliding motion of the rotor-stator grid geometry. 5. Read the case file back into FLUENT. As the mesh preview option advances the time step, thereby updating the mesh, it is essential to reread the case file to ensure that the mesh is at the proper position before the calculation is started. If the case file is not read again and the solution is initialized after the mesh preview, the solution time is initialized to zero but the mesh does not go back to its original position.

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Step 10: Solution: Unsteady Flow with Moving Rotor 1. Change the Courant number to 1 for the transient calculation. Solve −→ Controls −→Solution...

The Courant number controls the time step used by FLUENT during the inner iterations performed during each time step. A Courant number of 1 is a conservative setting that should ensure the stability of the inner iterations.


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2. Reset the lift force monitor. Solve −→ Monitors −→Force...

(a) In the File Name field, enter cl-hist.td. (b) Click Apply. (c) Click Clear. This will remove the lift coefficient data for the steady-state calculation (i.e., the contents of the file cl-hist.ss) from memory. (d) Click Yes when asked to confirm the data discard.

!

If you do not clear the old force-monitoring data, FLUENT will plot them with the new data, corrupting the new lift coefficient plot.

(e) Click on the Axes... button. This will open the Axes - Force Monitor Plot panel.

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(f) Under Axis, select X (the default). (g) Under Number Format, check that the Type is float. (h) Set the Precision to 4. (i) Click Apply.

(j) Under Axis, select Y. (k) Under Number Format, check that the Type is float and the Precision is 4. (l) Close the Axes - Force Monitor Plot and Force Monitors panels.


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Note: Monitoring the lift force is an ideal way to determine when the transient flow prediction becomes time-periodic (independent of the initial condition). In the time-periodic solution, the lift force variation will repeat identically from one passing period to the next. 3. Set the time step parameters. Solve −→Iterate...

(a) Set the Time Step Size to 0.0001 second. (b) Check that the Max Iterations per Time Step is set to 20. (c) Click Apply. Note: The selection of the time step is critical for accurate time-dependent flow predictions. Here, the time step is chosen to be about 1/70 of the passing period, T. The passing period is the time it takes for the rotor blade to pass from one stator blade row to the next: T = (0.1959 m)/(29.4 m/s) = 6.7 × 10−3 sec Using a time step of 0.0001 second, 67 time steps will be performed as the rotor performs one pass.

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!

The maximum number of iterations per time step should be set large enough so that the inner iterations converge before the solution moves to the next time value. The value of 20, selected here, is quite small: it is likely that the initial time steps will not fully converge within 20 inner iterations. While this would be unsuitable for prediction of most time-dependent flows, the current simulation does not require high accuracy during the initial time steps. The rotor-stator flow prediction will be continued in time until a time-periodic flow is obtained. Low accuracy during the initial passing periods is acceptable as long as convergence is achieved during each time step of the final passing periods.

4. Save the transient sliding mesh case file (slide td.cas). File −→ Write −→Case... 5. Start the transient calculation by requesting 1000 time steps.

!

Calculation of 1000 time steps will require significant CPU resources. Instead of calculating, you can read the case and data files saved after 0.1 seconds: slide01.cas and slide01.dat After reading the files, skip to Step 11: Postprocessing at t=0.1 Second. (The case and data files are available in the same directory where you found the mesh files.)


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By requesting 1000 time steps, you are asking FLUENT to compute until time is equal to 0.1 second. This will include roughly 15 passing periods (15 × 6.7e-3 sec = 0.10 sec). Experience shows that the flow becomes time-periodic after about 12 passing periods. The lift history display allows you to confirm this. Your lift force history should be similar to that shown in Figure 10.7. Notice the periodicity of the lift coefficient after approximately 0.05 seconds.

5.00e+01 4.00e+01 3.00e+01 2.00e+01

Cl

1.00e+01 0.00e+00 -1.00e+01 -2.00e+01 -3.00e+01 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Time

Lift Convergence (Time=1.0000e-01)

Nov 16, 2002 FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Figure 10.7: Lift Coefficient History: Unsteady Flow, Moving Rotor

6. Reset the lift coefficient history range to focus on the periodicity. Solve −→ Monitors −→Force... (a) Click the Axes... button. This will open the Axes - Force Monitor Plot panel.

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i. Under Axis, select X. ii. Under Options, deselect Auto Range. iii. Under Range, set the Minimum to 0.02, and the Maximum to 0.1. iv. Click Apply.

v. Under Axis, select Y. vi. Under Options, deselect Auto Range. vii. Under Range, set the Minimum to -9.2, and the Maximum to -7.6.


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viii. Click Apply and Close the panel. (b) In the Force Monitors panel, click Plot. In Figure 10.8, you can see the periodicity more clearly.

-7.4000 -7.6000 -7.8000 -8.0000 -8.2000

Cl -8.4000 -8.6000 -8.8000 -9.0000 -9.2000 0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.100

0.110

Time

Lift Convergence History (Time=1.0000e-01)

Jul 15, 2002 FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Figure 10.8: Lift Coefficient History: Narrowed Range

7. Save the case and data files at t = 0.1 second (slide01.cas and slide01.dat). File −→ Write −→Case & Data... !

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When the sliding mesh model is used, you must save a case file whenever a data file is saved. This is because the case file contains the grid information, which is changing with time.



Step 11: Postprocessing at t = 0.1 Second The solution data saved at t = 0.1 second can be reviewed using any of FLUENT’s postprocessing features. Time-dependent data are analyzed just like steady-state results: you read a case and data file for each time value of interest. Note that this means you must save case and data files (or graphics files) at all intermediate time values for which results are of interest. Automatic saving of results during a transient calculation is used in Step 12, Saving and Postprocessing Time-Dependent Data Sets. !

For sliding mesh cases, it is important that you read the associated case file whenever you read a data file, because the case file contains the grid information, which is changing with time. 1. Display the velocity vectors at t = 0.1 second (Figure 10.9). Display −→Vectors...


Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=1.0000e-01) Dec 17, 2002 FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Figure 10.9: Velocity Vectors at T = 0.1 Second: Unsteady Flow

Note: The velocity vectors in Figure 10.9 are displayed with respect to the absolute reference frame (default). If you want to display the vectors with respect to the moving reference frame, you can select Relative Velocity in the Vectors Of drop-down list and select the rotor fluid zone as the Reference Zone in the Reference Values panel. 2. Display contours of static pressure at t = 0.1 second (Figure 10.10). Display −→Contours...


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Contours of Static Pressure (pascal) (Time=1.0000e-01) Dec 17, 2002 FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Figure 10.10: Contours of Static Pressure at Time = 0.1 Second: Unsteady Flow

Note: Slight discontinuities in the pressure contours along the sliding interface are expected. This is because the contour plotting uses one-sided interpolation on either side of the sliding plane. This is purely a display issue. 3. Determine the instantaneous total pressure loss through the system. Report −→Surface Integrals...

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(a) In the Report Type drop-down list, select Mass-Weighted Average. (b) Select Pressure... and Total Pressure in the Field Variable drop-down lists. (c) In the Surfaces list, select pressure-outlet. (d) Click Compute. The mass-averaged (instantaneous) total pressure at the exit is about 98100 Pa, implying a loss of about 3200 Pa from the inlet total pressure of 101325 Pa. 4. Plot the instantaneous pressure coefficient on the rotor blade at t = 0.1 second (Figure 10.11). Plot −→XY Plot...


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(a) Select Pressure... and Pressure Coefficient in the Y Axis Function drop-down lists. (b) In the Surfaces list, select wall-16. (c) Click Plot.

wall-16 -2.00e+00 -4.00e+00 -6.00e+00 -8.00e+00 -1.00e+01


-1.20e+01 -1.40e+01 -1.60e+01 -1.80e+01 -2.00e+01 0.175

0.2

0.225

0.25

0.275

0.3

0.325

0.35

0.375

0.4

Position (m)

Pressure Coefficient (Time=1.0000e-01)


Figure 10.11: Pressure Coefficient on the Moving Rotor at Time = 0.1 Second

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Step 12: Saving and Postprocessing Time-Dependent Data Sets After 0.1 second, the sliding mesh flow prediction has achieved a time-periodic state. In order to study how the flow changes within a single passing period, you will now continue the time-marching through the next period and save results every 5 time steps. 1. Request saving of case and data files every 5 time steps. File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 5. (b) In the Filename field, enter slid.gz. (c) Click OK. FLUENT will append the time step value to the file name prefix (slid). The standard extensions (.cas and .dat will also be appended. This will yield file names of the form slid1005.cas and slid1005.dat, where 1005 is the time step number. The extension “.gz”, supplied in the panel above, instructs FLUENT to save the case and data files in compressed format, yielding file names of the form slid1005.cas.gz and slid1005.dat.gz. If you leave off the “.gz” extension, FLUENT will save the files as slid1005.cas and slid1005.dat, etc. !

When the sliding mesh model is used, you must save a case file whenever a data file is saved. This is because the case file contains the grid information, which is changing with time.

Extra: If you want to generate a solution animation by plotting, for example, pressure contours every 5 time steps, you can use the Solution Animation panel to set up the animation before you begin the calculation. Tutorial 4 demonstrates how to do this.


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2. Reset the lift force monitor. Supplying a new file name eliminates overwriting of the file stored during the previous time steps. Solve −→ Monitors −→Force...

(a) In the File Name field, enter cl-hist.cyc. (b) Click Apply. (c) Click Clear. This will remove the lift coefficient data for the previous time steps from memory (i.e., cl-hist.td). (d) Click Yes when asked to confirm the data discard. (e) Click on the Axes... button to reset the domain and range. This will open the Axes - Force Monitor Plot panel. i. Under Axis, select X. ii. Under Options, select Auto Range. This will deactivate the Minimum and Maximum range fields. iii. Click Apply. iv. Under Axis, select Y. v. Under Options, select Auto Range. This will deactivate the Minimum and Maximum range fields. vi. Click Apply, and Close the Axes - Force Monitor Plot panel. (f) Close the Force Monitors panel.

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3. Continue the calculation by requesting 70 time steps. This performs the time-marching iterations for the next passing period, starting from the current solution data at time = 0.1 second. Solve −→Iterate... Note: Requesting 70 time steps will march the solution through 0.007 seconds, or roughly one passing period. With the autosave and command monitor features active (as defined above), the case, data, and pressure contour plot files will be saved every 0.0005 seconds. The lift history should appear as in Figure 10.12.

-7.70e+00

-7.80e+00

-7.90e+00

Cl

-8.00e+00

-8.10e+00

-8.20e+00

-8.30e+00 0.1

0.101

0.102

0.103

0.104

0.105

0.106

0.107

0.108

Time

Lift Convergence (Time=1.0000e-01)


Figure 10.12: Lift History During the Final Passing Period

4. Examine the results at different time steps within a single passing period. (a) Read in the case and data files of interest. File −→ Read −→Case & Data... (b) Display contours of static pressure. The display of pressure contours every five time steps will show the timevarying pressure distribution and the motion of the rotor. Examples of two pressure contour plots at t = 0.1030 and t = 1.070 seconds are shown in Figures 10.13 and 10.14, respectively. Display −→Contours... Extra: If you generated a solution animation during the calculation as mentioned earlier in this tutorial, you could play it back inside FLUENT to see the pressure contour animation over time. See Tutorial 4 for details.


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Figure 10.13: Pressure Contours at Time = 0.103 Seconds



Figure 10.14: Pressure Contours at Time = 0.107 Seconds

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Summary: In this tutorial, you have modeled the time-periodic flow involving rotorstator interaction. You have learned how to merge the separate rotor and stator meshes using tmerge, and to create the grid-interface zones along the sliding interface. Similar procedures can be used to tie together meshes for non-sliding mesh analyses. You have used FLUENT’s time-dependent flow prediction capability, and you have learned how to set solution parameters for implicit time-stepping. These timedependent flow prediction procedures can also be applied to other, non-sliding mesh, analyses. The procedures in this tutorial, however, are applicable to timeperiodic calculations, in which the initial condition and initial phase of the transient calculation are treated without concern for time accuracy. You have also learned how to manage the file saving and graphical postprocessing for time-dependent flows, using file autosaving and command monitors to automatically save solution information as the transient calculation proceeds.


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Tutorial 11.

Using Dynamic Meshes

Introduction: This tutorial provides information for performing basic dynamic mesh calculations. In addition to combining the basic mesh-motion schemes, this tutorial will introduce rigid-body motion of a cell zone. This is useful for a multitude of realistic cases with moving meshes. In this tutorial you will learn how to: • Use the dynamic mesh capability of FLUENT to solve a simple flow-driven rigidbody motion problem • Set boundary conditions for internal flow • Use a compiled user-defined function (UDF) to specify flow-driven rigid-body motion • Calculate a solution using the segregated solver. Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem to be considered is shown schematically in Figure 11.1. A 2D axisymmetric valve geometry is used, consisting of a pressurized cavity on the left, driving the motion of a poppet that toggles the flow to the circumferential pressure outlets. A spring force is also acting on the poppet. In this case the transient closure of the valve is studied.


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Using Dynamic Meshes pressure outlets

mass flow inlet

moving poppet


Preparation 1. Copy the files valve.msh, and valve.c from the FLUENT documentation CD to your working directory (as described in Tutorial 1). A user-defined function will be used to define the rigid-body motion of the poppet in the valve geometry. This function has already been written (valve.c). You will only need to compile it within FLUENT. 2. Start the 2D version of FLUENT.

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Step 1: Grid 1. Read the grid file valve.msh. File −→ Read −→Case... 2. Check the grid. Grid −→Check Note: You should always make sure that the cell minimum volume is not negative, since FLUENT cannot begin a calculation if this is the case. 3. Scale the grid. Grid −→Scale...

(a) Under Units Conversion, select in from the drop-down list to complete the phrase Grid Was Created In in (inches). (b) Click Scale to scale the grid. (c) Click Change Length Units to set inches as the working units for length, and then close the panel.


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Grid


Figure 11.2: Initial Grid for the Valve

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Step 2: Units 1. For convenience, define new units for pressure and mass flow. In the problem description, pressure, length, and mass flow are specified in psi, in, and gpm, respectively. While the units for length were switched while scaling the grid in the previous step, psi and gpm are not the default units for pressure and mass flow. Define −→Units...

(a) Select pressure under Quantities, and psi under Units. (b) Select mass-flow under Quantities, and click New... The Define Unit panel will appear.

i. Enter gpm under Unit. ii. Enter 0.0536265 under Factor. iii. Click OK.


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Step 3: Models 1. Enable an axisymmetric time-dependent calculation. Define −→ Models −→Solver...

(a) Under Space, select Axisymmetric. (b) Select Unsteady under Time. (c) Keep the default Unsteady Formulation option of 1st-Order Implicit. !

Dynamic mesh simulations currently work only with first-order time advancement.

(d) Click OK.

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(a) Select k-epsilon as the Model, and retain the default setting of Standard under k-epsilon Model. (b) Click OK.


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Step 4: Materials You will create a new material called oil. Define −→Materials...

1. In the Name field, enter oil. 2. Specify 850 for the Density. 3. Specify 0.17 for the Viscosity. 4. Click Change/Create. 5. Click No when prompted to overwrite air.

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Step 5: Operating Conditions Set the operating pressure to 0 psi. Define −→Operating Conditions...

For this problem, you will work with absolute pressures.


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Step 6: Boundary Conditions Dynamic mesh motion and all related parameters are specified using the items in the Define/Dynamic Mesh submenu, not through the Boundary Conditions panel. You will set these conditions in the next step. Define −→Boundary Conditions... 1. Set the conditions for the mass flow inlet (inlet) as shown in the following figure.

2. Click OK.

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3. Set the conditions for the exit boundary (outlet) as shown in the following figure.

4. Click OK.


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Step 7: Grid Interfaces In this step, you will create a non-conformal grid interface between the deforming walls corresponding to the radial boundary of the pressure outlets, and the deforming wall corresponding to the radial boundary of the deforming fluid zone next to the poppet. Define −→Grid Interfaces...

1. Select ext intf in the Interface Zone 1 list. Note that when one interface zone is smaller than the other, it is recommended that you choose the smaller zone as Interface Zone 1. 2. Select int int in the Interface Zone 2 list. 3. Enter the name if under Grid Interface. 4. Click Create. Note: In the process of creating the grid interface, FLUENT creates two new wall boundary zones: wall-22 and wall-23. You will not be able to display these walls. wall-22 is the non-overlapping region of the ext intf zone that results from the intersection of the ext intf and int int boundary zones, and is listed under Boundary Zone 1 in the Grid Interfaces panel. wall-23 is the non-overlapping region of the int int zone that results from the intersection of the two interface zones, and is listed under Boundary Zone 2 in the Grid Interfaces panel.

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Note that in general, you will need to set boundary conditions for these new wall zones, when they are not empty. In this case, default settings are used.

Step 8: Mesh Motion 1. Read in and compile the user-defined function. Define −→ User-Defined −→ Functions −→Compiled...

(a) Under Source Files, click Add... A Select File panel will open. (b) In the Select File panel, select the source code valve.c, and click OK. (c) In the Compiled UDFs panel, click Build. The user-defined function has already been defined, but it needs to be compiled within FLUENT before it can be used in the solver. Here you will create a library with the default name of libudf in your working directory. If you would like to use a different name, you can enter it in the Library Name field. Note that in this case you need to make sure that you will open the correct library in the next step. (d) Click OK in the dialog box that will appear. (e) Click Load to load the user-defined function library you just compiled. !

Note that this UDF will write a file called udf loc velo in your working directory. This file will be written just before the first iteration in every time step, and will contain the location of the CG and the value of the velocity in


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the X direction for that time step. However, the UDF will first attempt to read information from this file. You will need to make sure that if there is a file of this name in your working directory, it contains the correct information, unless you are continuing the iteration process from the last case and data files you used. 2. Activate dynamic mesh motion and specify the associated parameters. Define −→ Dynamic Mesh −→Parameters...

(a) Under Model, select Dynamic Mesh. Selection of the In-Cylinder option allows input for IC-specific needs, including valve and piston motion. (b) Under Mesh Methods, select Smoothing and Remeshing. FLUENT will automatically flag the existing mesh zones for use of the different dynamic mesh methods where applicable. (c) Set the parameters under Smoothing as follows: i. Keep the default specification of 1 for the Spring Constant Factor. ii. Specify 0.7 for the Boundary Node Relaxation. iii. Keep the default specification of 0.001 for the Convergence Tolerance. iv. Specify 50 for the Number of Iterations.

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(d) Set the parameters under Remeshing as follows:

i. Under Options, be sure that the Must Improve Skewness option is selected. ii. Specify 1.1e-13 m3 for the Minimum Cell Volume. iii. Specify 1.2e-10 m3 for the Maximum Cell Volume. iv. Specify 0.7 for the Maximum Cell Skewness. v. Specify 1 for the Size Remesh Interval. If a cell exceeds these limits, the cell is marked for remeshing. Therefore, you will always need to specify problem-specific values under Remeshing Parameters. (e) Click OK. 3. Specify the motion of the poppet, the adjacent walls, and the fluid region left of the poppet. The poppet motion and the motion of the deforming wall side-wall-3 are specified by means of the user-defined function valve. Define −→ Dynamic Mesh −→Zones... (a) Specify the motion of the poppet.


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i. In the Zone Names drop-down list, select poppet. ii. Under Type, keep the default selection of Rigid Body. iii. Under Motion Attributes, select valve in the Motion UDF/Profile drop-down list. iv. Keep the default values of (0, 0) m for C.G. Location, and 0 for C.G. Orientation. FLUENT will automatically update the position of the CG based on the input you gave for the motion. v. Click the Meshing Options tab. vi. Specify 0.005 in for Cell Height. vii. Click Create. (b) Specify the motion of the deforming axis (def axis).

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i. In the Zone Names drop-down list, select def axis. ii. Under Type, select Deforming. The panel will expand to show the inputs for a deforming zone. iii. Click the Geometry Definition tab. iv. In the Definition drop-down list, select plane. The panel will expand again to show the inputs for a planar geometry. v. Under Point on Plane, enter 0, 0. vi. Under Plane Normal, enter 0, 1. vii. Click the Meshing Options tab. viii. Under Methods, keep the default selections of Smoothing and Remeshing, and set the Height to 0.005 in. ix. Set the Height Factor to 0.4, and keep the default value of 1 for Maximum Skewness. x. Click Create. (c) Specify the motion of the deforming wall corresponding to the radial boundary of the deforming fluid zone next to the poppet (int int). i. In the Zone Names drop-down list, select int int.


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ii. Under Type, keep the previous selection of Deforming. iii. Click the Geometry Definition tab. iv. In the Definition drop-down list, select plane. The panel will expand again to show the inputs for a planar geometry. v. Under Point on Plane, enter 0, 0.22625. vi. Under Plane Normal, keep the previous setting of 0, 1. vii. Click the Meshing Options tab. viii. Under Mesh Methods, be sure that Smoothing and Remeshing are selected, and keep the previous settings for Height (0.005 in), Height Factor (0.4), and Maximum Skewness (1). ix. Click Create. In many MDM problems, you may want to preview the mesh motion before proceeding any further. In this problem, the mesh motion is driven by the pressure exerted by the fluid on the poppet and acting against the inertia of the poppet and the force of a preloaded spring attached to it. Hence, for this problem, mesh motion in the absence of a flow field solution is meaningless, and you will not use this feature here.

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(a) Keep all default discretization schemes and values for under-relaxation factors. This problem has been found to converge satisfactorily with these default settings. Alternatively, you may want to try PISO discretization for PressureVelocity Coupling, in conjunction with higher under-relaxation factors. (b) Click OK. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual...


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3. Request that case and data files are automatically saved every 10 time steps. File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 10. (b) In the Filename field, enter valve. When FLUENT saves a file, it will append the time step value to the file name prefix (valve). The standard extensions (.cas and .dat) will also be appended. (c) Click OK. 4. Initialize the solution. You will initialize the flow field at this point in order to be able to display contours and vectors that you will use to define animations. Solve −→ Initialize −→Initialize...

(a) Set Gauge Pressure to 80 psi.

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(b) Set Axial Velocity to 3.097237 m/s. (c) Set Turbulence Kinetic Energy to 0.1438932. (d) Set Turbulence Dissipation Rate to 16.8147. (e) Click Init. 5. Create animation sequences for the static pressure contour plots and velocity vectors plots in the valve. You will use FLUENT’s solution animation feature to save contour plots of temperature every 5 time steps. After the calculation is complete, you will use the solution animation playback feature to view the animated temperature plots over time. Solve −→ Animate −→Define...

(a) Increase the number of Animation Sequences to 2. (b) Under Name, enter pressure for the first animation, and vv for the second one. (c) Under Every, increase the number to 2 for both sequences. The default value of 1 instructs FLUENT to update the animation sequence at every time step. For this case, this would generate a large number of files. (d) In the When drop-down list, select Time Step. (e) Define the animation sequence for pressure. i. Click Define... on the line for pressure to set the parameters for the sequence. The Animation Sequence panel will open.


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ii. Under Storage Type, keep the default selection of Metafile. Note: If you want to store the plots in a directory other than your working directory, enter the directory path in the Storage Directory field. If this field is blank (the default), the files will be saved in your working directory (i.e., the directory where you started FLUENT). iii. Increase the Window number to 1 and click Set. Graphics window number 1 will open. iv. Under Display Type, select Contours. The Contours panel will open.

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A. Under Options, turn on Filled. B. In the Contours Of drop-down lists, select Pressure... and Static Pressure. C. Click Display.


Contours of Static Pressure (psi) (Time=0.0000e+00) Nov 19, 2002 FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Figure 11.3: Contours of Static Pressure at t = 0 s


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v. Click OK in the Animation Sequence panel. The Animation Sequence panel will close, and the checkbox in the Active column next to pressure in the Solution Animation panel will become selected. vi. Click OK in the Solution Animation panel. (f) Define the animation sequence for the velocity vectors. i. Click Define... on the line for vv to set the parameters for the sequence. The Animation Sequence panel will open. ii. Under Storage Type, keep the default selection of Metafile. iii. Increase the Window number to 2 and click Set. Graphics window number 2 will open. iv. Under Display Type, select Vectors. The Vectors panel will open.

v. Click Display in the Vectors panel.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=0.0000e+00) Dec 17, 2002 FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Figure 11.4: Vectors of Velocity at t = 0 s vi. Click OK in the Animation Sequence panel. The Animation Sequence panel will close, and the checkbox in the Active column next to vv in the Solution Animation panel will become selected. vii. Click OK in the Solution Animation panel. 6. Set the time step parameters for the calculation. Solve −→Iterate... (a) Set the Time Step Size to 4e-6 s. (b) Increase the Max Iterations per Time Step to 100. In the accurate solution of a real-life time-dependent CFD problem, it is important to make sure that the solution converges at every time step to within the desired accuracy. Here the first few time steps will only come to a reasonably converged solution. (c) Click Apply. This will save the time step size to the case file (the next time a case file is saved).


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7. Save the initial case and data files (valve.cas and valve.dat). File −→ Write −→Case & Data... 8. Request 80 time steps. Solve −→Iterate... Extra: If you decide to read in the case file that is provided for this tutorial on the documentation CD, you will need to compile the UDF associated with this tutorial in your working directory. This is necessary because FLUENT will expect to find the correct UDF libraries in your working directory when reading the case file.

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Step 10: Postprocessing 1. Inspect the solution at the final time step. (a) Inspect the contours of static pressure in the valve (Figure 11.5).

1.74e+04 1.61e+04 1.47e+04 1.34e+04 1.20e+04 1.07e+04 9.34e+03 8.00e+03 6.65e+03 5.30e+03 3.95e+03 2.61e+03 1.26e+03 -8.73e+01 -1.43e+03 -2.78e+03 -4.13e+03 -5.48e+03 -6.82e+03 -8.17e+03 -9.52e+03

Contours of Static Pressure (psi) (Time=3.2000e-04) Nov 22, 2002 FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Figure 11.5: Contours of Static Pressure After 80 Time Steps (b) Inspect the velocity vectors in the valve (Figure 11.6). 2. Optionally, inspect the solution at different intermediate time steps. (a) Read in the corresponding case and data files (valve....cas and valve....dat). File −→ Read −→Case & Data... (b) Display the desired contours and vectors.


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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=3.2000e-04) Nov 22, 2002 FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Figure 11.6: Velocity Vectors After 80 Time Steps

3. Play back the animation of the pressure contours. Solve −→ Animate −→Playback...

(a) In the Sequences list, select pressure. The playback control buttons will become active.

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(b) Set the slider bar above Replay Speed about halfway in between Slow and Fast. (c) Keep the default settings in the rest of the panel and click the play button (the second from the right in the group of buttons under Playback). See Tutorial 4 in the Tutorial Guide and Section 24.17 of the User’s Guide for additional information on animating the solution. 4. Play back the animation of the velocity vectors. Solve −→ Animate −→Playback... (a) In the Sequences list, select vv. (b) Keep the default settings in the rest of the panel and click the play button. Summary: In this tutorial you learned how to use the dynamic mesh feature of FLUENT to simulate the rigid-body motion of a valve poppet in a flow field, driven by the flow-generated forces, and spring and inertial forces, by means of a user defined function (UDF).


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Tutorial 12. Modeling Species Transport and Gaseous Combustion Introduction: This tutorial examines chemical species mixing and combustion of a gaseous fuel. A cylindrical combustor burning methane (CH4 ) in air is studied using the finite-rate chemistry model in FLUENT. In this tutorial you will learn how to: • Enable physical models, select material properties, and define boundary conditions for a turbulent flow with chemical species mixing and reaction • Initiate and solve the combustion simulation using the segregated solver • Compare the results computed with constant and variable specific heat • Examine the reacting flow results using graphics • Predict thermal and prompt NOx production • Use custom field functions to compute NO parts per million Prerequisites: This tutorial assumes that you have performed Tutorial 1 and are familiar with the FLUENT interface. It also assumes that you have developed a basic familiarity with the solution of turbulent flows using FLUENT. You may find it helpful to read about chemical reaction modeling in the User’s Guide. Otherwise, no previous experience with chemical reaction or combustion modeling is assumed. Problem Description: The cylindrical combustor considered in this tutorial is shown in Figure 12.1. The flame considered is a turbulent diffusion flame. A small nozzle in the center of the combustor introduces methane at 80 m/s. Ambient air enters the combustor coaxially at 0.5 m/s. The overall equivalence ratio is approximately 0.76 (about 28% excess air). The high-speed methane jet initially expands with little interference from the outer wall, and entrains and mixes with the low-speed air. The Reynolds number based on the methane jet diameter is approximately 5.7 × 103 .


12-1

Wall: 300K

0.005m

Air, 0.5 m/s, 300K

Methane, 80 m/s, 300K

0.225 m

Modeling Species Transport and Gaseous Combustion

L

C 1.8 m

Figure 12.1: Combustion of Methane Gas in a Turbulent Diffusion Flame Furnace

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Background: In this tutorial, you will use the generalized finite-rate chemistry model to analyze the methane-air combustion system. The combustion will be modeled using a global one-step reaction mechanism, assuming complete conversion of the fuel to CO2 and H2 O. The reaction equation is CH4 + 2O2 → CO2 + 2H2 O

(12.1)

This reaction will be defined in terms of stoichiometric coefficients, formation enthalpies, and parameters that control the reaction rate. The reaction rate will be determined assuming that turbulent mixing is the rate-limiting process, with the turbulence-chemistry interaction modeled using the eddy-dissipation model.

Preparation 1. Copy the file gascomb/gascomb.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.


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Step 1: Grid 1. Read the grid file gascomb.msh. File −→ Read −→Case... After reading the grid file, FLUENT will report that 1615 quadrilateral fluid cells have been read, along with a number of boundary faces with different zone identifiers. 2. Check the grid. Grid −→Check The grid check lists the minimum and maximum x and y values from the grid, and reports on a number of other grid features that are checked. Any errors in the grid would be reported at this time. For instance, the cell volumes must never be negative. Note that the domain extents are reported in units of meters, the default unit of length in FLUENT. Since this grid was created in units of millimeters, the Scale Grid panel will be used to scale the grid into meters. 3. Scale the grid. Grid −→Scale... (a) Under Units Conversion, select mm from the drop-down list to complete the phrase Grid Was Created In mm. (b) Click on Scale and confirm that the maximum x and y values are 1.8 and 0.225 meters, respectively, as indicated in Figure 12.1. Note: Because the default SI units will be used in this tutorial, there is no need to change any units in this problem. 4. Display the grid. Display −→Grid...

Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENTconsole window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.

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Grid


Figure 12.2: The Quadrilateral Grid for the Combustor Model


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Step 2: Models 1. Define the domain as axisymmetric, and keep the default (segregated) solver. Define −→ Models −→Solver...

2. Enable the k- turbulence model. Define −→ Models −→Viscous...

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The panel will expand to provide further options. Click OK to accept the default Standard model and parameters. 3. Enable heat transfer by activating the energy equation. Define −→ Models −→Energy...

4. Enable chemical species transport and reaction. Define −→ Models −→Species...


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(a) Select Species Transport under Model. (b) Select Volumetric under Reactions. (c) Choose methane-air in the Mixture Material drop-down list. The Mixture Material list contains the set of chemical mixtures that exist in the FLUENT database. By selecting one of the pre-defined mixtures, you are accessing a complete description of the reacting system. The chemical species in the system and their physical and thermodynamic properties are defined by your selection of the mixture material. You can alter the mixture material selection or modify the mixture material properties using the Materials panel (see Step 3: Materials). (d) Select Eddy-Dissipation under Turbulence-Chemistry Interaction. The eddy-dissipation model computes the rate of reaction under the assumption that chemical kinetics are fast compared to the rate at which reactants are mixed by turbulent fluctuations (eddies).

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(e) Click OK. After you click OK in the Species Model panel, a warning about the symmetry zone will appear in the console window: Warning: It appears that symmetry zone 5 should actually be an axis (it has faces with zero area projections). Unless you change the zone type from symmetry to axis, you may not be able to continue the solution without encountering floating point errors.

In this axisymmetric model, the centerline should be treated using the axis boundary condition instead of symmetry. You will change the symmetry zone to an axis boundary in Step 4: Boundary Conditions. The console window will also list the properties that are required for the models you have enabled. You will see an Information dialog box, reminding you to confirm the property values that have been extracted from the database.

(f) Click OK to continue.


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Step 3: Materials Define −→Materials...

The Materials panel shows the mixture material, methane-air, that was enabled in the Species Model panel. The properties for this mixture material have been copied from the FLUENT database and can be modified by you. Here, you will modify the default setting for the mixture by enabling the gas law. By default, the mixture material uses constant properties: you will retain this constant property assumption for now, allowing only the mixture density to vary with temperature and composition. The influence of variable property inputs on the combustion prediction will be examined in a later part of this tutorial. 1. Retain incompressible-ideal-gas in the Density drop-down list. 2. Click the Edit... button to the right of Mixture Species. This opens the Species panel.

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You can add or remove species from the mixture material using this panel. Here, the species that make up the methane-air mixture are predefined and require no modification. 3. Click Cancel to close the panel without making any changes. 4. In the Materials panel, click the Edit... button to the right of the Reaction dropdown list. This will open the Reactions panel.


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The eddy-dissipation reaction model ignores chemical kinetics (the Arrhenius rate) and uses only the Mixing Rate parameters in the Reactions panel. The Arrhenius Rate section of the panel is therefore inactive. (The Rate Exponent and Arrhenius Rate entries are included in the database and are employed when the alternate finiterate/eddy-dissipation model is used.) See the User’s Guide for details. 5. Accept the default settings for the Mixing Rate constants by clicking the OK button. 6. In the Materials panel, select constant from the drop-down list next to Cp and enter 1000 for the specific heat value. 7. Use the scroll bar to review the remaining properties. Click on the Change/Create button to accept the material property settings and then Close the panel.

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As noted above, the initial calculation will be performed assuming that all properties except density are constant. Using constant transport properties (viscosity, thermal conductivity, and mass diffusion coefficients) is acceptable here because the flow is fully turbulent. The molecular transport properties will play a minor role compared to turbulent transport. The assumption of constant specific heat, in contrast, has a strong effect on the combustion solution, and you will change this property definition in Step 6: Solution Using NonConstant Heat Capacity.


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Step 4: Boundary Conditions 1. Convert the symmetry zone to the axis type. The symmetry zone must be converted to an axis to prevent numerical difficulties where the radius goes to zero. Define −→Boundary Conditions...

(a) Select symmetry-5 in the Zone list and then select axis in the Type list. You will be prompted to accept the change of boundary type:

(b) Click Yes to confirm the change.

(c) In the resulting Axis panel, click OK to accept the default axis zone name.

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2. Set the boundary conditions for the air inlet, velocity-inlet-8. Hint: Redisplay the grid without the fluid zone. This will show the boundaries. Use the right mouse button to probe the air inlet. The console window and the Boundary Conditions panel will show that the air inlet is labeled velocity-inlet-8.

(a) Rename the boundary air-inlet in the Zone Name text entry box. (b) Set the boundary conditions at the air inlet as shown in the panel. 3. Set the fuel inlet boundary conditions for velocity-inlet-6.


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(a) Rename this zone fuel-inlet and assign inlet conditions as shown in the panel. 4. Set the following conditions for the exit boundary, pressure-outlet-9:

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Note: The Backflow values in this panel are utilized only when backflow occurs at the pressure outlet. Reasonable values should always be assigned, since backflow may occur during intermediate iterations and could affect the solution stability. 5. Set the boundary conditions for the outer wall, wall-7. Hint: Use the mouse-probe method described above for the air inlet to determine which zone corresponds to the outer wall. The outer wall zone will be selected in the Boundary Conditions panel once the outer wall boundary is probed.


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(a) Rename this boundary outer-wall in the Zone Name text entry box. (b) Set the thermal condition to Temperature and keep the default temperature of 300 K. (c) Retain the default settings in the Momentum and Species sections of the panel. 6. Set the boundary conditions for wall-2, which represents the small fuel inlet nozzle.

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(a) Rename this boundary nozzle in the Zone Name text entry box. (b) Accept the default thermal condition of Heat Flux with a value of zero (adiabatic wall). (c) Retain the default settings in the Momentum and Species sections of the panel.


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Step 5: Initial Solution Using Constant Heat Capacity 1. Initialize the field variables. Solve −→ Initialize −→Initialize...

(a) Select all-zones in the Compute From drop-down list. (b) Adjust the Initial Values for Temperature to 2000 and ch4 Mass Fraction to 0.2. (c) Click Init to initialize the variables, and then close the panel. Initializing the flow using a high temperature and non-zero fuel content will allow the combustion reaction to begin. The initial condition acts as a numerical “spark” to ignite the methane-air mixture. This initialization is especially critical when you include finite-rate kinetics in the overall reaction rate. 2. Set the under-relaxation factors. The default under-relaxation parameters in FLUENT are set to high values. For a combustion model it may be necessary to reduce the under-relaxation to stabilize the solution. Some experimentation is typically necessary to establish the optimal under-relaxation. For this tutorial it is sufficient to reduce the species underrelaxation to 0.9. Solve −→ Controls −→Solution...

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(a) Use the slider bar next to the Under-Relaxation Factors list to locate each species and set its under-relaxation factor to 0.9. 3. Turn on residual plotting during the calculation. Solve −→ Monitors −→Residual...


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(a) Under Options, select Plot. (b) Click OK. 4. Save the case file (gascomb1.cas). File −→ Write −→Case... (a) Keep the Write Binary Files button on to produce a smaller, unformatted binary file. (b) Enter the file name gascomb1.cas in the Case File text entry box. (c) Click OK to proceed with the file writing. 5. Start the calculation by requesting 500 iterations. Solve −→Iterate...

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The solution converges in about 350 iterations. 6. Save the case and data files (gascomb1.cas and gascomb1.dat). File −→ Write −→Case & Data... Note: FLUENT will ask you to confirm that the previous case file is to be overwritten. 7. Review the current state of the solution by viewing contours of temperature (Figure 12.3). Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-down list. (b) Click Display. The temperature contours are shown in Figure 12.3. The peak temperature, predicted using a constant heat capacity of 1000 J/kg-K, is over 3000 K. This overprediction of the flame temperature can be remedied by a more realistic model for the temperature and composition dependence of the heat capacity, as illustrated in the next step of the tutorial.


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Nov 12, 2002 FLUENT 6.1 (axi, segregated, spe5, ske)

Figure 12.3: Temperature Contours: Constant cp

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Step 6: Solution Using Non-Constant Heat Capacity As noted above, the strong temperature and composition dependence of the specific heat will have a significant impact on the predicted flame temperature. In this step you will use the temperature-varying property information in the FLUENT database to recompute the solution. 1. Enable composition dependence of the specific heat. Define −→Materials...

(a) In the drop-down list next to Cp, select mixing-law as the specific heat method. (b) Click on the Change/Create button to render the mixture specific heat based on a local mass-fraction-weighted average of all the species. 2. Enable temperature dependence of the specific heat for each species.


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(a) In the Material Type drop-down list, select fluid. The fluid material type gives you access to each species in the mixture. (b) Select carbon-dioxide (co2) under Fluid Materials. (c) In the drop-down list for Cp, select piecewise-polynomial. This will open the Piecewise Polynomial Profile panel.

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i. Click OK to accept the default coefficients describing the temperature variation of cp for carbon dioxide. The default coefficients describe the polynomial cp (T ) and are extracted from the FLUENT property database. ii. Click on Change/Create in the Materials panel to accept the change in properties for CO2 . (d) Repeat steps (b) and (c) above for the remaining species (CH4 , N2 , O2 , and H2 O). Remember to click on Change/Create to accept the change for each species. 3. Request 500 more iterations. Solve −→Iterate... Note: The residuals will jump significantly as the solution adjusts to the new specific heat representation. The solution converges after about 300 additional iterations. 4. Save the new case and data files (gascomb2.cas and gascomb2.dat). File −→ Write −→Case & Data...


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Step 7: Postprocessing Review the solution by examining graphical displays of the results and performing surface integrations at the combustor exit. 1. View contours of temperature (Figure 12.4). Display −→Contours... (a) Select Temperature... and Static Temperature in the Contours Of drop-down list. (b) Click Display. The temperature contours are shown in Figure 12.4. The peak temperature has dropped to about 2300 K as a result of the temperature- and composition-dependent specific heat.




Figure 12.4: Temperature Contours: Variable cp

2. Plot contours of specific heat (Figure 12.5). Contours of the mixture specific heat will show how it varies through the domain. Display −→Contours... (a) Select Properties... and Specific Heat (Cp) in the Contours Of drop-down list. (b) Click Display.

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The contours are shown in Figure 12.5. The mixture specific heat is largest where the CH4 is concentrated, near the fuel inlet, and where the temperature and combustion product concentrations are large. The increase in heat capacity, relative to the constant value used before, substantially lowers the peak flame temperature.


Contours of Specific Heat (Cp) (j/kg-k)


Figure 12.5: Contours of Specific Heat

3. Display velocity vectors (Figure 12.6). Display −→Vectors...


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(a) Click the Vector Options... button. This opens the Vector Options panel.

(b) Select the Fixed Length option and click Apply. The fixed length option is useful when the vector magnitude varies dramatically. With fixed length vectors, the velocity magnitude is described only by color instead of by both vector length and color.

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(c) In the Vectors panel, reset the Scale to 0.01 and click Display. The velocity vectors are shown in Figure 12.6.




Figure 12.6: Velocity Vectors: Variable cp

4. Plot contours of stream function (Figure 12.7). Display −→Contours...


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(a) Select Velocity... and Stream Function in the Contours Of drop-down list. (b) Click Display. The stream function contours are shown in Figure 12.7. The entrainment of air into the high-velocity methane jet is clearly visible in the streamline display. 5. Plot contours of mass fraction for each species. Display −→Contours... (a) Select Species... and Mass fraction of ch4 in the Contours Of drop-down list. (b) Turn on the Filled button under Options. (c) Click Display. The CH4 mass fraction contours are shown in Figure 12.8. (d) Repeat for the remaining species. The mass fraction contours for O2 , CO2 , and H2 O are shown in Figures 12.9, 12.10, and 12.11.

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Figure 12.7: Stream Function Contours: Variable cp

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Mass fraction of ch4


Figure 12.8: CH4 Mass Fraction


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Contours of Mass fraction of o2


Figure 12.9: O2 Mass Fraction


Contours of Mass fraction of co2


Figure 12.10: CO2 Mass Fraction

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Contours of Mass fraction of h2o


Figure 12.11: H2 O Mass Fraction


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6. Determine the average exit temperature and velocity. Report −→Surface Integrals...

(a) Select Mass-Weighted Average in the Report Type drop-down list. (b) Select Temperature... and Static Temperature in the Field Variable drop-down list. The mass-averaged temperature will be computed as ~ T ρ~v · dA T = R ~ ρ~v · dA R

(12.2)

(c) Select pressure-outlet-9 as the surface over which to perform the integration. (d) Click Compute. The mass-weighted average exit temperature is about 1796 K.

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(e) Select Area-Weighted Average as the Report Type and Velocity Magnitude as the Field Variable. The area-weighted velocity-magnitude average will be computed as v¯ =

1Z v dA A

(12.3)

(f) Click Compute. The area-averaged exit velocity is about 3.14 m/s.


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Step 8: NOx Prediction In this section you will extend the FLUENT model to include the prediction of NOx . You will first calculate the formation of both thermal and prompt NOx , then calculate each separately to determine the contribution of each mechanism. 1. Enable the NOx model. Define −→ Models −→ Pollutants −→NOx...

(a) Under Models, enable Thermal NO and Prompt NO. (b) Select Temperature in the PDF Mode drop-down list under Turbulence Interaction to enable the turbulence-chemistry interaction. If turbulence interaction is not enabled, you will be computing NOx formation without considering the important influence of turbulent fluctuations on the time-averaged reaction rates. (c) Select Partial-equilibrium in the [O] Model drop down list under Thermal NO Parameters. The partial-equilibrium model is used to predict the O radical concentration required for thermal NOx prediction. (d) Set the Equivalence Ratio to 0.76 under Prompt NO Parameters, and keep the default Fuel Species and Fuel Carbon Number. The equivalence ratio defines the fuel-air ratio (relative to stoichiometric conditions) and is used in the calculation of prompt NOx formation. The Fuel Carbon Number is the number of carbon atoms per molecule of fuel and is used

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in the prompt NOx prediction. The Fuel Species designation is also used in the prompt NOx model. (e) Click OK to accept these changes. 2. Enable the calculation of only the NO species, and set the under-relaxation factor for this equation. Solve −→ Controls −→Solution...

(a) In the Equations list, deselect all variables except the NO species. (b) Increase the NO under-relaxation factor to 1.0. You will predict NOx formation in a “postprocessing” mode, with the flow field, temperature, and hydrocarbon combustion species concentrations fixed. Thus, only the NO equation is computed. Prediction of NO in this mode is justified on the grounds that the NO concentrations are very low and have negligible impact on the hydrocarbon combustion prediction. 3. Reduce the convergence criterion for the NO species equation. Solve −→ Monitors −→Residual...


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(a) Set the Convergence Criterion to 1e-6 and click OK. 4. Request 50 more iterations. Solve −→Iterate... The solution converges in about 10 iterations. 5. Save the new case and data files (gascomb3.cas and gascomb3.dat). 6. Review the solution by displaying contours of NO mass fraction (Figure 12.12). Display −→Contours... (a) Select NOx... and Mass fraction of NO in the Contours Of drop-down list. (b) Deselect Filled under Options and click Display. The NO mass fraction contours are shown in Figure 12.12. The peak concentration of NO is located in a region of high temperature where oxygen and nitrogen are available. 7. Calculate the average exit NO mass fraction. Report −→Surface Integrals...

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Contours of Mass fraction of NO


Figure 12.12: Contours of NO Mass Fraction: Prompt and Thermal NOx

(a) Select Mass-Weighted Average in the Report Type drop-down list and NOx... and Mass fraction of NO in the Field Variable drop-down list. (b) Select pressure-outlet-9 as the surface over which to perform the integration. (c) Click Compute. The mass-weighted average exit NO mass fraction is about 0.00469.


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8. Disable the prompt NOx mechanism and solve for thermal NOx only. Define −→ Models −→ Pollutants −→NOx... (a) Turn off Prompt NO under Models to disable the prompt NOx mechanism, and click OK. (b) Request 50 iterations. Solve −→Iterate... The solution converges in about 10 iterations. (c) Review the thermal NOx solution by viewing contours of NO mass fraction (Figure 12.13). Display −→Contours... i. Check that NOx... and Mass fraction of NO are selected in the Contours Of drop-down list. ii. Click Display. The NO mass fraction contours are shown in Figure 12.13. The concentration of NO is slightly lower without the prompt NOx mechanism.




Figure 12.13: Contours of NO Mass Fraction: Thermal NOx Formation (d) Compute the average exit NO mass fraction with only thermal NOx formation. Report −→Surface Integrals... Hint: Follow the same procedure you used earlier for the calculation with both thermal and prompt NOx formation.

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The mass-weighted average exit NO mass fraction, with thermal but no prompt NOx formation, is about 0.00457. 9. Solve for prompt NOx production only. Define −→ Models −→ Pollutants −→NOx... (a) Turn off Thermal NO and turn on Prompt NO under Models, and click OK. (b) Request 50 iterations. The solution converges in about 10 iterations. Solve −→Iterate... (c) Review the prompt NOx solution by viewing contours of NO mass fraction (Figure 12.14). Display −→Contours... The NO mass fraction contours are shown in Figure 12.14. The prompt NOx mechanism is most significant in fuel-rich flames. In this case the flame is lean and prompt NO production is low.




Figure 12.14: Contours of NO Mass Fraction: Prompt NOx Formation (d) Compute the average exit NO mass fraction with only prompt NOx formation. Report −→Surface Integrals... Hint: Follow the same procedure you used earlier for the calculation with both thermal and prompt NOx formation. The mass-weighted average exit NO mass fraction, with only prompt NOx formation, is about 0.000071.


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Note: The individual thermal and prompt NO mass fractions do not add up to the levels predicted with the two models combined. This is because reversible reactions are involved. NO produced in one reaction can be destroyed in another reaction. 10. Use a custom field function to compute NO parts per million (ppm). Define −→Custom Field Functions... NO ppm is computed from the following equation: NO ppm =

NO mole fraction × 106 1 − H2 O mole fraction

(12.4)

NO mass fraction × mixture MW 30

(12.5)

where NO mole fraction =

and the mixture molecular weight is 1 mixture MW = X mass fraction

(12.6)

MW

i

where MW is the molecular weight of each species. First you will create a function for Equation 12.6. Then you will substitute Equation 12.5 into Equation 12.4 and create a function for Equation 12.4. (a) Create a custom field function for the mixture molecular weight.

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i. Click on the 1 calculator button, then on /, and then on (. ii. Select Species... and Mass fraction of ch4 in the Field Functions drop-down list. Click Select to add this variable to the field function Definition. iii. Click on / and then click on 1 and 6 to enter 16 (the molecular weight of methane). iv. Continue in this fashion to complete the definition of the mixture molecular weight field function. v. Enter bulk-mw in the New Function Name text entry box. vi. Click Define to add the new field function to the variable list. (b) Create a field function for NO ppm.

i. Select NOx... and Mass fraction of NO in the Field Functions drop-down list. Click Select to add this variable to the field function Definition. ii. Click the × button to introduce the multiplication sign. iii. Select Custom Field Functions... and bulk-mw in the Field Functions dropdown list. Click Select to add this variable to the field function Definition. iv. Click on / and then click on 3 and 0 to enter 30 (the molecular weight of NO). v. Click the × button and then click on 1 and 0 to enter 10. vi. Click on y^x and then on 6. vii. Complete the definition of NO ppm as shown in the panel above. viii. Enter no-ppm in the New Function Name text entry box. ix. Click Define to add the new field function to the variable list.


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11. Plot contours of NO ppm (Figure 12.15). Display −→Contours... (a) Select Custom Field Functions... and no-ppm in the Contours Of drop-down list. (b) Click Display. The NO ppm contours are shown in Figure 12.15. The contours closely resemble the mass fraction contours (Figure 12.14), as expected.


Contours of no-ppm


Figure 12.15: Contours of NO ppm: Prompt NOx Formation

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Summary: In this tutorial you used FLUENT to model the transport, mixing, and reaction of chemical species. The reaction system was defined by using and modifying a mixture-material entry in the FLUENT database. The procedures used here for simulation of hydrocarbon combustion can be applied to other reacting flow systems. This exercise illustrated the important role of the mixture heat capacity in the prediction of flame temperature. The combustion modeling results are summarized in the following table. (Note that some of the values in the table were not explicitly calculated during the tutorial.)

Constant cp Variable cp

Peak Temp. Exit Temp. (K) (K) 3077 2198 2301 1796

Exit Velocity (m/s) 3.83 3.14

The use of a constant cp results in a significant overprediction of the peak temperature. The average exit temperature and velocity are also overpredicted. While the variable cp solution produces dramatic improvements in the predicted results, further improvements are possible by considering additional models and features available in FLUENT, as discussed below. The NOx production in this case was dominated by the thermal NO mechanism. This mechanism is very sensitive to temperature. Every effort should be made to ensure that the temperature solution is not overpredicted, since this will lead to unrealistically high predicted levels of NO. Further Improvements: Further improvements can be expected by including the effects of intermediate species and radiation, both of which will result in lower predicted combustion temperatures. The single-step reaction process used in this tutorial cannot account for the moderating effects of intermediate reaction products, such as CO and H2 . Multiple-step reactions can be used to address these species. If a multi-step Magnussen model is used, considerably more computational effort is required to solve for the additional species. Where applicable, the non-premixed combustion model can be used to account for intermediate species at a reduced computational cost. See the User’s Guide for more details on the non-premixed combustion model. Radiation heat transfer tends to make the temperature distribution more uniform, thereby lowering the peak temperature. In addition, radiation heat transfer to the wall can be very significant (especially here, with the wall temperature set at 300 K). The large influence of radiation can be anticipated by computing the Boltzmann number for the flow:


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Bo =

(ρUcp )inlet convection ∼ 3 σTAF radiation

where σ is the Boltzmann constant (5.729×10−8 W/m2 -K4 ) and TAF is the adiabatic flame temperature. For a quick estimate, assume ρ = 1 kg/m3 , U = 0.5 m/s, and cp = 1000 J/kg-K (the majority of the inflow is air). Assume TAF = 2000 K. The resulting Boltzmann number is Bo = 1.09, which shows that radiation is just about as important as convection for this problem. See the User’s Guide and Tutorial 5 for details on radiation modeling.

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Tutorial 13. Using the Non-Premixed Combustion Model Introduction: A pulverized coal combustion simulation involves modeling a continuous gas phase flow field and its interaction with a discrete phase of coal particles. The coal particles, traveling through the gas, will devolatilize and undergo char combustion, creating a source of fuel for reaction in the gas phase. Reaction can be modeled using either the species transport model or the non-premixed combustion model. In this tutorial you will model a simplified coal combustion furnace using the non-premixed combustion model for the reaction chemistry. In this tutorial you will learn how to: • Prepare a PDF table for a pulverized coal fuel using the prePDF preprocessor • Define FLUENT inputs for non-premixed combustion chemistry modeling • Define a discrete second phase of coal particles • Solve a simulation involving reacting discrete phase coal particles The non-premixed combustion model uses a modeling approach that solves transport equations for one or two conserved scalars, the mixture fractions. Multiple chemical species, including radicals and intermediate species, may be included in the problem definition and their concentrations will be derived from the predicted mixture fraction distribution. Property data for the species are accessed through a chemical database and turbulence-chemistry interaction is modeled using a Beta or double-delta probability density function (PDF). See the User’s Guide for more detail on the non-premixed combustion modeling approach. Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1 or its equivalent. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The coal combustion system considered in this tutorial is a simple 10 m by 1 m two-dimensional duct depicted in Figure 13.1. Only half of the domain width is modeled because of symmetry. The inlet of the 2D duct is split into two streams. A high-speed stream near the center of the duct enters at 50 m/s and spans 0.125 m. The other stream enters at 15 m/s and spans 0.375 m. Both streams are air at 1500 K. Coal particles enter the furnace near the center of the high-speed stream with a mass flow rate of 0.1 kg/s (total flow rate in the


13-1

Using the Non-Premixed Combustion Model

furnace is 0.2 kg/s). The duct wall has a constant temperature of 1200 K. The Reynolds number based on the inlet dimension and the average inlet velocity is about 100,000. Thus, the flow is turbulent. Details regarding the coal composition and size distribution are included in Step 5: Models: Continuous (Gas) Phase and Step 8: Materials: Discrete Phase.

T = 1200 K w

Air: 15 m/s, 1500 K

0.5 m Coal Injection: 0.1 kg/s 0.125 m

Air: 50 m/s, 1500 K Symmetry Plane 10 m

Figure 13.1: 2D Furnace with Pulverized Coal Combustion

Preparation for prePDF 1. Start prePDF. When you use the non-premixed combustion model, you prepare a PDF file with the preprocessor, prePDF. The PDF file contains information that relates species concentrations and temperatures to the mixture fraction values, and is used by FLUENT to obtain these scalars during the solution procedure.

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Step 1: Define the Preliminary Adiabatic System in prePDF 1. Define the prePDF model type. You can define either a single fuel stream, or a fuel stream plus a secondary stream. Enabling a secondary stream allows you to keep track of two mixture fractions. For coal combustion, this would allow you to track volatile matter (the secondary stream) separately from the char (fuel stream). In this tutorial, we will not follow this approach. Instead, we will model coal using a single mixture fraction. Setup −→Case...

(a) Under Heat transfer options, keep the default setting of Adiabatic. The coal combustor studied in this tutorial is a non-adiabatic system, with heat transfer at the combustor wall and heat transfer to the coal particles from the gas. Therefore, a non-adiabatic combustion system must be considered in prePDF. Because non-adiabatic calculations are more time-consuming than those for adiabatic systems, you will start the prePDF setup by considering the results of an adiabatic system. By computing the PDF/equilibrium chemistry results for the adiabatic system, you will determine appropriate system parameters that will make the non-adiabatic calculation more efficient. Specifically, the


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adiabatic calculation will provide information on the peak (adiabatic) flame temperature, the stoichiometric mixture fraction, and the importance of individual components to the chemical system. This process of beginning with an adiabatic system calculation should be followed in all PDF calculations that ultimately require a non-adiabatic model. (b) Under Chemistry models, keep the default setting of Equilibrium Chemistry. In most PDF-based simulations, the Equilibrium Chemistry option is recommended. The Stoichiometric Reaction (mixed is burned) option requires less computation but is generally less accurate. The Laminar Flamelets option offers the ability to include aerodynamic strain induced non-equilibrium effects, such as super-equilibrium radical concentration and sub-equilibrium temperatures. This can be important for NOx prediction, but is excluded here. (c) Keep the default setting of the PDF models. The Beta PDF integration is always recommended because it is more accurate than the Delta PDF approach. (d) Under Empirically Defined Streams, enable the Fuel stream option. This will allow you to define the fuel stream using the empirical input option. The empirical input option allows you to define the composition in terms of atom fractions of H, C, N, and O, along with the lower heating value and heat capacity of the fuel. This is a useful option when the ultimate analysis and heating value of the coal are known. (e) Click Apply and close the panel.

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2. Define the chemical species in the system. The choice of which species to include depends on the fuel type and combustion system. Guidelines on this selection are provided in the FLUENT User’s Guide. Here, you will assume that the equilibrium system consists of 13 species: C, C(s), CH4 , CO, CO2 , H, H2 , H2 O, N, N2 , O, O2 , and OH. C, H, O, and N are included because the fuel stream will be defined in terms of these atom fractions, using the “empirical” input method. !

You should include both C and C(S) in the system when the empirical input option is used.

Setup −→ Species −→Define...

(a) Set the Maximum # of Species to 13. Use the up and down arrows to set the maximum number of species, or enter the number in the text field followed by . (b) Select the top species in the Defined Species list (initially labeled UNDEFINED). (c) In the Database Species drop-down list, use the slider bar to scroll the list, and select C. The Defined Species list now shows C as the first entry. (d) Select the next species in the Defined Species list (or increment the Species # counter to 2). (e) In the Database Species drop-down list, use the slider bar to scroll the list, and select the next species (C(S)). (f) Repeat steps (d) and (e) until all 13 species are defined. (g) Click Apply and then close the panel.


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Note: In other combustion systems, you might want to include additional chemical species, but you should not add slow chemical species like NOx . 3. Determine the fuel composition inputs. The fuel considered here is known, from proximate analysis, to consist of 28% volatiles, 64% char, and 8% ash. You will use this information, along with the ultimate analysis given below, to define the coal composition in prePDF. The fuel stream composition (char and volatiles) is derived as follows. Begin by converting the proximate data to a dry-ash-free basis: Proximate Analysis Wt % (dry) Volatiles 28 Char (C(s)) 64 Ash 8

Wt % (DAF) 30.4 69.6 -

The ultimate analysis, for the dry-ash-free coal, is known to be: Element C H O N S

Wt % (DAF) 89.3 5.0 3.4 1.5 0.8

For modeling simplicity, the sulfur content of the coal can be combined into the nitrogen mass fraction, to yield: Element C H O N S

Wt % (DAF) 89.3 5.0 3.4 2.3 -

We can combine the proximate and ultimate analysis data to yield the following elemental composition of the volatile stream: Element C H O N Total

13-6

Wt % 89.3 5.0 3.4 2.3

Moles 7.44 5 0.21 0.16 12.81

Mole Fraction 0.581 0.390 0.016 0.013



You will enter the mole fractions in the final column, above, in order to define the fuel composition. prePDF will use this information, along with the coal heating value, to define the species present in the fuel. The lower heating value of coal (DAF) is known to be: • LCVcoal,DAF = 35.3 MJ/kg The specific heat and density of the coal are known to be 1000 J/kg-K and 1 kg/m3 respectively. 4. Enter the fuel and oxidizer compositions. Setup −→ Species −→Composition... (a) Enable the input of the oxidizer stream composition. The oxidizer (air) consists of 21% O2 and 79% N2 by volume.

i. Under Stream, select Oxidiser. ii. Under Specify Composition In, retain the default selection of Mole Fractions. iii. Select O2 in the Defined Species list and enter 0.21 in the Species Fraction field.


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iv. Select N2 in the Defined Species list and enter 0.79 in the Species Fraction field. (b) Enable the input of the fuel stream composition. Note: Because the empirical input option is enabled for the fuel stream, you will be prompted to enter atom mole fractions for C, H, O, and N, along with the heating value and heat capacity of the coal.

i. Under Stream, select Fuel. ii. Under Specify Composition In, retain the default selection of Mole Fractions. iii. Select C in the Defined Species list and enter 0.581 in the Atom Fraction field. iv. Select H in the Defined Species list and enter 0.390 in the Atom Fraction field. v. Select N in the Defined Species list and enter 0.016 in the Atom Fraction field. vi. Select O in the Defined Species list and enter 0.013 in the Atom Fraction field.

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vii. Enter 3.53e+07 J/kg for the Lower Caloric Value and 1000 J/kg-K for the Specific Heat. viii. Click Apply and close the panel. 5. Define the density of the solid carbon. Here, a value of 1300 kg/m3 is assumed. Setup −→ Species −→Density...

(a) Select C(S) in the Defined Species list. (b) Set the Density to 1300. (c) Click Apply and close the panel. Note: prePDF will use this information during computation of the mixture density for the fuel. You should enter the density of solid char. This input will differ from the coal density defined in FLUENT, which is the apparent density of the ash-containing coal particles.


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6. Define the system operating conditions. The system pressure and inlet stream temperatures are required for the equilibrium chemistry calculation. The fuel stream inlet temperature for coal combustion should be the temperature at the onset of devolatilization. The oxidizer inlet temperature should correspond to the air inlet temperature. In this tutorial, the coal devolatilization temperature will be set to 400 K and the air inlet temperature is 1500 K. The system pressure is one atmosphere. Setup −→Operating Conditions...

(a) Enter 400 K and 1500 K as the Fuel and Oxidiser inlet temperatures. (b) Click Apply and close the panel.

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Step 2: Compute and Review the Adiabatic System prePDF Look-Up Tables 1. Accept the default PDF solution parameters. Setup −→Solution Parameters...

The look-up table calculation performed by prePDF will result in a table of values for species mole fractions and temperature at a set of discrete mixture fraction values. You control the number and distribution of these discrete points using the Solution Parameters panel. You can also set the Fuel Rich Flamability Limit in this panel. The Fuel Rich Flamability Limit allows you to perform a “partial equilibrium” calculation, suspending equilibrium calculations when the mixture fraction exceeds the specified rich limit. This increases the efficiency of the PDF calculation, allowing you to bypass the complex equilibrium calculations in the fuel-rich region, and is more physically realistic than the assumption of full equilibrium. For empirically defined streams, the rich limit is always 1.0 and cannot be altered. (a) Keep the default setting for Automatic Distribution. This feature allows you to improve the prePDF prediction by optimizing the distribution of the discrete mixture fraction values, clustering them around the peak temperature value. If you choose not to use the Automatic Distribution, you should set the distribution center point on the rich side of the stoichiometric scale mixture fraction. (b) Click Apply and close the panel.


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2. Save your inputs (coal ad.inp). File −→ Write −→Input... 3. Calculate the adiabatic system chemistry. Calculate −→PDF Table During the calculation, prePDF first retrieves thermodynamic data from the database. Then the time-averaged values of temperature, composition, and density at the discrete mixture-fraction/mixture-fraction-variance points (21 points as defined in the Solution Parameters panel) are calculated. The result will be a set of tables containing time-averaged values of species mole fractions, density, and temperature at each discrete value of these two parameters. prePDF reports the progress of the look-up table construction in the console window. When the calculations are complete, prePDF will warn you that equilibrium calculations have been performed for the fuel inlet. You can simply acknowledge this warning, as the equilibrium conditions predicted do not impact your modeling inputs unless the fuel stream is representing a gaseous fuel inlet.

4. Save the adiabatic PDF file (coal ad.pdf). File −→ Write −→PDF... (a) Under File Type, select Write Formatted File. When you write a PDF file, prePDF will save a binary file by default. If you are planning to use the PDF file on the same machine, you can save the file using the default Write Binary File option. However, if you are planning to use the PDF file on a different machine, you should save an ASCII (formatted) file from prePDF. Note that ASCII files take up more disk space than binary files. (b) Under Solver, select FLUENT 6. (c) Enter coal ad.pdf as the Pdf File name. (d) Click OK to write the file.

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5. Examine the temperature/mixture-fraction relationship in the adiabatic system. The results of the adiabatic calculation provide insight into the system description that will be used for the non-adiabatic calculation. Display −→PDF Table...

(a) Select TEMPERATURE from the Plot Variable list and then click Display to generate the table (Figure 13.2). The temperature display shows how the time-averaged system temperature varies with the mean mixture fraction and its variance. The temperature/mixture-fraction relationship shows that the peak flame temperature is about 2750 K at fuel stoichiometric mixture fractions of approximately 0.1. The relatively high flame temperature is a result of the high preheat in the combustion air. Note: The adiabatic flame temperature predicted by the adiabatic system calculation will be used to select the maximum temperature in the non-adiabatic system calculation.


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2.8E+03

2.4E+03 T E M P E R A T U R E

2.0E+03

2.50E-01 2.00E-01

1.6E+03 1.50E-01 SCALED-F-VARIANCE

K

1.00E-01

1.2E+03 5.00E-02

7.6E+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 V4.11

Fluent Inc.

Figure 13.2: Time-Averaged Temperature: Adiabatic prePDF Calculation

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Step 3: Create and Compute the Non-Adiabatic prePDF System Creating a non-adiabatic PDF system description requires that you do the following: • Redefine the system as non-adiabatic. • Set the peak system temperature (based on the adiabatic result of 2750 K). After these modifications, you will recompute the system chemistry and save a nonadiabatic PDF file for use in FLUENT. 1. Define the prePDF model type as non-adiabatic. Setup −→Case...

(a) Select Non-Adiabatic under Heat transfer options and click Apply. 2. Set the system temperature limits. Minimum and maximum temperatures in the system are required when the PDF calculation is non-adiabatic. The minimum temperature should be a few degrees lower than the lowest boundary condition temperature (e.g., the inlet temperature or wall temperature). In coal


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combustion systems, the minimum system temperature should also be set below the temperature at which the volatiles begin to evolve from the coal. Here, the vaporization temperature at which devolatilization begins will be set to 400 K. Thus, the minimum system temperature is set to 298 K (the default). The maximum temperature should be at least 100 K higher than the peak flame temperature found in the preliminary adiabatic calculation. Here, the maximum temperature will be taken as 3000 K, well above the peak adiabatic system temperature of 2750 K. Setup −→Operating Conditions...

(a) Enter 298 for Min. Temperature and 3000 for Max. Temperature. (b) Click Apply and close the panel. 3. Save the non-adiabatic system inputs (coal.inp). File −→ Write −→Input... 4. Compute the non-adiabatic PDF look-up tables. Calculate −→PDF Table

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The non-adiabatic prePDF calculation requires much more computation than the adiabatic calculation. prePDF begins by accessing the thermodynamic data from the database. Next, the enthalpy field is initialized and the enthalpy grid adjusted to account for inlet conditions and solution parameters. Time-averaged values of temperature, composition, and density at the discrete mixture-fraction/mixture-fractionvariance/enthalpy points (21 points, as defined in the Solution Parameters panel) are then calculated. The result will be a set of tables containing time-averaged values of species mole fractions, density, and temperature at each discrete value of these three parameters. When the calculations are complete, prePDF will warn you that equilibrium calculations have been performed for the fuel inlet. As noted above, you can simply acknowledge this warning, which has no impact on your inputs when you are modeling coal or liquid fuels.

5. Write the PDF output file (coal.pdf). File −→ Write −→PDF... (a) Under File Type, select Write Formatted File. (b) Select FLUENT 6 under Solver. (c) Enter coal.pdf as the Pdf File name. (d) Click OK to write the file.


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6. Review one slice of the 3D look-up table prepared by prePDF. Display −→Nonadiabatic Table...

(a) Select TEMPERATURE from the Plot Variable drop-down list and click Display (Figure 13.3). Note: Review of the 3D look-up tables is accomplished on a slice-by-slice basis. By default, the slice selected is that corresponding to the adiabatic enthalpy values. This display should look very similar to the look-up table created during the adiabatic calculation. You can select other slices of constant enthalpy for display, as well. 7. Examine the species/mixture-fraction relationship in the non-adiabatic system. Display −→Nonadiabatic Table...

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2.8E+03

2.4E+03 T E M P E R A T U R E

2.0E+03

2.50E-01 2.00E-01

1.6E+03 1.50E-01 SCALED-F-VARIANCE

K

1.00E-01

1.2E+03 5.00E-02

7.6E+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 V4.11

MEAN FLAME TEMPERATURE FROM 3D-PDF-TABLE

Fluent Inc.

Figure 13.3: Non-Adiabatic Temperature Look-Up Table on the Slice Corresponding to Adiabatic Enthalpy

(a) Select SPECIES from the Plot Variable drop-down list. The Species Selection panel will open automatically. (b) In the Species Selection panel, select C(S) in the Species drop-down list and click OK.

(c) Click Display in the Nonadiabatic-Table panel to generate the table (Figure 13.4). 8. Follow the steps above to plot the instantaneous mole fractions for CO (Figure 13.5). 9. Exit from prePDF. File −→Exit


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7.6E-01

6.1E-01 M O L E F R A C T I O N

4.6E-01

2.50E-01 2.00E-01

3.1E-01 1.50E-01 SCALED-F-VARIANCE 1.00E-01

1.5E-01 5.00E-02

0.0E+00

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 SPECIES C(S)

prePDF V4.11

FROM 3D-PDF-TABLE

Fluent Inc.

Figure 13.4: Time-Averaged C(S) Mole Fractions: Non-Adiabatic prePDF Calculation

3.0E-01

2.4E-01 M O L E F R A C T I O N

1.8E-01

2.50E-01 2.00E-01

1.2E-01 1.50E-01 SCALED-F-VARIANCE 1.00E-01

6.0E-02 5.00E-02

0.0E+00

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 SPECIES CO

FROM 3D-PDF-TABLE

prePDF V4.11

Fluent Inc.

Figure 13.5: Time-Averaged CO Mole Fractions: Non-Adiabatic prePDF Calculation

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Preparation for FLUENT Calculation With the PDF file creation completed, you are ready to use the non-premixed combustion model in FLUENT to predict the combusting flow in the coal furnace. 1. Copy the file coal/coal.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). The mesh file coal.msh is a quadrilateral mesh describing the system geometry shown in Figure 13.1. 2. Start the 2D version of FLUENT.

Step 4: Grid 1. Read the 2D mesh file, coal.msh. File −→ Read −→Case... The FLUENT console window reports that the mesh contains 1357 quadrilateral cells. 2. Check the grid. Grid −→Check The grid check should not report any errors or negative volumes. 3. Display the grid (Figure 13.6). Display −→Grid... Due to the grid resolution and the size of the domain, you may find it more useful to display just the outline, or to zoom in on various portions of the grid display. Note: You can use the mouse probe button (right button, by default) to find out the boundary zone labels. As annotated in Figure 13.7, the upstream boundary contains two velocity inlets (for the low-speed and high-speed air streams), the downstream boundary is a pressure outlet, the top boundary is a wall, and the bottom boundary is a symmetry plane.


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Grid


Figure 13.6: 2D Coal Furnace Mesh Outline Display

wall-7

velocity-inlet-2

velocity-inlet-8

symmetry

Grid


Figure 13.7: Mesh Display with Annotated Boundary Types

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Step 5: Models: Continuous (Gas) Phase 1. Accept the default segregated solver. The non-premixed combustion model is available only with the segregated solver. Define −→ Models −→Solver...


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Note: As indicated in the problem description, the Reynolds number of the flow is about 105 . Thus, the flow is turbulent and the high-Re k- model is suitable. 3. Turn on the non-premixed combustion model. Define −→ Models −→Species... (a) Select Non-Premixed Combustion under Model. The panel will expand to show the related inputs.

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When you click OK, FLUENT will open the Select File dialog box, requesting input of the PDF file to be used in the simulation. (b) In the Select File dialog box, select and read the non-adiabatic PDF file (coal.pdf). FLUENT reports in the console window that it is reading the nonadiabatic PDF file containing 13 species. It also reports that a new material, called pdf-mixture, has been created. This mixture contains the 13 species that you defined in prePDF and their thermodynamic properties. FLUENT will present an Information dialog box telling you that available material properties have changed. You will be setting properties later, so you can simply click OK in the dialog box to acknowledge this information. Note: FLUENT will automatically activate solution of the energy equation when it reads the non-adiabatic PDF file, so you do not need to visit the Energy panel to enable heat transfer.


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4. Turn on radiation by selecting the P1 radiation model. Define −→ Models −→Radiation...

The P-1 model is one of the radiation models that can account for the exchange of radiation between gas and particulates.

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Step 6: Models: Discrete Phase The flow of pulverized coal particles will be modeled by FLUENT using the discrete phase model. This model predicts the trajectories of individual coal particles, each representing a continuous stream (or mass flow) of coal. Heat, momentum, and mass transfer between the coal and the gas will be included by alternately computing the discrete phase trajectories and the gas phase continuum equations. 1. Enable the discrete phase coupling to the continuous phase flow prediction. Define −→ Models −→Discrete Phase... (a) Under Interaction, turn on the Interaction with Continuous Phase option. This option enables coupling, in which the discrete phase trajectories (along with heat and mass transfer to the particles) are allowed to impact the gas phase equations. If you leave this option turned off, you can track particles but they will have no impact on the continuous phase flow.


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(b) Set the coupling parameter, the Number of Continuous Phase Iterations per DPM Iteration, to 20. You should use higher values of this parameter in problems that include a high particle mass loading or a larger grid size. Less frequent trajectory updates can be beneficial in such problems, in order to converge the gas phase equations more completely prior to repeating the trajectory calculation. (c) Under Tracking Parameters, set the Max. Number of Steps to 10000. The limit on the number of trajectory time steps is used to abort trajectories of particles that are trapped in the domain (e.g., in a recirculation). (d) Turn on Specify Length Scale and retain the default Length Scale of 0.01 m. The Length Scale controls the time step size used for integration of the discrete phase trajectories. The value of 0.01 m used here implies that roughly 1000 time steps will be used to compute trajectories along the 10 m length of the domain. (e) Under Options, turn on Particle Radiation Interaction.

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2. Create the discrete phase coal injections. The flow of the pulverized coal is defined by the initial conditions that describe the coal as it enters the gas. FLUENT will use these initial conditions as the starting point for its time integration of the particle equations of motion (the trajectory calculations). Here, the total mass flow rate of coal (in the half-width of the duct) is 0.1 kg/s (per unit meter depth). The particles will be assumed to obey a Rosin-Rammler size distribution between 70 and 200 micron diameter. Other initial conditions (velocity, temperature, position) are detailed below along with the appropriate input procedures. Define −→ Injections...

(a) Click the Create button in the Injections panel. This will open the Set Injection Properties panel where you will define the initial conditions defining the flow of coal particles.


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In the Set Injection Properties panel you will define the initial conditions of the flow of coal particles. The particle stream will be defined as a group of 10 distinct initial conditions, all identical except for diameter, which will obey the Rosin-Rammler size distribution law. (b) Select group in the Injection Type drop-down list. (c) Set the Number of Particle Streams to 10. These inputs tell FLUENT to represent the range of specified initial conditions by 10 discrete particle streams, each with its own set of discrete initial conditions. Here, this will result in 10 discrete particle diameters, as the diameter will be varied within the injection group. (d) Select Combusting under Particle Type. By selecting Combusting you are activating the submodels for coal devolatilization and char burnout. Similarly, selecting Droplet would enable the submodels for droplet evaporation and boiling.

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(e) Select coal-mv in the Material drop-down list. The Material list contains the combusting particle materials in the FLUENT database. You can select an appropriate coal from this list and then review or modify its properties in the Materials panel (see Step 8: Materials: Discrete Phase). (f) Select rosin-rammler in the Diameter Distribution drop-down list. The coal particles have a nonuniform size distribution with diameters ranging from 70 µm to 200 µm. The size distribution fits the Rosin-Rammler equation, with a mean diameter of 134 µm and a spread parameter of 4.52. (g) Select o2 (the default) in the Oxidizing Species drop-down list. (h) Specify the range of initial conditions under Point Properties starting with the following inputs for First Point: • X-Position: 0.001 m • Y-Position: 0.03124 m • X-Velocity: 10 m/s • Y-Velocity: 5 m/s • Temperature = 300 K • Total Flow Rate: 0.1 kg/s • Min. Diameter: 70e-6 m • Max. Diameter: 200e-6 m • Mean Diameter: 134e-6 m • Spread Parameter: 4.52 (i) Under Last Point, specify identical inputs for position, velocity, and temperature. (j) Define the turbulent dispersion. i. Click on Turbulent Dispersion. The panel will change to show the related inputs.


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ii. Under Stochastic Tracking, turn on Stochastic Model. Stochastic tracks model the effect of turbulence in the gas phase on the particle trajectories. Including stochastic tracking is important in coal combustion simulations, to simulate realistic particle dispersion. iii. Set the Number of Tries to 10. Note: The new injection (named injection-0, by default) now appears in the Injections panel.

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This panel can be used to copy and delete injection definitions. You can also select an existing injection and list the initial conditions of particle streams defined by that injection in the console window. The listing for the injection-0 group will show 10 particle streams, each with a unique diameter between the specified minimum and maximum value, obtained from the Rosin-Rammler distribution, and a unique mass flow rate.


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Step 7: Materials: Continuous Phase All thermodynamic data including density, specific heat, and formation enthalpies are extracted from the prePDF chemical database when the non-premixed combustion model is used. These properties are transferred to FLUENT as the pdf-mixture material, for which only transport properties, such as viscosity and thermal conductivity, need to be defined. Define −→Materials...

1. Set Thermal Conductivity to 0.025 (constant). 2. Set Viscosity to 2e-5 (constant). 3. Select wsggm-cell-based in the drop-down list for the Absorption Coefficient.

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This specifies a composition-dependent absorption coefficient, using the weightedsum-of-gray-gases model. See the User’s Guide for details. 4. Click the Change/Create button. Note: You can click on the View... button next to Mixture Species to view the species included in the pdf-mixture material. These are the species included during the system chemistry setup in prePDF. Note that the Density and Cp laws cannot be altered: these properties are stored in the non-premixed combustion look-up tables. prePDF uses the gas law to compute the mixture density and a mass-weighted mixing law to compute the mixture cp . Although it is possible for you to alter the properties of the individual species, you should not do so when the non-premixed combustion model is used. This would create an inconsistency with the look-up table created in prePDF.


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Step 8: Materials: Discrete Phase Define −→Materials...

1. Select combusting-particle from the Material Type list. The combusting-particle material type appears because you have activated combusting particles using the Set Injection Properties panel. Other discrete phase material types (droplets, inert particles) will appear in this list if you have created injections of those types. 2. Keep the current selection (coal-mv) in the Combusting Particle Materials list. This is the combusting particle material type that you selected from the list of database options in the Set Injection Properties panel. Additional combusting particle materials can be copied from the property database, if desired. You can click the

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Database... button in order to view the combusting-particle materials that are available. Here, you will simply modify the property settings for the selected material, coal-mv. 3. Set the following constant property values for the coal-mv material: Density Cp Thermal Conductivity Latent Heat Vaporization Temperature Volatile Component Fraction (%) Binary Diffusivity Particle Emissivity Particle Scattering Factor Swelling Coefficient Burnout Stoichiometric Ratio Combustible Fraction (%)

1300 kg/m3 1000 J/kg-K 0.0454 w/m-k 0 400 K 28 5e-4 m2 /s 0.9 0.6 2 2.67 64

FLUENT uses these inputs as follows: • Density impacts the particle inertia and body forces (when the gravitational acceleration is non-zero). • Cp determines the heat required to change the particle temperature. • Latent Heat is the heat required to vaporize the volatiles. This can usually be set to zero when the non-premixed combustion model is used for coal combustion. If the volatile composition has been selected in order to preserve the heating value of the fuel, the latent heat has been effectively included. (You would, however, use a non-zero latent heat if water content had been included in the volatile definition as vapor phase H2 O.) • Vaporization Temperature is the temperature at which the coal devolatilization begins. It should be set equal to the fuel inlet temperature used in prePDF. • Volatile Component Fraction determines the mass of each coal particle that is devolatilized. • Binary Diffusivity is the diffusivity of oxidant to the particle surface and is used in the diffusion-limited char burnout rate. • Particle Emissivity is the emissivity of the particles. It is used to compute radiation heat transfer to the particles. • Particle Scattering Factor is the scattering factor due to particles. • Swelling Coefficient determines the change in diameter during coal devolatilization. A swelling coefficient of 2 implies that the particle size will double as the volatile fraction is released.


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• Burnout Stoichiometric Ratio is used in the calculation of the diffusion-controlled burnout rate. Otherwise, this parameter has no impact when the non-premixed combustion model is used. When finite-rate chemistry is used instead, the stoichiometric ratio defines the mass of oxidant required per mass of char. The default value represents oxidation of C(s) to CO2 . • Combustible Fraction is the mass fraction of char in the coal particle. It determines the mass of each coal particle that is consumed by the char burnout submodel. !

The settings for the Vaporization Temperature, Combustible Fraction, and Volatile Component Fraction inputs should all be consistent with your prePDF inputs. (See Step 1: Define the Preliminary Adiabatic System in prePDF.)

4. Select the Single Rate Devolatilization Model for Devolatilization Model. (a) Select the single-rate option in the Devolatilization Model drop-down list. This opens the Single Rate Devolatilization Model panel.

(b) Accept the default devolatilization model parameters. 5. Select kinetics/diffusion-limited for the Combustion Model. (a) Select the kinetic/diffusion-limited option in the Combustion Model drop-down list. This opens the Kinetics/Diffusion Limited Combustion Model panel.

(b) Accept the default values. 6. Click Change/Create and then close the Materials panel.

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Step 9: Boundary Conditions Define −→Boundary Conditions... Hint: You can click your mouse probe button (the right button, by default) on the desired boundary zone in the graphics display window. FLUENT will then select that zone in the Boundary Conditions panel. 1. Set the following conditions for the velocity-inlet-2 zone (the low-speed inlet boundary). Note: Turbulence parameters are defined here based on intensity and hydraulic diameter. The relatively large turbulence intensity of 10% may be typical for combustion air flows. The hydraulic diameter has been set to twice the height of the 2D inlet stream. For the non-premixed combustion calculation, you need to define the inlet Mean Mixture Fraction and Mixture Fraction Variance. For coal combustion, all fuel comes from the discrete phase and thus the gas phase inlets have zero mixture fraction. Therefore, you can accept the zero default settings.


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2. Set the following conditions for the velocity-inlet-8 zone (the high-speed inlet boundary).


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3. Set the following conditions for the pressure-outlet-6 zone (the exit boundary).

The exit gauge pressure of zero simply defines the system pressure at the exit to be the operating pressure. The backflow conditions for scalars (temperature, mixture fraction, turbulence parameters) will be used only if flow is entrained into the domain through the exit. It is a good idea to use reasonable values in case flow reversal occurs at the exit at some point during the solution process.

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4. Set conditions for the wall-7 zone (the furnace wall). The furnace wall will be treated as an isothermal boundary with a temperature of 1200 K.

(a) Under Thermal Conditions, select Temperature. (b) Enter 1200 in the Temperature field. Note: The default boundary condition for particles that hit the wall is reflect, as shown under DPM. Alternate treatments can be selected, using the BC Type list, for particles that hit the wall.


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Step 10: Solution 1. Set the P1 under-relaxation factor to 1. Solve −→ Controls −→Solution... 2. Initialize the flow field using conditions at velocity-inlet-2. Solve −→ Initialize −→Initialize...

(a) Select velocity-inlet-2 in the Compute From list. (b) Click the Init button to initialize the flow field, and then close the panel. !

The Apply button does not initialize the flow field data. You must use the Init button. (Apply simply allows you to store your initialization parameters for later use.)

Note: Here, with very high pre-heat of the oxidizer stream, you can start the combustion calculation from the inlet-based initialization. In general, you may need to start your coal combustion calculations by patching a high-temperature region and performing a discrete phase trajectory calculation. This provides the initial volatile and char release required to initiate combustion. The Solve/Initialize/ Patch... menu item and the solve/dpm-update text command can be used to perform this initialization. 3. Enable the display of residuals during the solution process. Solve −→ Monitors −→Residual... 4. Save the case file (coal.cas). File −→ Write −→Case...

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5. Begin the calculation by requesting 400 iterations. Solve −→Iterate...

Note: The default convergence criteria will be met in about 170 iterations. 6. Save the converged flow data (coal.dat). File −→ Write −→Data...


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Step 11: Postprocessing 1. Display the predicted temperature field (Figure 13.8). Display −→Contours...

The peak temperature in the system is about 2260 K. Hint: Use the Views panel (Display/Views...) to mirror the display about the symmetry plane.

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Nov 26, 2002 FLUENT 6.1 (2d, segregated, pdf13, ske)

Figure 13.8: Temperature Contours


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2. Display the Mean Mixture Fraction distribution (Figure 13.9). Display −→Contours...

The mixture-fraction distribution shows where the char and volatiles released from the coal exist in the gas phase.

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Contours of Mean Mixture Fraction


Figure 13.9: Mixture-Fraction Distribution


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3. Display the devolatilization rate (Figure 13.10). Display −→Contours...

(a) Select Discrete Phase Model... and DPM Evaporation/Devolatilization in the drop-down lists under Contours Of. 4. Display the char burnout rate (Figure 13.11) by selecting DPM Burnout from the lower drop-down list. Note: The display of devolatilization rate shows that volatiles are released after the coal travels about one eighth of the furnace length. (The onset of devolatilization occurs when the coal temperature reaches the specified value of 400 K.) The char burnout occurs following complete devolatilization. Figure 13.11 shows that burnout is complete at about three-quarters of the furnace.

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Contours of DPM Evaporation/Devolatilization (kg/s)


Figure 13.10: Devolatilization Rate


Contours of DPM Burnout (kg/s)


Figure 13.11: Char Burnout Rate


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5. Display the particle trajectory of one particle stream (Figure 13.12). Display −→Particle Tracks...

(a) Select injection-0 in the Release From Injections list. (b) Select Particle Residence Time in the Color By drop-down list. (c) Turn on Track Single Particle Stream and set the Stream ID to 5. (d) Click Display.

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Particle Traces Colored by Particle Residence Time (s)


Figure 13.12: Trajectories of Particle Stream 5 Colored by Particle Residence Time


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6. Display the oxygen distribution (Figure 13.13). Display −→Contours...

Note: Although transport equations are solved only for the mixture fraction and its variance, you can still display the predicted chemical species concentrations. These are predicted by the PDF equilibrium chemistry model.

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Contours of Mass fraction of o2


Figure 13.13: O2 Distribution


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7. Select other species and display their mass fraction distributions (e.g., Figures 13.14– 13.16).


Contours of Mass fraction of co2


Figure 13.14: CO2 Distribution

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Contours of Mass fraction of h2o


Figure 13.15: H2 O Distribution


Contours of Mass fraction of co


Figure 13.16: CO Distribution


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Step 12: Energy Balances and Particle Reporting FLUENT can provide many useful reports, including overall energy accounting and detailed information regarding heat and mass transfer from the discrete phase. Here, you will examine these reports. 1. Compute the fluxes of heat through the domain boundaries. Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options. (b) Under Boundaries, select the pressure-outlet-6, velocity-inlet-2, velocity-inlet-8, and wall-7 zones. (c) Click Compute. Note: Positive flux reports indicate heat addition to the domain. Negative values indicate heat leaving the domain. In reacting flows, the heat report uses total enthalpy (sensible heat plus heat of formation of the chemical species). Here, the net “imbalance” of total enthalpy (about 14 kW) represents the total enthalpy addition from the discrete phase.

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2. Compute the volume sources of heat transferred between the gas and discrete particle phase. Report −→Volume Integrals...

(a) Select Sum under Options. (b) Select Discrete Phase Model... and DPM Enthalpy Source in the drop-down lists under Field Variable. (c) Select fluid-1 under Cell Zones. (d) Click Compute. The total enthalpy transfer to the discrete phase from the gas is about -13.4 kW, as expected based on the boundary flux report above. This represents the total enthalpy addition from the discrete phase to the gas during the devolatilization and char combustion processes. 3. Obtain a summary report on the particle trajectories. The discrete phase model summary report provides detailed information about the particle residence time, heat and mass transfer between the continuous and discrete phases, and (for combusting particles) char conversion and volatile yield. Display −→Particle Tracks... (a) Select Summary under Report Type. (b) Select injection-0. (c) Click Track. FLUENT will report the summary in the console window. (You can write the report to a file by selecting File under Report to. (d) Review the summary printed in the console window:


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DPM Iteration .... num tracked = 100, escaped = 0, aborted = 0, trapped = 0, evaporated = 0, incomp Fate

Number

---Escaped - Zone 6

-----100

Elapsed Time (s) Inj Min Max Avg Std Dev ---------- ---------- ---------- ---------- ------2.574e-01 5.153e-01 3.317e-01 5.311e-02 inj

(*)- Mass Transfer Summary -(*) Fate ---Escaped - Zone 6

Mass Flow (kg/s) Initial Final Change ---------- ---------- ---------1.000e-01 7.999e-03 -9.200e-02

(*)- Energy Transfer Summary -(*) Fate ---Escaped - Zone 6

Heat Content (W) Initial Final Change ---------- ---------- ----------3.712e+03 9.849e+03 1.356e+04

(*)- Combusting Particles -(*) Fate ---Escaped - Zone 6

Volatile Content (kg/s) Initial Final %Conv ---------- ---------- ------2.800e-02 0.000e+00 100.00

Char Content (kg/s) Initial Final %Conv ---------- ---------- ------6.400e-02 0.000e+00 100.00

The report shows that the average residence time of the coal particles is about 0.33 seconds. Volatiles are completely released within the domain and the char conversion is 100% . Extra: You can obtain a detailed report of the particle position, velocity, diameter, and temperature along the trajectories of individual particles. This type of detailed track reporting can be useful if you are trying to understand unusual or important details in the discrete model behavior. To generate the report, visit the Particle Tracks panel. Select Step By Step under Report Type, and File under Report to. Enable the Track Single Particle Stream option, and set the Stream ID to the desired particle stream. Clicking Track will bring up the Select File dialog box, where you will enter the name of the file to be written. This file can then be viewed with a text editor.

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Summary: Coal combustion modeling involves the prediction of volatile evolution and char burnout from the pulverized coal along with simulation of the combustion chemistry occurring in the gas phase. In this tutorial you learned how to use the non-premixed combustion model to represent the gas phase combustion chemistry. In this approach the fuel composition was defined in prePDF and the fuel was assumed to react according to the equilibrium system data. This equilibrium chemistry model can be applied to other turbulent, diffusion-reaction systems. Note that you can also model coal combustion using the finite-rate chemistry model. You also learned how to set up and solve a problem involving a discrete phase of combusting particles. You created discrete phase injections, activated coupling to the gas phase, and defined the discrete phase material properties. These procedures can be used to set up other simulations involving reacting or inert particles.


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Tutorial 14.

Modeling Surface Chemistry

Introduction: In chemically reacting laminar flows, such as those encountered in chemical vapor deposition (CVD) applications, accurate modeling of time-dependent hydrodynamics, heat and mass transfer, and chemical reactions (including wall surface reactions) is important. Tutorials 12 and 13 deal with reacting flows with applications in gaseous fuel and coal combustion. In this tutorial, surface reactions are considered. Modeling the reactions taking place at gas-solid interfaces is complex and involves several elementary physicochemical processes like adsorption of gas-phase species on the surface, chemical reactions occurring on the surface, and desorption of gases from the surface back to the gas phase. In this tutorial, you will learn how to: • Create new materials and set the mixture properties. • Model surface reactions involving site species. • Enable physical models and define boundary conditions for a chemically reacting laminar flow involving wall surface reactions. • Calculate the deposition solution using the segregated solver. • Examine the flow results using graphics. Prerequisites: This tutorial assumes that you are familiar with the FLUENT user interface, and that you have solved Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Before beginning, you should read Sections 13.1 and 13.2 in the User’s Guide. Section 13.1 deals with species transport and chemically reacting flows. In particular, you should be familiar with the Arrhenius rate equation, as this equation is used for the surface reactions modeled in this tutorial. Section 13.2 describes wall surface reaction modeling and chemical vapor deposition. Problem Description: A rotating disk CVD reactor for the growth of Gallium Arsenide (GaAs) shown in Figure 14.1 will be modeled. The process gases, Trimethyl Gallium (GaCh3 ) and Arsine (AsH3 ) enter the reactor at 293 K through the inlet at the top. These gases flow over the hot, spinning disk depositing thin layers of gallium and arsenide on it in a uniform, repeatable manner. The disk rotation generates a radially pumping effect, which forces the


14-1


Inlet Rotating Disk

Outlet

Figure 14.1: An Outline of the Reactor Configuration

gases to flow in a laminar manner down to the growth surface, outward across the disk, and finally to be discharged from the reactor. The semiconductor materials Ga(s) and As(s) are deposited on the heated surface governed by the following surface reactions. AsH3 + Ga s → Ga + As s + 1.5H2

(14.1)

GaCH3 + As s → As + Ga s + 3CH3

(14.2)

As mentioned earlier, the inlet gas is a mixture of trimethyl gallium and arsine. In the inlet mixture the mass fraction of GaCH3 is 0.15 and AsH3 is 0.4. The mixture velocity at the inlet is 0.02189 m/s. The disk rotates at 80 rad/sec, and the top wall (wall-1) is heated to 473 K, and the sidewalls (wall-2) of the reactor are maintained at 343 K. The susceptor (wall-4) is heated to a uniform temperature of 1023 K, and the bottom wall (wall-6) is at 303 K. In this tutorial, simultaneous deposition of Ga and As is simulated and examined. The mixture properties and the mass diffusivity are determined based on kinetic theory. Detailed surface reactions with multiple sites and site species, and full multi-component/thermal diffusion effects are also included in the simulation.

Preparation 1. Copy the files surface/surface.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 3ddp version of FLUENT.

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Step 1: Grid 1. Read in the mesh file surface.msh. File −→ Read −→Case... 2. Check the grid. Grid −→Check Note: The grid check lists the minimum and maximum x and y values from the grid, and reports on a number of other grid features that are checked. Any errors in the grid would be reported at this time. For instance, the cell volumes must never be negative. Note that the domain extents are reported in units of meters, the default unit of length in FLUENT. Since this grid was created in units of centimeters, the Scale Grid panel will be used to scale the grid into meters. 3. Scale the grid. Grid −→Scale...

(a) In the Units Conversion drop-down list, select cm to complete the phrase Grid Was Created In cm (centimeters). (b) Click Scale to scale the grid. The final Domain Extents should appear as in the panel above. Note: Because the default SI units will be used in this tutorial, there is no need to change any units.


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Extra: You can use the left mouse button to rotate the image and view it from different angles. You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its name and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly. Use the middle mouse button to zoom the image.

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Y Z Grid

X

Sep 20, 2002 FLUENT 6.1 (3d, dp, segregated, spe4, lam)

Figure 14.2: Grid Display


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Step 2: Models In this problem, the energy equation and the species conservation equations will be solved, along with the momentum and continuity equations. 1. Keep the default solver settings. Define −→ Models −→Solver...


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(a) Under Model, select Species Transport. This will expand the Species Model panel. (b) Under Reactions, select Volumetric and Wall Surface. (c) Under Wall Surface Reaction Options, select Mass Deposition Source. Mass Deposition Source is selected because there is a certain loss of mass due to the surface deposition reaction, i.e., As(s) and Ga(s) are being deposited out. If you were to do an overall mass balance without taking this fact into account, you would end up with a slight imbalance. (d) Keep the Diffusion Energy Source option turned on. Note: This includes the effect of enthalpy transport due to species diffusion in the energy equation, which contributes to the energy balance, especially for the case of Lewis numbers far from unity.


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(e) Select Full Multicomponent Diffusion and Thermal Diffusion. Note: The Full Multicomponent Diffusion activates Stefan-Maxwells equations and computes the diffusive fluxes of all species in the mixture to all concentration gradients. The Thermal Diffusion effects cause heavy molecules to diffuse less rapidly, and light molecules to diffuse more rapidly, towards heated surfaces. (f) Click OK. The console window will list the properties that are required for the models that you have enabled. You will see an Information dialog box, reminding you to confirm the property values that have been extracted from the database.

(g) Click OK in the Information dialog box to continue.

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Step 3: Materials Define −→Materials...

1. Create the gas-phase species (AsH3 , GaCH3 , CH3 , H2 ), the site species (Ga s and As s), and solid species (Ga and As). (a) Create species AsH3 . i. In the Materials panel, select fluid under Material Type. ii. Select nitrogen under Fluid Materials to create the new material. iii. Set the Mixture to none. iv. Enter arsine under Name. v. Enter ash3 under Chemical Formula. vi. Specify the following for each of the properties:


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Parameter Cp Thermal Conductivity Viscosity Molecular Weight Standard State Enthalpy Standard State Entropy Reference Temperature L-J Characteristic Length L-J Energy Parameter Degrees of Freedom

Value kinetic-theory kinetic-theory kinetic-theory 77.95 0 130579.1 298.15 4.145 259.8 0

Ignore the Density parameter as the density will be set to incompressibleideal-gas-law for mixture. vii. Click Change/Create to create the new material. viii. FLUENT will ask if you would like to overwrite nitrogen. Click No in the Question panel.

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(b) Create the other species following the same procedure as for AsH3 . i. The parameter values for each of the species is as per the table given below: Parameter Name Chemical Formula Cp

GaCH3 tmg gach3

kinetictheory Thermal Con- kineticductivity theory Viscosity kinetictheory Molecular 114.83 Weight Standard State 0 Enthalpy Standard State 130579.1 Entropy Reference 298.15 Temperature L-J Character- 5.68 istic Length L-J Energy Pa- 398 rameter Degrees of 0 Freedom

CH3 ch3g ch3

H2 Ga s hydrogen ga s h2 ga s

As s as s as s

Ga ga ga

As as as

kinetictheory kinetictheory kinetictheory 15

kinetictheory kinetictheory kinetictheory 2.02

520.64

520.64

1006.43

1006.43

0.0158

0.0158

2.125 e-05 69.72

2.125 e-05 74.92

kinetictheory kinetictheory 69.72

kinetictheory kinetictheory 74.92

2.044 0 -3117.71 -3117.71 0 e+07 257367.6 130579.1 154719.3 154719.3 0

0

298.15

298.15

298.15

298.15

298.15

298.15

3.758

2.827

-

-

0

0

148.6

59.7

-

-

0

0

0

5

-

-

-

-

0

ii. Click Change/Create to create the new material. iii. Click No in the Question panel. 2. Set the mixture species. (a) Under Material Type, select mixture. (b) Enter gaas deposition under Name. (c) Click Change/Create. (d) To overwrite the mixture-template, click Yes in the Question panel. (e) Under Properties, click the Edit... button to the right of Mixture Species. This will open the Species panel. Here you will set the Selected Species, Selected Site Species, and Selected Solid Species from the Available Materials list using the Add and Remove buttons.


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The species under each species type are: Selected Species ash3 gach3 ch3 h2

!

Selected Site Species ga s as s -

Selected Solid Species ga as -

The species should appear in the same order as shown in the above table. (f) To set the species follow the procedure listed below: i. To remove an unwanted species from the Selected Species list, select the species and click Remove under Selected Species. ii. Select the required species in the Available Materials list. iii. Click Add under the corresponding species list. iv. Click OK after all the species are set under the respective categories.

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3. Set the mixture reactions. (a) In the Materials panel, under Properties, click the Edit... button to the right of Reaction. This will open the Reactions panel. (b) In the Reactions panel, increase the Total Number of Reactions to 2, and define the following reactions, where PEF = Pre-Exponential Factor, AE = Activation Energy, and TE = Temperature Exponent.

Reaction Name Reaction ID Reaction Type Number of Reactants Species Stoich. Coefficient Rate Exponent Arrhenius Rate Number of Products Species Stoich. Coefficient Rate Exponent


AsH3 + Ga s → Ga + As s + 1.5H2

(14.3)

GaCH3 + As s → As + Ga s + 3CH3

(14.4)

gallium-dep 1 Wall Surface 2 ash3, ga s ash3=1, ga s=1 ash3=1, ga s=1 PEF=1e+06, AE=0, TE=0.5 3 ga, as s, h2 ga=1, as s=1, h2=1.5 as s=0, h2=0

arsenic-dep 2 Wall Surface 2 gach3, as s gach3=1, as s=1 gach3=1, as s=1 PEF=1e+12, AE=0, TE=0.5 3 as, ga s, ch3 as=1, ga s=1, ch3=3 ga s=0, ch3=0

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(c) Change the ID to 2 and set the parameters for the second equation as shown in the above table. (d) Click OK to save your data and close the panel. 4. Set the reaction mechanisms for the mixture. (a) In the Materials panel, under Properties, click the Edit... button to the right of Mechanism. This will open the Reaction Mechanisms panel. (b) Enter gaas-ald under Name. (c) Retain the Number of Mechanisms as 1. (d) Set the Reaction Type to Wall Surface. (e) Under Reactions, select gallium-dep and arsenic-dep. (f) Increase the Number of Sites to 1. (g) Set the Site Density as 1e-08.

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(h) Click Define... to the right of site-1. This opens the Site Parameters panel. i. In the Site Parameters panel, set the Total Number of Site Species to 2. ii. Select ga s as the first site species and set the Site Coverage to 0.7. iii. Select as s as the second site species and set the Site Coverage to 0.3.

(i) Click Apply and Close the panel. (j) Click OK in the Reaction Mechanisms panel to close the panel.


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5. In the Materials panel, set Density to incompressible-ideal-gas. 6. Set Cp to mixing-law. 7. Set Thermal Conductivity to mass-weighted-mixing-law. 8. Set Viscosity to mass-weighted-mixing-law. 9. Set Mass Diffusivity to kinetic-theory. 10. Set Thermal Diffusion Coefficient to kinetic-theory. 11. Click Change/Create and close the Materials panel.

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Step 4: Operating Conditions Define −→Operating Conditions... 1. Set the Operating Pressure to 10000 pascals. 2. Enable Gravity. 3. Set the Gravitational Acceleration in the Z direction as 9.81. 4. Set the Operating Temperature to 303 K. 5. Click OK to close the panel.


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Step 5: Boundary Conditions Define −→Boundary Conditions... 1. Keep the default settings for outflow.

2. Set the conditions for velocity-inlet. (a) Retain the default Velocity Specification Method as Magnitude,Normal to Boundary. (b) Retain the default Reference Frame as Absolute. (c) Set the Velocity Magnitude to 0.02189 m/s (d) Set the Temperature to 293 K. (e) Set the Species Mass Fractions for ash3 as 0.4, gach3 as 0.15, and ch3 as 0.

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(f) Click OK to close the panel. 3. Set the boundary conditions for wall-1. (a) Under Thermal Conditions, select Temperature and set the Temperature to 473 K.

(b) Click OK to close the panel. 4. Similarly, set the boundary conditions for wall-2. (a) Under Thermal Conditions, select Temperature and set the Temperature to 343 K. (b) Click OK to close the panel. 5. Set the boundary conditions for wall-4. (a) Under Thermal Conditions, select Temperature and set the Temperature to 1023 K. (b) In the Momentum section of the panel, set Wall Motion to Moving Wall, Motion to Absolute and Rotational and set the Speed to 80 rad/s. (c) Retain other defaults.


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(d) Under the Species section of the panel, enable Reaction and set Mechanisms to gaas-ald.

(e) Click OK to close the panel.

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6. Set the boundary conditions for wall-5. (a) Under Thermal Conditions, select Temperature and set the Temperature to 720 K. (b) In the Momentum section of the panel, set Wall Motion to Moving Wall, Motion to Absolute and Rotational and set the Speed to 80 rad/s. (c) Retain other defaults. (d) Click OK to close the panel. 7. Set the boundary conditions for wall-6. (a) Under Thermal Conditions, select Temperature and set the Temperature to 303 K. (b) Click OK to close the panel. 8. Use the TUI commands to turn off diffusion at the inlet. In the console window, type the commands shown in boxes in the dialog below. Hint: You may need to enter press the key to get the > prompt.

> define/models/species/inlet-diffusion? Include diffusion at inlets? [yes] no


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Step 5: Solution 1. Set the solution parameters. Solve −→ Controls −→Solution... (a) Change the Under-Relaxation Factor as follows: Parameter Pressure Density Body Forces Momentum

URF 0.1 0.3 1 0.2

Parameter ash3 gach3 ch3 Energy

URF 1 1 1 0.9

Hint: You will need to scroll down the Under-Relaxation Factors list to see the species and Energy. (b) Under Discretization, retain the default First Order Upwind for Momentum, all the species and Energy.

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2. Initialize the flow field using the boundary conditions set at velocity-inlet. Solve −→ Initialize −→Initialize...

(a) Select velocity-inlet in the Compute From drop-down list. (b) Click Init, and Close the panel.


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3. Turn on residual plotting during the calculation. Solve −→ Monitors −→Residual...

(a) Select Plot under Options. (b) Set the Convergence Criterion for Continuity to 1e-05. (c) Click OK to close the panel. 4. Save the case file (surface.cas). File −→ Write −→Case... 5. Start the calculation by requesting 2000 iterations. Solve −→Iterate...

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The solution converges in about 1900 iterations. Residuals continuity x-velocity y-velocity z-velocity energy ash3 gach3 ch3

1e+01 1e+00 1e-01 1e-02 1e-03 1e-04 1e-05 1e-06 1e-07 1e-08

Y

Z X

0

200

Scaled Residuals

400

600

800

1000

1200

1400

1600

1800

2000

Iterations


Figure 14.3: Scaled Residuals

6. Save the case and data files (surface.cas and surface.dat). File −→ Write −→Case & Data...


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Step 7: Postprocessing 1. Create an iso-surface near wall-4. Surface −→Iso-Surface... (a) In the Iso-Surface panel, select Grid and Z-Coordinate under Surface of Constant. (b) Click Compute. (c) Enter 0.075438 under Iso-Values. (d) Enter z=0.07 under New Surface Name. (e) Click Create.

2. Display contours of temperature on the plane surface. (Figure 14.4). Display −→Contours... (a) Select Temperature... and Static Temperature in the Contours Of drop-down list. (b) Enable Filled under Options. (c) Select z=0.07 under Surfaces. (d) Click Display.

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X Z Y



Figure 14.4: Temperature Contours near wall-4

The temperature contours shows the temperature distribution across a plane just above the rotating disk. You can see that the disk has a temperature of 1023 K..


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3. Display contours of surface deposition rates of ga.(Figure 14.5). Display −→Contours... (a) Select Species... and Surface Deposition Rate of ga in the Contours Of dropdown list. (b) Select wall-4 under Surfaces. (c) Click Display. You may need to use the left mouse button to rotate the image so that you can see the contours on the top side of wall-4 where the deposition takes place.


X Z Y

Contours of Surface Deposition Rate of ga (kg/m2-s)


Figure 14.5: Contours of Surface Deposition Rate of ga

Figure 14.5 shows the gradient of surface deposition rate of ga. The maximum deposition is seen at the center of the disk. 4. Display contours of surface coverage of ga s. (Figure 14.6). Display −→Contours... (a) Select Species... and Surface Coverage of ga s in the Contours Of drop-down list. (b) Select wall-4 under Surfaces. (c) Click Display.

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X Z Y

Contours of Surface Coverage of ga_s


Figure 14.6: Contours of Surface Coverage of ga s Figure 14.6 shows the rate of surface coverage of the site species ga s. 5. Create a line surface from the center of wall-4 to the edge. Surface −→Line/Rake... (a) In the Line/Rake Surface panel, select Select Points with Mouse. (b) In the graphic display, click at the center of wall-4 and at the edge with the right mouse button. (c) Click Create.


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6. Plot the surface deposition rate of Ga v/s radial distance(Figure 14.7). Plot −→XY Plot...

(a) Select Species... and Surface Deposition Rate of ga in the Y Axis Function drop-down list. (b) Under Options, deselect Node Values. The source/sink terms due to the surface reaction are deposited in the cell adjacent to the wall cells, so it is necessary to plot the cell values and not the node values. (c) In the Surfaces list, select line-7. (d) To set the scale of the XY plot, click Axes. i. In the Axes - Solution XY Plot panel, select Y under Axis. ii. Disable Auto Range under Options. iii. Under Range, set Minimum to 2e-05 and Maximum to 5e-05, click Apply and Close the panel. (e) In the Solution XY Plot, click Plot. The peak of the surface deposition rate occurs at the center of wall-4 (where the concentration of the mixture is highest).

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line-7 5.500000e-05

5.000000e-05

4.500000e-05

4.000000e-05

Surface Deposition3.500000e-05 Rate of ga3.000000e-05 (kg/m2-s) 2.500000e-05

2.000000e-05 -0.25

Y Z

X

Surface Deposition Rate of ga

-0.2

-0.15

-0.1

-0.05 1.38778e-170.05

0.1

0.15

0.2

0.25

Position (m)


Figure 14.7: Plot of Surface Deposition Rate of Ga

Extra: You can also perform all the above postprocessing steps to analyze the deposition of As. Summary: The main focus of this tutorial is the accurate modeling of macroscopic gas flow, heat and mass transfer, species diffusion, and chemical reactions (including surface reactions) in a rotating disk CVD reactor. In this tutorial, you learned how to use the two-step surface reactions involving site species, and computed simultaneous deposition of gallium and arsenide from a mixture of precursor gases on a rotating susceptor. Note that the same approach is valid if you are simulating multi-step reactions with multiple sites/site species.


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Tutorial 15. Spray

Modeling Evaporating Liquid

Introduction: In this tutorial, FLUENT’s air-blast atomizer model is used to predict the droplet behavior of an evaporating methanol spray. The air flow is modeled first as a steady-state problem without droplets. To predict the behavior of individual droplets in the atomizer, several other discrete-phase models, including collision and breakup, are used in an unsteady calculation. In this tutorial you will learn how to: • Create periodic zones • Define a discrete-phase spray injection for an air-blast atomizer • Calculate a transient solution using the second-order implicit unsteady formulation Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The geometry to be considered in this tutorial is shown in Figure 15.1. Methanol is cooled to −10◦ C before being introduced into an air-blast atomizer. The atomizer contains an inner air stream surrounded by a swirling annular stream. (The species include the components of air as well as water vapor, so the model can be expanded to include combustion, if desired.) To make use of the periodicity of the problem, only a 30-degree section of the atomizer will be modeled.

Preparation 1. Copy the file spray/sector.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 3D version of FLUENT.


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Modeling Evaporating Liquid Spray

inner air stream swirling annular stream

Z

Y

X


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Step 1: Grid 1. Read in the mesh file sector.msh. File −→ Read −→Case... 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...

(a) Under Options, select Faces. (b) Under Surfaces, select only atomizer-wall, central air, and swirling air. (c) Click the Colors... button.


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(d) In the Grid Colors panel, select Color By ID. This will assign a different color to each zone in the domain, rather than to each type of zone. (e) In the Grid Display panel, click Display. The graphics display will be updated to show the grid. You will now change the display again to zoom in on an isometric view of the atomizer section. 4. Change the display to an isometric view. Display −→Views...

(a) Select right in the Views list and click Restore. (b) Zoom in and rotate with your mouse to obtain the view shown in Figure 15.2.

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Z

Y

X Grid


Figure 15.2: Air-Blast Atomizer Mesh Display


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5. Using the text interface, change zones periodic-a and periodic-b from wall zones to periodic zones. (a) In the console window, type the commands shown in boxes in the dialog below.

> grid /grid> modify-zones /grid/modify-zones> list-zones id name type ---- ---------------- ----------------1 fluid fluid 2 atomizer-wall wall 3 central_air mass-flow-inlet 4 co-flow-air velocity-inlet 5 outlet pressure-outlet 6 swirling_air velocity-inlet 7 periodic-a wall 8 periodic-b wall 9 outer-wall wall 11 default-interior interior

material -----------------air aluminum

aluminum aluminum aluminum

kind ---cell face face face face face face face face face

/grid/modify-zones> make-periodic Periodic zone [()] 7 Shadow zone [()] 8 Rotational periodic? (if no, translational) [yes] yes Create periodic zones? [yes] yes all 1923 faces matched for zones 7 and 8. zone 8 deleted created periodic zones.

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6. Reorder the grid. To speed up the solution procedure, the mesh should be reordered, which will substantially reduce the bandwidth. Grid −→ Reorder −→Domain FLUENT will report its progress in the console window: >> Reordering domain using Reverse Cuthill-McKee method: zones, cells, faces, done. Bandwidth reduction = 3286/102 = 32.22 Done.


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3. Enable the realizable k- turbulence model. Define −→ Models −→Viscous...

The realizable k- model gives a more accurate prediction of the spreading rate of both planar and round jets than the standard k- model.


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(a) Select Species Transport under Model. (b) Choose methyl-alcohol-air in the Mixture Material drop-down list. The Mixture Material list contains the set of chemical mixtures that exist in the FLUENT database. By selecting one of the pre-defined mixtures, you are accessing a complete description of the reacting system. The chemical species in the system and their physical and thermodynamic properties are defined by your selection of the mixture material. You can alter the mixture material selection or modify the mixture material properties using the Materials panel (see Step 6: Solution: Unsteady Flow). !

When you click OK, the console window will list the properties that are required for the models you have enabled. You will see an Information dialog box, reminding you to confirm the property values that have been extracted from the database.

(c) Click OK in the Information dialog box to continue.

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Step 3: Boundary Conditions Define −→Boundary Conditions... 1. Set the following conditions for the inner air stream (central air).


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2. Set the following conditions for the air stream surrounding the atomizer (co-flowair).

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3. Set the following conditions for the exit boundary (outlet).


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4. Set the following conditions for the swirling annular stream (swirling air).

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5. Set the following conditions for the outer wall of the atomizer (outer-wall).


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Step 4: Initial Solution Without Droplets The airflow will first be solved and analyzed without droplets. 1. Initialize the flow field. Solve −→ Initialize −→Initialize...

(a) Select co-flow-air in the Compute From drop-down list. (b) Click Init to initialize the variables, and then close the panel.

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2. Keep the default under-relaxation factors. Solve −→ Controls −→Solution...


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3. Turn on residual plotting during the calculation. Solve −→ Monitors −→Residual...

(a) Under Options, select Plot. (b) Click OK. 4. Save the case file (spray1.cas). File −→ Write −→Case... 5. Start the calculation by requesting 200 iterations. Solve −→Iterate... The solution will converge after about 175 iterations. 6. Save the case and data files (spray1.cas and spray1.dat). File −→ Write −→Case & Data... Note: FLUENT will ask you to confirm that the previous case file is to be overwritten.

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7. Create a clip plane to examine the flow field at the midpoint of the atomizer section. Surface −→Iso-Surface...

(a) Select Grid... and Angular Coordinate in the Surface of Constant lists. (b) Click on Compute to update the minimum and maximum values. (c) Enter 15 in the Iso-Values field. (d) Enter angle=15 for the New Surface Name. (e) Click on Create to create the isosurface.


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8. Review the current state of the solution by examining contours of velocity magnitude (Figure 15.3). Display −→Contours...

(a) Select Velocity... and Velocity Magnitude in the Contours Of drop-down list. (b) Under Options, select Filled and Draw Grid. This will open the Grid Display panel.

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(c) Keep the current grid display settings and close the Grid Display panel. (d) In the Contours panel, select angle=15 in the Surfaces list. (e) Click Display. (f) Use your mouse to obtain the view shown in Figure 15.3.

9.91e+01 9.41e+01 8.92e+01 8.42e+01 7.92e+01 7.43e+01 6.93e+01 6.44e+01 5.94e+01 5.45e+01 4.95e+01 4.46e+01 3.96e+01 3.47e+01 2.97e+01 2.48e+01 1.98e+01 1.49e+01 9.91e+00 Y 4.95e+00 Z 0.00e+00 X

Contours of Velocity Magnitude (m/s)

Nov 18, 2002 FLUENT 6.1 (3d, segregated, spe5, ske)

Figure 15.3: Velocity Magnitude at Mid-Point of Atomizer Section 9. Display path lines of the air in the swirling annular stream (Figure 15.4). Display −→Path Lines...


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(a) In the Release From Surfaces list, select swirling air. You will need to scroll down to access this item. (b) Increase the Skip value to 5. (c) Under Options, select Draw Grid. This will open the Grid Display panel. (d) Keep the current grid display settings and close the Grid Display panel. (e) Click Display in the Path Lines panel. (f) Use your mouse to obtain the view shown in Figure 15.4.

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4.90e+01 4.65e+01 4.41e+01 4.17e+01 3.92e+01 3.68e+01 3.43e+01 3.19e+01 2.94e+01 2.70e+01 2.45e+01 2.20e+01 1.96e+01 1.71e+01 1.47e+01 1.22e+01 9.80e+00 7.35e+00 4.90e+00 Y 2.45e+00 Z 0.00e+00 X

Path Lines Colored by Particle ID

Nov 18, 2002 FLUENT 6.1 (3d, segregated, spe5, ske)

Figure 15.4: Path Lines of Air in the Swirling Annular Stream


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Step 5: Enable Time Dependence and Create a Spray Injection In this step you will define a transient flow and create a discrete phase spray injection. 1. Enable a time-dependent flow calculation. Define −→ Models −→Solver...

(a) Under Time, select Unsteady. (b) Under Unsteady Formulation, select 2nd-Order Implicit.

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2. Define the discrete phase modeling parameters. Define −→ Models −→Discrete Phase...

(a) Define the interphase interaction. i. Under Interaction, turn on Interaction with Continuous Phase. This will include the effects of the discrete phase trajectories on the continuous phase. ii. Under Number of Continuous Phase Iterations per DPM Iteration, enter a value of 1000. This option controls the iterative solution of the discrete phase within each gas-phase time step. Higher values are more desirable for sprays. (b) Specify the Tracking Parameters. i. Deselect the Specify Length Scale option.


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ii. Keep the default value of Step Length Factor. (c) Set the Unsteady Options. i. Under Spray Models, select Droplet Collision and Droplet Breakup. ii. Under Breakup Model, keep the default selection of TAB. iii. Under Constants, enter a value of 0.05 for y0. This parameter is the dimensionless droplet distortion at t = 0. (d) Under Drag Parameters, select dynamic-drag in the Drag Law drop-down list. The dynamic-drag law is available only when the Droplet Breakup model is used. 3. Create the spray injection. In this step, you will define the characteristics of the atomizer. Define −→Injections...

(a) Click the Create button at the top of the panel. This will open the Set Injection Properties panel.

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(b) In the Injection Type drop-down list, select air-blast-atomizer. (c) Increase the Number Of Particle Streams to 60. This option controls how many parcels of droplets are introduced into the domain at every time step. (d) Under Particle Type, select Droplet. (e) In the Material drop-down list, select methyl-alcohol-liquid. (f) Set the point properties for the injection. i. Set the X-Position, Y-Position, and Z-Position of the injection to 0, 0, and 0.0015. ii. Set the X-Axis, Y-Axis, and Z-Axis of the injection to 0, 0, and 1. iii. Set the Temperature to 263 K. iv. Set the Flow Rate to 1.7e-4 kg/s. This is the methanol flow rate for a 30-degree section of the atomizer. The actual atomizer flow rate is 12 times this value.


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v. Keep the default Start Time of 0 s and set the Stop Time to 100 s. For this problem, the injection should begin at t = 0 and not stop until long after the time period of interest. A large value for the stop time (e.g., 100 s) will ensure that the injection will essentially never stop. vi. Set the Injector Inner Diam. to 0.0035 m, and the Injector Outer Diam. to 0.0045 m. vii. Set the Spray Half Angle to -45 deg. The spray angle is the angle between the liquid sheet trajectory and the injector centerline. In this case, the value is negative because the sheet is initially converging toward the centerline. viii. Set the Relative Velocity to 82.6 m/s. The relative velocity is the expected relative velocity between the atomizing air and the liquid sheet. ix. Keep the default Azimuthal Start Angle of 0 deg and set the Azimuthal Stop Angle to 30 deg. This will restrict the injection to the 30-degree section of the atomizer that is being modeled. (g) Define the turbulent dispersion. i. Click the Turbulent Dispersion tab. The lower half of the panel will change to show options for the turbulent dispersion model. ii. Under Stochastic Tracking, turn on the Stochastic Model and Random Eddy Lifetime options. These models will account for the turbulent dispersion of the droplets. Note: In the case that the spray injection would be striking a wall, you would need to define the wall boundary conditions to reflect that event. In the Wall panel, you would select the DPM tab, and then select wall-jet from the Boundary Cond. Type drop-down list. Though this tutorial case does have wall zones, they are a part of the atomizer apparatus. Because these walls are not in the path of the spray droplets, you do not need to change the wall boundary conditions any further.

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4. Set the droplet material properties. Because the secondary atomization models (breakup and coalescence) are used, the droplet properties must be set. Define −→Materials...

(a) In the Material Type drop-down list, select droplet-particle. (b) Under Properties, enter a value of 0.0056 kg/m-s for Viscosity. (c) Under Properties, scroll down and enter a value of 0.0222 N/m for Droplet Surface Tension. (d) Click Change/Create to accept the change in properties for the methanol droplet material.


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Step 6: Solution: Unsteady Flow 1. Set the initial condition for the discrete phase. Resetting the discrete phase model sources will make sure that the interphase coupling is initialized. Solve −→ Initialize −→Reset DPM Sources 2. Set the time step parameters. The selection of the time step is critical for accurate time-dependent flow predictions. Solve −→Iterate...

(a) Set the Time Step Size to 5e-05 s. (b) Click Apply. 3. Save the transient solution case file (spray2.cas). File −→ Write −→Case...

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4. Calculate a solution for one time step. Solve −→Iterate... It is a good idea to do one time step initially so you can check the position of the atomizer droplets before they are significantly dispersed. (a) Set the Number of Time Steps to 1. (b) Click Iterate. !

You will notice that FLUENT will perform less than 20 iterations for the first time step. Since this is the specified Max Iterations per Time Step, the solution is converged. For a real problem, it is important that you allow the solution to converge at each time step, so you may need to increase the Max Iterations per Time Step. The default of 20 is used in this tutorial to speed up the calculation.

5. Save the new case and data files (spray2.cas and spray2.dat). File −→ Write −→Case & Data... 6. Display the trajectories of the droplets in the spray injection (Figure 15.5). This will allow you to review the location of the atomizer droplets after just one time step. They should therefore still be near their initial injection positions. Display −→Particle Tracks...


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(a) In the Style drop-down list, select point. (b) Click the Style Attributes... button. This will open the Path Style Attributes panel.

(c) Set the Marker Size to 0.25 and click OK. (d) In the Particle Tracks panel, select Draw Grid under Options. This will open the Grid Display panel.

(e) Keep the current display settings and close the panel. (f) In the Particle Tracks panel, select Particle Variables... and Particle Diameter in the Color By drop-down list. This will display the location of the droplets colored by their diameters. (g) In the Release From Injections list, select injection-0. (h) Click Display.

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(i) Use your mouse to obtain the view shown in Figure 15.4.

5.91e-05 5.63e-05 5.35e-05 5.07e-05 4.79e-05 4.51e-05 4.23e-05 3.95e-05 3.67e-05 3.39e-05 3.11e-05 2.83e-05 2.56e-05 2.28e-05 2.00e-05 1.72e-05 1.44e-05 1.16e-05 8.80e-06 Y 6.01e-06 Z 3.22e-06 X

Particle Traces Colored by Particle Diameter (m) (Time=5.0000e-05) Nov 18, 2002 FLUENT 6.1 (3d, segregated, spe5, ske, unsteady)

Figure 15.5: Particle Tracks for the Spray Injection After 1 Time Step The air-blast atomizer model assumes that a cylindrical liquid sheet exits the atomizer, which then disintegrates into ligaments and droplets. Appropriately, the model determines that the droplets should be input into the domain in a ring. The radius of this disk is determined from the inner and outer radii of the injector. Note that the maximum diameter of the droplets is about 10−4 m, or 0.1 mm. This is slightly smaller than the film height, which makes sense. Recall that the inner diameter and outer diameter of the injector are 3.5 mm and 4.5 mm, respectively. The film height is then 12 (4.5 − 3.5) = 0.5 mm. The range in the droplet sizes is due to the fact that the air-blast atomizer automatically uses a droplet distribution. Also note that the droplets are placed a slight distance away from the injector. Once the droplets are injected into the domain, they can collide/coalesce with other droplets as determined by the secondary models (breakup and collision). However, once a droplet has been introduced into the domain, the air-blast atomizer model no longer affects the droplet. 7. Request 10 more time steps. Solve −→Iterate... 8. Save the new case and data files (spray3.cas and spray3.dat).


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Step 7: Postprocessing 1. Display the particle trajectories again, to see how the droplets have dispersed. Display −→Particle Tracks... (a) Click Display in the Particle Tracks panel. (b) Use your mouse to obtain the view shown in Figure 15.6.

1.52e-04 1.45e-04 1.37e-04 1.30e-04 1.22e-04 1.15e-04 1.07e-04 9.95e-05 9.19e-05 8.43e-05 7.68e-05 6.92e-05 6.17e-05 5.41e-05 4.65e-05 3.90e-05 3.14e-05 2.39e-05 1.63e-05 Y 8.74e-06 Z 1.18e-06 X

Particle Traces Colored by Particle Diameter (m) (Time=5.5000e-04) Nov 18, 2002 FLUENT 6.1 (3d, segregated, spe5, ske, unsteady)

Figure 15.6: Particle Tracks for the Spray Injection After 11 Time Steps

2. Create an isosurface of the methanol mass fraction. Surface −→Iso-Surface...

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(a) Select Species... and Mass fraction of ch3oh in the Surface of Constant lists. (b) Click on Compute to update the minimum and maximum values. (c) Enter 0.001339 in the Iso-Values field. (d) Enter methanol-mf=0.001339 for the New Surface Name. (e) Click on Create to create the isosurface. 3. Display the isosurface you just created (methanol-mf=0.001339). Display −→Grid...

(a) Select methanol-mf=0.001339 in the Surfaces list.


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(b) Click the Colors... button.

(c) In the Grid Colors panel, select Color By Type. (d) Scroll down and select surface in the Types list and dark red in the Colors list. This will ensure that the isosurface is displayed in red, which contrasts better with the rest of the grid. (e) In the Grid Display panel, click Display. The graphics display will be updated to show the isosurface. 4. Modify the view to include the entire atomizer. Display −→Views...

(a) Increase the number of Periodic Repeats to 11. (b) Click Apply in the Views panel.

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(c) In the Grid Display panel, click Display. The graphics display will be updated to show the entire atomizer. (d) Use your mouse to obtain the view shown in Figure 15.7.

Y Z X

Grid (Time=5.5000e-04)

Aug 29, 2002 FLUENT 6.1 (3d, segregated, spe5, rke, unsteady)

Figure 15.7: Full Atomizer Display with Surface of Constant Methanol Mass Fraction


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Summary: In this tutorial, you defined a discrete-phase spray injection for an air-blast atomizer and calculated a transient solution using the second-order implicit unsteady formulation. You viewed the location of methanol droplet particles after they had exited the atomizer and examined an isosurface of the methanol mass fraction.

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Tutorial 16.

Using the VOF Model

Introduction: This tutorial illustrates the setup and solution of the two-dimensional turbulent fluid flow in a partially filled spinning bowl. In this tutorial you will learn how to: • Set up and solve a transient free-surface problem using the segregated solver • Model the effect of gravity • Copy a material from the property database • Patch initial conditions in a subset of the domain • Define a custom field function • Mirror and rotate the view in the graphics window • Examine the fluid flow and the free-surface shape using velocity vectors and volume fraction contours Prerequisites: This tutorial requires a basic familiarity with FLUENT. You may also find it helpful to read about VOF multiphase flow modeling in the FLUENT User’s Guide. Otherwise, no previous experience with multiphase modeling is required. Problem Description: The information relevant to this problem is shown in Figure 16.1. A large bowl, 1 m in radius, is one-third filled with water and is open to the atmosphere. The bowl spins with an angular velocity of 3 rad/sec. Based on the rotating water, the Reynolds number is about 106 , so the flow is modeled as turbulent.


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Using the VOF Model

2m

1m

Bowl: Ω = Air:

ρ =

µ = Water: ρ = µ =

3 rad/s 1.225 kg/m 3 -5

1.7894 x 10

kg/m-s

998.2 kg/m 3 1 x 10

-3

kg/m-s

Figure 16.1: Water and Air in a Spinning Bowl

Preparation 1. Copy the file vof/bowl.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). The mesh file bowl.msh is a quadrilateral mesh describing the system geometry shown in Figure 16.1. 2. Start the 2D version of FLUENT.

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Step 1: Grid 1. Read the 2D grid file, bowl.msh. File −→ Read −→Case... 2. Display the grid (Figure 16.2). Display −→Grid...

As shown in Figure 16.2, half of the bowl is modeled, with a symmetry boundary at the centerline. The bowl is shown lying on its side, with the region to be modeled extending from the centerline to the outer wall. When you begin to display data graphically, you will need to rotate the view and mirror it across the centerline to obtain a more realistic view of the model. This step will be performed later in the tutorial.


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Grid



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Step 2: Models 1. Specify a transient model with axisymmetric swirl. Define −→ Models −→Solver...

(a) Retain the default Segregated solver. The segregated solver must be used for multiphase calculations. (b) Under Space, select Axisymmetric Swirl. (c) Under Time, select Unsteady.


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2. Turn on the VOF model. Define −→ Models −→Multiphase...

(a) Select Volume of Fluid as the Model. The panel will expand to show inputs for the VOF model. (b) Under VOF Parameters, select Geo-Reconstruct (the default) as the VOF Scheme. This is the most accurate interface-tracking scheme, and is recommended for most transient VOF calculations. When you click OK, FLUENT will report that one of the zone types will need to be changed before proceeding with the calculation. You will take care of this step when you input boundary conditions for the problem.

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(a) Select k-epsilon as the Model, and retain the default setting of Standard under k-epsilon Model.


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Step 3: Materials 1. Copy water from the materials database so that it can be used for the secondary phase. Define −→Materials... (a) Click on the Database... button to open the Database Materials panel.

(b) In the Fluid Materials list (near the bottom), select water-liquid. (c) Click on Copy and close the Database Materials and Materials panels.

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Step 4: Phases Here, water is defined as the secondary phase mainly for convenience in setting up the problem. When you define the initial solution, you will be patching an initial swirl velocity in the bottom third of the bowl, where the water is. It is more convenient to patch a water volume fraction of 1 there than to patch an air volume fraction of 1 in the rest of the domain. Also, the default volume fraction at the pressure inlet is 0, which is the correct value if water is the secondary phase. 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. 1. Define the air and water phases within the bowl. Define −→Phases...

(a) Specify air as the primary phase. i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter air for the Name. iii. Keep the default selection of air for the Phase Material.


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(b) Specify water as the secondary phase. i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter water for the Name. iii. Select water-liquid from the Phase Material drop-down list.

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Step 5: Operating Conditions 1. Set the gravitational acceleration. Define −→Operating Conditions...

(a) Turn on Gravity. The panel will expand to show additional inputs. (b) Set the Gravitational Acceleration in the X direction to 9.81 m/s2 . Since the centerline of the bowl is the x axis, gravity points in the positive x direction. 2. Set the operating density. (a) Under Variable-Density Parameters, turn on the Specified Operating Density option and accept the Operating Density of 1.225. It is a good idea to set the operating density to be the density of the lighter phase. This excludes the buildup of hydrostatic pressure within the lighter phase, improving the round-off accuracy for the momentum balance. Note: The Reference Pressure Location (0,0) is situated in a region where the fluid will always be 100% of one of the phases (air), a condition that is essential for smooth and rapid convergence. If it were not, you would need to change it to a more appropriate location.


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Step 6: Boundary Conditions Define −→Boundary Conditions... 1. Change the bowl centerline from a symmetry boundary to an axis boundary. For axisymmetric models, the axis of symmetry must be an axis zone. (a) Select symmetry-2 in the Zone list in the Boundary Conditions panel. (b) In the Type list, choose axis. You will have to scroll to the top of the list. (c) Click Yes in the Question dialog box that appears.

(d) Click OK in the Axis panel to accept the default Zone Name. 2. Set the conditions at the top of the bowl (the pressure inlet). For the VOF model, you will specify conditions for the mixture (i.e., conditions that apply to all phases) and also conditions that are specific to the secondary phase. There are no conditions to be specified for the primary phase. (a) Set the conditions for the mixture. i. In the Boundary Conditions panel, keep the default selection of mixture in the Phase drop-down list and click Set....

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ii. Set the Turb. Kinetic Energy to 2.25e-2 and the Turb. Dissipation Rate to 7.92e-3. Since there is initially no flow passing through the pressure inlet, you need to specify k and explicitly rather than using one of the other turbulence specification methods. All of the other methods require you to specify the turbulence intensity, which is 0 in this case. The values for k and are computed as follows: k = (Iwwall )2

=

0.093/4 k 3/2 `

where the turbulence intensity I is 0.05 (close to zero), wwall is 3 m/s, and ` is 0.07 (obtained by multiplying 0.07 by the maximum radius of the bowl, which is 1). See the User’s Guide for details about the specification of turbulence boundary conditions at flow inlets and exits. (b) Check the volume fraction of the secondary phase. i. In the Boundary Conditions panel, select water from the Phase drop-down list and click Set....


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ii. Retain the default Volume Fraction of 0. A water volume fraction of 0 indicates that only air is present at the pressure inlet. 3. Set the conditions for the spinning bowl (the wall boundary). For a wall boundary, all conditions are specified for the mixture. There are no conditions to be specified for the individual phases. (a) In the Boundary Conditions panel, select mixture in the Phase drop-down list and click Set....

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(b) Select Moving Wall under Wall Motion. The panel will expand to show inputs for the wall motion. (c) Under Motion, choose Rotational and then set the rotational Speed (Ω) to 3 rad/s.


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Step 7: Solution In simple flows, the under-relaxation factors can usually be increased at the start of the calculation. This is particularly true when the VOF model is used, where high underrelaxation on all variables can greatly improve the performance of the solver. 1. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Set all Under-Relaxation factors to 1. !

Be sure to use the scroll bar to access the under-relaxation factors that are initially out of view.

(b) Under Discretization, choose the Body Force Weighted scheme in the drop-down list next to Pressure. The body-force-weighted pressure discretization scheme is recommended when you solve a VOF problem involving gravity. (c) Also under Discretization, select PISO as the Pressure-Velocity Coupling method. PISO is recommended for transient flow calculations. 2. Enable the display of residuals during the solution process. Solve −→ Monitors −→Residual...

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(a) Under Options, select Plot. (b) Click the OK button. 3. Enable the plotting of the axial velocity of water near the outer edge of the bowl during the calculation. For transient calculations, it is often useful to monitor the value of a particular variable to see how it changes over time. Here you will first specify the point at which you want to track the velocity, and then define the monitoring parameters. (a) Define a point surface near the outer edge of the bowl. Surface −→Point...


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i. Set the x0 and y0 coordinates to 0.75 and 0.65. ii. Enter point for the New Surface Name. iii. Click Create. (b) Define the monitoring parameters. Solve −→ Monitors −→Surface...

i. Increase the Surface Monitors value to 1. ii. Turn on the Plot and Write options for monitor-1. Note: When the Write option is selected in the Surface Monitors panel, the velocity history will be written to a file. If you do not select the Write option, the history information will be lost when you exit FLUENT. iii. In the drop-down list under Every, choose Time Step.

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iv. Click on Define... to specify the surface monitor parameters in the Define Surface Monitor panel.

v. Select Vertex Average from the Report Type drop-down list. This is the recommended choice when you are monitoring the value at a single point using a point surface. vi. Select Flow Time in the X Axis drop-down list. vii. Select Velocity... and Axial Velocity in the Report Of drop-down lists. viii. Select point in the Surfaces list. ix. Enter axial-velocity.out for the File Name. x. Click OK in the Define Surface Monitor panel and then in the Surface Monitors panel.


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(a) Select pressure-inlet-4 in the Compute From drop-down list. All initial values will be set to zero, except for the turbulence quantities. (b) Click Init and close the panel. 5. Patch the initial distribution of water (i.e., water volume fraction of 1.0) and a swirl velocity of 3 rad/s in the bottom third of the bowl (where the water is). In order to patch a value in just a portion of the domain, you will need to define a cell “register” for that region. You will use the same tool that is used to mark a region of cells for adaption. Also, you will need to define a custom function for the swirl velocity. (a) Define a register for the bottom third of the domain. Adapt −→Region...

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i. Set the (Xminimum,Yminimum) coordinate to (0.66,0), and the (Xmaximum,Ymaximum) coordinate to (1,1). ii. Click the Mark button. This creates a register containing the cells in this region. (b) Check the register to be sure it is correct. Adapt −→Manage...

i. Select the register (hexahedron-r0) in the Registers list and click Display. The graphics display will show the bottom third of the bowl in red.


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(c) Define a custom field function for the swirl velocity w = 3r. Define −→Custom Field Functions...

i. Click the 3 button on the calculator pad. The 3 will appear in the Definition field. If you make a mistake, click the DEL button to delete the last item you added to the function definition. ii. Click the X button on the calculator pad. iii. In the Field Functions drop-down list, select Grid... and Radial Coordinate. iv. Click the Select button. radial-coordinate will appear in the Definition. v. Enter a New Function Name of swirl-init. vi. Click Define. Note: If you wish to check the function definition, click on the Manage... button and select swirl-init.

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(d) Patch the water volume fraction in the bottom third of the bowl. Solve −→ Initialize −→Patch...

i. In the Phase drop-down list, select water. ii. Select Volume Fraction in the Variable list. iii. Select hexahedron-r0 in the Registers To Patch list. iv. Set the Value to 1. v. Click Patch. This sets the water volume fraction to 1 in the lower third of the bowl. That is, you have defined the lower third of the bowl to be filled with water.


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(e) Patch the swirl velocity in the bottom third of the bowl.

i. In the Phase drop-down list, select mixture. ii. Choose Swirl Velocity in the Variable list. iii. Enable the Use Field Function option and select swirl-init in the Field Function list. iv. Click Patch. It’s a good idea to check your patch by displaying contours of the patched fields.

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(f) Display contours of swirl velocity. Display −→Contours...

i. Select Velocity... and Swirl Velocity in the Contours Of lists. ii. Enable the Filled option and turn off the Node Values option. Since the values you patched are cell values, you should view the cell values, rather than the node values, to check that the patch has been performed correctly. (FLUENT computes the node values by averaging the cell values.) iii. Click Display. To make the view more realistic, you will need to rotate the display and mirror it across the centerline. (g) Rotate the view and mirror it across the centerline. Display −→Views...


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i. Select axis-2 in the Mirror Planes list and click Apply. ii. Use your middle and left mouse buttons to zoom and translate the view so that the entire bowl is visible in the graphics display. iii. Click on the Camera... button to open the Camera Parameters panel.

iv. Using your left mouse button, rotate the dial clockwise until the bowl appears upright in the graphics window (90◦ ). v. Close the Camera Parameters panel. vi. In the Views panel, click on the Save button under Actions to save the mirrored, upright view, and then close the panel. When you do this, view-0 will be added to the list of Views. The upright view of the bowl in Figure 16.3 correctly shows that w = 3r in the region of the bowl that is filled with water.

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Using the VOF Model

2.35e+00 2.23e+00 2.12e+00 2.00e+00 1.88e+00 1.76e+00 1.65e+00 1.53e+00 1.41e+00 1.29e+00 1.18e+00 1.06e+00 9.41e-01 8.23e-01 7.06e-01 5.88e-01 4.70e-01 3.53e-01 2.35e-01 1.18e-01 0.00e+00

Contours of Swirl Velocity (mixture) (m/s) (Time=0.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.3: Contours of Initial Swirl Velocity


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(h) Display contours of water volume fraction.

i. Select Phases... and Volume fraction of water in the Contours Of lists. ii. Select water in the Phase drop-down list. iii. Set the number of contour Levels to 2 and click Display. There are only two possible values for the volume fraction at this point: 0 or 1.

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Using the VOF Model

1.00e+00

5.00e-01

0.00e+00

Contours of Volume fraction (water) (Time=0.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.4: Contours of Initial Water Volume Fraction Figure 16.4 correctly shows that the bottom third of the bowl contains water. 6. Set the time-step parameters for the calculation. Solve −→Iterate... (a) Set the Time Step Size to 0.002 seconds. (b) Click Apply. This will save the time step size to the case file (the next time a case file is saved). 7. Request saving of data files every 100 time steps. File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency to 0 and the Autosave Data File Frequency to 100.


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(b) Enter the Filename bowl and then click OK. FLUENT will append the time step value to the file name prefix (bowl). The standard .dat extension will also be appended. This will yield file names of the form bowl100.dat, where 100 is the time step number. 8. Save the initial case and data files (bowl.cas and bowl.dat). File −→ Write −→Case & Data... 9. Request 1000 time steps. Solve −→Iterate... Since the time step is 0.002 seconds, you will be calculating up to t= 2 seconds. FLUENT will automatically save a data file after every 0.2 seconds, so you will have 10 data files for postprocessing. Figure 16.5 shows the time history for the axial velocity. The velocity is clearly oscillating, and the oscillations appear to be decaying over time (as the peaks become smaller). This periodic oscillation has a cycle of 1 second. The switch from a positive to a negative axial velocity indicates that the water is sloshing up and down the sides of the bowl in an attempt to reach an equilibrium position. The fact that the amplitude is decaying suggests that equilibrium will be reached at some point. The periodic behavior in evidence will therefore be present only during the initial startup phase of the bowl rotation.

0.3000

0.2000

0.1000

Average of Surface Vertex Values (m/s)

0.0000

-0.1000

-0.2000

-0.3000 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

Flow Time

Convergence history of Axial Velocity on point (Time=2.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.5: Time History of Axial Velocity

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Step 8: Postprocessing As indicated by changes in axial velocity in Figure 16.5, the flow field is oscillating periodically. In this step, you will examine the flow field at several different times. (Recall that FLUENT saved 10 data files for you during the calculation.) 1. Read in the data file of interest. File −→ Read −→Data... 2. Display filled contours of water volume fraction. Display −→Contours... Hint: Follow the instructions in substep 5h of Step 7: Solution (on page 16-28), but turn Node Values back on. Figures 16.6–16.9 show that the water level decreases from t = 0.4 to t = 0.6, then increases from t = 0.6 to t = 1. At t = 1, the water level in the center of the bowl has risen above the initial level, so you can expect the cycle to repeat as the water level begins to decrease again in an attempt to return to equilibrium. (You can read in the data files between t = 1 and t = 2 to confirm that this is in fact what happens. Since the time history of axial velocity (Figure 16.5) shows that the velocity oscillation is decaying over time, you can expect that if you were to continue the calculation, the water level would eventually reach some point where the gravitational and centrifugal forces balance and the water level reaches a new equilibrium point. Extra: Try continuing the calculation to determine how long it takes for the axial velocity oscillations in Figure 16.5 to disappear.


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1.00e+00

5.00e-01

0.00e+00

Contours of Volume fraction (water) (Time=4.0000e-01) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.6: Shape of the Free Surface at t = 0.4

1.00e+00

5.00e-01

0.00e+00



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1.00e+00

5.00e-01

0.00e+00



1.00e+00

5.00e-01

0.00e+00

Contours of Volume fraction (water) (Time=1.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.9: Shape of the Free Surface at t = 1


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3. Plot contours of stream function. (a) Select Stream Function (in the Velocity... category) in the Contours Of dropdown list. (b) Turn off the Filled option and increase the number of contour Levels to 30. (c) Click on Display. In Figures 16.10–16.13, you can see a recirculation region that falls and rises as the water level changes. To get a better sense of these recirculating patterns, you will next look at velocity vectors.

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2.64e+01 2.46e+01 2.29e+01 2.11e+01 1.93e+01 1.76e+01 1.58e+01 1.41e+01 1.23e+01 1.05e+01 8.79e+00 7.03e+00 5.27e+00 3.52e+00 1.76e+00 0.00e+00

Contours of Stream Function (mixture) (kg/s) (Time=4.0000e-01) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.10: Contours of Stream Function at t = 0.4





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8.42e+00 7.86e+00 7.30e+00 6.74e+00 6.18e+00 5.62e+00 5.05e+00 4.49e+00 3.93e+00 3.37e+00 2.81e+00 2.25e+00 1.68e+00 1.12e+00 5.62e-01 0.00e+00

Contours of Stream Function (mixture) (kg/s) (Time=1.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.13: Contours of Stream Function at t = 1

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4. Plot velocity vectors in the bowl. Display −→Vectors...

(a) In the Style drop-down list, select arrow. This will make the velocity direction easier to see. (b) Increase the Scale factor to 6 and increase the Skip value to 1. (c) Click on Vector Options... to open the Vector Options panel.


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i. Turn off the Z Component. This allows you to examine the non-swirling components only. ii. Click Apply and close the panel. (d) Click on Display. Figures 16.14–16.17 show the changes in water and air flow patterns between t = 0.4 and t = 1. In Figure 16.14, you can see that the flow in the middle of the bowl is being pulled down by gravitational forces, and pushed out and up along the sides of the bowl by centrifugal forces. This causes the water level to decrease in the center of the bowl, as shown in the volume fraction contour plots, and also results in the formation of a recirculation region in the air above the water surface. In Figure 16.15, the flow has reversed direction, and is slowly rising up in the middle of the bowl and being pulled down along the sides of the bowl. This reversal occurs because the earlier flow pattern caused the water to overshoot the equilibrium position. The gravity and centrifugal forces now act to compensate for this overshoot.

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1.93e+00 1.80e+00 1.67e+00 1.54e+00 1.42e+00 1.29e+00 1.16e+00 1.03e+00 9.05e-01 7.77e-01 6.49e-01 5.21e-01 3.93e-01 2.65e-01 1.37e-01 8.68e-03

Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=4.0000e-01) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.14: Velocity Vectors for the Air and Water at t = 0.4





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Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=1.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Figure 16.17: Velocity Vectors for the Air and Water at t = 1

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In Figure 16.16 you can see that the flow is rising up more quickly in the middle of the bowl, and in Figure 16.17 you can see that the flow is still moving upward, but more slowly. These patterns correspond to the volume fraction plots at these times. As the upward motion in the center of the bowl decreases, you can expect the flow to reverse as the water again seeks to reach a state of equilibrium. Summary: In this tutorial, you have learned how to use the VOF free surface model to solve a problem involving a spinning bowl of water. The time-dependent VOF formulation is used in this problem to track the shape of the free surface and the flow field inside the spinning bowl. You observed the changing pattern of the water and air in the bowl by displaying volume fraction contours, stream function contours, and velocity vectors at t = 0.4, t = 0.6, t = 0.8, and t = 1 second.


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Tutorial 17.

Modeling Cavitation

Introduction: This tutorial examines the pressure-driven cavitating flow of water through a sharp-edged orifice. This is a typical configuration in fuel injectors, and brings a challenge to the physics and numerics of cavitation models, because of the high pressure differentials involved, and the high ratio of liquid to vapor density. Using FLUENT’s multiphase modeling capability, you will be able to predict the strong cavitation near the orifice after flow separation at a sharp edge. In this tutorial you will learn how to: • Set boundary conditions for internal flow • Use the mixture model with cavitation effects • Calculate a solution using the segregated solver Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem considers the cavitation caused by the flow separation after a sharp-edged orifice. The flow is pressure driven, with an inlet pressure of 5 × 105 Pa, and an outlet pressure of 9.5 × 104 Pa. The orifice diameter is 4 × 10− 3 m, and geometrical parameters of the orifice are D/d = 2.88 and L/d = 8, where D, d, and L are inlet diameter, orifice diameter, and orifice length respectively. The geometry of the orifice is shown in Figure 17.1.

Preparation 1. Copy the file cav/cav.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.


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Modeling Cavitation

pressure inlet = 5e5 Pa

Wall

pressure outlet = 9.5e4 Pa

Axis


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Modeling Cavitation

Step 1: Grid 1. Read the grid file (cav.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...

(a) Display the grid using the default settings (Figure 17.2). As shown in Figure 17.2, half of the problem geometry is modeled, with an axis boundary (consisting of two separate lines) at the centerline. Especially when you begin to display data graphically, you may want to mirror the view across the centerline to obtain a more realistic view of the model. This step will be performed later in the tutorial. The mesh is quadrilateral, slightly graded in the plenum to be finer toward the orifice. In the orifice, the mesh is uniform, with aspect ratios close to 1, as the flow is expected to exhibit two-dimensional gradients.


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Grid


Figure 17.2: The Grid in the Orifice

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Modeling Cavitation

Step 2: Models 1. Specify a steady-state axisymmetric model. Define −→ Models −→Solver... The segregated solver must be used for multiphase calculations.

(a) Under Space, select Axisymmetric. (b) Keep the default settings for everything else. Note: A computationally-intensive unsteady calculation is necessary to accurately simulate the irregular cyclic process of bubble formation, growth, filling by water jet re-entry, and breakoff. In this tutorial, you will perform a steadystate calculation to simulate the presence of a bubble in the separation region in the time-averaged flow.


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2. Enable the multiphase mixture model with cavitation effects. Define −→ Models −→Multiphase... (a) Select Mixture as the Model. The panel will expand. (b) Under Mixture Parameters, turn off the Slip Velocity option. Since there is no significant difference in velocities for the different phases, there is no need to solve for the slip velocity equation. (c) Select Cavitation under Interphase Mass Transfer. The panel will expand again to show the cavitation inputs.

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(d) Enter 3540 for the Vaporization Pressure. The vaporization pressure is a property of the working liquid, which depends mainly on the liquid temperature. The default value is the vaporization pressure of water at a temperature of 300 K. (e) Enter 1.5e-5 for Non Condensable Gas. This is the mass fraction of non condensable gas dissolved in the working liquid. 1.5e − 5 (15 ppm) is a typical value for air dissolved in water. (f) Enter 0.0717 for the Liquid Surface Tension. Like the vaporization pressure, the liquid-vapor surface tension is a property of the liquid, which depends mainly on temperature. Here too, the default value is the surface tension for water and vapor at a temperature of 300 K. 3. Turn on the standard k- turbulence model with standard wall functions. Define −→ Models −→Viscous... (a) Select k-epsilon as the Model.


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(b) Keep the default selection of Standard under k-epsilon Model. The standard k-model used in conjunction with standard wall functions is a suitable choice for this problem. For different cavitation problems, you may use other turbulence models. See Chapter 22 of the User’s Guide for more information on the choice of turbulence models to be used in conjunction with FLUENT’s cavitation model. (c) Keep the default selection of Standard Wall Functions under Near-Wall Treatment.

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Modeling Cavitation

Step 3: Materials 1. Create a new material to be used for the primary phase. Copy water vapor from the materials database so that it can be used for the secondary phase, and modify its density. Define −→Materials... (a) In the Name field, type water. (b) Clear the Chemical Formula field. (c) In the Density drop-down list, keep the default selection of constant, and enter a value of 1000. (d) In the Viscosity drop-down list, keep the default selection of constant, and enter a value of 0.001. (e) Click Change/Create, and then click Yes in the dialog box prompting whether you want to overwrite the definition of air. (f) Click the Database... button in the Materials panel. The Database Materials panel will open.


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Modeling Cavitation

i. In the list of Fluid Materials, select water-vapor (h2o). ii. Click Copy to copy the information for water vapor to your model. iii. Close the Database Materials panel. (g) Change the value of Density for water-vapor (h2o) to 0.02558. (h) Change the value of Viscosity for water-vapor (h2o) to 1.26e-6.

17-10


Modeling Cavitation

Step 4: Phases 1. Define the liquid water and water vapor phases that flow through the orifice. Define −→Phases...

(a) Specify liquid water as the primary phase. i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter liquid for the Name. iii. Select water from the Phase Material drop-down list.


17-11

Modeling Cavitation

(b) Specify water vapor as the secondary phase. i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter vapor for the Name. iii. Select water-vapor from the Phase Material drop-down list.

Step 5: Operating Conditions 1. Set the operating pressure to 0 pascal. Define −→Operating Conditions...

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Modeling Cavitation

Step 6: Boundary Conditions For this problem, you need to set the boundary conditions for two boundaries: the pressure inlet (consisting of two boundary zones), and the pressure outlet. The pressure outlet is the downstream boundary, opposite the pressure inlets. 1. Set the conditions for the pressure inlets (inlet-1, inlet-2). For the multiphase mixture model, you will specify conditions for the mixture (i.e., conditions that apply to all phases) and also conditions that are specific to the primary and secondary phases. In this tutorial, boundary conditions are needed for the mixture and secondary phase only. (a) Set the conditions for the mixture. Define −→Boundary Conditions... i. In the Boundary Conditions panel, keep the default selection of mixture in the Phase drop-down list and click Set.... ii. Enter 500000 for the Gauge Total Pressure. iii. Enter 449000 for the Supersonic/Initial Gauge Pressure. 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 (the Gauge Total Pressure) to compute initial values according to the isentropic relations (for compressible flow) or Bernoulli’s equation (for incompressible flow). Otherwise, in an incompressible flow calculation, the Supersonic/Initial Gauge Pressure input will be ignored by FLUENT. In this problem the velocity will be initialized based on the difference between these two values. iv. In the Direction Specification Method drop-down list, keep the default selection of Normal to Boundary. v. In the Turbulence Specification Method drop-down list, keep the default selection of K and Epsilon. vi. Under Turb. Kinetic Energy, enter 0.02.


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Modeling Cavitation

(b) Check the volume fraction of the secondary phase. i. In the Boundary Conditions panel, select vapor from the Phase drop-down list and click Set....

ii. Keep the default Volume Fraction of 0. (c) Copy the boundary conditions defined for the first pressure inlet zone (inlet-1) to the second one (inlet-2). i. In the Boundary Conditions panel, select mixture from the Phase drop-down list. ii. In the Boundary Conditions panel, click Copy... This will open the Copy BCs panel.

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Modeling Cavitation

iii. Select inlet-1 in the From Zone list, and then select inlet-2 in the To Zones list. iv. Click Copy. 2. Set the boundary conditions for the pressure outlet (outlet). The turbulence conditions you input at the pressure outlet will be used only if flow enters the domain through this boundary. You can set them equal to the inlet values, as no flow reversal is expected at the pressure outlet. In general, however, it is important to set reasonable values for these downstream scalar values, in case flow reversal occurs at some point during the calculation. (a) Set the conditions for the mixture. i. In the Boundary Conditions panel, keep the default selection of mixture in the Phase drop-down list and click Set....


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Modeling Cavitation

ii. Under Gauge Pressure, enter 95000. iii. Keep the default selection of K and Epsilon for the Turbulence Specification Method. iv. Set the Backflow Turb. Kinetic Energy to 0.02. (b) Check the volume fraction of the secondary phase. i. In the Boundary Conditions panel, select vapor from the Phase drop-down list and click Set.... ii. Retain the default Volume Fraction of 0.

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Modeling Cavitation


(a) Under Under-Relaxation Factors, set the under-relaxation factor for Pressure to 0.4. (b) Set the under-relaxation factor for Momentum to 0.4. (c) Scroll down and set the under-relaxation factors for Turbulence Kinetic Energy, Turbulence Dissipation Rate, and Turbulent Viscosity to 0.5. FLUENT’s new cavitation model follows a different numerical approach from the previous one. In general it is more robust and gives more accurate results. Typically, for more complex cases, with very high pressure drops or large liquidvapor density ratios, the under-relaxation factors may need to be reduced to between 0.1 and 0.2. For the Vaporization Mass, it is generally advised to use a value of 0.1, even though for this term you can use an under-relaxation factor of 0.001 to 1, as necessary. (d) Under Discretization, select Linear in the Pressure drop-down list and SIMPLEC in the Pressure-Velocity Coupling drop-down list.


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Modeling Cavitation


(a) Change the convergence criterion for continuity to 1e-7 for improved accuracy. (b) Change all other convergence criteria except for vf-vapor to 1e-5 for improved accuracy. (c) Select Plot under Options, and click OK.

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Modeling Cavitation

3. Initialize the solution from either of the pressure inlet zones (inlet-1 or inlet-2). Solve −→ Initialize −→Initialize...

(a) Select inlet-1 or inlet-2 in the Compute From drop-down list. (b) Under Reference Frame, select Absolute. (c) Click Init to initialize the solution. 4. Save the case file (cav.cas). File −→ Write −→Case... 5. Start the calculation by requesting 2500 iterations. The solution will converge to within the specified criteria in approximately 2100 iterations. Solve −→Iterate... 6. Save the data file (cav.dat). File −→ Write −→Data...


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Modeling Cavitation

Step 8: Postprocessing 1. Plot the pressure in the orifice. Display −→Contours...

(a) Select Pressure... and Static Pressure in the drop-down lists under Contours Of. (b) Select Filled under Options. (c) Click Display. Note the dramatic pressure drop at the flow restriction in Figure 17.3. Low static pressure is the major factor to cause cavitation, though turbulence also contributes to cavitation, due to the effect of pressure fluctuation and turbulent diffusion, as will be shown in the following plots. To make the view more realistic, you will need to mirror it across the centerline.

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Modeling Cavitation


Contours of Static Pressure (mixture) (pascal)

Nov 26, 2002 FLUENT 6.1 (axi, segregated, mixture, ske)



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Modeling Cavitation

2. Mirror the display across the centerline. Display −→Views...

(a) Select symm-1 and symm-2 in the Mirror Planes list and click Apply.



Dec 17, 2002 FLUENT 6.1 (axi, segregated, mixture, ske)

Figure 17.4: Mirrored View of Contours of Static Pressure

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Modeling Cavitation

3. Plot the turbulent kinetic energy. Display −→Contours... (a) Select Turbulence... and Turbulent Kinetic Energy in the drop-down lists under Contours Of. (b) Click Display.


Contours of Turbulent Kinetic Energy (k) (mixture) (m2/s2) Dec 17, 2002 FLUENT 6.1 (axi, segregated, mixture, ske)

Figure 17.5: Contours of Turbulent Kinetic Energy

In this example, the grid used is fairly coarse. However, in cavitating flows the pressure distribution is the dominant factor, and is not very sensitive to grid size. 4. Plot the volume fraction of water vapor. Display −→Contours... (a) Select Phases... and Volume fraction in the drop-down lists under Contours Of. (b) Select vapor in the Phase drop-down list. (c) Click Display.


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Modeling Cavitation


Contours of Volume fraction (vapor)

Dec 17, 2002 FLUENT 6.1 (axi, segregated, mixture, ske)

Figure 17.6: Contours of Vapor Volume Fraction

Note that the high turbulent kinetic energy region near the neck of the orifice (Figure 17.5) coincides with the highest volume fraction of vapor in Figure 17.6. This indicates the correct prediction of a localized high phase change rate. The vapor then gets convected downstream by the main flow. Summary: This tutorial demonstrated how to set up and resolve a strongly cavitating pressure driven flow through an orifice, using FLUENT’s multiphase mixture model with cavitation effects. You learned how to set the boundary conditions for an internal flow. A steady-state solution was calculated to simulate the formation of a vapor bubble in the neck of the flow after the section restriction at the orifice. A more computationally-intensive unsteady calculation is necessary to accurately simulate the irregular cyclic process of bubble formation, growth, filling by water jet re-entry, and breakoff.

17-24


Tutorial 18. Using the Mixture and Eulerian Multiphase Models Introduction: This tutorial examines the flow of water and air in a tee junction. First you will solve the problem using the less computationally-intensive mixture model, and then you will turn to the more accurate Eulerian model. Finally, you will compare the results obtained with the two approaches. In this tutorial you will learn how to: • Use the mixture model with slip velocities • Set boundary conditions for internal flow • Calculate a solution using the segregated solver • Use the Eulerian model • Compare the results obtained with the two approaches Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: This problem considers an air-water mixture flowing upwards in a duct and then splitting in a tee-junction. The ducts are 25 mm in width, the inlet section of the duct is 125 mm long, and the top and the side ducts are 250 mm long. The geometry and data for the problem are shown in Figure 18.1.

Preparation 1. Copy the file tee/tee.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.


18-1

Using the Mixture and Eulerian Multiphase Models

velocity inlet water: v = - 0.31 m/s air: v = - 0.45 m/s

pressure outlet

velocity inlet water: ρ=1000 kg/m3 µ=9e-4 kg/m-s v=1.53 m/s

air: ρ=1.2 kg/m3 µ=2e-5 kg/m-s v=1.6 m/s vol frac=0.02 bubble diam=1


18-2



Step 1: Grid 1. Read the grid file (tee.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...

(a) Display the grid using the default settings (Figure 18.2). Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.


18-3


Grid


Figure 18.2: The Grid in the Tee Junction

18-4



Step 2: Models 1. Keep the default settings for the 2D segregated steady-state solver. Define −→ Models −→Solver... The segregated solver must be used for multiphase calculations.


18-5


2. Enable the multiphase mixture model with slip velocities. Define −→ Models −→Multiphase... (a) Select Mixture as the Model. The panel will expand to show the inputs for the mixture model. (b) Under Mixture Parameters, keep the Slip Velocity turned on. Since there will be significant difference in velocities for the different phases, you need to solve the slip velocity equation. (c) Under Body Force Formulation, select Implicit Body Force. This treatment improves solution convergence by accounting for the partial equilibrium of the pressure gradient and body forces in the momentum equations. It is used when body forces are large in comparison to viscous and convective forces, namely in VOF and mixture problems.

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3. Turn on the standard k- turbulence model with standard wall functions. Define −→ Models −→Viscous...

(a) Select k-epsilon as the Model. (b) Under k-epsilon Model, keep the default selection of Standard. The standard k- model has been found to be quite effective in accurately resolving mixture problems when standard wall functions are used. (c) Keep the default selection of Standard Wall Functions under Near-Wall Treatment. This problem does not require a particularly fine grid, and standard wall functions will be used.


18-7


4. Set the gravitational acceleration. Define −→Operating Conditions... (a) Turn on Gravity. The panel will expand to show additional inputs.

(b) Set the Gravitational Acceleration in the Y direction to -9.81 m/s2 .

18-8



Step 3: Materials 1. Copy liquid water from the materials database so that it can be used for the primary phase. Define −→Materials... (a) Click the Database... button in the Materials panel. The Database Materials panel will open.

(b) In the list of Fluid Materials, select water-liquid (h2o). (c) Click Copy to copy the information for liquid water to your model. (d) Close the Database Materials panel and the Materials panel.


18-9


Step 4: Phases 1. Define the liquid water and air phases that flow in the tee junction. Define −→Phases...

(a) Specify liquid water as the primary phase. i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter water for the Name. iii. Select water-liquid from the Phase Material drop-down list.

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(b) Specify air as the secondary phase. i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter air for the Name. iii. Select air from the Phase Material drop-down list. iv. Set the Diameter to 0.001 m.


18-11


2. Check the slip velocity formulation to be used. (a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, click the Slip tab. (c) Keep the default selection of manninen-et-al in the Slip Velocity drop-down list.

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Step 5: Boundary Conditions For this problem, you need to set the boundary conditions for three boundaries: the upper and lower velocity inlets and the pressure outlet. Define −→Boundary Conditions... 1. Set the conditions for the lower velocity inlet (velocity-inlet-4). For the multiphase mixture model, you will specify conditions at a velocity inlet for the mixture (i.e., conditions that apply to all phases) and also conditions that are specific to the primary and secondary phases. (a) Set the conditions at velocity-inlet-4 for the mixture. i. In the Boundary Conditions panel, keep the default selection of mixture in the Phase drop-down list and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity and Length Scale. iii. Set Turbulence Intensity to 10% and Turbulence Length Scale to 0.025 m.


18-13


(b) Set the conditions for the primary phase. i. In the Boundary Conditions panel, select water from the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to 1.53. (c) Set the conditions for the secondary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to 1.6. iv. Set the Volume Fraction to 0.02.

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2. Set the conditions for the upper velocity inlet (velocity-inlet-5). (a) Set the conditions at velocity-inlet-5 for the mixture. i. In the Boundary Conditions panel, select mixture in the Phase drop-down list and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity and Length Scale. iii. Set Turbulence Intensity to 10% and Turbulence Length Scale to 0.025 m. (b) Set the conditions for the primary phase. i. In the Boundary Conditions panel, select water from the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to -0.31. In this problem, outflow characteristics at the upper velocity inlet are assumed to be known, and therefore imposed as a boundary condition.


18-15


(c) Set the conditions for the secondary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to -0.45. iv. Set the Volume Fraction to 0.02.

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3. Set the boundary conditions for the pressure outlet (pressure-outlet-3). For the multiphase mixture model, you will specify conditions at a pressure outlet for the mixture and for the secondary phase. There are no conditions to be set for the primary phase. The turbulence conditions you input at the pressure outlet will be used only if flow enters the domain through this boundary. You can set them equal to the inlet values, as no flow reversal is expected at the pressure outlet. In general, however, it is important to set reasonable values for these downstream scalar values, in case flow reversal occurs at some point during the calculation. (a) Set the conditions at pressure-outlet-3 for the mixture. i. In the Boundary Conditions panel, select mixture in the Phase drop-down list and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity and Length Scale. iii. Set the Backflow Turbulence Intensity to 10%. iv. Set the Backflow Turbulence Length Scale to 0.025. (b) Set the conditions for the secondary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set.... ii. Set the Backflow Volume Fraction to 0.02.


18-17


Step 6: Solution Using the Mixture Model 1. Set the solution parameters. Solve −→ Controls −→Solution...

(a) Keep all default Under-Relaxation Factors. (b) Under Discretization, select PRESTO! in the Pressure drop-down list. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual...

18-18




4. Save the case file (tee.cas). File −→ Write −→Case... 5. Start the calculation by requesting 1000 iterations. Solve −→Iterate... The solution will converge in approximately 600 iterations. 6. Save the case and data files (tee.cas and tee.dat). File −→ Write −→Case & Data...


18-19


Step 7: Postprocessing for the Mixture Solution 1. Display the pressure field in the tee (Figure 18.3). Display −→Contours...

(a) Select Pressure... and Static Pressure in the Contours Of drop-down lists. (b) Select Filled under Options. (c) Click Display.

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2.34e+03 2.15e+03 1.95e+03 1.76e+03 1.56e+03 1.36e+03 1.17e+03 9.73e+02 7.77e+02 5.81e+02 3.85e+02 1.89e+02 -7.51e+00 -2.04e+02 -4.00e+02 -5.96e+02 -7.92e+02 -9.88e+02 -1.18e+03 -1.38e+03 -1.58e+03


Nov 18, 2002 FLUENT 6.1 (2d, segregated, mixture, ske)



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2. Display contours of velocity magnitude (Figure 18.4). Display −→Contours... (a) Select Velocity... and Velocity Magnitude in the Contours Of drop-down lists. (b) Click Display.


Contours of Velocity Magnitude (mixture) (m/s)


Figure 18.4: Contours of Velocity Magnitude 3. Display the volume fraction of air (Figure 18.5). Display −→Contours... (a) Select Phases... and Volume fraction in the Contours Of drop-down lists. (b) Select air in the Phase drop-down list. (c) Click Display. In Figure 18.5, note the small bubble of air that separates at the sharp edge of the horizontal arm of the tee junction, and the small layer of air that floats in the same area above the water, marching towards the pressure outlet.

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Contours of Volume fraction (air)


Figure 18.5: Contours of Air Volume Fraction


18-23


Step 8: Setup and Solution for the Eulerian Model You will use the solution obtained with the mixture model as an initial condition for the calculation with the Eulerian model. 1. Turn on the Eulerian model. Define −→ Models −→Multiphase...

(a) Under Models, select Eulerian.

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2. Specify the drag law to be used for computing the interphase momentum transfer. Define −→Phases... (a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, keep the default selection of schiller-naumann in the Drag Coefficient drop-down list. Note: For this problem there are no parameters to be set for the individual phases, other than those that you specified when you set up the phases for the mixture model calculation. If you use the Eulerian model for a flow involving a granular secondary phase, there are additional parameters that you need to set. There are also other options in the Phase Interaction panel that may be relevant for other applications. See the User’s Guide for complete details on setting up an Eulerian multiphase calculation.


18-25


3. Select the multiphase turbulence model. Define −→ Models −→Viscous...

(a) Under k-epsilon Multiphase Model, keep the default selection of Mixture. The mixture turbulence model 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. See Chapter 22 of the User’s Guide for more information on turbulence models for the Eulerian multiphase model.

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4. Continue the solution by requesting 1000 additional iterations. Solve −→Iterate... The solution will converge after about 300 additional iterations. 5. Save the case and data files (tee2.cas and tee2.dat). File −→ Write −→Case & Data...


18-27


Step 9: Postprocessing for the Eulerian Model 1. Display the pressure field in the tee (Figure 18.6). Display −→Contours...

2.54e+03 2.34e+03 2.14e+03 1.94e+03 1.75e+03 1.55e+03 1.35e+03 1.15e+03 9.54e+02 7.55e+02 5.57e+02 3.59e+02 1.61e+02 -3.74e+01 -2.36e+02 -4.34e+02 -6.32e+02 -8.30e+02 -1.03e+03 -1.23e+03 -1.42e+03


Nov 18, 2002 FLUENT 6.1 (2d, segregated, eulerian, ske)


2. Display contours of velocity magnitude for the water (Figure 18.7). Display −→Contours... (a) In the Contours Of drop-down lists, select Velocity... and water Velocity Magnitude. Because the Eulerian model solves individual momentum equations for each phase, you have the choice of which phase to plot solution data for. (b) Click Display. 3. Display the volume fraction of air (Figure 18.8). Display −→Contours... Note that the air bubble at the tee junction in Figure 18.8 is slightly different from the one that you observed in the solution obtained with the mixture model (Figure 18.5). The Eulerian model generally offers better accuracy than the mixture model, as it solves separate sets of equations for each individual phase, rather than modeling slip velocity between phases. See Chapter 22 of the User’s Guide for more information about the mixture and Eulerian models.

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Contours of Velocity Magnitude (water) (m/s)


Figure 18.7: Contours of Water Velocity Magnitude


Contours of Volume fraction (air)


Figure 18.8: Contours of Air Volume Fraction


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Summary: This tutorial demonstrated how to set up and solve a multiphase problem using the mixture model and the Eulerian model. You learned how to set boundary conditions for the mixture and both phases. The solution obtained with the mixture model was used as a starting point for the calculation with the Eulerian model. After completing calculations with both models, you compared the results obtained with the two approaches.

18-30


Tutorial 19. Using the Eulerian Multiphase Model for Granular Flow Introduction: Mixing tanks are used to maintain solid particles or droplets of heavy fluids in suspension. Mixing may be required to enhance reaction during chemical processing or to prevent sedimentation. In this tutorial, you will use the Eulerian multiphase model to solve the particle suspension problem. The Eulerian multiphase model solves momentum equations for each of the phases, which are allowed to mix in any proportion. In this tutorial you will learn how to: • Use the granular Eulerian multiphase model • Specify fixed velocities with a user-defined function (UDF) to simulate an impeller • Set boundary conditions for internal flow • Calculate a solution using the segregated solver • Solve a time-accurate transient problem Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem involves the transient startup of an impellerdriven mixing tank. The primary phase is water, while the secondary phase consists of sand particles with a 111 micron diameter. The sand is initially settled at the bottom of the tank, to a level just above the impeller. A schematic of the mixing tank and the initial sand position is shown in Figure 19.1. The domain is modeled as 2D axisymmetric. The fixed-values option will be used to simulate the impeller. Experimental data are used to represent the time-averaged velocity and turbulence values at the impeller location. This approach avoids the need to model the impeller itself. These experimental data are provided in a user-defined function.


19-1

Using the Eulerian Multiphase Model for Granular Flow

.4446 m

.016 m water .4446 m

impeller settled .1728 m sand bed .116 m

.0864 m


19-2



Preparation 1. Copy the files mixtank/mixtank.msh and mixtank/fix.c from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.

Step 1: Grid 1. Read the grid file (mixtank.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid... (a) Display the grid using the default settings (Figure 19.2). Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.


19-3


Grid



19-4



(b) Click the Colors... button. This will open the Grid Colors panel. The Grid Colors panel allows you to control the colors that are used to draw grids.

i. In the Grid Colors panel, select Color By ID. This will assign a different color to each zone in the domain, rather than to each type of zone. (c) In the Grid Display panel, click Display. (Figure 19.3). The graphics display will be updated to show the grid.

Grid


Figure 19.3: Grid Display (Color by ID option)


19-5


4. Manipulate the grid display to show the full tank upright. Display −→Views...

(a) Under Mirror Planes, select axis. (b) Click Apply. The grid display will be updated to show both sides of the tank. (c) Click Auto Scale. This option is used to scale and center the current display without changing its orientation (Figure 19.4).

Grid


Figure 19.4: Grid Display with Both Sides of the Tank

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(d) Click on Camera... to display the tank in an upright position. This will open the Camera Parameters panel.

(e) Click with the left mouse button on the indicator of the dial and drag it in the counter-clockwise direction till the upright view is displayed (Figure 19.5). (f) Click Apply and close the Camera Parameters and Views panels.

Grid


Figure 19.5: Grid Display of the Upright Tank Note: 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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Step 2: Models 1. Specify a transient, axisymmetric model. Define −→ Models −→Solver...

(a) Retain the default Segregated solver. The segregated solver must be used for multiphase calculations. (b) Under Space, select Axisymmetric. (c) Under Time, select Unsteady.

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2. Enable the Eulerian multiphase model. Define −→ Models −→Multiphase... (a) Select Eulerian as the Model. The panel will expand to show the inputs for the Eulerian model.

(b) Keep the default settings for the Eulerian model. 3. Turn on the k- turbulence model with standard wall functions. Define −→ Models −→Viscous...


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(a) Select k-epsilon as the Model. (b) Keep the default selection of Standard Wall Functions under Near-Wall Treatment. This problem does not require a particularly fine grid, and standard wall functions will be used. (c) Under k-epsilon Multiphase Model, select the Dispersed model. The dispersed turbulence model is applicable in this case because there is clearly one primary continuous phase and the material density ratio of the phases is about 2.5. Furthermore, the Stokes number is much less than 1. Therefore, the particle’s kinetic energy will not depart significantly from that of the liquid. 4. Set the gravitational acceleration. Define −→Operating Conditions... (a) Turn on Gravity. The panel will expand to show additional inputs.

(b) Set the Gravitational Acceleration in the X direction to -9.81 m/s2 .

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Step 3: Materials In this step, you will add liquid water to the list of fluid materials by copying it from the materials database, and create a new material called sand. Define −→Materials... 1. Copy liquid water from the materials database so that it can be used for the primary phase. (a) Click the Database... button in the Materials panel. The Database Materials panel will open.

(b) In the list of Fluid Materials, select water-liquid (h2o). (c) Click Copy to copy the information for liquid water to your model. (d) Close the Database Materials panel.


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2. Create a new material called sand.

(a) Type the name sand in the Name text-entry box. (b) Under Properties, enter 2500 kg/m3 as the Density. (c) Remove the entry for Chemical Formula so the field is blank. (d) Click on Change/Create and close the Materials panel. When you click Change/Create, a question dialog box will appear, asking you if water-liquid should be overwritten. Click No to retain water-liquid and add the new material, sand, to the list. The Materials panel will be updated to show the new material name in the Fluid Materials list.

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Step 4: Phases 1. Define the primary (water) and secondary (sand) phases. Define −→Phases...

(a) Specify water as the primary phase. i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter water for the Name. iii. Select water-liquid from the Phase Material drop-down list.


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(b) Specify sand as the secondary phase. i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter sand for the Name. iii. Select sand from the Phase Material drop-down list. iv. Turn on the Granular option. v. Define the properties of the sand phase. A. Enter 0.000111 as the Diameter. B. Select syamlal-obrien from the Granular Viscosity drop-down list. C. Select lun-et-al from the Granular Bulk Viscosity drop-down list. D. Enter 0.6 as the Packing Limit.

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(c) Specify the drag law to be used for computing the interphase momentum transfer. i. Click the Interaction... button in the Phases panel.

ii. In the Phase Interaction panel, select gidaspow in the Drag Coefficient dropdown list.


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Step 5: Boundary Conditions For this problem, there are no conditions to be specified on the outer boundaries. Within the domain, there are three fluid zones, representing the impeller region, the region where the sand is initially located, and the rest of the tank. There are no conditions to be specified in the latter two zones, so you will need to set conditions only in the zone representing the impeller. As mentioned earlier, a UDF is used to specify the fixed velocities that simulate the impeller. The values of the time-averaged impeller velocity components and turbulence quantities are based on experimental measurement. The variation of these values may be expressed as a function of radius, and imposed as polynomials according to: variable = A1 + A2 r + A3 r2 + A4 r3 + ... The order of polynomial to be used depends on the behavior of the function being fitted. For this tutorial, the polynomial coefficients shown in Table 19.1 are provided in the UDF fix.c. Table 19.1: Impeller Profile Specifications Variable A1 A2 A3 u velocity -7.1357e-2 54.304 -3.1345e+3 v velocity 3.1131e-2 -10.313 9.5558e+2 kinetic energy 2.2723e-2 6.7989 -424.18 dissipation -6.5819e-2 88.845 -5.3731e+3 Variable A4 A5 A6 u velocity 4.5578e+4 -1.9664e+5 – v velocity -2.0051e+4 1.1856e+5 – kinetic energy 9.4615e+3 -7.7251e+4 1.8410e+5 dissipation 1.1643e+5 -9.1202e+5 1.9567e+6

See the separate UDF Manual for details about setting up a UDF using the DEFINE PROFILE macro. Note that, while this macro is usually used to specify a profile condition on a boundary face zone, it is used in fix.c to specify the condition in a fluid cell zone. The arguments of the macro have been changed accordingly.

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1. Compile the UDF, fix.c, using the Interpreted UDFs panel. Define −→ User-Defined −→ Functions −→Interpreted...

(a) Enter fix.c under Source File Name. !

Make sure that the C source code for your UDF and your mesh file reside in your working directory. If your source code is not in your working directory, then when you compile the UDF you must enter the file’s complete path in the Interpreted UDFs panel, instead of just the filename.

(b) Keep the default Stack Size setting of 10000. (c) Turn on the Display Assembly Listing option. Turning on the Display Assembly Listing option will cause a listing of the assembly language code to appear in your console window when the function compiles. (d) Click Compile to compile your UDF. Note: The name and contents of your UDF will be stored in your case file when you write the case file.


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2. Set the conditions for the fluid zone representing the impeller (fix-zone). You will specify the conditions for the water and the sand separately. There are no conditions to be specified for the mixture (i.e., conditions that apply to all phases); the default conditions for the mixture are acceptable. Define −→Boundary Conditions... (a) Set the conditions on fix-zone for the water. All of the conditions for the water will come from the UDF. i. In the Boundary Conditions panel, select water from the Phase drop-down list and click Set....

ii. Turn on the Fixed Values option. The panel will expand to show the related inputs. iii. Select udf fixed u from the drop-down list to the right of Axial Velocity. iv. Select udf fixed v for Radial Velocity. v. Select udf fixed ke for Turbulence Kinetic Energy. vi. Select udf fixed diss for Turbulence Dissipation Rate.

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(b) Set the conditions on fix-zone for the sand. All of the conditions for the sand will come from the UDF. i. In the Boundary Conditions panel, select sand from the Phase drop-down list and click Set....

ii. Turn on the Fixed Values option. The panel will expand to show the related inputs. iii. Select udf fixed u for Axial Velocity. iv. Select udf fixed v for Radial Velocity.


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(a) For the Under-Relaxation Factors, set Pressure to 0.5, Momentum to 0.2, and Turbulent Viscosity to 0.8. (b) Under Discretization, keep the default settings. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual... 3. Initialize the solution using the default initial values. Solve −→ Initialize −→Initialize...

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4. Patch the initial sand bed configuration. Solve −→ Initialize −→Patch...

(a) Select sand in the Phase drop-down list. (b) In the Variable list, select Volume Fraction. (c) Select initial-sand in the Zones To Patch list. (d) Set the Value to 0.56. (e) Click Patch. 5. Set the time stepping parameters. Solve −→Iterate... (a) Set the Time Step Size to 0.005. (b) Under Iteration, set the Max Iterations per Time Step to 40. (c) Click Apply.


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6. Save the initial case and data files (mixtank.cas and mixtank.dat). File −→ Write −→Case & Data... The problem statement is now complete. As a precaution, you should review the impeller velocity fixes and sand bed patch after running the calculation for a single time step. Since you are using a UDF for the velocity profiles, you need to perform one time step in order for the profiles to be calculated and available for viewing. 7. Run the calculation for 0.005 seconds. Solve −→Iterate... (a) Set the Number of Time Steps to 1. (b) Click Iterate.

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8. Check the initial velocities and sand volume fraction. In order to display the initial velocities in the fluid zone where you have fixed their values (fix-zone), you will need to create a zone surface for it. (a) Create a zone surface for fix-zone. Surface −→Zone...

i. In the Zone list, select fix-zone. ii. Under New Surface Name, retain the default name. The default name is the same as the zone name. FLUENT will automatically assign the default name to the new surface when it is created. iii. Click on Create and close the panel. The new surface will be added to the Surfaces list in the Zone Surface panel.


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(b) Display the initial impeller velocities for water. Display −→Vectors...

i. Select Velocity in the Vectors Of drop-down list. ii. Select water in the Phase drop-down list. iii. Select Velocity... and Velocity Magnitude in the Color By drop-down lists. iv. Select water in the Phase drop-down list below the Color By drop-down lists.

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v. In the Surfaces list, select fix-zone. vi. In the Style drop-down list, select arrow. vii. Click Display. FLUENT will display the water velocity vector fixes at the impeller location, as shown in Figure 19.6.


water-velocity Colored By Velocity Magnitude (water) (m/s) (Time=5.0000e-03) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.6: Initial Impeller Velocities for Water


19-25


(c) Display the initial impeller velocities for sand. Display −→Vectors... i. Select sand in the Phase drop-down list below the Vectors Of drop-down list. ii. Select sand in the Phase drop-down list below the Color By drop-down lists. iii. Click Display. FLUENT will display the sand velocity vector fixes at the impeller location, as shown in Figure 19.7.


sand-velocity Colored By Velocity Magnitude (sand) (m/s) (Time=5.0000e-03) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.7: Initial Impeller Velocities for Sand

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(d) Display contours of sand volume fraction. Display −→Contours...

i. Select Phases... and Volume fraction in the Contours Of drop-down lists. ii. Select sand in the Phase drop-down list. iii. Select Filled under Options. iv. Click Display. FLUENT will display the initial location of the settled sand bed, shown in Figure 19.8. 9. Run the calculation for 1 second. Solve −→Iterate... (a) Set the Number of Time Steps to 199. (b) Click Iterate. After 200 time steps have been computed (a total of 1 second of operation), you will review the results before continuing. 10. Save the case and data files (mixtank1.cas and mixtank1.dat). File −→ Write −→Case & Data...


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Contours of Volume fraction (sand) (Time=5.0000e-03) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.8: Initial Settled Sand Bed

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11. Examine the results of the calculation after 1 second. (a) Display the velocity vectors in the whole tank for the water. Display −→Vectors... !

Remember to deselect fix-zone in the Surfaces list.

Figure 19.9 shows the water velocity vectors after 1 second of operation. The circulation is confined to the region near the impeller, and has not yet had time to develop in the upper portions of the tank.


water-velocity Colored By Velocity Magnitude (water) (m/s) (Time=1.0000e+00) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.9: Water Velocity Vectors after 1 Second (b) Display the velocity vectors for the sand. Display −→Vectors... Figure 19.10 shows the sand velocity vectors after 1 second of operation. The circulation of sand around the impeller is significant, but note that no sand vectors are plotted in the upper part of the tank, where the sand is not yet present.


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sand-velocity Colored By Velocity Magnitude (sand) (m/s) (Time=1.0000e+00) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.10: Sand Velocity Vectors after 1 Second

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(c) Display contours of sand volume fraction. Display −→Contours... Notice that the action of the impeller draws clear fluid from above the originally settled bed and mixes it into the sand. To compensate, the sand bed is lifted up slightly. The maximum sand volume fraction has decreased as a result of the mixing of water and sand.


Contours of Volume fraction (sand) (Time=1.0000e+00) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.11: Contours of Sand Volume Fraction after 1 Second 12. Continue the calculation for another 19 seconds. Solve −→Iterate... (a) Set the Time Step Size to 0.01. The initial calculation was performed with a very small time step size to stabilize the solution. After the initial calculation, you can usually increase the time step to speed up the calculation. (b) Set the Number of Time Steps to 1900. (c) Click Iterate. The transient calculation will continue to 20 seconds. 13. Save the case and data files (mixtank20.cas and mixtank20.dat). File −→ Write −→Case & Data...


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Step 7: Postprocessing You will now examine the progress of the sand and water in the mixing tank after a total of 20 seconds.The mixing tank has nearly, but not quite, reached a steady flow solution. 1. Display the velocity vectors for the water. Display −→Vectors... Figure 19.12 shows the water velocity vectors after 20 seconds of operation. The circulation of water is now very strong in the lower portion of the tank, though modest near the top.


water-velocity Colored By Velocity Magnitude (water) (m/s) (Time=2.0000e+01) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.12: Water Velocity Vectors after 20 Seconds

2. Display the velocity vectors for the sand. Display −→Vectors... Figure 19.13 shows the sand velocity vectors after 20 seconds of operation. The sand has now been suspended much higher within the mixing tank, but does not reach the upper region of the tank. The water velocity in that region is not sufficient to overcome the gravity force on the sand particles. 3. Display contours of sand volume fraction. Display −→Contours... Figure 19.14 shows the contours of sand volume fraction after 20 seconds of operation.

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sand-velocity Colored By Velocity Magnitude (sand) (m/s) (Time=2.0000e+01) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.13: Sand Velocity Vectors after 20 Seconds


Contours of Volume fraction (sand) (Time=2.0000e+01) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.14: Contours of Sand Volume Fraction after 20 Seconds


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4. Display filled contours of static pressure in the mixing tank. (a) Select Pressure... and Static Pressure in the Contours Of drop-down lists. (b) Select mixture in the Phase drop-down list. (c) Click Display. Figure 19.15 shows the pressure distribution after 20 seconds of operation. Notice that the pressure field represents the hydrostatic pressure except for some slight deviations due to the flow of the impeller near the bottom of the tank.

1.51e+02 6.12e+01 -2.83e+01 -1.18e+02 -2.07e+02 -2.97e+02 -3.86e+02 -4.76e+02 -5.65e+02 -6.55e+02 -7.44e+02 -8.33e+02 -9.23e+02 -1.01e+03 -1.10e+03 -1.19e+03

Contours of Static Pressure (mixture) (pascal) (Time=2.0000e+01) Nov 14, 2002 FLUENT 6.1 (axi, segregated, eulerian, ske, unsteady)

Figure 19.15: Contours of Pressure after 20 Seconds

Summary: This tutorial demonstrated how to set up and solve a granular multiphase problem using the Eulerian multiphase model. The problem involved the 2D modeling of particle suspension in a mixing tank, and postprocessing showed the nearsteady-state behavior of the sand in the mixing tank, under the assumptions made.

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Tutorial 20.

Modeling Solidification

Introduction: This tutorial illustrates how to set up and solve a problem involving solidification. In this tutorial, you will learn how to: • Define a solidification problem • Define pull velocities for simulation of continuous casting • Define a surface tension gradient for Marangoni convection • Solve a solidification problem Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: This tutorial demonstrates the setup and solution procedure for a fluid flow and heat transfer problem involving solidification, namely the Czochralski growth process. The geometry considered is a 2D axisymmetric bowl (shown in Figure 20.1), containing a liquid metal. The bottom and sides of the bowl are heated above the liquidus temperature, as is the free surface of the liquid. The liquid is solidified by heat loss from the crystal and the solid is pulled out of the domain at a rate of 0.001 m/s and a temperature of 500 K. There is a steady injection of liquid at the bottom of the bowl with a velocity of 1.01 × 10−3 and a temperature of 1300 K. Material properties are listed in Figure 20.1. Starting with an existing 2D mesh, the details regarding the setup and solution procedure for the solidification problem are presented. The steady conduction solution for this problem is computed as an initial condition. Then, the fluid flow is turned on to investigate the effect of natural and Marangoni convection in an unsteady fashion.

Preparation 1. Copy the file solid/solid.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D version of FLUENT.


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T = 1400 K

g

Free Surface 2

h = 100 W/m K T = 1500 K env

T = 1300 K

0.05 m 0.1 m T = 500 K u = 0.001 m/s T = 500 K u = 0.00101 m/s 0.03 m Ω = 1 rad/s

T = 1300 K

Mushy Region

Crystal

0.1 m

ρ µ k cp ∂σ/∂T Tsolidus Tliquidus L Amush

= 8000 − 0.1*T kg/m = 5.53 x 10-3 kg/m-s = 30 W/m-K = 680 J/kg-K = −3.6 x 10-4 N/m-K = 1100 K = 1200 K 5 = 1 x 10 J/kg = 1 x 104 kg/m3-s

3

Figure 20.1: Solidification in Czochralski model

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Step 1: Grid 1. Read the mesh file solid.msh. File −→ Read −→Case... As this mesh is read by FLUENT, messages appear in the console window reporting the progress of the reading. 2. Check the grid. Grid −→Check FLUENT performs various checks on the mesh and reports the progress in the console window. Pay particular attention to the minimum volume. Make sure this is a positive number. 3. Display the grid (Figure 20.2). Display −→ Grid...

Grid

Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam)

Figure 20.2: Graphics Display of Grid


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Step 2: Models 1. Enable the modeling of axisymmetric swirl. Define −→ Models −→Solver...

(a) Under Space, select Axisymmetric Swirl. (b) Keep the default settings for everything else.

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2. Define the solidification model. Define −→ Models −→Solidification & Melting... (a) Under Model, turn on Solidification/Melting. The panel will expand to show the related inputs.

(b) Under Parameters, keep the default value for the Mushy Zone Constant. The default value of 100000 is acceptable for most cases. (c) Turn on Include Pull Velocities. The panel will expand to show an additional input. Including the pull velocities accounts for the movement of the solidified material as it is continuously withdrawn from the domain in the continuous casting process. Note: It is possible to have FLUENT compute the pull velocities during the calculation, but this approach is computationally expensive, and is recommended only if the pull velocities are strongly dependent on the location of the liquid-solid interface. In this tutorial, you will patch values for the pull velocities instead of having FLUENT compute them. See the User’s Guide for more information. Note: When you click OK in the Solidification/Melting panel, FLUENT will present an Information dialog box telling you that available material properties have changed for the solidification model. You will be setting properties later, so you can simply click OK in the dialog box to acknowledge this information. Note: FLUENT will automatically enable the energy calculation when you enable the solidification model, so you need not visit the Energy panel.


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3. Add the effect of gravity on the model. Define −→Operating Conditions...

(a) Turn on Gravity. The panel will expand to show additional inputs. (b) Set the Gravitational Acceleration in the X direction to -9.81 m/s2 .

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Step 3: Materials In this step, you will create a new material and specify its properties, including the melting heat, solidus temperature, and liquidus temperature. Define −→Materials...

1. In the Name field, enter liquid-metal. 2. Specify the density as a function of temperature. As shown in Figure 20.1, the density of the material is defined by a polynomial function: ρ = 8000 − 0.1T . (a) Select Polynomial in the Density drop-down list. The Polynomial Profile panel will open.


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(b) Increase the value of Coefficients to 2. (c) Enter 8000 for coefficient 1 and -0.1 for coefficient 2. When you click OK in the Polynomial Profile panel, a question dialog box will appear, asking you if air should be overwritten. Click No to retain air and add the new material, liquid-metal, to the list. The Materials panel will be updated to show the new material name in the Fluid Materials list. You will need to select liquid-metal in the Fluid Materials drop-down list to set the other material properties. 3. Set the specific heat, Cp, to 680 J/kg-K. 4. Set the Thermal Conductivity to 30 W/m-K. 5. Set the Viscosity to 0.00553 kg/m-s. 6. Set the Melting Heat to 100000 J/kg. 7. Set the Solidus Temperature to 1100 K. 8. Set the Liquidus Temperature to 1200 K. 9. Click on Change/Create and close the Materials panel.

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Step 4: Boundary Conditions Define −→Boundary Conditions... 1. Set the boundary conditions for the fluid.

(a) Select liquid-metal in the Material Name drop-down list. 2. Set the boundary conditions for the velocity inlet.

(a) Set the Velocity Magnitude to 0.00101 m/s. (b) Set the Temperature to 1300 K.


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3. Set boundary conditions for the outlet. Here, the solid is pulled out with a specified velocity, so a velocity inlet is used with the velocities pointing outwards.

(a) In the Velocity Specification Method drop-down list, select Components. The panel will change to show related inputs. (b) Set the Axial-Velocity to 0.001 m/s. (c) Set the Swirl Angular Velocity to 1 rad/s. (d) Set the Temperature to 500 K.

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4. Set the boundary conditions for the bottom wall.

(a) Select Temperature under Thermal Conditions. (b) Set the Temperature to 1300 K.


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5. Set the boundary conditions for the free surface. 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. A free surface condition is an example of such a situation. In this case, the conduction is Marangoni stress driven and the shear stress is dependent on the surface tension, which is a function of temperature.

(a) Specify the thermal conditions. i. Select Convection under Thermal Conditions. The panel will change to show related inputs. ii. Set the Heat Transfer Coefficient to 100 W/m2 -K. iii. Set the Free Stream Temperature to 1500 K.

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(b) Specify the shear conditions. i. Click the Momentum tab. The wall motion and shear condition will be displayed.

ii. Under Shear Condition, select Marangoni Stress. The Marangoni Stress condition allows you to specify the gradient of the surface tension with respect to temperature at a wall boundary. iii. Set the Surface Tension Gradient to -0.00036 N/m-K. 6. Set the boundary conditions for the side wall. (a) Select Temperature under Thermal Conditions. (b) Set the Temperature to 1400 K.


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7. Set the boundary conditions for the solid wall. (a) Specify the thermal conditions. i. Select Temperature under Thermal Conditions. ii. Set the Temperature to 500 K. (b) Specify the wall motion. i. Click the Momentum tab.

ii. Under Wall Motion, select Moving Wall. The panel will expand to show additional parameters. iii. Under Motion, select Rotational. The panel changes to show the rotational speed. iv. Under Speed, set the rotational velocity to 1.0 rad/s.

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Step 5: Solution: Steady Conduction In this step, you will disable the calculation of the flow and swirl velocity equations, and calculate the conduction only. This steady-state solution will be used as the initial condition for the time-dependent fluid flow and heat transfer calculation. 1. Set the solution parameters. In this step, you will specify the discretization schemes to be used, and temporarily turn off the calculation of the flow and swirl velocity equations. Solve −→ Controls −→Solution...

(a) In the Equations list, deselect Flow and Swirl Velocity. (b) Keep the default values for all Under-Relaxation Factors. (c) Under Discretization, select PRESTO! for Pressure, SIMPLE for Pressure-Velocity Coupling, and First Order Upwind for Momentum, Swirl Velocity, and Energy.


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(a) Check that the value for Temperature is set to 300 K. Since you are solving only the steady conduction problem, the initial values for the pressure and velocities will not be used. (b) Click on Init and Close the panel.

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3. Define a custom field function for the swirl pull velocity. You will use this field function to patch a variable value for the swirl pull velocity in the next step. The swirl pull velocity is equal to Ωr, where Ω is the angular velocity and r is the radial coordinate. Since Ω = 1 rad/s, you can simplify the equation to simply r. In this example, the value of Ω is included for demonstration purposes. Define −→Custom Field Functions...

(a) In the Field Functions drop-down lists, select Grid... and Radial Coordinate. (b) Click the Select button. radial-coordinate will appear in the Definition field. If you make a mistake, click the DEL button on the calculator pad to delete the last item you added to the function definition. (c) Click the X button on the calculator pad. (d) Click on 1. (e) Enter omegar as the New Function Name. (f) Click Define and close the panel. If you wish to check the function definition, click on Manage... and select omegar.


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4. Patch the pull velocities. As noted earlier, you will patch values for the pull velocities, rather than having FLUENT compute them. Since the radial pull velocity is zero, you will patch just the axial and swirl pull velocities. Solve −→ Initialize −→Patch...

(a) Specify the value of the axial pull velocity. i. In the Variable list, select Axial Pull Velocity. ii. Select fluid in the Zones To Patch list. iii. Set the Value to 0.001 m/s. iv. Click Patch.

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(b) Specify the value of the swirl pull velocity.

i. In the Variable list, select Swirl Pull Velocity. ii. Enable the Use Field Function option. iii. Select omegar in the Field Function list. iv. Click Patch.


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(a) Under Options, select Plot. (b) Click OK. 6. Save the initial case and data files (solid0.cas and solid0.dat). File −→ Write −→Case & Data... 7. Start the calculation by requesting 20 iterations. Solve −→Iterate...

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8. Display filled contours of temperature (Figure 20.3). Display −→Contours...

(a) Under Options, select Filled. (b) Select Temperature... and Static Temperature in the Contours Of drop-down lists. (c) Click Display. The thickness of the mushy zone can be determined from the contours of temperature. The mushy zone is the region where the temperature is between the liquidus temperature and solidus temperature. 9. Save the case and data files for the steady conduction solution (solid.cas and solid.dat). File −→ Write −→Case & Data...


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Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam)

Figure 20.3: Contours of Temperature for Steady Conduction Solution

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Step 6: Solution: Unsteady Flow and Heat Transfer In this step, you will turn on time dependence and include the flow and swirl velocity equations in the calculation. You will then solve the unsteady problem using the steady conduction solution as the initial condition. 1. Enable a time-dependent solution. Define −→ Models −→Solver...

(a) Under Time, select Unsteady. (b) Under Unsteady Formulation, retain 1st-Order Implicit. 2. Enable the solution of the flow and swirl velocity equations. Solve −→ Controls −→Solution... (a) Select Flow and Swirl Velocity in the Equations list and keep the selection of Energy. Now all three items in the Equations list will be selected. (b) Keep the default values for all Under-Relaxation Factors. (c) Under Discretization, retain the settings for all parameters.


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3. Save the initial case and data files (solid01.cas and solid01.dat). File −→ Write −→Case & Data... 4. Run the calculation for 2 time steps. Solve −→Iterate...

(a) Under Time, set the Time Step Size to 0.1 seconds. (b) Set the Number of Time Steps to 2. (c) Under Iteration, retain the default value of 20 for Max Iterations per Time Step. (d) Click Iterate. 5. Examine the results of the calculation after 0.2 seconds. (a) Display filled contours of temperature (Figure 20.4). Display −→Contours... i. Select Temperature... and Static Temperature in the Contours Of dropdown lists. ii. Click Display. The temperature contours show the gradient in temperature from the hot walls on the left to the cooler zone on the right.

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Contours of Static Temperature (k) (Time=2.0000e-01) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.4: Contours of Temperature at t = 0.2 s (b) Display contours of stream function (Figure 20.5). i. Under Options, deselect Filled. ii. Select Velocity... and Stream Function in the Contours Of drop-down lists. iii. Click Display. As shown in Figure 20.5, the liquid is beginning to circulate in a large eddy, driven by natural convection and Marangoni convection on the free surface. (c) Display contours of liquid fraction (Figure 20.6). i. Under Options, select Filled. ii. Select Solidification/Melting... and Liquid Fraction in the Contours Of dropdown lists. iii. Click Display. The liquid fraction contours show the current position of the melt front. Note that in Figure 20.6, the mushy zone divides the liquid and solid regions roughly in half. 6. Continue the calculation for 48 additional time steps. Solve −→Iterate... After a total of 50 time steps have been completed, the elapsed time will be 5 seconds.


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Contours of Stream Function (kg/s) (Time=2.0000e-01) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.5: Contours of Stream Function at t = 0.2 s


Contours of Liquid Fraction (Time=2.0000e-01)

Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.6: Contours of Liquid Fraction at t = 0.2 s

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7. Examine the results of the calculation after 5 seconds. (a) Display filled contours of temperature (Figure 20.7).


Contours of Static Temperature (k) (Time=5.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.7: Contours of Temperature at t = 5 s As shown in Figure 20.7, the temperature contours are fairly uniform through the melt front and solid material. The distortion of the temperature field due to the recirculating liquid is also clearly evident. In a continuous casting process, it is important to pull out the solidified material at the proper time. If the material is pulled out too soon, it will not have solidified; that is, it will still be in a mushy state. If it is pulled out too late, it solidifies in the casting pool and cannot be pulled out in the required shape. The optimal rate of pull can be determined from the contours of liquidus temperature and solidus temperature.


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(b) Display contours of stream function (Figure 20.8). Display −→Contours...


Contours of Stream Function (kg/s) (Time=5.0000e+00) Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.8: Contours of Stream Function at t = 5 s Note that the flow has developed more fully now, as compared with Figure 20.5 after 0.2 seconds. The main eddy, driven by natural convection and Marangoni stress, dominates the flow. To examine the position of the melt front and the extent of the mushy zone, you will plot the contours of liquid fraction. (c) Display filled contours of liquid fraction (Figure 20.9). The introduction of liquid material at the left of the domain is balanced by the pulling of the solidified material from the right. After 5 seconds, the equilibrium position of the melt front is beginning to be established. 8. Save the case and data files for the solution at 5 seconds (solid5.cas and solid5.dat). File −→ Write −→Case & Data...

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Contours of Liquid Fraction (Time=5.0000e+00)

Nov 18, 2002 FLUENT 6.1 (axi, swirl, segregated, lam, unsteady)

Figure 20.9: Contours of Liquid Fraction at t = 5 s


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Summary: In this tutorial, you studied the setup and solution for a fluid flow problem involving solidification for the Czochralski growth process. The solidification model in FLUENT can be used to model the continuous casting process where a solid material is continuously pulled out from the casting domain. In this tutorial, you patched a constant value and a custom field function for the pull velocities instead of computing them. For cases where the pull velocity is not changing over the domain, this approach is used as it is computationally less expensive than having FLUENT compute the pull velocities during the calculation. For more information about the solidification/melting model, see the User’s Guide.

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Tutorial 21. Using the Eulerian Granular Multiphase Model with Heat Transfer Introduction: This tutorial examines the flow of air and a granular solid phase consisting of glass beads in a hot gas fluidized bed, in uniform minimum fluidization conditions. Finally, you will compare the results obtained for the local wall-to-bed heat transfer coefficient in FLUENT with analytical results. In this tutorial you will learn how to: • Use the Eulerian granular model • Set boundary conditions for internal flow • Use a user defined function (UDF) to specify a phase-specific velocity inlet profile • Calculate a solution using the segregated solver • Compare the results obtained with analytical results. Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have solved or read Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: This problem considers a hot gas fluidized bed in which air flows upwards through the bottom of the domain and through an additional small orifice next to a heated wall. For this problem, a uniformly fluidized bed is examined, for the sake of comparison with analytical results [1]. The geometry and data for the problem are shown in Figure 21.1.


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Using the Eulerian Granular Multiphase Model with Heat Transfer

pressure outlet 101325 Pa

insulated wall

heated wall T = 373 K

0.598 volume fraction of solids

uniform velocity inlet u = 0.25 m/s T = 293 K

orifice u = 0.25 m/s T = 293 K


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Preparation 1. Copy the files fluid-bed/fluid-bed.msh and fluid-bed/gasvel.c from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 2D double-precision version of FLUENT.

Step 1: Grid 1. Read the grid file (fluid-bed.msh). File −→ Read −→Case... As FLUENT reads the grid file, it will report its progress in the console window. 2. Check the grid. Grid −→Check FLUENT will perform various checks on the mesh and will report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number. 3. Display the grid. Display −→Grid...


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Grid (Time=0.0000e+00)

Nov 25, 2002 FLUENT 6.1 (2d, dp, segregated, lam, unsteady)

Figure 21.2: The Grid in the Fluidized Bed (a) Display the grid using the default settings (Figure 21.2). Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries in the graphics window, its zone number, name, and type will be printed in the FLUENT console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.

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Step 2: Models 1. Keep the default settings for the 2D segregated unsteady solver. The segregated solver must be used for multiphase calculations. Define −→ Models −→Solver... (a) Under Time, select Unsteady.


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2. Enable the Eulerian multiphase model with 2 phases. Define −→ Models −→Multiphase...

(a) Select Eulerian as the Model. (b) Click OK in the dialog box that appears. Although for this problem you will be using the Eulerian granular multiphase model with heat transfer, no further inputs are necessary in the Multiphase model panel. You will set the conditions for the granular phase and heat transfer in the next steps. 3. Enable heat transfer by activating the energy equation. Define −→ Models −→Energy...

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4. Keep the default laminar model. Experiments have shown negligible three-dimensional effects in the flow field for the case modeled, suggesting very weak turbulent behavior. Define −→ Models −→Viscous...

5. Set the gravitational acceleration. Define −→Operating Conditions...

(a) Turn on Gravity. The panel will expand to show additional inputs. (b) Set the Gravitational Acceleration in the Y direction to -9.81 m/s2 .


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Step 3: Materials 1. Read in and compile the user-defined functions. Define −→ User-Defined −→ Functions −→Compiled...

(a) Under Source Files, click Add... A Select File panel will open. (b) In the Select File panel, select the source code gasvel.c, which includes all the user-defined macros you will need to run this tutorial, and click OK. (c) In the Compiled UDFs panel, click Build. FLUENT will build a libudf directory and compile the UDF. (d) Click OK in the dialog box that will appear. (e) Click Load to open the directory and load the UDF. 2. Modify the properties for air, which will be used for the primary phase. The properties used for air are modified to match data used by Kuipers et al. [1] Define −→Materials... (a) Specify 1.2 for Density. (b) Specify 994 for Cp. (c) In the Thermal Conductivity drop-down list, select user-defined. The User Defined Functions panel will automatically open. (d) In the User Defined Functions panel, select conduct gas, and click OK. (e) Click Change/Create.

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3. Define a new fluid material for the granular phase (the glass beads).

(a) In the Name field, enter solids. (b) Specify 2660 for the Density. (c) Specify 737 for Cp. (d) Keep the current selection of user-defined in the Thermal Conductivity dropdown list, and click Edit... (e) In the User Defined Functions panel, select conduct solid, and click OK. (f) Click No in the dialog box asking if you want to overwrite air. (g) Select solids under Fluid Materials. (h) Click Change/Create.


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Step 4: Phases 1. Define the air and granular phases that exist in the fluidized bed. Define −→Phases... (a) Specify air as the primary phase. i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter air for the Name. iii. Select air from the Phase Material drop-down list. iv. Click OK. (b) Specify the glass beads as the secondary phase. i. Select phase-2 and click the Set... button.

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ii. In the Secondary Phase panel, enter solids for the Name. iii. Select solids from the Phase Material drop-down list. iv. Turn on Granular. v. Set the Diameter to 0.0005 m. vi. In the Granular Viscosity drop-down list, select syamlal-obrien. vii. In the Granular Bulk Viscosity drop-down list, select lun-et-al. viii. In the Granular Conductivity drop-down list, select syamlal-obrien. Hint: You will have to scroll down in the Properties list to change the settings for some of the properties. ix. Click OK. The Phases panel is now updated.


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2. Check the inter-phase interactions formulations to be used. (a) Click the Interaction... button in the Phases panel.

(b) In the Drag Coefficient drop-down list, select syamlal-obrien. (c) Click the Heat tab, and select gunn in the Heat Transfer Coefficient drop-down list. For this problem, you will be simulating interphase heat exchange, using a drag coefficient, the default restitution coefficient for granular collisions of 0.9, and a heat transfer coefficient. Granular phase lift is not very relevant in this problem, and in fact is rarely used. (d) Click OK.

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Step 5: Boundary Conditions For this problem, you need to set the boundary conditions for all boundaries. Define −→Boundary Conditions... 1. Set the conditions for the lower velocity inlet (v uniform). For the Eulerian multiphase model, you will specify conditions at a velocity inlet that are specific to the primary and secondary phases. (a) Set the conditions at v uniform for the primary phase. i. In the Boundary Conditions panel, select air in the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to 0.25. iv. Set the Temperature to 293. v. Click OK. (b) Set the conditions at v uniform for the secondary phase. i. In the Boundary Conditions panel, select solids from the Phase drop-down list and click Set.... ii. Keep the default Velocity Specification Method and Reference Frame. iii. Keep the default value of 0 for the Velocity Magnitude. iv. Set the Temperature to 293. v. Set the Granular Temperature to 0.0001. vi. Keep the default value of 0 for the Volume Fraction. vii. Click OK.


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2. Set the conditions for the orifice velocity inlet (v jet). (a) Set the conditions at v jet for the primary phase. i. In the Boundary Conditions panel, select air in the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Set the Velocity Magnitude to 0.25. In order for a comparison with analytical results [1] to be meaningful, in this simulation you will use a uniform value for the air velocity equal to the minimum fluidization velocity at both inlets on the bottom of the bed. iv. Set the Temperature to 293. v. Click OK.

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(b) Set the conditions at v jet for the secondary phase. i. In the Boundary Conditions panel, select solids from the Phase drop-down list and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame. iii. Keep the default value of 0 for the Velocity Magnitude. iv. Set the Temperature to 293. v. Set the Granular Temperature to 0.0001. vi. Keep the default value of 0 for the Volume Fraction. vii. Click OK. 3. Set the boundary conditions for the pressure outlet (poutlet). For the Eulerian granular model, you will specify conditions at a pressure outlet for the mixture and for both phases. The thermal conditions at the pressure outlet will be used only if flow enters the domain through this boundary. You can set them equal to the inlet values, as no flow reversal is expected at the pressure outlet. In general, however, it is important to set reasonable values for these downstream scalar values, in case flow reversal occurs at some point during the calculation. (a) Set the conditions at poutlet for the mixture. i. In the Boundary Conditions panel, select mixture in the Phase drop-down list and click Set.... ii. Keep the default value of 0 for the Gauge Pressure. iii. Click OK.


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(b) Set the conditions for the primary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set....

ii. Set the Backflow Total Temperature to 293. iii. Click OK. (c) Set the conditions for the secondary phase. i. In the Boundary Conditions panel, select solids from the Phase drop-down list and click Set....

ii. Set the Backflow Total Temperature to 293. iii. Set the Backflow Granular Temperature to 0.0001. iv. Set the Backflow Volume Fraction to 0. v. Click OK.

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4. Set the boundary conditions for the heated wall (wall hot). For the heated wall, you will set thermal conditions for the mixture, and momentum conditions (zero shear) for both phases. (a) Set the conditions for the mixture. i. In the Boundary Conditions panel, select mixture from the Phase drop-down list and click Set....

ii. Select Temperature under Thermal Conditions, and input 373 for the Temperature. iii. Click OK.


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(b) Set the conditions for the primary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set....

ii. Click the Momentum tab. iii. Select Specified Shear under Shear Condition (the panel will expand), and keep the default values of 0 for the X-Component and Y-Component. (c) Set the conditions for the secondary phase. For the secondary phase, you will set the same conditions of zero shear as for the primary phase.

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5. Set the boundary conditions for the adiabatic wall (wall ins). For the adiabatic wall, you will retain the default thermal conditions for the mixture (zero heat flux), and set momentum conditions (zero shear) for both phases. (a) Set the conditions for the primary phase. i. In the Boundary Conditions panel, select air from the Phase drop-down list and click Set....

ii. Select Specified Shear under Shear Condition (the panel will expand), and keep the default values of 0 for the X-Component and Y-Component. iii. Click OK. (b) Set the conditions for the secondary phase. For the secondary phase, you will set the same conditions of zero shear as for the primary phase.


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(a) Set the under-relaxation factor for Pressure to 0.5. (b) Set the under-relaxation factor for Momentum to 0.2. (c) Set the under-relaxation factor for Volume Fraction to 0.5. You will have to scroll the Under Relaxation Factors list to display the underrelaxation factor for Volume Fraction. (d) Keep all default Discretization schemes. (e) Click OK. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual...

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3. Define a surface monitor for the heat transfer coefficient at a point surface in the cell next to the wall, on a plane of y = 0.24. (a) Define a custom field function for the heat transfer coefficient. First you will define functions for the mixture temperature, and thermal conductivity, then you will use these to define a function for the heat transfer coefficient. Define −→Custom Field Functions... i. Define function t mix. A. In the Field Functions drop-down list, select Temperature... and Static Temperature. B. In the Phase drop-down list, select air, and click Select. C. Click the multiplication symbol in the calculator pad. D. In the Field Functions drop-down list, select Phases... and Volume Fraction. E. In the Phase drop-down list, select air, and click Select. F. Click the addition symbol in the calculator pad. G. Repeat the steps above to add the term solids-temperature * solids-vof. H. In the New Function Name field, enter t mix as the name of the defined function. I. Click Define.


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ii. Define function k mix. A. In the Field Functions drop-down list, select Properties.... B. In the Phase drop-down list, select air C. Set the property as Thermal Conductivity and click Select. D. Click the multiplication symbol in the calculator pad. E. In the Field Functions drop-down list, select Phases... and Volume Fraction. F. In the Phase drop-down list, select air, and click Select. G. Click the addition symbol in the calculator pad. H. Repeat the steps above to add the term solids-thermalconductivity-lam * solids-vof. I. In the New Function Name field, enter k mix. J. Click Define.

iii. Define function ave htc. A. Click the subtraction symbol in the calculator pad. B. In the Field Functions drop-down list, select Custom Field Functions... and t mix. C. Use the calculator pad and the Field Functions list as you did in the previous steps to complete the definition of the function as shown below. −k mix × (t mix − 373)/(58.5 × 10(−6) )/80

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D. In the New Function Name field, enter ave htc. E. Click Define.

(b) Define the point surface on the plane y = 0.24. Surface −→Point...

i. Under Coordinates, enter 0.28494 for x0, and 0.24 for y0. ii. Enter y=0.24 for the New Surface Name. iii. Click Create.


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(c) Define the surface monitor for the heat transfer coefficient. Solve −→ Monitors −→Surface... i. Increase the number of Surface Monitors to 1. ii. Enable Plot, Print, and Write for monitor-1. iii. In the Every drop-down list, select Time Step, and click Define... The Define Surface Monitor panel will open.

iv. Enter htc in the Name field. v. In the Report Type drop-down list, select Vertex Average. vi. In the X Axis drop-down list, select Flow Time. vii. Increase the Plot Window to 1. viii. In the Report Of drop-down lists, select Custom Field Functions..., and ave htc. ix. In the Surfaces list, select y=0.24. x. Under File Name, enter htc-024. xi. Click OK. xii. Click OK in the Surface Monitors panel.

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(a) Under Initial Values, set air Temperature to 293. (b) Set solids Granular Temperature to 0.0001. (c) Set solids Temperature to 293. (d) Click Apply to save the above settings. (e) Click Init.


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5. Define an adaption register for the lower half of the fluidized bed. You will use this register to patch the initial volume fraction of solids in the next step. Adapt −→Region... (a) Under Input Coordinates, specify the Xmaximum value as 0.3 and the Ymaximum value as 0.5. (b) Click Mark.

(c) Click Manage... The Manage Adaption Registers panel will open. (d) Under Registers, in the Manage Adaption Registers panel, select hexahedron-r0, and click Display. After you define a region for adaption, it is good practice to display it to visually verify that it encompasses the intended area.

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6. Patch the initial volume fraction of solids in the lower half of the fluidized bed. Solve −→ Initialize −→Patch...

(a) In the Phase drop-down list, select solids. (b) In the Variable drop-down list, select Volume Fraction. (c) In the Value field, enter 0.598. (d) In the Registers to Patch list, select hexahedron-r0. (e) Click Patch. At this point, it is good practice to display contours of the variable you just patched, to ensure that the desired field was obtained. 7. Display contours of Volume Fraction of solids. Display −→Contours... 8. Save the case file (fluid-bed.cas). File −→ Write −→Case...


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Contours of Volume fraction (solids) (Time=0.0000e+00) Nov 25, 2002 FLUENT 6.1 (2d, dp, segregated, eulerian, lam, unsteady)

Figure 21.3: Initial Volume Fraction of Granular Phase (solids).

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9. Set a time step size of 0.00025 s and start the calculation by requesting 7000 time steps. Solve −→Iterate... The plot of the value of the mixture-averaged heat transfer coefficient in the cell next to the heated wall versus time is in excellent agreement with results published for the same case [1].

1600.0000 1400.0000 1200.0000 1000.0000

Average of Surface Vertex Values

800.0000 600.0000 400.0000 200.0000 0.0000 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000

Flow Time

Convergence history of ave_htc on y=0.24 (Time=1.7500e+00) Nov 25, 2002 FLUENT 6.1 (2d, dp, segregated, eulerian, lam, unsteady)

Figure 21.4: Plot of Mixture-Averaged Heat Transfer Coefficient in the Cell Next to the Heated Wall Versus Time

10. Save the case and data files (fluid-bed.cas and fluid-bed.dat). File −→ Write −→Case & Data... Extra: If you decide to read in the case file that is provided for this tutorial on the documentation CD, you will need to compile the UDF associated with this tutorial in your working directory. This is necessary because FLUENT will expect to find the correct UDF libraries in your working directory when reading the case file.


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Step 7: Postprocessing 1. Display the pressure field in the fluidized bed. Display −→Contours...

(a) Select Pressure... and Static Pressure in the Contours Of drop-down lists. (b) Select Filled under Options. (c) Click Display. Note the build-up of static pressure in the granular phase. 2. Display the volume fraction of solids. Display −→Contours... (a) Select Phases... and Volume fraction in the Contours Of drop-down lists. (b) Select solids in the Phase drop-down list. (c) Click Display. (d) Zoom in to show the contours close to the region where the change in volume fraction is the greatest.

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7.79e+03 7.40e+03 7.01e+03 6.62e+03 6.23e+03 5.84e+03 5.45e+03 5.06e+03 4.68e+03 4.29e+03 3.90e+03 3.51e+03 3.12e+03 2.73e+03 2.34e+03 1.95e+03 1.56e+03 1.17e+03 7.79e+02 3.90e+02 -4.96e-02

Contours of Static Pressure (mixture) (pascal) (Time=1.7500e+00) Nov 25, 2002 FLUENT 6.1 (2d, dp, segregated, eulerian, lam, unsteady)



Contours of Volume fraction (solids) (Time=1.7500e+00) Nov 25, 2002 FLUENT 6.1 (2d, dp, segregated, eulerian, lam, unsteady)

Figure 21.6: Contours of Volume Fraction of Solids


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Note that the region occupied by the granular phase has expanded slightly, as a result of fluidization. Summary: This tutorial demonstrated how to set up and solve a granular multiphase problem with heat transfer, using the Eulerian model. You learned how to set boundary conditions for the mixture and both phases. The solution obtained is in excellent agreement with analytical results from Kuipers et al. [1]. References: 1. J. A. M. Kuipers, W. Prins, and W. P. M. Van Swaaij “Numerical Calculation of Wall-to-Bed Heat Transfer Coefficients in Gas-Fluidized Beds”, Department of Chemical Engineering, Twente University of Technology, in AIChE Journal, July 1992, Vol. 38, No. 7.

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Tutorial 22.

Postprocessing

Introduction: In this tutorial, the postprocessing capabilities of FLUENT are demonstrated for a 3D laminar flow involving conjugate heat transfer. The flow is over a rectangular heat-generating electronics chip which is mounted on a flat circuit board. The heat transfer involves the coupling of conduction in the chip and conduction and convection in the surrounding fluid. The physics of conjugate heat transfer such as this is common in many engineering applications, including the design and cooling of electronic components. In this example, you will read the case and data files (without doing the calculation) and perform a number of postprocessing exercises. In the process, you will learn how to: • Create surfaces for the display of 3D data • Display velocity vectors • Display filled contours of temperature on several surfaces • Mirror a display about a symmetry plane • Add lights to the display at multiple locations • Use the Scene Description and Animate panels to animate the graphics display • Use the Sweep Surface panel to display results on successive slices of the domain • Display pathlines • Plot quantitative results • Overlay and “explode” a display • Annotate your display Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Problem Description: The problem to be considered is shown schematically in Figure 22.1. The configuration consists of a series of side-by-side electronic chips, or modules, mounted on a circuit board. Air flow, confined between the circuit board and an upper wall, cools the modules. To take advantage of the symmetry present in the problem, the model will extend from the middle of one module to the plane of symmetry between it and the next module.


22-1

Postprocessing

As shown in the figure, each half-module is assumed to generate 2.0 Watts and to have a bulk conductivity of 1.0 W/m2 -K. The circuit board conductivity is assumed to be one order of magnitude lower: 0.1 W/m2 -K. The air flow enters the system at 298 K with a velocity of 1 m/s. The Reynolds number of the flow, based on the module height, is about 600. The flow is therefore treated as laminar.

Symmetry Planes Top Wall Externally Cooled Bottom Wall Externally Cooled Air Flow 1.0 m/s 298 K

Electronic Module (one half) k = 1.0 W/m2-K Q = 2.0 Watts Circuit Board k = 0.1 W/m2-K Figure 22.1: Problem Specification

Preparation 1. Copy the files chip/chip.cas and chip/chip.dat from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 3D version of FLUENT.

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Postprocessing

Step 1: Reading the Case and Data Files 1. Read in the case and data files (chip.cas and chip.dat). File −→ Read −→Case & Data... Once you select chip.cas, chip.dat will be read automatically.

Step 2: Grid Display 1. Display the grid. Display −→Grid...

(a) Under Options, select Edges. (b) In the Surfaces list, select board-top and chip. (c) Click Display. Note: You may want to scroll through the Surfaces list to be sure that no other surfaces are selected. You can also deselect all surfaces by clicking on the farright button at the top of the Surfaces list, and then select the desired surfaces for display.


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Postprocessing

Y X Z

Grid


Figure 22.2: Graphics Display of the Chip and Board Surfaces

2. Use your left mouse button to rotate the view, and your middle mouse button to zoom the view until you obtain an enlarged isometric display of the circuit board in the region of the chip, as shown in Figure 22.2. Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries displayed in the graphics window, its zone number, name, and type will be printed in the console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly. 3. Create a filled surface display. (a) In the Grid Display panel under Options, deselect Edges and select Faces. (b) Click Display. The surfaces run together with no shading to separate the chip from the board.

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Postprocessing

4. Add shading effects by enabling lights. Display −→Options...

(a) Under Lighting Attributes, enable the Lights On. (b) Click Apply. Shading will be added to the surface grid display (Figure 22.3).

Y X Z

Grid


Figure 22.3: Graphics Display of the Chip and Board Surfaces with Default Lighting


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Postprocessing

(c) In the Display Options panel, click on the Lights... button. This will open the Lights panel.

Note: When you turn lights on, the default settings are for light 0 (indicated by the Light ID), corresponding to a white light at the position (1, 1, 1), as indicated by the unit vectors under Direction. (d) Add a light at (-1,1,1). i. Increase the Light ID to 1 and enable the Light On option. ii. Set X, Y, and Z to -1, 1, and 1. iii. Click Apply. (e) Repeat this procedure to add a second light (Light ID=2) at (-1,1,-1). The result is a more softly shaded display (Figure 22.4). Note: The Lights panel contains a Headlight On option that is turned on by default. When you create additional lights using this panel, FLUENT will automatically turn on a light in the direction of the flow. You can turn off the headlight by deselecting the Headlight On option (Figure 22.5).

Extra: You can use your left mouse button to rotate the ball in the Active Lights window in the Lights panel, as shown below. By doing so, you can gain a perspective view on the relative locations of the lights that are currently active, and see the shading effect on the ball at the center.

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Postprocessing

Y X Z

Grid


Figure 22.4: Graphics Display of the Chip and Board Surfaces with Additional Lighting

Y X Z

Grid


Figure 22.5: Graphics Display of the Chip and Board Surfaces with Additional Lighting: Headlight Off


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Postprocessing

You can also change the color of one or more of the lights by typing the name of a color in the Color field or moving the Red, Green, and Blue sliders.

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Postprocessing

Step 3: Isosurface Creation To display results in a 3D model, you will need surfaces on which the data can be displayed. FLUENT creates surfaces for all boundary zones automatically. In the case file that you have read, several of these surfaces have been renamed. Examples are board-sym and board-ends, which correspond to the side and end faces of the circuit board. In general, you may want to define additional surfaces for the purpose of viewing your results, such as a plane in Cartesian space, for example. In this exercise, you will create a horizontal plane cutting through the middle of the module. This surface will have a y value of 0.25 inches, and will be used in a later step for displaying the temperature and velocity fields. 1. Create a surface of constant y coordinate. Surface −→Iso-Surface...

(a) In the Surface of Constant drop-down lists, select Grid... and Y-Coordinate. (b) Click Compute. The Min and Max fields will display the y extents of the domain. (c) Enter 0.25 under Iso-Values. (d) Enter y=0.25in under New Surface Name. (e) Click Create, and Close the panel.


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Postprocessing

Step 4: Contours 1. Plot filled contours of temperature on the symmetry plane (Figure 22.6). Display −→Contours...

(a) Under Options, select Filled. (b) Select Temperature... and Static Temperature in the Contours Of drop-down lists. (c) In the Surfaces list, select board-sym, chip-sym, and fluid-sym. (d) Click Display. The temperature contour will be displayed. (e) Rotate and zoom the display using the left and middle mouse buttons, respectively, to obtain the view shown in Figure 22.6. Hint: If the display disappears from the screen at any time, or if you are having difficulty manipulating it with the mouse, you can open the Views panel from the Display pull-down menu and use the Default button to reset the view. Alternatively, you can revert to a previous graphics display using the keyboard shortcut -L. Hint: You can revert to previous views in the graphics display window using the keyboard shortcut -L.

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Postprocessing


Y X Z



Figure 22.6: Filled Contours of Temperature on the Symmetry Surfaces

Note the peak temperatures in the chip where the heat is generated, along with the higher temperatures in the wake where the flow is recirculating. 2. Plot filled contours of temperature on the horizontal plane at y=0.25 in (Figure 22.7). (a) In the Contours panel under Surfaces, deselect the symmetry planes and select y=0.25in. (b) Click Display. (c) Zoom the display using your middle mouse button to obtain the view shown in Figure 22.7. In the contour display (Figure 22.7), the high temperatures in the wake of the module are clearly visible. You may want to display other quantities using the Contours panel, such as velocity magnitude or pressure).


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Postprocessing


Y X Z



Figure 22.7: Filled Contours of Temperature on the y = 0.25 in. Surface

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Postprocessing

Step 5: Velocity Vectors Velocity vectors provide an excellent visualization of the flow around the module, depicting details of the wake structure. 1. Display velocity vectors on the symmetry plane through the module centerline (Figure 22.8). Display −→Vectors...

(a) In the Surfaces list, select fluid-sym. (b) Set the Scale Factor to 1.9. (c) Click Display. (d) Rotate and zoom the display to observe the vortex near the stagnation point and in the wake of the module (Figure 22.8). Note: The vectors in Figure 22.8 are shown without arrowheads. You can modify the arrow style in the Vectors panel by selecting a different option from the Style drop-down list.


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Postprocessing


Y X Z



Figure 22.8: Velocity Vectors in the Module Symmetry Plane

Extra: If you want to decrease the number of vectors displayed, you can increase the Skip factor to a non-zero value.

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Postprocessing

2. Plot velocity vectors in the horizontal plane intersecting the module (Figure 22.10). After plotting the vectors, you will enhance your view by mirroring the display about the module centerline and by adding the display of the module surfaces. Display −→Vectors...

(a) Deselect all surfaces by clicking the unshaded icon to the right of Surfaces. (b) In the Surfaces list, select y=0.25in. (c) Set the Scale to 3.8. (d) Under Options, select Draw Grid. This will open the Grid Display panel.


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Postprocessing

(e) Under Options, check that Faces is selected. (f) In the Surfaces list, select board-top and chip. (g) Click Colors.... This will open the Grid Colors panel.

(h) In the Types list, select wall. (i) In the Colors list, select light blue, and then Close the panel. (j) In the Grid Display panel, click Display and then Close the panel. (k) Use your mouse to obtain the view shown in Figure 22.9. (l) In the Vectors panel, click Display. (m) Rotate the display with your mouse to obtain the view shown in Figure 22.10.

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Postprocessing

Y X Z

Grid


Figure 22.9: Filled Surface Display for the Chip and Board Top


Y X Z



Figure 22.10: Velocity Vectors and Chip and Board Top Surfaces


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Postprocessing

3. Mirror the view about the chip symmetry plane (Figure 22.11). Display −→Views...

(a) In the Mirror Planes list, select symmetry-18. Note: This zone is the centerline plane of the module, and its selection will create a mirror of the entire display about the centerline plane. (b) Click Apply. The display will be updated in your graphics window (Figure 22.11). Extra: You may want to experiment with different views and/or scale factors for the velocities to examine different regions (upstream and downstream of the chip, for example).

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Postprocessing


Y X Z



Figure 22.11: Velocity Vectors and Chip and Board Top Surfaces after Mirroring


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Postprocessing

Step 6: Animation The surface temperature distribution on the module and on the circuit board can be displayed by selecting these boundaries for display of temperature contours. You can then view the display dynamically, using the animation feature. While effective animation is best conducted on “high-end” graphics workstations, you can follow the procedures below on any workstation. If your graphics display speed is slow, the animation playback will take some time and will appear choppy, with the redrawing very obvious. On fast graphics workstations, the animation will appear smooth and continuous and will provide an excellent visualization of the display from a variety of spatial orientations. On many machines, you can improve the smoothness of the animation by turning on the Double Buffering option in the Display Options panel. 1. Display filled contours of surface temperature on the board-top and chip, excluding the symmetry surfaces (Figure 22.12). Display −→Contours...

(a) Under Options, select Filled. (b) Select Temperature... and Static Temperature in the Contours Of drop-down lists. (c) Deselect all surfaces by clicking the unshaded icon to the right of Surfaces. (d) In the Surfaces list, select board-top and chip.

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Postprocessing

(e) Click Display. (f) Zoom the display as needed to obtain the view shown in Figure 22.12.


Y X Z



Figure 22.12: Filled Temperature Contours on the Chip and Board Top Surfaces The temperature display (Figure 22.12) shows the high temperatures on the downstream portions of the module and the relatively localized heating of the circuit board around the module. 2. Animate the surface temperature display by changing the point of view. Display −→Scene Animation...


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Postprocessing

You will use the current display (Figure 22.12) as the starting view for the animation (Frame = 1). (a) Under Key Frames, click Add. This will store the current display as Key-1. (b) Zoom the view to focus on the module region. (c) Under Key Frames, change the Frame number to 10. (d) Click Add. This will store the new display as Key-10.

The zoomed view will be the tenth keyframe of the animation, with intermediate displays (2 through 9) to be filled in during the animation. (e) Rotate the view and un-zoom the display so that the downstream side of the module is in the foreground, as shown in Figure 22.13. (f) Change the Frame number to 20. (g) Click Add. This will store the new display as Key-20. 3. To animate the view, click on the “play” arrow button (second from the right in the row of playback buttons) in the Playback section of the Animate panel. Note: You can also make use of FLUENT’s animation tools for transient cases as demonstrated in Tutorial 4. Extra: You can change the Playback mode if you want to “auto repeat” or “auto reverse” the animation. When you are in either of these Playback modes, you can click on the “stop” button (square) to stop the continuous animation.

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Postprocessing

4.09e+02 4.03e+02 3.98e+02 3.92e+02 3.87e+02 3.81e+02 3.76e+02 3.70e+02 3.64e+02 3.59e+02 3.53e+02 3.48e+02 3.42e+02 3.37e+02 3.31e+02 3.26e+02 3.20e+02 3.15e+02 3.09e+02 Y 3.04e+02 X 2.98e+02Z



Figure 22.13: Filled Temperature Contours on the Chip and Board Top Surfaces


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Postprocessing

Step 7: Displaying Pathlines Pathlines are the lines traveled by neutrally buoyant particles in equilibrium with the fluid motion. Pathlines are an excellent tool for visualization of complex three-dimensional flows. In this example, you will use pathlines to examine the flow around and in the wake of the module. 1. Create a rake from which the pathlines will emanate. Surface −→Line/Rake...

(a) In the Type drop-down list, select Rake. A rake surface consists of a specified number of points equally spaced between two specified endpoints. A line surface (the other option in the Type list) is a line that includes the specified endpoints and extends through the domain; data points on a line surface will not be equally spaced. (b) Keep the default of 10 for the Number of Points along the rake. This will generate 10 pathlines. (c) Under End Points, enter the coordinates of the line, using a starting coordinate of (1.0, 0.105, 0.07) and an ending coordinate of (1.0, 0.25, 0.07), as shown in the panel above. This will define a vertical line in front of the module, about halfway between the centerline and edge.

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Postprocessing

(d) Enter pathline-rake for the New Surface Name. You will refer to the rake by this name when you plot the pathlines. (e) Click Create, and Close the panel. 2. Draw the pathlines (Figure 22.14). Display −→Path Lines...

(a) In the Release From Surfaces list, select pathline-rake. (b) Set the Step Size to 0.001 inch and the number of Steps to 6000. Note: A simple rule of thumb to follow when you are 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. (c) Under Options, select Draw Grid. This will open the Grid Display panel. (d) In the Surfaces list, select board-top and chip. These surfaces should already be selected from the earlier exercise where the grid was displayed with velocity vectors, Step 5: Velocity Vectors. (e) Under Options, check that Faces is selected, and then Close the panel. (f) In the Path Lines panel, click Display. The pathlines will be drawn on the surface.


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Postprocessing

9.00e+00 8.55e+00 8.10e+00 7.65e+00 7.20e+00 6.75e+00 6.30e+00 5.85e+00 5.40e+00 4.95e+00 4.50e+00 4.05e+00 3.60e+00 3.15e+00 2.70e+00 2.25e+00 1.80e+00 1.35e+00 9.00e-01 4.50e-01 0.00e+00

Y X Z



Figure 22.14: Pathlines Shown on a Display of the Chip and Board Surfaces.

(g) Rotate the display so that the flow field in front and in the wake of the chip is visible, as shown in Figure 22.14. 3. Display pathlines as spheres. Display −→Path Lines...

(a) In the Release From Surfaces list, keep the selection of pathline-rake.

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Postprocessing

(b) Select sphere from the Style drop-down list. (c) Click the Style Attributes button. This displays the Path Style Attributes panel.

i. In the Path Style Attributes panel, set the Diameter to 0.0005. ii. Click OK to dismiss the Path Style Attributes panel with the new diameter setting. (d) Set the Step Size to 1 inch and the number of Steps to 1000. (e) Set Skip to 2. (f) In the Path Lines panel, click Display. The spherical pathlines will be drawn along the surface. (g) Rotate the display so that the flow field in front and in the wake of the chip is visible, as shown in Figure 22.15. Note: Path lines can be colored by the surface they are released from using the Color By drop-down lists. Select Particle Variables... and Surface ID and then select Display in the Path Lines panel. An example of coloring path lines based on the surface can be seen in Figure 22.16.


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Postprocessing

9.00e+00 8.55e+00 8.10e+00 7.65e+00 7.20e+00 6.75e+00 6.30e+00 5.85e+00 5.40e+00 4.95e+00 4.50e+00 4.05e+00 3.60e+00 3.15e+00 2.70e+00 2.25e+00 1.80e+00 1.35e+00 9.00e-01 4.50e-01 0.00e+00

Y X Z



Figure 22.15: Sphere Pathlines Shown on a Display of the Chip and Board Surfaces.


Y X Z

Path Lines Colored by Surface ID


Figure 22.16: Sphere Pathlines Colored by Surface ID

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Postprocessing

Step 8: Overlaying Velocity Vectors on the Pathline Display The overlay capability, provided in the Scene Description panel, allows you to display multiple results on a single plot. You can exercise this capability by adding a velocity vector display to the pathlines just plotted. 1. Enable the overlays feature. Display −→Scene...

(a) Under Scene Composition, select Overlays. (b) Click Apply.


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Postprocessing

2. Add a plot of vectors on the chip centerline plane. Display −→Vectors...

(a) Under Options, deselect Draw Grid. (b) Deselect all surfaces by clicking the unshaded icon to the right of Surfaces. (c) In the Surfaces list, select fluid-sym. (d) Set the Scale to 3.8. Because the grid surfaces are already displayed and overlaying is active, there is no need to redisplay the grid surfaces. (e) Click Display. (f) Use your mouse to obtain the view that is shown in Figure 22.17.

Note: The final display (Figure 22.17) does not require mirroring about the symmetry plane because the vectors obscure the mirrored image. You may turn off the mirroring option in the Views panel at any stage during this exercise.

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Postprocessing


Y X Z



Figure 22.17: Overlay of Velocity Vectors and Pathlines Display


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Postprocessing

Step 9: Exploded Views The Scene Description panel stores each display that you request and allows you to manipulate the displayed items individually. This capability can be used to generate “exploded” views, in which results are translated or rotated out of the physical domain for enhanced display. Below, you can experiment with this capability by displaying “side-by-side” velocity vectors and temperature contours on a streamwise plane in the module wake. 1. Delete the velocity vectors and pathlines from the current display. Display −→Scene...

(a) In the Names list, select the velocity vectors and pathlines. (b) Click Delete Geometry. (c) Click Apply. The Scene Description panel should then contain only the two grid surfaces (board-top and chip). 2. Create a plotting surface at x=3 inches (named x=3.0in), just downstream of the trailing edge of the module. Surface −→Iso-Surface...

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Postprocessing

Hint: If you forget how to create an isosurface, see Step 3: Isosurface Creation. 3. Add the display of filled temperature contours on the x=3.0in surface. Display −→Contours...

(a) Under Options, deselect Draw Grid. (b) Deselect all surfaces by clicking on the unshaded icon to the right of Surfaces.


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Postprocessing

(c) In the Surfaces list, select x=3.0in. (d) Click Display, and Close the panel. The filled temperature contours will be displayed on the x=3.0 in. surface. 4. Add the velocity vectors on the x=3.0in plotting surface. Display −→Vectors...

(a) Under Options, deselect Draw Grid. (b) Deselect all surfaces by clicking on the unshaded icon to the right of Surfaces. (c) In the Surfaces list, select x=3.0in. (d) Increase the Skip to 2. (e) Change the Scale to 1.9. (f) Click Display. The display will show the vectors superimposed on the contours of temperature at x=3.0 in.

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Postprocessing

5. Create the exploded view (Figure 22.18) by translating the contour display, placing it above the vectors. Display −→Scene... (a) In the Scene Description panel, select contour-6-temperature in the Names list. (b) Click Transform.... This will open the Transformations panel.

(c) Under Translate, enter 1 inch for Y. (d) Click Apply, and Close the Transformations panel. The exploded view allows you to see the contours and vectors as distinct displays in the final scene (Figure 22.18). 6. Turn off the Overlays. (a) In the Scene Description panel, deselect the Overlays option. (b) Click Apply, and Close the panel.


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Postprocessing


Y X Z



Figure 22.18: Exploded Scene Display of Temperature and Velocity

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Postprocessing

Step 10: Animating the Display of Results in Successive Streamwise Planes Often, you may want to march through the flow domain, displaying a particular variable on successive slices of the domain. While this task could be accomplished manually, plotting each plane in turn, or using the Scene Description and Animate panels, here you will use the Sweep Surface panel to facilitate the process. To illustrate the display of results on successive slices of the domain, you will plot contours of velocity magnitude on planes of constant x coordinate. 1. Delete the vectors and temperature contours from the display. Display −→Scene... (a) In the Scene Description panel, select contour-6-temperature and vv-6-velocitymagnitude in the Names list. (b) Click Delete Geometry. (c) Click Apply, and Close the panel. The panel and display window will be updated to contain only the grid surfaces. 2. Use your mouse to un-zoom the view in the graphics window so that the entire board surface is visible. 3. Generate contours of velocity magnitude and sweep them through the domain along the x axis. Display −→Sweep Surface...


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Postprocessing

(a) Keep the default Sweep Axis (the x axis). (b) Under Animation, set the Initial Value to 0 m and the Final Value to 0.1651 m. !

The units for the initial and final values are in meters, regardless of the length units being used in the model. Here, the initial and final values are set to the Min Value and Max Value, to generate an animation through the entire domain.

(c) Set the number of Frames to 20. (d) Select Contours under Display Type. This will open the Contours panel.

i. In the Contours panel, select Velocity... and Velocity Magnitude in the Contours Of drop-down lists. ii. In the Contours panel, click OK. (e) Click on Animate in the Sweep Surface panel. You will see the velocity contour plot displayed at 20 successive streamwise planes. FLUENT automatically interpolates the contoured data on the streamwise planes between the specified end points. Especially on high-end graphics workstations, this can be an effective way to study how a flow variable changes throughout the domain. Note: You can also make use of FLUENT’s animation tools for transient cases as demonstrated in Tutorial 4.

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Postprocessing

Step 11: XY Plots XY plotting can be used to display quantitative results of your CFD simulations. Here, you will complete your review of the module cooling simulation by plotting the temperature distribution along the top centerline of the module. 1. Define the line along which to plot results. Surface −→Line/Rake...

(a) In the Type drop-down list, select Line. (b) Under End Points, enter the coordinates of the line, using a starting coordinate of (2.0, 0.4, 0.01) and an ending coordinate of (2.75, 0.4, 0.01), as shown in the panel above. These coordinates define the top centerline of the module. (c) Enter top-center-line as the New Surface Name. (d) Click Create.


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Postprocessing

2. Plot the temperature distribution along the top centerline of the module (Figure 22.19). Plot −→XY Plot...

(a) Select Temperature... and Static Temperature in the Y Axis Function drop-down lists. (b) In the Surfaces list, select top-center-line. (c) Keep the default Plot Direction of X. This will plot temperature vs. the x coordinate along the selected line (topcenter-line). (d) Click Axes... to modify the axis range. This will open the Axes - Solution XY Plot panel .

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Postprocessing

(e) Under Axis, select X. (f) Under Options, deselect Auto Range. (g) Set the Range using a Minimum of 2.0 and a Maximum of 2.75. (h) Click Apply, and Close the panel. (i) In the Solution XY Plot panel, click Plot. The temperature distribution (Figure 22.19) shows the temperature increase across the module surface as the thermal boundary layer develops in the cooling air flow.


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Postprocessing

top-center-line 4.02e+02

4.00e+02

3.98e+02

3.96e+02


3.94e+02

3.92e+02

3.90e+02

3.88e+02 1.9

Y X Z

Static Temperature

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Position (in)


Figure 22.19: Temperature Along the Top Centerline of the Module

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Postprocessing

Step 12: Annotation You can annotate your display with the text of your choice. Display −→Annotate...

1. In the Annotation Text field, enter the text describing your plot (e.g., Temperature Along the Top Centerline). 2. Click Add. A Working dialog box will appear telling you to select the desired location of the text using the mouse-probe button, which is, by default, the right button. 3. Click your right mouse button in the graphics display window where you want the text to appear, and you will see the text displayed at the desired location (Figure 22.20). Extra: If you want to move the text to a new location on the screen, click Delete Text in the Annotate panel, and click Add once again, defining a new position with your mouse. Note: Depending on the size of your graphics window and the hardcopy file format you choose, the font size of the annotation text you see on the screen may be different from the font size in a hardcopy file of that graphics window. The annotation text font size is absolute, while the rest of the items in the graphics window are scaled to the proportions of the hardcopy.


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Postprocessing

top-center-line Temperature Along The Top Centerline

4.02e+02

4.00e+02

3.98e+02

3.96e+02


3.94e+02

3.92e+02

3.90e+02

3.88e+02 1.9

Y X Z

Static Temperature

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Position (in)


Figure 22.20: Temperature Along the Top Centerline of the Module

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Postprocessing

Step 13: Saving Hardcopy Files You can save hardcopy files of the graphics display in many different formats, including PostScript, encapsulated PostScript, TIFF, PICT, and window dumps. Here, the procedure for saving a color PostScript file is shown. File −→Hardcopy...

1. Under Format, select PostScript. 2. Under Coloring, select Color. 3. Click Save.... This will open the Select File dialog box. 4. In the Select File dialog box, enter a name for the hardcopy file. Summary: This tutorial has demonstrated the use of many of the extensive postprocessing features available in FLUENT. For more information on these and related features, see Chapter 27 and Chapter 28 in the User’s Guide.


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Postprocessing

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Tutorial 23.

Turbo Postprocessing

Introduction: This tutorial demonstrates the turbomachinery postprocessing capabilities of FLUENT. In this example, you will read the case and data files (without doing the calculation) and perform a number of turbomachinery-specific postprocessing exercises. In the process, you will learn how to: • Define the topology of a turbomachinery model • Create surfaces for the display of 3D data • Revolve 3D geometry to display a 360-degree image • Report turbomachinery quantities • Display averaged contours for turbomachinery • Display 2D contours for turbomachinery • Display averaged XY plots for turbomachinery Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Some steps will not be shown explicitly. Problem Description: The problem to be considered is shown schematically in Figure 23.1. The flow of air through a centrifugal compressor is simulated. The model consists of a single 3D sector of the compressor, to take advantage of the circumferential periodicity in the problem. FLUENT’s postprocessing capabilities readily allow you to display realistic full 360-degree images of the solution obtained.


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inlet

shroud side

hub side

outlet


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Preparation 1. Copy the files turbo/turbo.cas and turbo/turbo.dat from the FLUENT documentation CD to your working directory (as described in Tutorial 1). 2. Start the 3D version of FLUENT.

Step 1: Reading the Case and Data Files 1. Read in the case and data files (turbo.cas and turbo.dat). File −→ Read −→Case & Data... Once you select turbo.cas, turbo.dat will be read automatically.


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Step 2: Grid Display Display −→Grid...

1. Under Options, keep the default selection of Edges. 2. Under Edge Type, select Outline. 3. Deselect all surfaces, and then click on Outline at the bottom of the panel. 4. Click Display. 5. Use your left mouse button to rotate the view, and your middle mouse button to zoom the view until you obtain an isometric display of the compressor duct, as shown in Figure 23.2.

Extra: You can use the right mouse button to check which zone number corresponds to each boundary. If you click the right mouse button on one of the boundaries displayed in the graphics window, its zone number, name, and type will be printed in the console window. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly.

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Y X Z Grid

Nov 20, 2002 FLUENT 6.1 (3d, coupled imp, rke)

Figure 23.2: Graphics Display of the Edges of the Compressor Mesh


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Step 3: 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. Specifically, you will select boundary zones that comprise the hub, shroud, inlet, outlet, and periodics. Note that boundaries may consist of more than one zone. See Section 25.9.1 of the User’s Guide for more information. 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. Define −→Turbo Topology...

1. Specify the surfaces representing the hub. (a) Under Boundaries, keep the default selection of Hub. (b) In the Surfaces list, select the surfaces that represent the hub (wall-diffuser-hub, wall-hub, and wall-inlet-hub.) 2. Specify the surfaces representing the casing. (a) Under Boundaries, select Casing. (b) In the Surfaces list, select wall-diffuser-shroud, wall-inlet-shroud, and wall-shroud.

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3. Specify the surfaces representing the periodic boundaries. (a) Under Boundaries, select Theta Periodic. (b) In the Surfaces list, select periodic.33, periodic.34, and periodic.35. Note: While Theta Periodic represents periodic boundary zones on the circumferential boundaries of the flow passage, Theta Min and Theta Max are wall surfaces at the minimum and maximum θ position on a circumferential boundary. There are no such wall surfaces in this problem. 4. Specify the surface representing the Inlet (inlet). 5. Specify the surface representing the Outlet (outlet). 6. Specify the surface representing the Blade (wall-blade). 7. Keep the default Turbo Topology Name of new-topology-1. 8. Click Define to set all of the turbomachinery 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. Note: You can display the selected surfaces by clicking on Display at the bottom of the panel. This is useful as a graphical check to ensure that all relevant surfaces have been selected. Note: In the Turbo Topology panel, you can define any number of turbo topologies. This is especially useful when you have a model consisting of multiple blade rows and you need to define more than one blade row simultaneously. Each topology can be assigned a specific name and accessed using the drop-down list in the Turbo Topology panel. For more information on defining turbo topologies, see Section 27.9.1 of the User’s Guide.


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Step 4: Isosurface Creation To display results in a 3D model, you will need surfaces on which the data can be displayed. FLUENT creates surfaces for all boundary zones automatically. In a general application, you may want to define additional surfaces for the purpose of viewing results. FLUENT’s turbo postprocessing capabilities allow you to define more complex surfaces, specific to the application and the particular topology that you defined. In this step, you will create surfaces of iso-meridional (marching along the streamwise direction) and spanwise (distance between the hub and the shroud) coordinates in the compressor. Surface −→Iso-Surface... 1. Create surfaces of constant meridional coordinate.

(a) In the Surface of Constant drop-down lists, select Grid... and Meridional Coordinate. (b) Enter 0.2 under Iso-Values. (c) Enter meridional-0.2 under New Surface Name. (d) Click Create. Note: The iso-values you enter for these turbo-specific surfaces are expressed as a percentage of the entire domain (i.e., you just defined a surface of meridional coordinate equal to 20% of the path along the duct). (e) Repeat the steps above to define surfaces of meridional coordinates equal to 0.4, 0.6, and 0.8.

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2. Create surfaces of constant spanwise coordinate.

(a) In the Surface of Constant drop-down lists, select Grid... and Spanwise Coordinate (b) Enter 0.25 under Iso-Values. (c) Enter spanwise-0.25 under New Surface Name. (d) Click Create. (e) Repeat the steps above to define surfaces of spanwise coordinates equal to 0.5 and 0.75.


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Step 5: Contours 1. Plot filled contours of pressure on the meridional isosurfaces (Figure 23.3). Display −→Contours...

(a) Under Options, select Filled. (b) Select Pressure... and Static Pressure in the Contours Of drop-down lists. (c) In the Surfaces list, select inlet, meridional-0.2, meridional-0.4, meridional-0.6, meridional-0.8, and outlet. (d) Under Options, select Draw Grid, and keep the current settings in the Grid Display panel. (e) Click Display in the Contours panel. (f) Rotate and zoom the display using the left and middle mouse buttons, respectively, to obtain the view shown in Figure 23.3. In Figure 23.3, you can observe the buildup of static pressure along the duct. 2. Plot filled contours of Mach number (Figure 23.4). (a) Select Velocity... and Mach Number in the Contours Of drop-down lists. (b) Click Display.

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1.84e+00 1.78e+00 1.73e+00 1.67e+00 1.62e+00 1.56e+00 1.50e+00 1.45e+00 1.39e+00 1.34e+00 1.28e+00 1.22e+00 1.17e+00 1.11e+00 1.06e+00 1.00e+00 9.44e-01 8.88e-01 8.32e-01 Y 7.76e-01 Z 7.20e-01X

Contours of Static Pressure (atm)

Dec 17, 2002 FLUENT 6.1 (3d, coupled imp, rke)

Figure 23.3: Filled Contours of Pressure on the Meridional Isosurfaces

1.04e+00 9.85e-01 9.35e-01 8.85e-01 8.35e-01 7.84e-01 7.34e-01 6.84e-01 6.34e-01 5.83e-01 5.33e-01 4.83e-01 4.33e-01 3.82e-01 3.32e-01 2.82e-01 2.32e-01 1.81e-01 1.31e-01 Y 8.07e-02 Z 3.05e-02X



Figure 23.4: Filled Contours of Mach Number on the Meridional Isosurfaces


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In Figure 23.4, you can observe locations at which the flow becomes slightly supersonic, about halfway through the duct. 3. Plot filled contours of Mach number on the spanwise isosurfaces (Figure 23.5). (a) In the Surfaces list, deselect all surfaces, and then select spanwise-0.25, spanwise0.5, and spanwise-0.75. (b) Click Display.

1.04e+00 9.85e-01 9.35e-01 8.85e-01 8.35e-01 7.84e-01 7.34e-01 6.84e-01 6.34e-01 5.83e-01 5.33e-01 4.83e-01 4.33e-01 3.82e-01 3.32e-01 2.82e-01 2.32e-01 1.81e-01 1.31e-01 8.07e-02 Y 3.05e-02X

Z Contours of Mach Number


Figure 23.5: Filled Contours of Mach Number on the Spanwise Isosurfaces

The display in Figure 23.5 allows you to further study the variation of the Mach number inside the duct. You may want to explore using different combinations of surfaces to display the same or additional variables. 4. Display a 360-degree image of the Mach number contours on the 0.5 spanwise isosurface (Figure 23.6). (a) Redisplay the contours, just on the 0.5 spanwise isosurface. i. In the Surfaces list, deselect spanwise-0.25 and spanwise-0.75. ii. Click Display.

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(b) Display the full 360-degree geometry. Display −→Views...

i. Set Periodic Repeats to 20. ii. Click Apply. The display will be updated to show the entire geometry.

1.04e+00 9.85e-01 9.35e-01 8.85e-01 8.35e-01 7.84e-01 7.34e-01 6.84e-01 6.34e-01 5.83e-01 5.33e-01 4.83e-01 4.33e-01 3.82e-01 3.32e-01 2.82e-01 2.32e-01 1.81e-01 1.31e-01 8.07e-02 3.05e-02 Y

X Z



Figure 23.6: Filled Contours of Mach Number on the 0.5 Spanwise Iso Surface Note: This step demonstrates a typical view-manipulation task. See Tutorial 22 for further examples of postprocessing features.


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Step 6: Reporting Turbo Quantities The turbomachinery report gives you some tabulated information specific to the application and the defined topology. See Section 27.9.2 of the User’s Guide for details. Turbo −→Report...

1. Under Averages, keep the default of Mass-Weighted. 2. Click Compute.

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Step 7: 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. 1. Turn off the periodic repeats. Display −→Views... (a) In the Views panel, enter 0 in the Periodic Repeats field. (b) Click Apply. 2. Display filled contours of averaged static pressure (Figure 23.7). Turbo −→Averaged Contours...

(a) In the Contours Of drop-down lists, select Pressure... and Static Pressure. (b) Click Display.


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1.80e+00 1.76e+00 1.72e+00 1.67e+00 1.63e+00 1.58e+00 1.54e+00 1.50e+00 1.45e+00 1.41e+00 1.36e+00 1.32e+00 1.28e+00 1.23e+00 1.19e+00 1.14e+00 1.10e+00 1.06e+00 1.01e+00 9.68e-01 9.24e-01

Y Z

X

Averaged Turbo Contour - pressure (atm) (atm)


Figure 23.7: Filled Contours of Averaged Static Pressure

23-16



Step 8: 2D Contours In postprocessing a turbomachinery solution, it is often desirable to display contours on constant pitchwise, spanwise, or meridional coordinates, and then project these contours onto a plane. This permits easier evaluation of the contours, especially for surfaces that are highly three-dimensional. FLUENT allows you to display contours in this fashion using the Turbo 2D Contours panel. 1. Display 2D contours of Mach number. Turbo −→2D Contours...

(a) Under Surface of Constant, keep the default selection of Pitchwise Value. (b) In the Contours Of drop-down lists, select Velocity... and Mach Number. (c) Under Fractional Distance, enter 0.25. (d) Under Projection Type, select Radial. (e) Click Display. (f) Use your mouse to obtain the view shown in Figure 23.8.


23-17


8.30e-01 7.96e-01 7.63e-01 7.29e-01 6.95e-01 6.62e-01 6.28e-01 5.95e-01 5.61e-01 5.27e-01 4.94e-01 4.60e-01 4.26e-01 3.93e-01 3.59e-01 3.25e-01 2.92e-01 2.58e-01 2.25e-01 1.91e-01 Y 1.57e-01 X Z

2D Turbo Contour - mach-number


Figure 23.8: 2D Contours of Mach Number on Surface of Pitchwise Value 0.25.

23-18



Step 9: Averaged XY Plots In addition to displaying data on different combinations of complex 3D and flattened surfaces, FLUENT’s turbo postprocessing capabilities allow you to display XY plots of averaged variables, relevant to the specific topology of a turbomachinery problem. In particular, you will be able to plot circumferentially-averaged values of variables as a function of either the spanwise coordinate or the meridional coordinate. 1. Plot temperature as a function of the meridional coordinate. Turbo −→Averaged XY Plot...

(a) In the Y Axis Function drop-down lists, select Temperature... and Static Temperature. (b) In the X Axis Function drop-down list, select Meridional Distance. (c) Under Fractional Distance, enter 0.9. (d) Click Plot. Summary: This tutorial has demonstrated the use of some of the turbomachineryspecific postprocessing features of FLUENT. These features can be accessed once you have defined the topology of the problem. More extensive general-purpose postprocessing features are demonstrated in Tutorial 22. Also refer to Chapter 27 and Chapter 28 in the User’s Guide.


23-19


3.50e+02

3.40e+02

3.30e+02

3.20e+02


3.10e+02

3.00e+02

2.90e+02

2.80e+02 0

Y X Z Averaged XY - temperature

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Meridional Distance

Nov 20, 2002 FLUENT 6.1 (3d, coupled imp, rke)

Figure 23.9: Averaged XY Plot of Static Temperature on Spanwise Surface of 0.9 Isovalue

23-20


Tutorial 24.

Parallel Processing

Introduction: This tutorial illustrates the setup and solution of a simple 2D problem using FLUENT’s parallel processing capabilities. In order to be run in parallel, the mesh must be divided into smaller, evenly sized partitions. Each FLUENT process, called a compute node, will solve on a single partition, and information will be passed back and forth across all partition interfaces. FLUENT’s solver allows parallel processing on a dedicated parallel machine, or a network of heterogeneous workstations running UNIX, or a network of workstations running Windows. The tutorial assumes that both FLUENT and network communication software have been correctly installed (see the separate installation instructions and related information for details). The case chosen is the mixing elbow problem you solved in Tutorial 1. In this tutorial you will learn how to: • Start the parallel version of FLUENT • Partition a grid for parallel processing • Use a parallel network of workstations • Check the performance of the parallel solver Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1. Problem Description: The problem to be considered is shown schematically in Figure 24.1. A cold fluid at 26◦ C enters through the large pipe and mixes with a warmer fluid at 40◦ C in the elbow. The pipe dimensions are in inches, and the fluid properties and boundary conditions are given in SI units. The Reynolds number at the main inlet is 2.03 × 105 , so that a turbulent model will be necessary.


24-1

Parallel Processing

Density:

ρ= 1000 kg/m

Viscosity:

µ = 8 x 10

-4

3

Pa-s 32 ″

Conductivity: k = 0.677 W/m-K Specific Heat: C p = 4216 J/kg-K

39.9 3°

Ux= 0.2 m/s T = 26°C I = 5%

39.9

16 ″

3°

16 ″ 12 ″ 32 ″

4″ Uy= 1 m/s T = 40° C I = 5%


24-2


Parallel Processing

Preparation 1. Copy the file parallel/elbow3.cas from the FLUENT documentation CD to your working directory (as described in Tutorial 1). You can partition the grid before or after you set up the problem (by defining models, boundary conditions, etc.). It is best to partition after the problem is set up, since partitioning has some model dependencies (e.g., sliding-mesh and shell-conduction encapsulation). Because you already set up this problem in Tutorial 1, you can save the effort of redefining the models and boundary conditions.

Step 1: Starting the Parallel Version of FLUENT Since the procedure for starting the parallel version of FLUENT is dependent upon the type of machine(s) you are using, four versions of this step are provided here. Follow the procedure for the machine configuration that is appropriate for you. • Step 1A: Multiprocessor UNIX Machine • Step 1B: Multiprocessor Windows Machine • Step 1C: Network of UNIX Workstations • Step 1D: Network of Windows Workstations


24-3

Parallel Processing

Step 1A: Multiprocessor UNIX Machine 1. At the command prompt, type fluent. !

Do not specify any argument (e.g., 2d).

2. Specify the 2D parallel version. File −→Run...

(a) Under Versions, turn on Parallel. (b) Under Options, specify 2 as the number of Processes. (c) Under Options, keep the Default selection in the Communicator drop-down list. (d) Click Run. Note: It is also possible to start the multiprocessor parallel version of FLUENT from the command line instead of using the Select Solver panel. See Chapter 30 of the User’s Guide for details.

24-4


Parallel Processing

Step 1B: Multiprocessor Windows Machine 1. At the DOS command prompt, type fluent 2d -t2 to start the 2D parallel version with two processes.


24-5

Parallel Processing

Step 1C: Network of UNIX Workstations 1. At the command prompt, type fluent. !

Do not specify any argument (e.g., 2d).

2. Specify the 2D network parallel version. File −→Run...

(a) Under Versions, turn on Parallel. (b) Under Options, keep the default value of 1 as the number of Processes. You will spawn processes to other machines in the next step. (c) Under Options, select Socket in the Communicator drop-down list. (d) Click Run. Note: It is also possible to start the network parallel version from the command line instead of using the Select Solver panel. See Chapter 30 of the User’s Guide for details.

24-6


Parallel Processing

3. Spawn one additional computational node. Parallel −→ Network −→Configure...

(a) Specify the machine on which you want to spawn the process. i. Under Host Entry, specify the machine name in the Hostname field. ii. Enter your user ID in the Username field. iii. Click Add. The machine will be added to the Available Hosts list. Note: It is possible to create a list of available machines and add them to the hosts database, rather than adding machines manually. See Chapter 30 of the User’s Guide for details. (b) Select the newly added host in the Available Hosts list. Note: If you do not have access to another machine, you can spawn the second node on your own machine by selecting it from the Available Hosts list, although you will incur a performance penalty on a single processor machine. (c) Under Spawn Count, keep the default value of 1. This will give you the desired total number of 2 computational nodes.


24-7

Parallel Processing

(d) Click Spawn. FLUENT will inform you in a Working dialog box that it is spawning the new node. When it is done, the new node will appear in the Spawned Compute Nodes list, as shown below.

Hint: If you accidentally spawn an undesired computational node, you can remove it by selecting it from the Spawned Compute Nodes list and clicking on Kill. 4. Check the network connectivity information. Although FLUENT displays a message confirming the connection to each new compute node and summarizing the host and node processes defined, you may find it useful to review the same information at some time during your session, especially if more compute nodes are spawned to several different machines. Parallel −→Show Connectivity...

(a) Specify the number of the Compute Node of interest (0).

24-8


Parallel Processing

For information about all defined compute nodes, you will select node 0, since this is the node from which all other nodes are spawned. (b) Click Print. -------------------------------------------------------------------ID Comm. Hostname O.S. PID Mach ID HW ID Name -------------------------------------------------------------------n1 net dori hpux 11681 1 7 Fluent Node host net bilbo hpux 12697 0 3 Fluent Host n0* net bilbo hpux 12698 0 -1 Fluent Node

ID is the sequential denomination of each compute node (the host process is always host), Hostname is the name of the machine hosting the compute node (or the host process), O.S is the architecture, PID is the process ID number, Mach ID is the compute node ID, and HW ID is an identifier specific to the communicator used.


24-9

Parallel Processing

Step 1D: Network of Windows Workstations The procedure below is for using the RSHD communicator software that is included with FLUENT. You can use a different communicator if one is available on your system. See the User’s Guide for more information. 1. At the DOS command prompt, type fluent 2d -pnet -t1 to start the 2D network parallel version with one process. You will spawn a second compute node in the next step. 2. Spawn an additional compute node, following the procedure described in Step 1C, substep 3, for a network of UNIX machines. 3. Check the network connectivity, following substep 4 of Step 1C.

24-10


Parallel Processing

Step 2: Reading and Partitioning the Grid When you use the parallel solver, you need to subdivide (or partition) the grid into groups of cells that can be solved on separate processors. If you read an unpartitioned grid into the parallel solver, FLUENT will automatically partition it, using the default partition settings. You can then check the partitions, to see if you need to modify the settings and repartition the grid. 1. Inspect the automatic partitioning settings. Parallel −→Auto Partition...

If the Case File option is turned on (the default setting), and there exists a valid partition section in the case file (i.e., one where the number of partitions in the case file divides evenly into the number of compute nodes), then that partition information will be used rather than repartitioning the mesh. You need to turn off the Case File option only if you want to change other parameters in the Auto Partition Grid panel. (a) Keep all defaults in the Auto Partition Grid panel. When you keep the Case File option turned on, FLUENT will automatically select a partitioning method for you. This is the preferred initial approach for most problems. In the next step you will inspect the partitions created and be able to change them, if you so choose. 2. Read the case file elbow3.cas. File −→ Read −→Case... 3. Display the grid (Figure 24.2). Display −→Grid...


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Parallel Processing

Grid


Figure 24.2: Triangular Grid for the Mixing Elbow

24-12


Parallel Processing

4. Check the partition information. Parallel −→Partition...

(a) Click Print Active Partitions. FLUENT will print the active partition statistics to the console window. Note: FLUENT distinguishes between two cell partition schemes within a parallel problem: the active cell partition, and the stored cell partition. Here, both are set to the cell partition that was created 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 on 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 of machines and solve it on a different one. See Chapter 30 of the User’s Guide for more information.


24-13

Parallel Processing

>> 2 Active Partitions: P Cells I-Cells Cell Ratio 0 612 10 0.016 1 612 13 0.021

Faces I-Faces Face Ratio Neigh 985 13 0.013 1010 13 0.013

----------------------------------------------------------------Collective Partition Statistics: Minimum Maximum Total ----------------------------------------------------------------Cell count 612 612 1224 Mean cell count deviation 0.0% 0.0% Partition boundary cell count 10 13 23 Partition boundary cell count ratio 1.6% 2.1% 1.9% Face count Mean face count deviation Partition boundary face count Partition boundary face count ratio

985 -1.3% 13 1.3%

1010 1.3% 13 1.3%

1982 13 0.7%

Partition neighbor count 1 1 ----------------------------------------------------------------Partition Method Principal Axes Original Partition Count 2 Done.

(b) Review the partition statistics. An optimal partition should produce an equal number of cells in each partition for load balancing, a minimum number of partition interfaces to reduce interpartition communication bandwidth, and a minimum number of partition neighbors to reduce the startup time for communication. Here, you will be looking for relatively small values of mean cell and face count deviation and total partition boundary cell and face count ratio.

24-14


Parallel Processing

5. Examine the partitions graphically. (a) Initialize the solution. Even though you are not going to start a solution at this point, you have to perform a solution initialization in order to use the Contours panel to inspect the partition you just created. Solve −→ Initialize −→Initialize... (b) Display the cell partitions (Figure 24.3). Display −→Contours...

i. In the Contours Of drop-down lists, select Cell Info... and Active Cell Partition. ii. Under Options, select Filled. iii. Set the number of Levels to 2, the number of compute nodes. iv. Click Display. As shown in Figure 24.3, the cell partitions are acceptable for this problem. The position of the interface reveals that the criteria mentioned above will be matched. If you were unsatisfied with the partitions, you could use the Partition Grid panel to repartition the grid. See the User’s Guide for details about the procedure and options for manually partitioning a grid. Recall that, if you wish to use the modified partitions for a calculation, you will need to make


24-15

Parallel Processing

1.00e+00

5.00e-01

0.00e+00

Contours of Active Cell Partition


Figure 24.3: Cell Partitions the Stored Cell Partition the Active Cell Partition by either clicking on the Use Stored Partitions button in the Partition Grid panel or saving the case file and reading it back into FLUENT. 6. Save the case file with the partitioned mesh (elbow4.cas). File −→ Write −→Case...

24-16


Parallel Processing

Step 3: Solution 1. Initialize the flow field using the boundary conditions set at velocity-inlet-5. Solve −→ Initialize −→Initialize...

(a) Choose velocity-inlet-5 from the Compute From list. (b) Click on Init and Close the panel. 2. Enable the plotting of residuals during the calculation. Solve −→ Monitors −→Residual... 3. Start the calculation by requesting 100 iterations. Solve −→Iterate... The solution will converge in approximately 72 iterations. 4. Save the data file (elbow4.dat). File −→ Write −→Data...


24-17

Parallel Processing

Step 4: Checking Parallel Performance Generally, you will use the parallel solver for large, computationally-intensive problems, and you will want to check the parallel performance to determine if any optimization is required. See Chapter 30 of the User’s Guide for details. Although the example in this tutorial is a simple 2D case, here you will check the parallel performance as an exercise. Parallel −→ Timer −→Usage Performance Timer for 71 iterations on 2 compute nodes Average wall-clock time per iteration: 0.021 sec Global reductions per iteration: 80 ops Global reductions time per iteration: 0.000 sec (0.0%) Message count per iteration: 199 messages Data transfer per iteration: 0.009 MB LE solves per iteration: 6 solves LE wall-clock time per iteration: 0.005 sec (23.7%) LE global solves per iteration: 2 solves LE global wall-clock time per iteration: 0.000 sec (0.8%) AMG cycles per iteration: 9 cycles Relaxation sweeps per iteration: 276 sweeps Relaxation exchanges per iteration: 61 exchanges Total wall-clock time: Total CPU time:

1.463 sec 2.900 sec

The most accurate way to evaluate parallel performance is by running the same parallel problem on 1 CPU and on n CPUs, and comparing the Total wall-clock time (elapsed time for the iterations) in both cases. Ideally you would want to have the Total wall-clock time with n CPUs be 1/n times the Total wall-clock time with 1 CPU. In practice, this improvement will be reduced by the performance of the communication subsystem of your hardware, and the overhead of the parallel process itself. As a rough estimate of parallel performance, you can compare the Total wall-clock time with the CPU time. In this case the CPU time was approximately 1.98 times the Total wall-clock time. For a parallel process run on two compute nodes, this reveals very good parallel performance, even though the advantage over a serial calculation is small, as expected for this simple 2D problem.

24-18


Parallel Processing

Step 5: Postprocessing See Tutorial 1 for complete postprocessing exercises for this example. Here, two plots are generated so that you can confirm that the results you obtained with the parallel solver are the same as those you obtained with the serial solver. 1. Display an XY plot of temperature across the exit (Figure 24.4). Plot −→ XY Plot...

(a) Select Temperature... and Static Temperature in the Y Axis Function drop-down lists. (b) Select pressure-outlet-7 in the Surfaces list. (c) Click on Plot.


24-19

Parallel Processing

Figure 24.4: Temperature Distribution at the Outlet

24-20


Parallel Processing

2. Display filled contours of the custom field function dynam-head (Figure 24.5). Display −→ Contours...

(a) Select Custom Field Functions... in the drop-down list under Contours Of. The function you created in Tutorial 1, dynam-head, will be shown in the lower drop-down list. (b) Change the number of Levels back to 20. (c) Click on Display, and then Close the panel.


24-21

Parallel Processing


Contours of dynam-head


Figure 24.5: Contours of the Custom Field Function, Dynamic Head

Summary: In this tutorial you learned how to solve a simple 2D problem using FLUENT’s parallel solver. Here the automatic grid partitioning performed by FLUENT when you read the mesh into the parallel version was found to be acceptable. You also learned how to check the performance of the parallel solver to determine if optimizations are required. See the User’s Guide for additional details about using the parallel solver.

24-22


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