Analysis of turbulent flows

Cover ......Page 1
Elsevier ......Page 2
Title page ......Page 3
Date-line ......Page 4
Preface to the Second Edition ......Page 5
Contents ......Page 9
1.1 Introductory Remarks ......Page 15
1.2 Turbulence - Miscellaneous Remarks ......Page 17
1.3 The Ubiquity of Turbulence ......Page 21
1.4 The Continuum Hypothesis ......Page 23
1.5 Measures of Turbulence - Intensity ......Page 24
1.6 Measures of Turbulence - Scale ......Page 28
1.7 Measures of Turbulence - The Energy Spectrum ......Page 32
1.8 Measures of Turbulence - Intermittency ......Page 34
1.9 The Diffusive Nature of Turbulence ......Page 35
1.10 Turbulence Simulation ......Page 38
References ......Page 41
Problems ......Page 43
2.2 The Navier-Stokes Equations ......Page 45
2.3 Conventional Time-Averaging and Mass-Weighted-Averaging Procedures ......Page 47
2.4 Relation Between Conventional Time-Averaged Quantities and Mass-Weighted-Averaged Quantities ......Page 50
2.6 Energy Equations ......Page 52
2.7 Mean-Kinetic-Energy Equation ......Page 53
2.8 Reynolds-Stress Transport Equations ......Page 54
2.9 Reduced Forms of the Navier-Stokes Equations ......Page 58
Problems ......Page 61
3.2 Boundary-Layer Approximations for Compressible Flows ......Page 63
3.2.1 Laminar Flows ......Page 65
3.2.2 Turbulent Flows ......Page 68
3.3.1 Two-Dimensional Flows ......Page 73
3.3.2 Axisymmetric Flows ......Page 78
3.3.3 Three-Dimensional Flows ......Page 79
3.4 Mean-Kinetic-Energy Flows ......Page 81
3.5 Reynolds-Stress Transport Equations ......Page 82
3.6.1 Momentum Integral Equation ......Page 86
3.6.2 Mean Energy Integral Equation ......Page 87
3.6.3 Turbulent Energy Integral Equation ......Page 88
3.6.4 Energy Integral Equation ......Page 89
Problems ......Page 91
4.2 Composite Nature of a Turbulent Boundary Layer ......Page 95
4.3 Eddy-Viscosity, Mixing-Length, Eddy-Conductivity and Turbulent Prandtl Number Concepts ......Page 103
4.4 Mean-Velocity and Temperature Distributions in Incompressible Flows on Smooth Surfaces ......Page 109
4.4.1 Viscous and Conductive Sublayers ......Page 111
4.4.2 Fully Turbulent Part of the Inner Region ......Page 112
4.4.3 Inner Region ......Page 113
4.4.4 Outer Region ......Page 115
4.4.5 Equilibrium Boundary Layers ......Page 119
4.4.6 Velocity and Temperature Distributions for the Whole Layer ......Page 120
4.5 Mean-Velocity Distributions in Incompressible Turbulent Flows on Rough Surfaces with Zero Pressure Gradient ......Page 126
4.6 Mean-Velocity Distributions on Smooth Porous Surfaces with Zero Pressure Gradient ......Page 132
4.7 The Crocco Integral for Turbulent Boundary Layers ......Page 134
4.8.1 The Law of the Wall for Compressible Flows ......Page 137
4.8.2 Van Driest Transformation for the Law of the Wall ......Page 141
4.8.3 Transformations for Compressible Turbulent Flows ......Page 142
4.8.4 Law of the Wall for Compressible Flow with Mass Transfer ......Page 145
4.9 Effect of Pressure Gradient on Mean-Velocity and Temperature Distributions in Incompressible and Compressible Flows ......Page 147
References ......Page 148
Problems ......Page 150
5.1 Introduction ......Page 155
5.2 Eddy Viscosity and Mixing Length Models ......Page 156
5.3 CS Model ......Page 159
5.3.1 Effect of Low Reynolds Number ......Page 160
5.3.2 Effect of Transverse Curvature ......Page 163
5.3.3 Effect of Streamwise Wall Curvature ......Page 164
5.3.4 The Effect of Natural Transition ......Page 166
5.3.5 Effect of Roughness ......Page 170
5.4.1 Johnson-King Approach ......Page 173
5.4.2 Cebeci-Chang Approach ......Page 175
5.5 Extensions of the CS Model to Navier-Stokes Methods ......Page 179
5.6 Eddy Conductivity and Turbulent Prandtl Number Models .... ......Page 183
5.7 CS Model for Three-Dimensional Flows ......Page 190
5.7.1 Infinite Swept Wing Flows ......Page 193
5.7.2 Full Three-Dimensional Flows ......Page 196
5.8 Summary ......Page 199
References ......Page 200
Problems ......Page 204
6.1 Introduction ......Page 207
6.2.1 k-e Model ......Page 210
6.2.2 k-u Model ......Page 216
6.2.3 SST Model ......Page 218
6.3.1 Bradshaw's Model ......Page 221
6.3.2 Spalart-Allmaras Model ......Page 222
6.4 Stress-Transport Models ......Page 224
References ......Page 227
Problems ......Page 228
7.1 Introduction ......Page 231
7.2.1 Incompressible Flow on a Smooth Flat Plate ......Page 232
7.2.2 Incompressible Flow on a Rough Flat Plate ......Page 241
7.2.3 Compressible Flow on a Smooth Flat Plate ......Page 243
7.2.4 Compressible Flow on a Rough Flat Plate ......Page 248
7.3 Flows with Pressure Gradient: Integral Methods ......Page 250
7.4 Prediction of Flow Separation in Incompressible Flows ......Page 255
7.5 Free Shear Flows ......Page 259
7.5.1 Two-Dimensional Turbulent Jet ......Page 260
7.5.2 Turbulent Mixing Layer Between Two Uniform Streams at Different Temperatures ......Page 265
7.5.3 Power Laws for the Width and the Center line Velocity of Similar Free Shear Layers ......Page 271
Appendix 7A ......Page 272
References ......Page 274
Problems ......Page 275
8.1 Introduction ......Page 285
8.2 Numerical Solution of the Boundary-Layer Equations with Algebraic Turbulence Models ......Page 286
8.2.1 Numerical Formulation ......Page 288
8.2.2 Newton's Method ......Page 290
8.2.4 Subroutine SOLV3 ......Page 292
8.3.1 Impermeable Surface with Zero Pressure Gradient ......Page 295
8.3.2 Permeable Surface with Zero Pressure Gradient ......Page 296
8.3.3 Impermeable Surface with Pressure Gradient ......Page 299
8.3.4 Permeable Surface with Pressure Gradient ......Page 303
8.4 Axisymmetric Incompressible Flows ......Page 304
8.5.1 Impermeable Surface with Zero Pressure Gradient ......Page 306
8.5.2 Permeable Surface with Zero Pressure Gradient ......Page 309
8.5.3 Impermeable Surface with Pressure Gradient ......Page 310
8.7 Prediction of Two-Dimensional Incompressible Flows with Separation ......Page 311
8.7.1 Interaction Problem ......Page 313
8.7.2 Results for Airfoil Flows ......Page 314
8.8 Prediction of Three-Dimensional Flows with Separation ......Page 317
References ......Page 319
Problems ......Page 321
9.1 Introduction ......Page 329
9.2.1 Turbulence Equations and Boundary Conditions ......Page 330
9.2.2 Solution Procedure ......Page 331
9.3 Solution of the k-e Model Equations with and without Wall Functions ......Page 340
9.3.1 Solution of the k-e Model Equations without Wall Functions ......Page 341
9.4 Evaluation of Four Turbulence Models ......Page 344
9.4.1 Free-Shear Flows ......Page 345
9.4.2 Attached and Separated Turbulent Boundary Layers.... ......Page 351
9.4.3 Summary ......Page 356
9A. Appendix: Coefficients of the Linearized Finite-Difference Equations for the k-e Model ......Page 359
Problems ......Page 364
10.2 Integral Methods ......Page 375
10.2.3 Head's Method ......Page 376
10.3.1 MAIN ......Page 377
10.3.2 Subroutine INPUT ......Page 378
10.3.4 Subroutine GROWTH ......Page 380
10.3.8 Subroutine OUTPUT ......Page 381
10.6 Differential Method with CS Model: Infinite Swept-Wing Flows ......Page 382
10.10 Useful Subroutines ......Page 383
10.10.3 Subroutine MSA ......Page 384
References ......Page 385
Subject Index ......Page 387