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| Bird G.A. — Molecular gas dynamics and the direct simulation of gas flows |
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| Ïðåäìåòíûé óêàçàòåëü |
Acceptance-rejection method 105 424
Accommodation coefficient 118—121
Activation energy 124
Adiabatic, atmosphere 311—312
Adiabatic, surface temperature 169 354
Apse line 33 35 39 95
Arrhenius equation 124
Atomic mass constant 5
Average (see mean)
Averages, ensemble 11
Averages, instantaneous 10
Averages, time 10
Avogadro’s number 5 19 124
Axially symmetric flows 370—388
BBGKY equations 50
beta function 112 422
BGK equation 195
Bimodal distribution 148—150 156 191—196 295 305
Bimolecular reaction 124—125 129—133
Binary collision 7 27 30—36 88 129 137
Blunt-body problem, axially symmetric 374—377
Blunt-body problem, two-dimensional 353—359
Boltzmann CFD 200
Boltzmann constant 14 25 211 243
Boltzmann distribution 114 116 146 239—240 245
Boltzmann equation 1 50—53 61 183—186 199 202 209 292
Borgnakke-Larsen (see Larsen-Borgnakke)
Breakdown parameter 4
Bridging formulae 189
Burnett equations 70 293
Cellular automata 204
Cercignani-Lampis-Lord (CLL), surface reflection model 120—121 360—361 366
Chapman — Enskog solution of 64
Chapman-Enskog, distribution function 3 73—74 91 173
Chapman-Enskog, second approximation to 74
Chapman-Enskog, theory 3 20 64—75
Characteristic temperature of dissociation 25 245 412
Characteristic temperature of ionization 412
Characteristic temperature of rotation 25 412
Characteristic temperature of vibration 25 113 241 412
Chemical reactions 123—144 245—251
Coefficient of diffusion (see Diffusion)
Coefficient of heat conduction (see Heat conduction)
Coefficient of viscosity (see Viscosity)
Collapse of cylindrical cavity 331
Collision cross-section in mixture 16
Collision cross-section, differential 33
Collision cross-section, reference 67 72
Collision cross-section, relative speed dependence 20 38
Collision cross-section, total 5 34—39 67
Collision cut-off 20 37
Collision integral 56—57
Collision integral, evaluation of 60 68
Collision lifetime 129
Collision term 54 196
Collisional invariants 58
Collisionless 156 160
Collisionless for gas mixture 54
Collisionless, Boltzmann equation 156
Collisionless, derivation of 50—53
Collisionless, direct CFD for 200
Collisionless, flow 2
Collisionless, generalized 54 64
Collisionless, moment of 55
Collisionless, normal solution of 65
Collisionless, piston problem 160—162 (see also Free-molecule)
Collisionless, relationship to simulation 208—210
Collisionless, unsteady flows free expansion 157—160
Complete rarefaction wave 325—327
Computational grids (see Grids)
Conservation equations 58—60
Conservation equations of energy 59
Conservation equations of mass 58
Conservation equations of momentum 58
Continuum breakdown parameter (see Breakdown parameter)
Couette flow 154 212 262 271 275
Couette flow, Taylor (see Taylor-Couette)
Coulomb molecules 26
Cross-section (see Collision cross-section)
Cumulative distribution function 110 239 423—427
Cylindrical symmetry 260
de Broglie wavelength 24
Debye length 204
Deflection angle 36
Degree of dissociation 130
Degrees of freedom 25 408
Degrees of freedom, internal 83
density 9
Density of mixture 17
Diffuse reflection 97
Diffusion, coefficient Chapman — Enskog result 69
Diffusion, coefficient for GHS molecules 73
Diffusion, coefficient for VHS molecules 69
DSMC determination of 282—285
DSMC procedures 370—371
Effusion 151
Einstein coefficients 29 145
Elastic collisions 30
electric dipole moment 145
electric field 204
Ensemble average 11
Equation of change 56
Equilibrium 8
Equilibrium, air composition 27
Equilibrium, collision rate 90
Equilibrium, collision rate DSMC result 224—227
Equilibrium, collision rate in mixtures 96
Equilibrium, collisional energy 93—5
Equilibrium, constant 130
Equilibrium, distribution function 64 77—98
Equilibrium, distribution function in cylindrical coordinates 80
Equilibrium, distribution function in polar coordinates 77
Equilibrium, distribution function of internal energy 104
Equilibrium, distribution function, rotational from DSMC 234—237
Equilibrium, distribution function, vibrational from DSMC 240
Equilibrium, flux energy translational 83
Equilibrium, internal 83
Equilibrium, internal, total 84
Equilibrium, mean free path 91 93
Equilibrium, mean free path in mixtures 96
Equilibrium, momentum normal, parallel 82
Equilibrium, number 82
Equilibrium, relative speeds in collisions 89
Ergodic 11
Error function 79 420—421
Euler equations 60 186
Exchange reactions 140
Fiat plate, free-molecule 169—172
Fiat plate, supersonic 360—366
Fiat plate, three-dimensional 401—404
Field molecules 7 16 52
Flux vector 12
Forced diffusion 75
Four moment method 187—194
Free expansion problem 157
Free-molecule, aerodynamics 162—172
Free-molecule, aerodynamics, flat plate 169—172
Free-molecule, aerodynamics, heat transfer coefficient 167
Free-molecule, aerodynamics, number flux 164
Free-molecule, aerodynamics, pressure coefficient 165
Free-molecule, aerodynamics, skin friction coefficient 165
Free-molecule, internal flow 175—181
Free-molecule, one-dimensional heat transfer 154—156
Free-molecule, piston problem 160
Free-molecule, test particle method for 176 (see also Collisionless)
Frozen flow 28
Gamma function 94 112 126 417
Gas, centrifuge 313—315
Gas, constants 14
Gas, Dilute 7 12
| Gas, equilibrium 8
Gas, properties 19—29 408—416
Gas, simple 5
Gas-surface interactions 97 118— 121 360—361
Gaussian (see Normal distribution)
Generalized hard sphere (GHS) model 44
Grad’s thirteen moment equations 186
Gravitational field 258 311
Grids, effect of cell-size 346—348
Grids, sub-cells 216
Grids, three-dimensional 389—393
Grids, two-dimensional 335—339
H-Theorem 61—63
Hard sphere 5 39—40
harmonic oscillator (see Vibrational excitation)
Heat conduction, coefficient Chapman — Enskog result for 66
Heat flux vector 15 74
Heisenburg uncertainty principle 24
Hypersonic limit 84—86
Impact parameters 33
Information theory 124
Intermolecular, force field 6 35
Intermolecular, potential 35
Inverse collision 33
Inverse-cumulative method 424
Ionization 26 140—142
Ionized gas 204
Isentrflpic 9
Knudsen layer 191
Knudsen number 2
Knudsen number, local 2
Knudsen number, overall 2
Kronecker delta 14
Lapse rate 311—312
Larsen — Borgnakke model 104—107
Larsen — Borgnakke model, distribution functions general internal energy 107
Larsen — Borgnakke model, DSMC implementation general 109—112
Larsen — Borgnakke model, DSMC implementation rotation 228—237
Larsen — Borgnakke model, DSMC implementation vibration 238—245
Larsen — Borgnakke model, method 100 104—116
Larsen — Borgnakke model, method for simple gas 104—107
Larsen — Borgnakke model, method for vibration 112—116
Larsen — Borgnakke model, method for vibration quantum version 114—115
Larsen — Borgnakke model, method in a mixture 108—109
Larsen — Borgnakke model, serial application 111
Larsen — Borgnakke model, translational energy 106
Lattice gas method 204
Leading-edge problem 340—346
Lennard — Jones model 43
Liouville equation 50 156
List of symbols xiii
Local thermodynamic equilibrium 9 146
Loschmidt’s number 19
Mach number 165
Macroscopic model 1
Mass average velocity 17
Mass velocity 13
Maximum entropy principle 124
Maxwell model 43
Maxwellian distribution (see Equilibrium distribution)
Mean, collision frequency 7
Mean, collision rate 7
Mean, collision rate in gas mixture 16
Mean, collision time 7
Mean, collision time, free path 2 8
Mean, collision time, free path in equilibrium gas 90
Mean, collision time, free path in mixture 17
Mean, molecular spacing 5
Mean, radiative lifetime 145
Mean, square molecular speed 20
Mean, translational energy in collisions 93 97
Mean, values in collisions 92
Mean, velocity 17
Microscopic model 1
Model equation (see BGK)
Molecular, angular velocity 101 145
Molecular, chaos 49—50 88 204 209
Molecular, cross-section (see Collision cross-section)
Molecular, diameter, hard sphere 5
Molecular, diameter, reference value 92 409
Molecular, diameter, VHS 68 93 97
Molecular, diameter, VHS in mixture 69
Molecular, diameter, VSS 70
Molecular, dynamics (MD) method 202 209
Molecular, effusion 151
Molecular, elastic models 39—44
Molecular, elastic models, GHS 44
Molecular, elastic models, GHS hard sphere 5 39—40
Molecular, elastic models, GHS Lennard — Jones 43
Molecular, elastic models, GHS Maxwell 43
Molecular, elastic models, GHS square-well 43
Molecular, elastic models, GHS Sutherland 43
Molecular, elastic models, GHS VHS 20 40—41
Molecular, elastic models, GHS VSS 41—42
Molecular, elastic models, GHS VSS, scattering parameter 42 410
Molecular, force field 6
Molecular, inelastic models, rough-sphere 99 101—103
Molecular, inelastic models, sphero-cylinder 99
Molecular, inelastic models, two centres of repulsion 99 (see also Larsen-Borgnakke)
Molecular, inverse power law 37
Molecular, mass 5 408
Molecular, mass, reduced 31
Molecular, mean spacing 5
Molecular, reflection at surfaces diffuse 97
Molecular, specular 97
Molecular, speed ratio 82
Molecular, transpiration 151
Molecular, weight 5
Moment equation 55
Moment methods 184
Momentum cross-section 38—42
Monte Carlo, direct simulation see direct simulation Monte Carlo method test particle method free-molecule 176
Monte Carlo, transition regime 203
Morse potential 245—246
Most probable thermal speed 78
Mott — Smith solution 191—194
Navier — Stokes equations 1—2 74 186
Nomenclature xiii-xvii
Normal distribution 9
Normal shock wave (see Shock wave)
NTC method 219
Number density 5
Number density in gas mixture 16
Number density, standard 19
One-dimensional heat transfer, DSMC result for 280—281
One-dimensional heat transfer, four moment method 187—191
Ordinary gas constant 14
Partition functions 131 415
Peculiar velocity 13
Phase space 1
Phenomenological models 100
Photophoresis 174
Physical space 46
Piston problem 317—324
Piston problem, collisionless 160—162
Piston problem, spherical 328—331
Planck’s constant 24
plasma 204
Poisson distribution 9
Poisson equation 204
Prandtl number 66
Prandtl number, DSMC result for 271
Prandtl — Meyer expansion 367—369
Pressure, diffusion 75
Pressure, scalar 14
Pressure, tensor 13
Quantum vibration model 114
Radiation (see Thermal radiation)
Random numbers 203 432 435
Random velocity 13
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