 | Marciniak V. Pnenomenological transition modelling for turbomachinery flows: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Antriebstechnik, Köln. - Köln: DLR, 2016. - x, 117 p.: ill. - (Forschungsbericht; 2016-15). - Res. also Germ. - Bibliogr.: p.105-113. - ISSN 1434-8454
Шифр: (Pr 1120/2016-15) 02
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Nomenclature ................................................... ix
1 Introduction ............................................... 1
2 Transition in Turbomachines ................................ 3
2.1 States of Motion in a Boundary Layer ....................... 3
2.2 Transition Modes ........................................... 4
2.2.1 Natural Transition .................................. 4
2.2.2 Bypass Transition ................................... 5
2.2.3 Separation-induced Transition ....................... 5
2.2.4 Wake-induced Transition ............................. 7
2.3 Factors Influencing Transition ............................. 7
2.4 Role of Transition in Turbomachine Design ................. 10
2.4.1 Fans and Compressors ............................... 10
2.4.2 High-pressure Turbines ............................. 12
2.4.3 Low-pressure Turbines .............................. 12
2.5 Overview of Transition Prediction ......................... 15
2.5.1 Experimental Correlations .......................... 15
2.5.2 Linear Stability Theory ............................ 15
2.5.3 Numerical Simulations .............................. 15
2.6 Objectives of this Work ................................... 17
3 Derivation of the Transition Model ........................ 19
3.1 Experimental Observations ................................ 19
3.1.1 Boundary Layers .................................... 19
3.1.2 Shear Layers ....................................... 22
3.1.3 Stagnation Point Flows ............................. 28
3.1.4 Summary of the Experimental Observations ........... 29
3.2 Theoretical Concepts ...................................... 30
3.2.1 Laminar Kinetic Energy ............................. 30
3.2.2 Transport Equations for Fluctuations ............... 31
3.3 Formulation of the Transition Model ....................... 32
3.3.1 Modelling Concepts ................................. 32
3.3.2 Modelling Principles ............................... 34
3.3.3 Boundary Conditions ................................ 35
3.3.4 Transport Equation for the Laminar Kinetic Energy .. 36
3.3.5 Modification of the Turbulence Model ............... 40
3.3.6 Complete Formulation of the Model .................. 42
3.4 Concluding Remarks ....................................... 44
4 Numerical Methods ......................................... 45
4.1 General Equations ......................................... 45
4.1.1 Favre-averaged Navier-Stokes Equations ............. 45
4.1.2 Boundary Conditions ................................ 47
4.2 Discretization ............................................ 47
4.3 Resolution of the Partial Differential Equations .......... 48
5 Calibration of the Model .................................. 49
5.1 Low-pressure Turbine Cascade T107 ......................... 49
5.1.1 Description of the Cascade ......................... 49
5.1.2 Investigated Flows ................................. 50
5.2 Calibration Methodology ................................... 51
5.3 Evaluation of the Results ................................. 53
5.3.1 Cascade Performance ................................ 53
5.3.2 Flow Details ....................................... 54
5.3.3 Boundary Layer Analysis ............................ 58
5.4 Concluding Remarks ........................................ 61
6 Application of the Model .................................. 63
6.1 Low-pressure Turbine Cascade T108 ......................... 63
6.1.1 Description of the Cascade ......................... 63
6.1.2 Investigated Flows ................................. 64
6.1.3 Results ............................................ 65
6.1.4 Concluding Remarks ................................. 68
6.2 Low-pressure Turbine Cascade T106C ........................ 68
6.2.1 Description of the Cascade ........................ 68
6.2.2 Investigated Flows ................................. 69
6.2.3 Results ............................................ 69
6.2.4 Concluding Remarks ................................. 72
6.3 Low-pressure Turbine Cascade Design С ..................... 72
6.3.1 Description of the Cascade ......................... 72
6.3.2 Investigated Flows ................................. 73
6.3.3 Results ............................................ 74
6.3.4 Concluding Remarks ................................. 78
6.4 Controlled Diffusion Airfoil Compressor Cascade ........... 79
6.4.1 Description of the Cascade ......................... 79
6.4.2 Investigated Flows ................................. 80
6.4.3 Results ............................................ 81
6.4.4 Concluding Remarks ................................. 92
7 Conclusion .................................................. 95
List of Figures ................................................ 98
List of Tables ................................................ 103
Bibliography .................................................. 104
A Appendix ................................................. 115
A.l Influence of the Span-wise Resolution ................ 115
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