Abstract ...................................................... 111
Table of Contents ............................................. vii
Nomenclature .................................................. xui
Chapter 1 Introduction ......................................... 1
Chapter 2 Transition phenomena ................................. 5
2.1 Transition mechanisms ...................................... 6
2.1.1 Attachment line transition .......................... 6
2.1.2 Crossflow transition ................................ 6
2.1.3 Streamwise transition ............................... 8
2.1.4 Other transition mechanisms ........................ 11
2.2 Transition prediction ..................................... 12
DNS or LES ................................................ 12
2.2.2 Local linear stability theory ...................... 13
2.2.3 Empirical transition criteria ...................... 19
2.2.4 Transition transport models ........................ 19
Chapter 3 γ-Reθt transition model ............................. 21
3.1 Introduction .............................................. 21
3.2 Streamwise transition modeling ............................ 23
3.2.1 Vorticity Reynolds number and Reg formulation ...... 23
3.2.2 λ2 and Tu .......................................... 24
3.3 Crossflow transition modeling ............................. 24
3.3.1 Recalling the semi-local C1 approach ............... 25
3.3.2 Local C1-based approach ............................ 30
3.3.3 Local helicity-based approach ...................... 39
Chapter 4 Coupling of γ-Reθt and a Reynolds stress model
and model calibration .......................................... 45
4.1 The γ-Reθt RSM transition model ........................... 46
4.1.1 SSG/LRR-ω model .................................... 46
4.1.2 Coupling of the models ............................. 48
4.1.3 Sustaining turbulence .............................. 50
4.1.4 Length-scale equation modification ................. 51
4.2 Streamwise transition calibration ......................... 54
4.2.1 New onset function ................................. 57
4.2.2 New correlation function ........................... 58
4.3 CF transition calibration ................................. 59
4.3.1 Local C1-based approach ............................ 60
4.3.2 Local helicity-based approach ...................... 61
Chapter 5 Grid influences and best practice ................... 63
5.1 Grid convergence .......................................... 64
5.1.1 Streamwise transition .............................. 64
5.1.2 Crossflow transition ............................... 66
5.2 Numerical scheme settings ................................. 67
5.3 Sustaining turbulence ..................................... 69
5.4 Other settings ............................................ 69
Chapter 6 Validation cases .................................... 71
6.1 Zero pressure-gradient flat plate ......................... 71
6.1.1 T3-series ZPG flat plate ........................... 72
6.1.2 Schubauer & Klebanoff flat plate ................... 74
6.2 2D airfoils and infinite swept wing ....................... 76
6.2.1 NLF(1)-0416 airfoil ................................ 76
6.2.2 NACA0021 airfoil ................................... 79
6.2.3 CAST 10-2 airfoil .................................. 81
6.2.4 A310 3-element airfoil ............................. 83
6.2.5 NLF (2)-0415 swept wing ............................ 84
6.3 3D cases .................................................. 87
6.3.1 DLR-F5 wing ........................................ 87
6.3.2 DLR 6:1 prolate Spheroid ........................... 93
6.3.3 Sickle wing ........................................ 95
6.3.4 DLR-F4 wing body ................................... 98
Chapter 7 Summary and Outlook ................................ 105
7.1 Summary .................................................. 105
7.2 Open questions ........................................... 106
7.2.1 Streamwise transition ............................. 106
7.2.2 CF transition ..................................... 107
Outlook .................................................. 108
Bibliography ............................................. 109
Publication .............................................. 115
Appendix A C2-criterion ...................................... A-l
Appendix В SST & 4-equation model ............................ B-3
B.l Menter SST model ......................................... B-3
B.2 Langtry & Menter γ-Reθt SST model ........................ B-4
B.3 4-equation model with CF-extension ....................... B-7
B.3.1 Local C1-based approach ........................... B-8
B.3.2 Local helicity-basedapproach ...................... B-8
Appendix С Calibration of model correlations for
CF-extensions ................................................. C-9
C.l Local C1-based model ..................................... C-9
C.2 Local helicity-based model .............................. C-l1
Appendix D Calibration details .............................. D-15
D.l Improvement of the transition length behavior ........... D-15
D.2 Effect of Flength,cf ...................................... D-16
D.3 Influence from the turbulence settings at farfiled ...... D-16
Appendix E SSG/LRR-g model + 9-equation model ............... E-19
E.1 SSG/LRR-g model ......................................... E-19
E.2 γ-Reθt RSM model (SSG/LRR-g model) ....................... E-20
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