This book elucidates the methods of molecular gas dynamics or rarefied gas dynamics which treat the problems of gas flows when the discrete molecular effects of the gas prevail under the circumstances of low density, the emphasis being on the basis of the methods, the direct simulation Monte Carlo method applied to the simulation of non-equilibrium effects and the frontier subjects related to low speed microscale rarefied gas flows. It provides a solid basis for the study of molecular gas dynamics for senior students and graduates in the aerospace and mechanical engineering departments of universities and colleges. It gives a general acquaintance of modern developments of rarefied gas dynamics in various regimes and leads to the frontier topics of non-equilibrium rarefied gas dynamics and low speed microscale gas dynamics. It will be also of benefit to the scientific and technical researchers engaged in aerospace high altitude aerodynamic force and heating design and in the research on gas flow in MEMS.
Author(s): Ching Shen
Series: Heat and Mass Transfer
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 421
Contents......Page 17
Preface......Page 5
Nomenclature......Page 10
0.1 The Conception of Rarefied Gas Dynamics......Page 22
0.2 The Molecular Model of Gases......Page 24
0.3 Mean Free Path of Molecules......Page 25
0.4 Division of Flow Regimes......Page 26
0.5 Nonequilibrium Phenomena and Rarefied Gas Dynamics......Page 30
0.6 Similarity Criteria......Page 34
References......Page 39
1.1 Diatomic Molecules......Page 41
1.2 Energy Distribution of Molecules......Page 50
1.2.1 Boltzmann's Relation......Page 52
1.2.2 Calculation of The Number Ω of Microscopic States......Page 54
1.2.3 Boltzmann Distribution......Page 57
1.3 Internal Energy Distribution Functions......Page 63
References......Page 70
2.1 The Velocity Distribution Function......Page 71
2.2 Macroscopic Properties......Page 73
2.3 Binary Elastic Collisions of Molecules......Page 81
2.4 Collision Cross-sections and Molecule Models......Page 89
2.4.1 Hard Sphere Model......Page 92
2.4.2 The Inverse Power Law Model......Page 94
2.4.3 Maxwell Model......Page 96
2.4.4 Variable Hard Sphere (VHS) Model......Page 97
2.4.5 Variable Soft Sphere (VSS) Model......Page 100
2.4.6 Generalized Hard Sphere (GHS) Model......Page 105
2.4.7 Generalized Soft Sphere (GSS) Model......Page 107
2.5 The Eight Velocity Gas Model......Page 108
2.6 Boltzmann Equation......Page 112
2.7 Collision Integral and The Total Number of Collisions......Page 118
2.8 Evaluation of Collision Integrals......Page 120
2.9 The Maxwell Transport Equation – The Moment Equation......Page 124
2.10 Maxwell Distribution......Page 126
2.11.1 Some Peculiar Speeds of Gas......Page 132
2.11.2 Molecular Collision Frequency and The Mean Free Path......Page 135
2.11.3 The Mean Value of Collision Quantities......Page 140
2.11.4 The Reference Diameter of The VSS Model and The VHS Model......Page 143
2.12.1 The Macroscopic Properties......Page 144
2.12.3 Number of Collisions, Collision Frequency and Mean Free Path......Page 146
2.12.4 Collision Frequency of a Molecule of species A with Molecules of Species B in Gas Mixture of VSS (or VHS) Molecules......Page 147
References......Page 148
3.1 Introduction......Page 150
3.2 Specular and Diffuse Reflection......Page 151
3.3 The Reciprocity Principle......Page 159
3.4 The CLL Gas Surface Interaction Model......Page 161
References......Page 177
4 Free Molecular Flow......Page 178
4.1 The Number Flux and The Momentum Flux of Molecules in Gases......Page 179
4.2 The Aerodynamic Forces Acted on Bodies......Page 182
4.3 Heat Transfer to Surface Element......Page 189
4.4 Free Molecular Effusion and Thermal Transpiration......Page 193
4.5 Couette Flow and Heat Transfer between Plane Plates......Page 196
4.6 The General Solutions, Unsteady Flow......Page 201
References......Page 209
5.1 Introduction......Page 210
5.2.1 Equations of Mass, Momentum and Energy Conservation......Page 211
5.2.2 Chapman-Enskog Expansion......Page 212
5.2.4 Navier-Stokes Equations......Page 213
5.2.5 Burnett Equations......Page 215
5.2.6 Grad's Thirteen Moment Equations......Page 220
5.2.7 The Asymptotic Theory for Small Knudsen Numbers......Page 222
5.3.1 The Simple Derivation......Page 223
5.3.2 The Conservation of Momentum and Energy Fluxes in The Knudsen Layer......Page 225
5.3.3 The Derivation of The Slip Velocity Formula......Page 226
5.3.4 The Derivation of The Temperature Jump Expression......Page 228
5.4 The Solution of Some Simple Problems......Page 231
5.4.1 Couette Flow......Page 232
5.4.2 The Poiseuille Flow......Page 234
5.4.3 The Rayleigh Problem......Page 237
5.5 Thermal Creep and Thermophoresis......Page 239
5.6 Second Order Slip-jump Conditions......Page 246
References......Page 247
6.1 General Overview......Page 250
6.2 Linearized Boltzmann Equation......Page 252
6.3 The Moment Method......Page 258
6.4 Model Equations......Page 266
6.5 The Finite Difference Method......Page 274
6.6 Discrete Ordinate Method......Page 276
6.7 Integral Methods......Page 282
6.8 Direct Simulation Methods......Page 283
References......Page 288
7.1 Introduction......Page 293
7.2 Sampling of Collisions......Page 296
7.3 Example of Solution of Problem by The DSMC Method......Page 299
7.4.1 Introduction of Phenomenological Models......Page 306
7.4.2 Implementation of Larsen-Borgnakke Model......Page 307
7.4.3 Cases of Distributions with Singularities, Generalized Acceptance-rejection Method......Page 311
7.4.4 Larsen-Borgnakke Method for Discrete Energy Levels......Page 313
7.4.5 Relaxation Collision Number and Vibrational Exchange Probability......Page 315
7.5.1 Chemical Reaction Rate Coefficient......Page 317
7.5.2 Phenomenological Chemical Reaction Model of Bird......Page 318
7.5.3 A Sterically Dependent Chemical Reaction Model......Page 320
7.6 Computation of Complicated Flow Fields......Page 328
References......Page 331
8.1 Introduction......Page 334
8.2 Methods for Solving The Rarefied Gas Flows in MEMS......Page 338
8.3.1 The Description of The Method......Page 343
8.3.2 The Validation of The Method......Page 346
8.3.3 Program Demonstrating The Method......Page 349
8.4 Unidirectional Flows......Page 350
8.5 The MicroChannel Flow Problem......Page 355
8.6 Thin Film Air Bearing Problem......Page 365
8.7 Use of Degenerated Reynolds Equation in Channel Flow......Page 372
8.8 Some Actual Problems and Concluding Remarks......Page 377
References......Page 380
Appendix I Gas Properties......Page 383
References......Page 384
II.1 The gamma Function and Error Function......Page 385
II.2 Some Definite Integrals......Page 386
II.3 The beta Function......Page 389
References......Page 390
III.1 Inversion of Cumulative Distribution Function......Page 391
III.3 Generalized Acceptance-rejection Method......Page 394
References......Page 397
Appendix IV Program of The Couette Flow......Page 398
B......Page 414
D......Page 415
F......Page 416
K......Page 417
M......Page 418
R......Page 419
T......Page 420
W......Page 421
