Computational fluid dynamics

Title page  ......Page 1
Date-line  ......Page 2
CONTENTS  ......Page 3
Preface  ......Page 7
20.1 Introductory Remarks  ......Page 9
20.2 Fundamental Concepts and Definitions  ......Page 12
20.3 Introduction to Transition  ......Page 13
20.3.1 Stability Theory  ......Page 15
20.4 Conceptual Model for Turbulent Flows  ......Page 17
20.5 Production, Diffusion, and Dissipation of Turbulence  ......Page 20
20.6 Length and Time Scales of Turbulence  ......Page 21
20.7 Free Shear Layer Flows  ......Page 23
20.8 Numerical Techniques for Turbulent Flows  ......Page 24
20.9 Concluding Remarks  ......Page 26
21.2 Fundamental Concepts  ......Page 28
21.2.1 Universal Velocity Distribution  ......Page 31
21.3 Modification of the Equations of Fluid Motion  ......Page 35
21.3.1 Reynolds Averaged Navier-Stokes Equations  ......Page 36
21.3.1.1 Turbulent Shear Stress and Heat Flux  ......Page 42
21.3.1.2 Flux Vector RANS Formulation  ......Page 45
21.4 Turbulence Models  ......Page 46
21.4.1 Zero-Equation Turbulence Models  ......Page 47
21.4.2 One-Equation Turbulence Models  ......Page 50
21.4.2.1 Baldwin-Barth One-Equation Turbulence Model  ......Page 51
21.4.2.1.1 Nondimensional form  ......Page 52
21.4.2.1.2 Baldwin-Barth turbulence model in computational space  ......Page 53
21.4.2.2 Spalart-Allmaras One-Equation Turbulence Model  ......Page 56
21.4.2.2.1 Nondimensional form  ......Page 58
21.4.2.2.2 Spalart-Allmaras turbulence model in computational space  ......Page 59
21.4.3 Two-Equation Turbulence Models  ......Page 61
21.4.3.1 $k-\varepsilon$ Two-Equation Turbulence Model  ......Page 62
21.4.3.1.1 Low Reynolds number $k-\varepsilon$ model  ......Page 64
21.4.3.1.3 Initial and boundary conditions  ......Page 66
21.4.3.2 $k-\omega$ Two-Equation Turbulence Model  ......Page 67
21.4.3.3 Combined $k-\varepsilon$/$k-\omega$ Two-Equation Turbulence Model  ......Page 68
21.4.3.3.1 Baseline model  ......Page 71
21.4.3.3.2 Initial and boundary conditions  ......Page 72
21.4.3.3.5 Nondimensional form  ......Page 73
21.4.3.3.6 $k-\varepsilon$/$k-\omega$ turbulence model in computational space  ......Page 74
21.5 Numerical Considerations  ......Page 76
21.6 Finite Difference Formulations  ......Page 77
21.6.1.1 Implicit Formulation  ......Page 78
21.6.1.2 Explicit Formulation  ......Page 83
21.6.2.1 Implicit Formulation  ......Page 85
21.6.2.2 Explicit Formulation  ......Page 92
21.6.3 Two-Equation Turbulence Models  ......Page 94
21.7.1 Shock/Boundary Layer Interaction  ......Page 100
21.7.2 Two-Dimensional Base Flow  ......Page 103
21.7.3 Axisymmetric, Supersonic, Turbulent Exhaust Flow  ......Page 108
21.8 Favre-Averaged Navier-Stokes Equations  ......Page 113
21.8.1 Turbulent Viscosity  ......Page 121
21.9 Concluding Remarks  ......Page 123
22.1 Introductory Remarks  ......Page 125
22.2 Compact Finite Difference Formulations for the First-Order Derivatives  ......Page 126
22.2.1 One-Sided Approximations  ......Page 133
22.3 Compact Finite Difference Formulations for the Second-Order Derivatives  ......Page 134
22.4 Error Analysis  ......Page 135
22.5 Application to a Hyperbolic Equation  ......Page 138
22.6 Problems  ......Page 145
23.1 Introductory Remarks  ......Page 147
23.2.1 Filtered Navier-Stokes Equations  ......Page 148
23.2.2 Subgridscale Models  ......Page 154
23.2.2.1 Eddy Viscosity  ......Page 155
23.2.2.1.1 Smagorinsky model  ......Page 156
23.2.2.1.2 Dynamic model  ......Page 157
23.3 Direct Numerical Simulation  ......Page 160
Appendix J: Transformation of Turbulence Models from Physical Space to Computational Space  ......Page 163
Appendix K: The Transport Equation for the Turbulence Kinetic Energy  ......Page 167
References  ......Page 174
Index  ......Page 178