In recent decades, numerical algorithms and computer power have advanced to the point where computer simulations of the equations fluid flow have become routine. How does that affect the way we teach fluid dynamics? This book seizes on that question. One of its objectives is to integrate computer solutions into fluid dynamics education; another is to review important concepts of fluid dynamics that a computationalist needs in order to understand computed flows. This book provides a development of fluid flow theory in concert with a perspective on how computations are formulated and effected.
Author(s): Paul A. Durbin, Gorazd Medic
Edition: 1
Publisher: Cambridge University Press
Year: 2007
Language: English
Commentary: 61102
Pages: 363
City: Oxford; New York
Tags: Механика;Механика жидкостей и газов;
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1.1 Why Study Fluid Dynamics?......Page 15
1.2 Viscosity......Page 16
1.3 Navier–Stokes Equations......Page 19
1.4 Reynolds Number......Page 24
1.5.1 Couette–Poiseuille Flow......Page 28
1.5.2 Oscillatory Boundary Layer......Page 33
1.6 Some Basics......Page 35
1.6.1 One-Dimensional Conservation Laws......Page 36
1.6.2 Bernoulli's Equation......Page 38
1.6.3 Unsteady Flow......Page 43
1.7 Swirl......Page 45
1.7.1 Computation of Swirling Flow in an Expansion......Page 48
1.8 Vorticity and Its Dynamics......Page 49
1.8.1 Vortex Kinematics and Dynamics......Page 51
1.8.2 Stretching and Rotation......Page 56
1.8.3 Origin of Vorticity......Page 58
1.8.4 Circulation and Lift......Page 60
1.8.5 Diffusion of Vorticity......Page 63
1.8.6 Visualization of Vortices......Page 66
1.9 Turbulence......Page 69
2 Elements of Computational Analysis......Page 75
2.1.1 Computational Domain......Page 77
2.1.2 Discrete Representation of the Geometry......Page 81
2.1.3 Structured Grids......Page 82
2.1.4 Unstructured Meshes......Page 86
2.1.5 Mesh Quality......Page 88
2.2 Computation of Fluid Flow......Page 92
2.2.1 Discrete Equations......Page 93
2.2.2 Centered and Upwind Differencing......Page 96
2.2.3 Solvers......Page 100
2.2.4 Boundary Conditions......Page 104
2.3.1 Residuals and Convergence......Page 107
2.3.2 Grid Independence......Page 108
2.4 Postprocessing and Visualization......Page 111
2.4.1 Streamlines......Page 112
2.4.2 Vectors and Contours......Page 114
2.4.3 Quantitative Data......Page 116
2.5 Packages and Codes......Page 117
3 Creeping Flow......Page 122
3.1 The Low Reynolds Number Limit......Page 123
3.1.1 Stokes Flow around a Sphere......Page 125
3.1.2 Resistance Matrix......Page 130
3.1.3 Resistance Due to Relative Motion......Page 133
3.1.4 Computation of Resistance Coefficients......Page 134
3.1.5 Eddies in Stokes Flow......Page 136
3.2 Hydrodynamic Lubrication......Page 138
4.1 Separation, Vorticity, and Vortex Shedding......Page 146
4.1.1 Five Examples......Page 147
4.1.2 Secondary Circulation......Page 165
4.2 Wakes, Jets, and Mixing Layers......Page 169
4.2.1 Scaling Shear Layer Evolution......Page 170
4.2.2 Entrainment......Page 173
4.2.3 Free and Impinging Round Jets......Page 174
5 High Reynolds Number Flow and Boundary Layers......Page 181
5.1 Formal Definition of the Boundary Layer......Page 182
5.1.1 Growth of the Boundary Layer......Page 186
5.1.2 Pressure Gradients and Separation......Page 189
5.1.3 Gridding......Page 192
5.2 Approximate Equations......Page 195
5.3 Three-Dimensional Boundary Layers......Page 197
5.4 Separation in Three Dimensions and Critical Points......Page 199
5.5 High Reynolds Number Flow over a Spheroid......Page 202
5.6 Potential Flow......Page 205
5.6.1 Point Sources......Page 206
5.6.2 Images......Page 210
5.6.3 Point Vortices and Circulation......Page 211
5.6.4 Stream Function......Page 213
5.6.5 Added Mass......Page 215
6 Turbulent Flow......Page 224
6.2 Statistically Averaged Method......Page 225
6.2.1 Eddy Viscosity Model......Page 229
6.2.2 Computed Example......Page 234
6.2.3 Limitations of Scalar Eddy Viscosity Models......Page 236
6.3.1 Boundary Layers......Page 239
6.3.2 Wall Functions......Page 247
6.3.3 Free Shear Layers......Page 250
6.3.4 Computed Axisymmetric Jets......Page 251
6.4.1 Spectrum of Turbulence......Page 253
6.4.2 Direct Numerical Simulation......Page 256
6.4.3 DNS of Isotropic Turbulence......Page 258
6.4.4 Approximate Simulation of Large Eddies......Page 260
6.5 Instability Theory......Page 268
6.5.1 Inflection Point Theorem......Page 270
6.5.2 Instability in Boundary Layers......Page 273
7.1 Thermodynamics......Page 278
7.1.1 First Law......Page 279
7.1.3 Entropy and Irreversibility......Page 280
7.1.4 First Law with Flow......Page 282
7.1.5 Isentropic Relations......Page 284
7.2 Mach Waves......Page 285
7.2.1 Speed of Sound......Page 286
7.2.2 Occurrence of Shock Waves......Page 287
7.3.1 Normal Shock......Page 290
7.3.2 Supersonic Flow over a Hemisphere......Page 292
7.3.3 Expansion Fan......Page 295
7.3.4 Supersonic Flow over a Wedge......Page 298
7.4 Quasi-One-Dimensional Gas Dynamics......Page 300
7.4.1 Shock Patterns and Shock-Induced Separation......Page 306
7.5 Computation of Compressible Flows......Page 314
8 Interfaces......Page 321
8.1 Interface Conditions......Page 322
8.2 Surface Tension......Page 325
8.2.1 Capillarity and Contact Angle......Page 328
8.2.2 Disintegration by Capillarity......Page 330
8.2.3 Simulation of Capillary Breakup......Page 334
8.3 Inviscid Free Surface......Page 335
8.3.1 Group Velocity and Its Connection to Surface Excrescence......Page 337
8.3.2 Sloshing......Page 342
8.3.3 Numerical Simulation of Sloshing......Page 346
8.4 Volume of Fluid Method......Page 348
8.4.1 Pouring a Viscous Liquid......Page 350
Bibliography......Page 357
Index......Page 359
