Fluid Dynamics - Theory, Computation, and Numerical Simulation

Front Matter......Page 1
Preface......Page 3
Subject Index......Page 0
Table of Contents......Page 5
1.1 Fluids and Solids......Page 10
1.2 Fluid Parcels and Flow Kinematics......Page 11
1.3 Coordinates, Velocity, and Acceleration......Page 13
1.4 Fluid Velocity and Streamlines......Page 24
1.5 Point Particles and Their Trajectories......Page 27
1.6 Material Surfaces and Elementary Motions......Page 36
1.7 Interpolation......Page 47
2.1 Fundamental Modes of Fluid Parcel Motion......Page 58
2.2 Fluid Parcel Expansion......Page 70
2.3 Fluid Parcel Rotation and Vorticity......Page 71
2.4 Fluid Parcel Deformation......Page 77
2.5 Numerical Differentiation......Page 81
2.6 Areal and Volumetric Flow Rate......Page 87
2.7 Mass Flow Rate, Mass Conservation, and the Continuity Equation......Page 97
2.8 Properties of Point Particles......Page 103
2.9 Incompressible Fluids and Stream Functions......Page 111
2.10 Kinematic Conditions at Boundaries......Page 116
3.1 Flow Classification Based on Kinematics......Page 121
3.2 Irrotational Flows and the Velocity Potential......Page 124
3.3 Finite-Difference Methods......Page 132
3.4 Linear Solvers......Page 141
3.5 Two-Dimensional Point Sources and Point-Source Dipoles......Page 145
3.6 Three-Dimensional Point Sources and Point-Source Dipoles......Page 159
3.7 Point Vortices and Line Vortices......Page 164
4.1 Body Forces and Surface Forces......Page 174
4.2 Traction and the Stress Tensor......Page 176
4.3 Traction Jump across a Fluid Interface......Page 183
4.4 Stresses in a Fluid at Rest......Page 191
4.5 Viscous and Newtonian Fluids......Page 195
4.6 Simple Non-Newtonian Fluids......Page 204
4.7 Stresses in Polar Coordinates......Page 207
4.8 Boundary Condition on the Tangential Velocity......Page 213
4.9 Wall Stresses in Newtonian Fluids......Page 215
5.1 Equilibrium of Pressure and Body Forces......Page 218
5.2 Force Exerted on Immersed Surfaces......Page 227
5.3 Archimedes' Principle......Page 234
5.4 Shapes of Two-Dimensional Interfaces......Page 237
5.5 A Semi-Infinite Interface Attached to an Inclined Plate......Page 241
5.6 Meniscus between Two Parallel Plates......Page 245
5.7 A Two-Dimensional Drop on a Horizontal Plane......Page 251
5.8 Axisymmetric Shapes......Page 256
6.1 Newton's Second Law for the Motion of a Parcel......Page 262
6.2 Integral Momentum Balance......Page 268
6.3 Cauchy's Equation of Motion......Page 273
6.4 Euler's and Bernoulli's Equations......Page 280
6.5 The Navier-Stokes Equation......Page 291
6.6 Vorticity Transport......Page 298
6.7 Dynamic Similitude, the Reynolds Number, and Dimensionless Numbers in Fluid Dynamics......Page 306
7.1 Steady Flow in a Two-Dimensional Channel......Page 316
7.2 Steady Film Flow Down an Inclined Plane......Page 325
7.3 Steady Flow through a Circular or Annular Tube......Page 329
7.4 Steady Flow through Channels and Tubes with Various Cross-Sections......Page 337
7.5 Steady Swirling Flow......Page 346
7.6 Transient Flow in a Channel......Page 349
7.7 Oscillatory Flow in a Channel......Page 357
7.8 Transient and Oscillatory Flow in a Circular Tube......Page 364
8.1 Choice of Governing Equations......Page 374
8.2 Unidirectional Flow; Velocity/Pressure Formulation......Page 376
8.3 Unidirectional Flow; Velocity/Vorticity Formulation......Page 387
8.4 Unidirectional Flow; Stream Function/Vorticity Formulation......Page 392
8.5 Two-Dimensional Flow; Stream Function/Vorticity Formulation......Page 396
8.6 Velocity/Pressure Formulation......Page 405
8.7 Operator Splitting and Solenoidal Projection......Page 409
9. Flows at Low Reynolds Numbers......Page 420
9.1 Flows in Narrow Channels......Page 421
9.2 Film Flow on a Horizontal or Down Plane Wall......Page 434
9.3 Two-Layer Channel Flow......Page 446
9.4 Flow Due to the Motion of a Sphere......Page 454
9.5 Point Forces and Point Sources in Stokes Flow......Page 461
9.6 Two-Dimensional Stokes Flow......Page 470
9.7 Flow near Corners......Page 476
10. Flows at High Reynolds Numbers......Page 486
10.1 Changes in the Structure of a Flow with Increasing Reynolds Number......Page 487
10.2 Prandtl Boundary-Layer Analysis......Page 490
10.3 Prandtl Boundary Layer on a Flat Surface......Page 496
10.4 Von Karman's Integral Method......Page 512
10.5 Instability of Shear Flows......Page 524
10.6 Turbulent Motion......Page 537
10.7 Analysis of Turbulent Motion......Page 551
11. Vortex Motion......Page 560
11.1 Vorticity and Circulation in Two-Dimensional Flow......Page 561
11.2 Motion of Point Vortices......Page 563
11.3 Two-Dimensional Flow with Distributed Vorticity......Page 578
11.4 Vorticity, Circulation, and Three-Dimensional Flow Induced by Vorticity......Page 593
11.5 Axisymmetric Flow Induced by Vorticity......Page 598
11.6 Three-Dimensional Vortex Motion......Page 612
12. Aerodynamics......Page 618
12.1 General Features of Flow Past an Aircraft......Page 619
12.2 Airfoils and the Kutta-Joukowski Condition......Page 621
12.3 Vortex Panels......Page 624
12.4 Vortex Panel Method......Page 632
12.5 Vortex Sheet Representation......Page 641
12.6 Point-Source-Dipole Panels......Page 650
12.7 Point-Source Panels and Green's Third Identity......Page 657
FDLIB Software Library......Page 663
FDLIB Directories......Page 665
References......Page 678
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W......Page 697