Preface ......................................................... v
1 Introduction ................................................. 1
2 Properties of Liquids and Gases ............................. 15
2.1 Properties of Liquids .................................. 15
2.2 State of Stress ........................................ 16
2.3 Liquid Pressure ........................................ 18
2.4 Properties of Gases .................................... 24
2.5 Gas Pressure ........................................... 26
2.6 Interaction Between Gas Pressure and Liquid Pressure ... 29
2.7 Equilibrium in Other Force Fields ...................... 32
2.8 Surface Stress (Capillarity) ........................... 36
2.9 Problems ............................................... 40
3 Kinematics of Fluid Flow .................................... 43
3.1 Methods of Representation .............................. 43
3.2 Acceleration of a Flow ................................. 47
3.3 Topology of a Flow ..................................... 48
3.4 Problems ............................................... 55
4 Dynamics of Fluid Flow ...................................... 59
4.1 Dynamics of Inviscid Liquids ........................... 59
4.1.1 Continuity and the Bernoulli Equation ........... 59
4.1.2 Consequences of the Bernoulli Equation .......... 63
4.1.3 Pressure Measurement ............................ 71
4.1.4 Interfaces and Formation of Vortices ............ 73
4.1.5 Potential Flow .................................. 76
4.1.6 Wing Lift and the Magnus Effect ................. 88
4.1.7 Balance of Momentum for Steady Flows ............ 91
4.1.8 Waves on a Free Liquid Surface .................. 99
4.1.9 Problems ....................................... 109
4.2 Dynamics of Viscous Liquids ........................... 114
4.2.1 Viscosity (Inner Friction), the Navier-Stokes
Equation ....................................... 114
4.2.2 Mechanical Similarity, Reynolds Number ......... 118
4.2.3 Laminar Boundary Layers ........................ 119
4.2.4 Onset of Turbulence ............................ 122
4.2.5 Fully Developed Turbulence ..................... 132
4.2.6 Flow Separation and Vortex Formation ........... 140
4.2.7 Secondary Flows ................................ 147
4.2.8 Flows with Prevailing Viscosity ................ 149
4.2.9 Flows Through Pipes and Channels ............... 156
4.2.10 Drag of Bodies in Liquids ...................... 161
4.2.11 Flows in Non-Newtonian Media ................... 170
4.2.12 Problems ....................................... 175
4.3 Dynamics of Gases ..................................... 181
4.3.1 Pressure Propagation, Velocity of Sound ........ 181
4.3.2 Steady Compressible Flows ...................... 185
4.3.3 Conservation of Energy ......................... 190
4.3.4 Theory of Normal Shock Waves ................... 191
4.3.5 Flows past Corners, Free Jets .................. 195
4.3.6 Flows with Small Perturbations ................. 199
4.3.7 Flows past Airfoils ............................ 203
4.3.8 Problems ....................................... 208
4.4 Aerodynamics .......................................... 212
4.4.1 Bird Flight .................................... 213
4.4.2 Airfoils and Wings ............................. 215
4.4.3 Airfoil and Wing Theory ........................ 222
4.4.4 Aerodynamic Facilities ......................... 237
4.4.5 Transonic Aerodynamics, Swept Wings ............ 238
4.4.6 Shock-Boundary-Layer Interaction ............... 244
4.4.7 Flow Separation ................................ 250
4.4.8 Supersonic Aerodynamics, Delta Wings ........... 252
4.4.9 Problems ....................................... 259
5 Fundamental Equations of Fluid Mechanics ................... 265
5.1 Continuity Equation ................................... 265
5.2 Navier-Stokes Equations ............................... 266
5.2.1 Laminar Flows .................................. 266
5.2.2 Reynolds Equations for Turbulent Flows ......... 273
5.3 Energy Equation ....................................... 278
5.3.1 Laminar Flows .................................. 278
5.3.2 Turbulent Flows ................................ 282
5.4 Fundamental Equations as Conservation Laws ............ 284
5.4.1 Hierarchy of Fundamental Equations ............. 284
5.4.2 Navier-Stokes Equations ........................ 287
5.4.3 Derived Model Equations ........................ 290
5.4.4 Reynolds Equations for Turbulent Flows ......... 298
5.4.5 Turbulence Models .............................. 299
5.4.6 Multiphase Flows ............................... 317
5.4.7 Reactive Flows ................................. 329
5.5 Differential Equations of Perturbations ............... 332
5.6 Problems .............................................. 338
6 Instabilities and Turbulent Flows .......................... 345
6.1 Fundamentals of Turbulent Flows ....................... 345
6.2 Onset of Turbulence ................................... 346
6.2.1 Fluid-Mechanical Instabilities ................. 347
6.2.2 Linear Stability Analysis ...................... 350
6.2.3 Transition to Turbulence ....................... 373
6.3 Developed Turbulence .................................. 378
6.3.1 The Notion of a Mixing Length .................. 378
6.3.2 Turbulent Mixing ............................... 380
6.3.3 Energy Relations in Turbulent Flows ............ 381
6.4 Classification of Turbulent Flows ..................... 384
6.4.1 Free Turbulence ................................ 385
6.4.2 Turbulence near Solid Boundaries ............... 388
6.4.3 Rotating and Stratified Flows .................. 391
6.4.4 Turbulence in Wind Tunnels ..................... 392
6.4.5 Two-Dimensional Turbulence ..................... 396
6.4.6 Structures and Statistics ..................... 399
6.5 Some New Developments in Turbulence ................... 400
6.5.1 Decomposition into small and large scales ...... 400
6.5.2 Lagrangian Investigations of Turbulence ........ 406
6.5.3 Field-Theoretic Methods ........................ 407
6.5.4 Outlook ........................................ 407
7 Convective Heat and Mass Transfer .......................... 409
7.1 Fundamentals of Heat and Mass Transfer ................ 410
7.1.1 Free and Forced Convection ..................... 410
7.1.2 Heat Conduction and Convection ................. 412
7.1.3 Diffusion and Convection ....................... 414
7.2 Free Convection ....................................... 415
7.2.1 Rayleigh-Benard Convection ..................... 415
7.2.2 Convection at a Vertical Plate ................. 426
7.2.3 Convection at a Horizontal Cylinder ............ 432
7.3 Forced Convection ..................................... 433
7.3.1 Pipe Flows ..................................... 433
7.3.2 Boundary-Layer Flows ........................... 438
7.3.3 Bodies in Flows ................................ 443
7.4 Heat and Mass Exchange ................................ 444
7.4.1 Diffusion Convection ........................... 444
7.4.2 Mass Exchange at a Flat Plate .................. 451
8 Multiphase Flows ........................................... 455
8.1 Fundamentals of Multiphase Flows ...................... 455
8.1.1 Definitions .................................... 456
8.1.2 Flow Patterns .................................. 459
8.1.3 Flow Pattern Maps .............................. 459
8.2 Flow Models ........................................... 462
8.2.1 The One-Dimensional Two-Fluid Model ............ 463
8.2.2 Mixing Models .................................. 466
8.2.3 The Drift-Flow Model ........................... 468
8.2.4 Bubbles and Drops .............................. 470
8.2.5 Spray Flows .................................... 475
8.2.6 Liquid-Solid Transport ......................... 479
8.2.7 Fluidization of Particle Beds .................. 482
8.3 Pressure Loss and Volume Fraction in Hydraulic
Components ............................................ 484
8.3.1 Friction Loss in Horizontal Straight Pipes ..... 485
8.3.2 Acceleration Losses ............................ 489
8.4 Propagation Velocity of Density Waves and Critical
Mass Fluxes ........................................... 493
8.4.1 Density Waves .................................. 493
8.4.2 Critical Mass Fluxes ........................... 496
8.4.3 Cavitation ..................................... 503
8.5 Instabilities in Two-Phase Flows ...................... 507
8.6 Turbulence in Dispersed Two-Phase Flows ............... 513
8.6.1 General Aspects ................................ 513
8.6.2 The Mixing Length Concept ...................... 518
8.6.3 Transport Equation Models for Turbulence ....... 520
9 Reactive Flows ............................................. 523
9.1 Fundamentals of Reactive Flows ........................ 523
9.1.1 Rate Laws and Reaction Orders .................. 525
9.1.2 Relation Between Forward and Reverse
Reactions ...................................... 526
9.1.3 Elementary Reactions and Reaction
Molecularity ................................... 527
9.1.4 Temperature Dependence of Rate Coefficients .... 531
9.1.5 Pressure Dependence of Rate Coefficients ....... 532
9.1.6 Characteristics of Reaction Mechanisms ......... 535
9.2 Laminar Reactive Flows ................................ 540
9.2.1 Structure of Premixed Flames ................... 540
9.2.2 Flame Velocity of Premixed Flames .............. 542
9.2.3 Sensitivity Analysis ........................... 543
9.2.4 Nonpremixed Counterflow Flames ................. 544
9.2.5 Nonpremixed Jet Flames ......................... 547
9.2.6 Nonpremixed Flames with Fast Chemistry ......... 548
9.2.7 Exhaust Gas Cleaning with Plasma Sources ....... 550
9.2.8 Flows in Etching Reactors ...................... 551
9.2.9 Heterogeneous Catalysis ........................ 553
9.3 Turbulent Reactive Flows .............................. 555
9.3.1 Overview and Concepts .......................... 555
9.3.2 Direct Numerical Simulation .................... 556
9.3.3 Mean Reaction Rates ............................ 558
9.3.4 Eddy-Break-Up Models ........................... 563
9.3.5 Turbulent Nonpremixed Flames ................... 563
9.3.6 Turbulent Premixed Flames ...................... 575
9.4 Hypersonic Flows ...................................... 581
9.4.1 Physical-Chemical Phenomena in Re-Entry
Flight ......................................... 581
9.4.2 Chemical Nonequilibrium ........................ 583
9.4.3 Thermal Nonequilibrium ......................... 585
9.4.4 Surface Reactions on Re-entry Vehicles ......... 588
10 Flows in the Atmosphere and in the Ocean ................... 593
10.1 Fundamentals of Flows in the Atmosphere and in the
Ocean ................................................. 593
10.1.1 Introduction ................................... 593
10.1.2 Fundamental Equations in Rotating Systems ...... 593
10.1.3 Geostrophic Flow ............................... 597
10.1.4 Vorticity ...................................... 599
10.1.5 Ekman Layer .................................... 602
10.1.6 Prandtl Layer .................................. 605
10.2 Flows in the Atmosphere ............................... 607
10.2.1 Thermal Wind Systems ........................... 607
10.2.2 Thermal Convection ............................. 611
10.2.3 Gravity Waves .................................. 613
10.2.4 Vortices ....................................... 616
10.2.5 Global Atmospheric Circulation ................. 621
10.3 Flows in the Ocean ............................... 623
10.3.1 Wind-Driven Flows .............................. 624
10.3.2 Water Waves .................................... 626
10.4 Application to Atmospheric and Oceanic Flows .......... 629
10.4.1 Weather Forecast ............................... 629
10.4.2 Greenhouse Effect and Climate Prediction ....... 631
10.4.3 Ozone Hole ..................................... 635
11 Microflows ................................................. 639
11.1 Fundamentals of Microflows ............................ 639
11.1.1 Application of Microflows ...................... 639
11.1.2 Fluid Models ................................... 641
11.1.3 Microfiows of Gases ............................ 643
11.1.4 Microfiows of Liquids .......................... 645
11.2 Molecular Models ...................................... 647
11.2.1 Fundamentals of Molecular Models ............... 647
11.2.2 Monte-Carlo-Simulation ......................... 650
11.2.3 Molecular Dynamic Simulation ................... 653
11.3 Continuum Models ...................................... 655
11.3.1 Similarity Discussion .......................... 655
11.3.2 Modifications of Boundary Conditions ........... 657
11.3.3 Electrokinetic Effects ......................... 661
11.3.4 Wetting and Thin Films ......................... 670
11.4 Experiments ........................................... 678
11.4.1 Pressure Drop .................................. 679
11.4.2 Laminar-Turbulent Transition ................... 681
11.4.3 Heat Transfer .................................. 682
12 Biofluid Mechanics ......................................... 685
12.1 Fundamentals of Biofluid Mechanics .................... 685
12.1.1 Biofluid Mechanics of Animals .................. 687
12.1.2 Biofluid Mechanics of Humans ................... 690
12.1.3 Blood Rheology ................................. 697
12.2 Swimming and Flight ................................... 700
12.2.1 Motion of Protozoa ............................. 700
12.2.2 Swimming of Fish ............................... 703
12.2.3 Flow Control ................................... 705
12.2.4 Bird Flight .................................... 707
12.3 Human Heart Flow ...................................... 712
12.3.1 Physiology and Anatomy of the Heart ............ 713
12.3.2 Structure of the Heart ......................... 715
12.3.3 Excitation Physiology of the Heart ............. 719
12.3.4 Flow in the Heart .............................. 722
12.3.5 Cardiac Valves ................................. 731
12.4 Flow in Blood Vessels ................................. 734
12.4.1 Unsteady Pipe Flow ............................. 738
12.4.2 Unsteady Arterial Flow ......................... 742
12.4.3 Arterial Branchings ............................ 745
12.4.4 Microcirculation ............................... 749
Selected Bibliography ......................................... 753
Index ......................................................... 785
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