 | Morsbach C. Reynolds stress modelling for turbomachinery flow applications: Diss. … Dr. rer. nat. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Antriebstechnik, Köln. - Köln: DLR, 2016. - XI, 163 p.: ill. - (Forschungsbericht; 2016-41). - Res. also Germ. - Bibliogr.: p.135-144.( - ISSN 1434-8454
Шифр: Pr 1120/2016-41) 02
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1 Introduction and motivation ................................ 1
1.1 Computational Fluid Dynamics - CFD ......................... 1
1.2 Reynolds-Averaged Navier-Stokes approach - RANS ............ 2
1.3 Differential Reynolds stress modelling - DRSM .............. 3
1.4 Outline of the thesis ...................................... 4
2 State of the art ........................................... 7
2.1 Statistical turbulence modelling ........................... 7
2.2 Differential Reynolds stress modelling ..................... 8
3 Turbulence modelling ...................................... 13
3.1 Statistical turbulence modelling .......................... 13
3.2 Differential Reynolds stress modelling .................... 16
3.2.1 Reynolds stress transport equations ................ 16
3.2.2 Reynolds stress anisotropy and its visualisation ... 17
3.2.3 Pressure-strain correlation ........................ 20
3.2.4 Dissipation correlation ............................ 21
3.2.5 Diffusion of Reynolds stresses ..................... 21
3.3 Studied DRSMs ............................................. 22
3.3.1 SSG/LRR-ω model .................................... 22
3.3.2 Jakirlic, Hanjalic and Maduta's ui-uj-ωh model ..... 23
3.4 Numerical properties of pressure-strain models ............ 30
3.4.1 Model problem ...................................... 31
3.4.2 Dynamical systems analysis ......................... 33
3.4.3 Numerical phase space analysis ..................... 35
4 Numerical method .......................................... 43
4.1 Flow solver ............................................... 43
4.2 Discretisation of transport equations ..................... 46
4.3 Linearisation of the residual ............................. 48
4.4 Boundary conditions for turbulent flows ................... 51
4.4.1 Solid walls ........................................ 51
4.4.2 Rotationally periodic boundaries ................... 51
4.4.3 Mixing planes ...................................... 52
4.4.4 Inflow ............................................. 53
4.4.5 Symmetry plane ..................................... 54
4.5 Numerical performance ..................................... 54
5 Model validation in generic flows ......................... 57
5.1 Channel flow .............................................. 57
5.2 Boundary layer ............................................ 70
5.3 Curved boundary layer ..................................... 74
5.4 Separated boundary layer .................................. 78
5.5 Shock wave/boundary layer interaction ..................... 83
6 Model application to turbomachinery flows ................. 87
6.1 Compressor cascade ........................................ 87
6.1.1 Description ........................................ 87
6.1.2 Numerical setup .................................... 87
6.1.3 Discussion ......................................... 89
6.2 Ranque-Hilsch vortex tube ................................. 96
6.2.1 Description ........................................ 96
6.2.2 Numerical setup .................................... 98
6.2.3 Discussion ......................................... 98
6.3 One and a half stage cold air turbine .................... 107
6.3.1 Description ....................................... 107
6.3.2 Numerical setup ................................... 109
6.3.3 Post-processing ................................... 110
6.3.4 Discussion ........................................ 111
7 Summary and Outlook ...................................... 125
Nomenclature .................................................. 129
Bibliography .................................................. 134
List of figures ............................................... 145
List of tables ................................................ 151
A Model specifications ..................................... 153
A.l Menter SST k-ω ........................................... 153
A.2 Hellsten EARSM k-ω ....................................... 154
A.3 DRSM: common terms ....................................... 157
А.4 SSG/LRR-ω model .......................................... 158
A.5 Jakirlić, Hanjalić and Maduta's ui-uj-ωh model ........... 159
В Vortex detection methods ................................. 163
B.l The λ2-criterion ......................................... 163
B.2 Streamwise vorticity ..................................... 163
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