Boundary-Layer Transition Prediction for Reynolds

Edward Anthony Mayda December 2007 Mechanical and Aeronautical Engineering Boundary-Layer Transition Prediction for Reynolds-Averaged Navier-Stokes Methods

Abstract Boundary layer transition plays a critical role in many fluid dynamic applications, but it is still not well understood. While engineering methods do exist for predicting the onset of turbulent flow, they are rarely incorporated in Reynolds-averaged Navier Stokes (R ANS) solvers which continue to increase in popularity as design and analysis tools. This report begins with a brief literature survey of boundary layer stability and transition, engineering methods for transition prediction and recent efforts to couple transition models with R ANS codes. Next, the process of coupling an existing simplified eN envelope transition model with the A RC 2 D solver is described. Transitional R ANS solutions for a flat plate, a stationary NLF(1)-0416 airfoil and a pitching NACA0015 airfoil are presented. Results show good agreement with available experiment data. A method for generating a compressible database eN method applicable to unsteady flows is outlined. The L ASTRAC boundary layer stability program was used in conjunction with compressible, near-similarity boundary layer velocity profiles and non-similar separated velocity profiles to generate a database, or look-up table, of amplification rates. The amplification rates are stored for use in a full eN model which utilizes an efficient, local four-dimensional Lagrangian interpolation scheme for amplification rate retrieval. The database eN transition model was validated against results generated by L ASTRAC for several model problems. The database results agreed very well with those produced by L ASTRAC but were generated roughly 3,600 times as fast. Finally, the database model was tested on several steady and unsteady real-world aerodynamic analysis problems. Predicted performance for steady subsonic and transonic

2 airfoil cases closely matched the available experimental data and highlighted the need to include boundary layer transition in the design cycle of future airfoil geometries. Unsteady, transitional results for test cases including pitching NACA0015 and NACA0012 airfoils and static extremely thick airfoils sensitive to surface roughness effects illustrate the need for time-accurate transition prediction. The gross trends of the “drag crisis” for the cylinder-in-crossflow are produced when transition prediction is enabled.

Boundary-Layer Transition Prediction for Reynolds-Averaged Navier-Stokes Methods By EDWARD ANTHONY MAYDA B.S. (University of California, Davis) 2001 M.S. (University of California, Davis) 2003 DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical and Aeronautical Engineering in the OFFICE OF GRADUATE STUDIES of the UNIVERSITY OF CALIFORNIA DAVIS Approved:

Committee in charge 2007 –i–

Boundary-Layer Transition Prediction for Reynolds-Averaged Navier-Stokes Methods

Copyright 2007 by Edward Anthony Mayda

Acknowledgments I would not be writing these specific words today if Dr. Earl Duque had not taught undergraduate fluid mechanics as a visiting lecturer in the fall of 1999. His enthusiasm for the subject rubbed off on me to the point that I added aeronautical engineering as a major midway through the term. If that wasn’t influential enough, at the end of the quarter Earl offered me a NASA internship for the following summer. Those three months at Ames Research Center exposed me to the field of computational fluid dynamics, laid the foundation for a very fulfilling graduate school experience, and introduced me to Dr. Case van Dam, my now long-time graduate advisor, mentor and friend. For the past seven years, Case has pushed me academically and technically and has provided me every opportunity to excel. Because of Case, I have been able to write conference papers and journal articles, travel to numerous technical meetings around the country and the world, and apply for and receive a patent on the work I did for my Master’s degree. He generously shared his knowledge, interests and experiences with me, and in doing so nurtured my developing skill set and curiosities. I know what Case has taught me will take me far, and I will be forever thankful. This research project would not have been possible without the technical and financial support of Dr. Roger Strawn and the U.S. Army Aeroflightdynamics Directorate. Roger was a pleasure to work with on both my qualifying exam and dissertation committees, and I hope that I have the opportunity to work with him again in the future. Similarly, Dr. Jean-Jacques Chattot, Dr. Roger Davis, Dr. Harry Dwyer and Dr. Bruce White deserve recognition for sitting on one or both of my qualifying and dissertation committees. I am also thankful for the efforts of Dr. Chau-Lyan Chang to develop L ASTRAC and Dr. Thomas Pulliam to develop A RC 2 D. These two computer codes were indispensable throughout this project. If one is lucky, by the end of grad school they have acquired two very important things: a diploma and friendships. I consider myself lucky. Over the years, The Farm has been –ii–

my second home. Past and present Farm members, my friends, have made working in a windowless office perfectly (dare I say it?) enjoyable. They were always willing to help me take a break from coding by pointing out the latest Piled, Higher & Deeper comic strip, arranging group lunch outings, forming less-than-stellar IM softball teams, flying things around the office... A job is only as good as the people you work with, and being a grad student has been a very good job indeed. Finally, the people who have had the largest impact on my life and success so far are my family. My parents, Kathy and Michael, and sister, Julia, have supported me throughout it all. From my first Mite hockey game to my Ph.D. exit seminar, my family has cheered me on, and I surely would not be where I am today without them. Lastly, but most importantly, I cannot thank my wife, Adriane, enough for her unwavering patience, encouragement and love throughout this entire process. Adriane, a graduate student herself, knew the stressfulness of qualifying exams and the like, and somehow always knew how to keep me calm and relaxed. I hope that I can do the same for her as she completes her studies and in the “real life” that awaits us afterwards. Adriane, I love you and thank you with all my heart and dedicate this thesis to you.

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Contents List of Figures

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List of Tables

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Nomenclature

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Abstract

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Introduction 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Laminar Flow Stability . . . . . . . . . . . . . 1.1.2 Boundary Layer Transition . . . . . . . . . . . 1.1.3 Engineering Methods for Transition Prediction 1.1.4 Coupling Flow Solvers and Transition Models 1.2 Research Objectives and Motivation . . . . . . . . . .

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Coupling an Existing Transition Model with a R ANS Flow Solver 2.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Local Coordinate System and Variables . . . . . . . . 2.2.2 Determination of Boundary Layer Edge Variables . . . 2.2.3 Robust Determination of the Boundary Layer Edge . . 2.2.4 Calculation of Boundary Layer Parameters . . . . . . 2.2.5 Comments on Artificial Dissipation Effects . . . . . . 2.2.6 Simplified eN Envelope Method . . . . . . . . . . . . 2.2.7 Transition Length and Intermittency Factor . . . . . . 2.2.8 Implementation Details . . . . . . . . . . . . . . . . . 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Flat Plate . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 NLF(1)-0416 Airfoil . . . . . . . . . . . . . . . . . . 2.3.3 Pitching NACA0015 Airfoil . . . . . . . . . . . . . . 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Database eN Transition Model Development 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Boundary Layer Stability Analysis . . . . . . . . . . . . . . . . 3.3 Database Velocity Profiles . . . . . . . . . . . . . . . . . . . . 3.3.1 Horton’s Near-similarity Compressible Velocity Profiles 3.3.2 Numerical Generation of Horton’s Velocity Profiles . . . 3.3.3 Validation of Numerical Horton Solutions . . . . . . . . 3.3.4 Separated Velocity Profiles . . . . . . . . . . . . . . . . 3.4 Database Generation . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Database Input Parameters – Attached Flow . . . . . . . 3.4.2 Database Input Parameters – Separated Flow . . . . . . 3.4.3 Mean Flow Input File Creation . . . . . . . . . . . . . . 3.4.4 Running L ASTRAC . . . . . . . . . . . . . . . . . . . . 3.5 Database Model Implementation . . . . . . . . . . . . . . . . . 3.5.1 Database Storage . . . . . . . . . . . . . . . . . . . . . 3.5.2 Retrieving Data from the Database . . . . . . . . . . . . 3.5.3 Database eN Transition Prediction . . . . . . . . . . . . 3.5.4 Implementation for Time-accurate Simulations . . . . . 3.6 Database Validation . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Flat Plate Flow . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Flow with Pressure Gradient . . . . . . . . . . . . . . . 3.7 Relative Performance of Stability Analysis Methods . . . . . . . 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Database eN Transition Model Results and Discussion 4.1 Steady Cases . . . . . . . . . . . . 4.1.1 NLF(1)-0416 Airfoil . . . . 4.1.2 HSNLF(1)-0213 Airfoil . . 4.1.3 NACA0012 Airfoil . . . . . 4.2 Unsteady Cases . . . . . . . . . . . 4.2.1 Pitching Airfoils . . . . . . 4.2.2 Blunt Trailing Edge Airfoils 4.2.3 Cylinder in Crossflow . . . 4.3 Conclusions . . . . . . . . . . . . .

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Conclusions and Recommendations

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Bibliography

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A A RC 2 D Overview A.1 The Navier-Stokes Equations . . . . . . A.2 Curvilinear Coordinate Transformation . A.3 Numerical Schemes . . . . . . . . . . . A.3.1 Implicit Time Differencing . . .

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A.3.2 Spatial Differencing . . . . . . . . . . . . . . . . . A.3.3 Unfactored and Approximate Factorization Methods A.3.4 Reduced Formulations . . . . . . . . . . . . . . . . A.3.5 Artificial Dissipation . . . . . . . . . . . . . . . . . A.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . A.5 Spalart-Allmaras One-Equation Turbulence Model . . . . . B Transition Model Inputs for A RC 2 D B.1 VISINP Namelist Group . . . . . . . . . . . . B.2 TIMACU Namelist Group . . . . . . . . . . . . B.3 Usage Guidelines - Steady Simulations . . . . . B.4 Usage Guidelines - Time-accurate Simulations . C Airfoil Coordinates C.1 NLF(1)-0416 . . . . . . . . . . . . . C.2 HSNLF(1)-0213 . . . . . . . . . . . . C.3 NACA0012 with Sharp Trailing Edge C.4 NACA0015 with Sharp Trailing Edge

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List of Figures 1.1 1.2 1.3 1.4 1.5 1.6

Classical example of the stability of four systems . . . . . . . . . . . . . Generic thumb plot showing neutral stability curves . . . . . . . . . . . . Hotwire measurements in a flat plate boundary layer . . . . . . . . . . . Flow structures present at different stages of transition to turbulence . . . Determining transition location for Blasius flat plate flow using Michel’s criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N -factor curves for constant frequency disturbances in a Blasius flat plate boundary layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

General two-dimensional and thin shear layer coordinate systems and grid index conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ∗ 2.2 Normalized flat plate velocity profile and I δ and I θ integrands . . . . . . 2.3 Demonstration of artificial dissipation effects on the boundary layer shape factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The simplified envelope concept used by Drela and Giles . . . . . . . . . 2.5 Flowchart depicting the processes involved with coupling a transition prediction method with a R ANS flow solver . . . . . . . . . . . . . . . . . . 2.6 Calculated flat plate skin friction coefficient for varying critical N -factors 2.7 NLF(1)-0416 lift, drag and pitching moment coefficients . . . . . . . . . 2.8 NLF(1)-0416 transition locations as predicted by A RC 2 D and reported by experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 NACA0015 lift coefficient limit cycle . . . . . . . . . . . . . . . . . . . 2.10 NACA0015 drag coefficient limit cycle . . . . . . . . . . . . . . . . . . 2.11 NACA0015 pitching moment coefficient limit cycle . . . . . . . . . . . . 2.12 NACA0015 transition location limit cycles . . . . . . . . . . . . . . . . .

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3.1 3.2 3.3 3.4 3.5

Sensitivity of F to the choice of ηmax . . . . . . Sensitivity of F to varying mesh resolution . . . Sensitivity of G to varying mesh resolution . . . Comparison of the present numerical solutions to second derivative of velocity . . . . . . . . . . . Comparison of the present numerical solutions to second derivative of static enthalpy . . . . . . . .

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3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13

Comparison of the present numerical solutions to those of Horton for the wall shear stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the present numerical solutions to those of Horton for the wall temperature recovery factor . . . . . . . . . . . . . . . . . . . . . . Comparison of the present numerical solutions to those of Horton for the transformed shape factor . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of measured and Falkner-Skan separated flow velocity profiles at two streamwise locations showing the effect of varying pressure gradient parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Green’s two-parameter separated flow velocity profile . . . . . . . . . . . Comparison of measured and Green’s two-parameter separated flow velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic tangent approximation to Green’s profile . . . . . . . . . . . Flowchart depicting the processes involved with running L ASTRAC over the desired Reδ∗ and F × Reδ∗ ranges . . . . . . . . . . . . . . . . . . . Diagram of three L ASTRAC frequency sweeps at constant Reδ∗ . . . . . . Definition of Reynolds number and frequency bounds used to normalize an amplification rate surface . . . . . . . . . . . . . . . . . . . . . . . . . . Normalization approach for a single velocity profile . . . . . . . . . . . . Schematic outlining the process of two-dimensional interpolation . . . . . Connectivity diagram for the separated Green’s profile database . . . . . Flowchart depicting the dual-time subiteration process with transition prediction for time accurate simulations . . . . . . . . . . . . . . . . . . . . N-factor distributions for flat plate flow comparing results from the present eN database method and L ASTRAC for various Mach numbers . . . . . . N-factor distributions for the HSNLF(1)-0313 airfoil comparing results from L ASTRAC, the present eN database method and published computational data from Viken and Wagner . . . . . . . . . . . . . . . . . . . .

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NLF(1)-0416 computational grid . . . . . . . . . . . . . . . . . . . . . . . 89 NLF(1)-0416 lift and pitching moment curves . . . . . . . . . . . . . . . . 91 NLF(1)-0416 pressure ditributions . . . . . . . . . . . . . . . . . . . . . . 92 NLF(1)-0416 drag polars and transition locations . . . . . . . . . . . . . . 93 Nearbody view of the HSNLF(1)-0213 computational grid . . . . . . . . . 95 HSNLF(1)-0213 lift and quarter-chord pitching moment coefficients . . . . 95 HSNLF(1)-0213 drag polars and transition locations . . . . . . . . . . . . 96 Mach number dependence of the HSNLF(1)-0213 drag coefficient and transition locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Mach number dependence of the NACA0012 drag coefficient and transition locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Nearbody view of the NACA0015 computational grid for dynamic stall cases102 NACA0015 hysteresis loops for inviscid lift, drag and pitching moment coefficients and transition locations . . . . . . . . . . . . . . . . . . . . . . 103 NACA0015 pressure distributions at α = 4.11◦ during the down stroke . . . 105 Nearbody view of the NACA0012 computational grid for dynamic stall cases106

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4.14 NACA0012 dynamic stall hysteresis loops for the pressure-based lift, drag and quarter-chord pitching moment coefficients for three different conditions108 4.15 Experimentally measured and numerically predicted upper surface transition locations for the pitching NACA0012 airfoil during the upstroke . . . . 110 4.16 FB-3500 computational grids . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.17 FB-3500-0050 experimental and computational lift and drag coefficients and transition locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.18 FB-3500-0875 experimental and computational lift and drag coefficients and transition locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.19 FB-3500-1750 experimental and computational lift and drag coefficients and transition locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.20 Computational lift-to-drag ratio for the FB-3500 airfoil series under clean and soiled conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.21 Cylinder computational grid . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.22 Cylinder drag coefficient at a function of Reynolds number . . . . . . . . . 120 4.23 Cylinder transition location iteration histories . . . . . . . . . . . . . . . . 122 A.1 Curvilinear coordinate transformation from the physical to the computational domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

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List of Tables 1.1

Suggested Ncrit values for various freestream conditions . . . . . . . . . . 11

2.1

Predicted flat plate transition locations and lengths . . . . . . . . . . . . . 34

3.1 3.2 3.3 3.4 3.5

Database input variables and their ranges . . . . . . . . . . . . . . . . . . Database input ranges for the separated branch of the stability database . . Green’s profiles included in the database . . . . . . . . . . . . . . . . . . Shape factor bounds used for normalization . . . . . . . . . . . . . . . . Timing study results comparing the performance of L ASTRAC, the database model and the simplified envelope model . . . . . . . . . . . . . . . . .

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63 64 65 73

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Nomenclature a

speed of sound

c

airfoil chord length, or small disturbance wave speed

Cd

two-dimensional drag coefficient

C`

two-dimensional lift coefficient

Cm

two-dimensional quarter-chord pitching moment coefficient

d

cylinder diameter

F

nondimensional small disturbance frequency

f

small disturbance frequency, or nondimensional stream function

G

total enthalpy function

H

boundary layer shape factor, or specific total enthalpy

h

specific static enthalpy

Ix

local value for integrand used to determine x via numerical integration

k

reduced frequency –xi–

`tr

transition length

M

Mach number

n ˜

transition amplification variable

N

amplification factor in the eN transition model

p

static pressure

Pr

Prandtl number