Performance of modern Eddy-Viscosity turbulence models

257 Pages·2004·4.718 MB·English

by  Alan Celic

Performance of Modern
Eddy-Viscosity Turbulence Models
Von der Fakult¨at fu¨r Luft- und Raumfahrttechnik und Geod¨asie
der Universit¨at Stuttgart zur Erlangung der Wu¨rde
eines Doktor-Ingenieurs (Dr.-Ing.)
genehmigte Abhandlung
Vorgelegt von
Alan Celi´c
geboren in Tu¨bingen
Hauptberichter: Prof. Dr.-Ing. habil. Ernst H. Hirschel
1. Mitberichter: Prof. Dr.-Ing. Siegfried Wagner
2. Mitberichter: Prof. Peter Bradshaw
Tag der mu¨ndlichen Pru¨fung: 23.07.2004
Institut fu¨r Aerodynamik und Gasdynamik
Universit¨at Stuttgart
2004

Berichte aus der Luft- und Raumfahrttechnik
Alan Celi ´c
Performance of Modern Eddy-Viscosity
Turbulence Models
.
D 93 (Diss. Universität Stuttgart)
Shaker Verlag
Aachen 2004
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the internet at http://dnb.ddb.de.
Zugl.: Stuttgart, Univ., Diss., 2004
.
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Acknowledgments
ThisworkwasconductedduringmytimeasaresearchengineerattheInsti-
tut fu¨r Aerodynamik und Gasdynamik (IAG) of the University of Stuttgart,
Germany, and was funded by the Deutsche Forschungsgemeinschaft (Grants
Hi 342/4-1 to 342/4-4).
I am deeply grateful to my thesis adviser Professor Dr.-Ing. habil. Ernst
H. Hirschel for his great personal support and help, and technical advice.
Professor Hirschel always believed in my work, which gave me confidence
especially during difficult periods when things did not go as smoothly as
hoped. I highly appreciate that I could be one of his doctoral students.
IamalsodeeplygratefultoProfessorPeterBradshawfromStanfordUni-
versity who was a distant adviser and a “Mitberichter” (co-referee) for this
Ph.D. thesis. ProfessorBradshaw’sinvaluable professional andlinguistic ad-
vice as well as his personal support made this work a great experience and
joy for me. I have learned so much from him.
I also wish to thank Professor Dr.-Ing. Siegfried Wagner for his commit-
ment as a Mitberichter and for offering me the opportunity to perform this
study at his institute. The IAG is a great place to work at and I also thank
all my former colleagues for creating such a great atmosphere.
Very special thanks go to Dr.-Ing. Werner Haase from EADS Munich.
Dr. Haase put me on track at the beginning of this work by supplying his
CFD code and his great experience in turbulence modeling. He always took
the time to teach me about CFD and turbulence modeling which I sincerely
appreciate. I am likewise grateful to Dr.-Ing. Markus Kloker from the IAG
forprovidinghisinvaluableadvicewhenIhadquestionsconcerningnumerics.
I am indebted to Professor Stefan Staudacher who, on short notice, at-
tended my Ph.D. exam in place of Professor Bradshaw who unfortunately
could not take the burden of the long travel to Stuttgart because at that
time he had not completely recovered from an accident.
Last but not least, I wish to thank my family and my close friends who
have supported me in many ways and without whom I would have not been
able to master this work.
Alan Celi´c
Toulouse, October 24th, 2004

Contents
Notation 9
Abstract 15
Zusammenfassung 17
1 Introduction 25
1.1 The Present Study . . . . . . . . . . . . . . . . . . . . . . . . 33
1.2 Contents and Organization of the Thesis . . . . . . . . . . . . 34
I Topological Approach to Turbulence Modeling 37
2 Basic Considerations 38
3 Governing Equations and Numerical Method 42
3.1 Governing Equations of the Mean Flow . . . . . . . . . . . . 42
3.2 The Baldwin-Lomax Model . . . . . . . . . . . . . . . . . . . 44
3.3 The Johnson-King Model . . . . . . . . . . . . . . . . . . . . 46
3.4 Numerical Method (I) . . . . . . . . . . . . . . . . . . . . . . 48
4 Demonstration 50
4.1 Description of Flow Case . . . . . . . . . . . . . . . . . . . . 50
4.2 Computational Grid . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Computational Results and Discussion . . . . . . . . . . . . . 53
4.3.1 Topology of the Velocity Field . . . . . . . . . . . . . 53
4.3.2 Pressure and Skin-Friction Distributions . . . . . . . . 55
4.3.3 Boundary-Layer Profiles . . . . . . . . . . . . . . . . . 60
4.3.4 Numerical Experiment in the Recirculation Zone . . . 67
4.3.5 Comments Regarding Hidden Three-Dimensional Ef-
fects in Nominally Two-Dimensional Flows . . . . . . 70
II Analysis of Modern Turbulence Models 73
5 Numerical Method (II) 74
6 Models Investigated 75
6.1 The k, ω Models of Wilcox . . . . . . . . . . . . . . . . . . . 76
6.2 The k, ω Shear-Stress Transport (SST) Model of Menter . . . 79
6.3 The Turbulent/Non-turbulent (TNT) k, ω Model of Kok. . . 81
6.4 The Local Linear Realizable (LLR) k, ω Model of Rung . . . 82
6.5 The Explicit Algebraic Reynolds-Stress Model (EARSM) of
Wallin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.6 Boundary Conditions for the k, ω Models . . . . . . . . . . . 87
6.6.1 Free-Stream Boundary Conditions . . . . . . . . . . . 87
6.6.2 Wall Boundary Conditions . . . . . . . . . . . . . . . 88
6.7 The One-Equation Model of Spalart & Allmaras . . . . . . . 89
6.8 The One-Equation Model of Edwards & Chandra . . . . . . . 91
6.9 The Strain-Adaptive Linear Spalart-Allmaras (SALSA) Model 91
6.10 Boundary Conditions for the One-Equation Models . . . . . . 93
7 Test Cases Selected 94
7.1 Flat-Plate Boundary Layer (Case FPBL) . . . . . . . . . . . 95
7.1.1 Computational Setup . . . . . . . . . . . . . . . . . . 95
7.1.2 Computational Results and Discussion . . . . . . . . . 96
7.1.3 Some Modifications of the k, ω SST Model . . . . . . 101
7.1.4 Effects of Low-Reynolds-Number Modifications . . . . 105
7.2 Boundary Layer with Adverse Pressure Gradient (Case BS0) 107
7.2.1 Computational Setup . . . . . . . . . . . . . . . . . . 108
7.2.2 Computational Results and Discussion . . . . . . . . . 111
7.3 Boundary Layer with Pressure-Induced Separation (Case CS0) 118
7.3.1 Computational Results and Discussion . . . . . . . . . 119
7.4 Separated Airfoil Flow (Case AAA) . . . . . . . . . . . . . . 127
7.4.1 Computational Results and Discussion . . . . . . . . . 127
8 Numerical Issues 137
8.1 Grid Convergence. . . . . . . . . . . . . . . . . . . . . . . . . 137
8.2 Local Preconditioning for Low Mach Numbers. . . . . . . . . 141
8.3 Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.4 Artificial Damping in Boundary Layers. . . . . . . . . . . . . 149
8.5 Boundary-Value Dependences . . . . . . . . . . . . . . . . . . 153
8.5.1 Dependences on Wall Value of ω . . . . . . . . . . . . 153
8.5.2 Dependence on Free-Stream Value of ω . . . . . . . . 154
9 Summary and General Conclusions 156
10 Outlook 160
III Appendices 161
A RANSLESS – A New Approach to RANS/LES Coupling 162
A.1 Brief Review of Turbulence Physics at Turbulent Separation . 162
A.2 RANS/LES Coupling for Separated Flows . . . . . . . . . . . 162
A.2.1 Inflow Conditions for LES . . . . . . . . . . . . . . . . 164
A.2.2 Outflow Conditions for LES . . . . . . . . . . . . . . . 167
A.2.3 Inflow Conditions for RANS. . . . . . . . . . . . . . . 167
A.2.4 Outflow Conditions for RANS. . . . . . . . . . . . . . 167
A.3 Closing Note . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B Details of the Johnson-King Model 169
C Graphs of Computational Results 172
C.1 Boundary Layer with Adverse Pressure Gradient (Case BS0) 172
C.2 Boundary Layer with Pressure-Induced Separation (Case CS0) 185
C.3 Separated Airfoil Flow (Case AAA) . . . . . . . . . . . . . . 207
D Overview of Algorithmic Accomplishments 232
E Typical FLOWer Input Decks 234
E.1 Typical FLOWer Input Deck for Case FPBL . . . . . . . . . 234
E.2 Typical FLOWer Input Deck for Case BS0 and CS0 . . . . . 238
E.3 Typical FLOWer Input Deck for Case AAA . . . . . . . . . . 242
Bibliography 254