Rarefied gas dynamics: fundamentals, simulations and micro flows
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| Main Author: | |
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| Format: | Book |
| Language: | English Chinese |
| Published: |
Berlin
Springer
2005
|
| Series: | Heat and mass transfer
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXIII, 406 S. graph. Darst. |
| ISBN: | 354023926X 9783642062957 |
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Record in the Search Index
| _version_ | 1804133295736225792 |
|---|---|
| adam_text | CHING SHEN
RAREFIED GAS DYNAMICS
FUNDAMENTALS, SIMULATIONS AND MICRO FLOWS
WITH 53 FIGURES
FYJ
SPRINGER
CONTENTS
PREFACE V
NOMENCLATURE X
I
0 INTRODUCTION 1
0.1 THE CONCEPTION OF RAREFIED GAS DYNAMICS 1
0.2 THE MOLECULAR MODEL O
F GASES 3
0.3 MEAN FREE PATH OF MOLECULES 4
0.4 DIVISION OF FLOW REGIMES 5
0.5 NONEQUILIBRIUMPHENOMENA AND RAREFIED GAS DYNAMICS 9
0.6 SIMILARITY CRITERIA 13
REFERENCES 18
1 MOLECULAR STRUCTURE AND ENERGY STATES 21
1.1 DIATOMIC MOLECULES 21
1.2 ENERGY DISTRIBUTION OF MOLECULES 30
1.2.1 BOLTZMANN S RELATION 32
1.2.2 CALCULATION OF THE NUMBER
Q
OF MICROSCOPIC STATES 34
1.2.3 BOLTZMANN DISTRIBUTION 37
1.3 INTERNAL ENERGY DISTRIBUTION FUNCTIONS 43
REFERENCES 50
2 SOME BASIC CONCEPTS OF KINETIC THEORY 51
2.1 THE VELOCITY DISTRIBUTION FUNCTION 51
2.2 MACROSCOPIC PROPERTIES 53
2.3 BINARY ELASTIC COLLISIONS OF MOLECULES 61
2.4 COLLISION CROSS-SECTIONS AND MOLECULE MODELS 69
2.4.1 HARD SPHERE MODEL 72
XX CONTENTS
2.4.2 THE INVERSE POWER LAW MODEL 74
2.4.3 MAXWELL MODEL 76
2.4.4 VARIABLE HARD SPHERE (VHS) MODEL 77
2.4.5 VARIABLE SOFT SPHERE (VSS) MODEL 80
2.4.6 GENERALIZED HARD SPHERE (GHS) MODEL 85
2.4.7 GENERALIZED SOFT SPHERE (GSS) MODEL 87
2.5 THE EIGHT VELOCITY GAS MODEL 88
2.6 BOLTZMANN EQUATION 92
2.7 COLLIS ION INTEGRAL AND THE TOTAL NUMBER OF COLLISIONS 98
2.8 EVALUATION OF COLLISION INTEGRALS 100
2.9 THE MAXWELL TRANSPORT EQUATION - THE MOMENT EQUATION 104
2.10 MAXWELL DISTRIBUTION 106
2.11 EQUILIBRIUM STATE OF GASES 112
2.11.1 SOME PECULIAR SPEEDS OF GAS 112
2.11.2 MOLECULAR COLLISION FREQUENCY AND THE MEAN FREE PATH .... 115
2.11.3 THE MEAN VALUE OF COLLISION QUANTITIES 120
2.11.4 THE REFERENCE DIAMETER OF THE VSS MODEL AND THE VHS
MODEL 123
2.12 GAS MIXTURE 124
2.12.1 THE MACROSCOPIC PROPERTIES 124
2.12.2 THE BOLTZMANN EQUATIONS 126
2.12.3 NUMBER OF COLLISIONS, COLLISION FREQUENCY AND MEAN FREE
PATH 126
2.12.4 COLLISION FREQUENCY OF A MOLECULE OF SPECIES A WITH
MOLECULES OF SPECIES B IN GAS MIXTURE OF VSS (OR VHS)
MOLECULES 127
REFERENCES 128
INTERACTION OF MOLECULES WITH SOLID SURFACE 131
3.1 INTRODUCTION 131
3.2 SPECULAR AND DIFFUSE REFLECTION 132
3.3 THE RECIPROCITY PRINCIPLE 140
3.4 THE CLL GAS SURFACE INTERACTION MODEL 142
REFERENCES 158
CONTENTS XXI
FREE MOLECULAR FLOW 159
4.1 THE NUMBER FLUX AND THE MOMENTUM FLUX OF MOLECULES IN GASES
160
4.2 THE AERODYNAMIC FORCES ACTED ON BODIES 163
4.3 HEAT TRANSFER TO SURFACE ELEMENT 170
4.4 FREE MOLECULAR EFFUSION AND THERMAL TRANSPIRATION 174
4.5 COUETTE FLOW AND HEAT TRANSFER BETWEEN PLANE PLATES 177
4.6 THE GENERAL SOLUTIONS, UNSTEADY FLOW 182
REFERENCES 190
CONTINUUM MODELS 191
5.1 INTRODUCTION 191
5.2 BASIC EQUATIONS 192
5.2.1 EQUATIONS OF MASS, MOMENTUM AND ENERGY CONSERVATION.. 192
5.2.2 CHAPMAN-ENSKOG EXPANSION 193
5.2.3 EULER EQUATION 194
5.2.4 NAVIER-STOKES EQUATIONS 194
5.2.5 BURNETT EQUATIONS 196
5.2.6 GRAD S THIRTEEN MOMENT EQUATIONS 201
5.2.7 THE ASYMPTOTIC THEORY FOR SMALL KNUDSEN NUMBERS 203
5.3 SLIP BOUNDARY CONDITIONS 204
5.3.1 THE SIMPLE DERIVATION 204
5.3.2 THE CONSERVATION OF MOMENTUM AND ENERGY FLUXES IN THE
KNUDSEN LAYER 206
5.3.3 THE DERIVATION OF THE SLIP VELOCITY FORMULA 207
5.3.4 THE DERIVATION OF THE TEMPERATURE JUMP EXPRESSION 209
5.3.5 THE EXTENSION TO CASES OF MULTI-COMPONENT GASES AND
NON-EQUILIBRIUM FLOWS 212
5.4 THE SOLUTION OF SOME SIMPLE PROBLEMS 212
5.4.1 COUETTE FLOW 213
5.4.2 THE POISEUILLE FLOW 215
5.4.3 THE RAYLEIGH PROBLEM 218
5.5 THERMAL CREEP AND THERMOPHORESIS 220
5.6 SECOND ORDER SLIP-JUMP CONDITIONS 227
XXII CONTENTS
REFERENCES 228
TRANSITIONAL REGIME 231
6.1 GENERAL OVERVIEW 231
6.2 LINEARIZED BOLTZMANN EQUATION 233
6.3 THE MOMENT METHOD 239
6.4 MODEL EQUATIONS 247
6.5 THE FINITE DIFFERENCE METHOD 255
6.6 DISCRETE ORDINATE METHOD 257
6.7 INTEGRAL METHODS 263
6.8 DIRECT SIMULATION METHODS 264
REFERENCES 269
DIRECT SIMULATION MONTE-CARLO (DSMC) METHOD 275
7.1 INTRODUCTION 275
7.2 SAMPLING OF COLLISIONS 278
7.3 EXAMPLE OF SOLUTION OF PROBLEM BY THE DSMC METHOD 281
7.4 THE EXCITATION AND RELAXATION OF THE INTERNAL ENERGIES 288
7.4.1 INTRODUCTION OF PHENOMENOLOGICAL MODELS 288
7.4.2 IMPLEMENTATION OF LARSEN-BORGNAKKE MODEL 289
7.4.3 CASES OF DISTRIBUTIONS WITH SINGULARITIES, GENERALIZED
ACCEPTANCE-REJECTION METHOD 293
7.4.4 LARSEN- BORGNAKKE METHOD FOR DISCRETE ENERGY LEVELS 295
7.4.5 RELAXATION COLLISION NUMBER AND VIBRATIONAL EXCHANGE
PROBABILITY 297
7.5 SIMULATION OF CHEMICAL REACTIONS 299
7.5.1 CHEMICAL REACTION RATE COEFFICIENT 299
7.5.2 PHENOMENOLOGICAL CHEMICAL REACTION MODEL OF BIRD 300
7.5.3 A STERICALLY DEPENDENT CHEMICAL REACTION MODEL 302
7.6 COMPUTATION OF COMP LICATED FLOW FIELDS 310
REFERENCES 313
MICROSCALE SLOW GAS FLOWS, INFORMATION PRESERVATION METHOD 317
8.1 INTRODUCTION 317
CONTENTS XXIII
8.2 METHODS FOR SOLVING THE RAREFIED GAS FLOWS IN MEMS 321
8.3 INFORMATION PRESERVATION (IP) METHOD 326
8.3.1 THE DESCRIPTION OF THE METHOD 326
8.3.2 THE VALIDATION OF THE METHOD 329
8.3.3 PROGRAM DEMONSTRATING THE METHOD 332
8.4 UNIDIRECTIONAL FLOWS 333
8.5 THE MICROCHANNEL FLOW PROBLEM 338
8.6 THIN FILM AIR BEARING PROBLEM 348
8.7 USE OF DEGENERATED REYNOLDS EQUATION IN CHANNEL FLOW 355
8.8 SOME ACTUAL PROBLEMS AND CONCLUDING REMARKS 360
REFERENCES 363
APPENDIX I GAS PROPERTIES 367
REFERENCES 368
APPENDIX II SOME INTEGRALS 369
11.1 THE GAMMA FUNCTION AND ERROR FUNCTION 369
11.2 SOME DEFINITE INTEGRALS 370
11.3 THE BET
A FUNCTION 373
REFERENCES 374
APPENDIX III SAMPLING FROM A PRESCRIBED DISTRIBUTION
37
5
III. 1
INVERSION OF CUMULATIVE DISTRIBUTION FUNCTION 375
111.2 ACCEPTANCE-REJECTION METHOD 378
111.3 GENERALIZED ACCEPTANCE-REJECTION METHOD 378
REFERENCES 381
APPENDIX IV PROGRAM OF THE COUETTE FLOW 383
SUBJECT INDEX 399
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:27Z |
| institution | BVB |
| isbn | 354023926X 9783642062957 |
| language | English Chinese |
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| physical | XXIII, 406 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Springer |
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| series2 | Heat and mass transfer |
| spelling | Shen, Ching 1935- Verfasser (DE-588)129755168 aut Rarefied gas dynamics fundamentals, simulations and micro flows Ching Shen Berlin Springer 2005 XXIII, 406 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Heat and mass transfer Literaturangaben Rarefied gas dynamics Dynamik hochverdünnter Gase (DE-588)4130419-6 gnd rswk-swf Dynamik hochverdünnter Gase (DE-588)4130419-6 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shen, Ching 1935- Rarefied gas dynamics fundamentals, simulations and micro flows Rarefied gas dynamics Dynamik hochverdünnter Gase (DE-588)4130419-6 gnd |
| subject_GND | (DE-588)4130419-6 |
| title | Rarefied gas dynamics fundamentals, simulations and micro flows |
| title_auth | Rarefied gas dynamics fundamentals, simulations and micro flows |
| title_exact_search | Rarefied gas dynamics fundamentals, simulations and micro flows |
| title_full | Rarefied gas dynamics fundamentals, simulations and micro flows Ching Shen |
| title_fullStr | Rarefied gas dynamics fundamentals, simulations and micro flows Ching Shen |
| title_full_unstemmed | Rarefied gas dynamics fundamentals, simulations and micro flows Ching Shen |
| title_short | Rarefied gas dynamics |
| title_sort | rarefied gas dynamics fundamentals simulations and micro flows |
| title_sub | fundamentals, simulations and micro flows |
| topic | Rarefied gas dynamics Dynamik hochverdünnter Gase (DE-588)4130419-6 gnd |
| topic_facet | Rarefied gas dynamics Dynamik hochverdünnter Gase |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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