Title Page
Abstract
Contents
Ch 1. Introduction 14
1.1. Motivation 14
1.2. Preconditioning Methods 15
1.3. Artificial Compressibility Methods 18
1.4. Objectives 18
1.5. Overviews of Thesis 19
Ch 2. Governing Equations of Incompressible/Compressible Fluids 21
2.1. Governing Equations of Compressible Fluids 21
2.2. Governing Equations of Incompressible Fluids 23
2.3. Unified Formulations 24
2.4. Turbulence Modeling 27
2.4.1. Spalart-Allmaras One Equation Model 27
2.4.2. K-ω SST Two Equations Model 28
2.5. Non-dimensionalization 32
Ch 3. Unification of Methods 33
3.1. Preconditioning Methods 33
3.1.1. Y.-H. Choi-Merkle's Viscous Preconditioners 36
3.1.2. Weiss-Smith's Preconditioners 37
3.1.3. Turkel's Preconditioners 38
3.2. Artificial Compressibility Methods 40
3.2.1. Chorin's Artificial Compressibility Method 41
3.2.2. Turkel's Artificial Compressibility Method 42
3.3. Unified Preconditioner 43
3.3.1. Low Mach Preconditioning of Unified Preconditioner 44
3.3.2. Artificial Compressibility of Unified Preconditioner 44
Ch 4. Numerical Implementation 48
4.1. Spatial Discretization 48
4.1.1. Roe's Approximate Riemann Solver 52
4.1.2. Jameson-Schmidt-Turkel Artificial Dissipation 57
4.1.3. Viscous Flux 58
4.2. Temporal Discretization 59
4.3. Implicit Boundary Conditions 62
4.3.1. Farfield Boundary Conditions 63
4.3.2. Inviscid Slip Wall 67
4.3.3. Viscous Non-slip Wall 68
4.3.4. Prescribed Velocity Boundary Condition 70
Ch 5. Validations of Unified Preconditioner 74
5.1. 2D Zero Pressure Gradient Flat Plate 74
5.2. Fully-Developed Square Duct Flow 83
5.3. Incompressible Square Duct with 90° Bend 86
5.4. 3D Bump-in-channel 95
5.5. 2D Multielement Airfoil Verification Case 101
5.6. Onera M6 Wing 104
5.7. DLR F6 Wing-Body 111
Ch 6. Conclusion 118
References 120
Appendices 123
Appendix A 123
Appendix B 126
Appendix C 128
Table 1. Model Coefficients of Spalart-Allmaras One Equation Model 30
Table 2. Model Coefficients of K-ω SST Two Equations Model 31
Table 3. Preconditioners defined using modified αp and βT[이미지참조] 47
Table 4. Artificial Compressibility Methods in Unified Preconditioner 47
Table 5. Temporal Discretization Depending on θ 61
Table 6. Results of parametric studies of proposed artificial compressibility method 77
Figure 1. Control volume Vi at vertex i and neighboring vertex j with shared surface k[이미지참조] 51
Figure 2. Axis orientation of square duct inlet 73
Figure 3. Geometry of grid for 2D zero pressure gradient flat plate 76
Figure 4. Comparison of Cƒ distributions on the wall of 2D zero pressure gradient flat plate[이미지참조] 78
Figure 5. Comparison of Cƒ distributions with experimental data[이미지참조] 78
Figure 6. Comparison of μt/μ∞ contours of 2D zero pressure gradient flat plate[이미지참조] 79
Figure 7. Residual histories (M=0, Roe, α'p=5.0)[이미지참조] 80
Figure 8. Residual histories (M=0, Roe, α'p=1.0)[이미지참조] 80
Figure 9. Residual histories (M=0, Roe, α'p=0.1)[이미지참조] 81
Figure 10. Residual histories (M=0, JST, α'p=5.0)[이미지참조] 81
Figure 11. Residual histories (M=0, JST, α'p=1.0)[이미지참조] 82
Figure 12. Residual histories (M=0, JST, α'p=0.1)[이미지참조] 82
Figure 13. Geometry of grid for square duct 84
Figure 14. Error analyses of proposed artificial compressibility method 84
Figure 15. x-component of velocity contours at mid-point of square duct 85
Figure 16. Geometry of grid for L-shaped square duct 87
Figure 17. Velocity magnitude contours in bending section 88
Figure 18. Velocity magnitude contour of S6 89
Figure 19. Velocity magnitude contours of S6 computed(left) and measured(right) 89
Figure 20. Velocity magnitude of S1-L1 90
Figure 21. Velocity magnitude of S4-L1 90
Figure 22. Velocity magnitude of S5-L1 91
Figure 23. magnitude of S6-L1 91
Figure 24. Velocity magnitude of S1-L2 92
Figure 25. Velocity magnitude of S4-L2 92
Figure 26. Velocity magnitude of S5-L2 93
Figure 27. Velocity magnitude of S6-L2 93
Figure 28. Residual histories for Roe scheme 94
Figure 29. Residual histories for JST scheme 94
Figure 30. Geometry of grid for 3D bump-in-channel 96
Figure 31. Pressure Residual History of 3D Bump-in-channel 97
Figure 32. Pressure Residual History of 3D Bump-in-channel 97
Figure 33. Cp distributions of the wall for 3D bump-in-channel (M=0, α'p=1.0, α=0.0)[이미지참조] 98
Figure 34. Cp distributions of the wall for 3D bump-in-channel[이미지참조] 99
Figure 35. Comparison of μt/μ∞ contours for 3D bump-in-channel at x=0.3[이미지참조] 100
Figure 36. Geometry of grid for 2D Multielement Airfoil 102
Figure 37. Locally Compressible Regions in the Leading Edge 103
Figure 38. Comparison of abs(cƒ) distributions on the wall of 2D Multielement Airfoil[이미지참조] 103
Figure 39. Configuration of grid of Onera M6 wing 105
Figure 40. Locations where Cp distributions are compared[이미지참조] 105
Figure 41. λ shock in Cp contour on upper surface[이미지참조] 106
Figure 42. Comparison of Cp distribution at η=0.2[이미지참조] 107
Figure 43. Comparison of Cp distribution at η=0.44[이미지참조] 107
Figure 44. Comparison of Cp distribution at η=0.65[이미지참조] 108
Figure 45. Comparison of Cp distribution at η=0.8[이미지참조] 108
Figure 46. Comparison of Cp distribution at η=0.9[이미지참조] 109
Figure 47. Comparison of Cp distribution at η=0.96[이미지참조] 109
Figure 48. Comparison of Cp distribution at η=0.99[이미지참조] 110
Figure 49. Configuration of grid of DLR F6 Wing Body 112
Figure 50. Locations where Cp distributions are compared[이미지참조] 112
Figure 51. Cp contours of upper and lower surfaces[이미지참조] 113
Figure 52. Comparison of Cp distribution at η=0.15[이미지참조] 114
Figure 53. Comparison of Cp distribution at η=0.239[이미지참조] 114
Figure 54. Comparison of Cp distribution at η=0.331[이미지참조] 115
Figure 55. Comparison of Cp distribution at η=0.377[이미지참조] 115
Figure 56. Comparison of Cp distribution at η=0.411[이미지참조] 116
Figure 57. Comparison of Cp distribution at η=0.514[이미지참조] 116
Figure 58. Comparison of Cp distribution at η=0.638[이미지참조] 117
Figure 59. Comparison of Cp distribution at η=0.847[이미지참조] 117
Figure C-1. Temperature fields of incompressible & compressible fluid flows near inviscid adiabatic wall 131
Figure C-2. Temperature fields near wall with constant temperature 132