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E-raamat: Nonequilibrium Gas Dynamics and Molecular Simulation

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(University of Minnesota), (University of Michigan, Ann Arbor)
  • Formaat: EPUB+DRM
  • Sari: Cambridge Aerospace Series
  • Ilmumisaeg: 23-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316871225
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Nonequilibrium Gas Dynamics and Molecular SimulationSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Cambridge Aerospace Series
  • Ilmumisaeg: 23-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316871225
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"The book is divided into two parts based on the overall goals, with the first part focusing on fundamental considerations, and the second part dedicated to describing computer simulation methods. The first section covers three different areas: (1) kinetic theory, (2) quantum mechanics, and (3) statistical mechanics. Important results from these three areas are then brought together to allow analysis of nonequilibrium processes in a gas based on molecular level considerations. Chapter 1 covers kinetic theory, in which the basic idea is to develop techniques to relate the properties and behavior of particles, representing atoms and molecules, to the fluid mechanical aspects of a gas at the macroscopic level. This requires us to provide a basic definition by what is meant by a particle, and how these particles interact with one another through the mechanism of inter-molecular collisions. This leads us into a discussion of modeling of macroscopic molecular transport processes, such as viscosity and thermal conductivity, that represents one of the first key successes of kinetic theory. We will find that kinetic theory relies on the use of statistical analysis techniques, such as probability density functions, due to the very large volumes of information involved in tracking the behavior of every single particle in a real gas flow"--

Muu info

This current, comprehensive book provides an updated treatment of molecular gas dynamics topics and the DSMC method for aerospace engineers.
List of Illustrations
ix
List of Tables
xv
Preface xvii
Acknowledgments xxi
Part I Theory
1 Kinetic Theory
3(51)
1.1 Introduction
3(1)
1.2 Fundamental Concepts
3(17)
1.2.1 Particle Model
4(2)
1.2.2 Macroscopic Quantities from Molecular Behavior
6(6)
1.2.3 Molecular Collisions
12(2)
1.2.4 Molecular Transport Processes
14(6)
1.3 Kinetic Theory Analysis
20(30)
1.3.1 Velocity Distribution Function
20(2)
1.3.2 The Boltzmann Equation
22(4)
1.3.3 The H-Theorem of Boltzmann
26(3)
1.3.4 Maxwellian VDF
29(6)
1.3.5 Equilibrium Collision Properties
35(2)
1.3.6 Free Molecular Flow onto a Surface
37(7)
1.3.7 Kinetic-Based Analysis of Nonequilibrium Flow
44(4)
1.3.8 Free Molecular Flow Analysis
48(2)
1.4 Summary
50(1)
1.5 Problems
51(3)
2 Quantum Mechanics
54(30)
2.1 Introduction
54(1)
2.2 Quantum Mechanics
54(15)
2.2.1 Heisenberg Uncertainty Principle
56(1)
2.2.2 The Schrodinger Equation
57(3)
2.2.3 Solutions of the Schrodinger Equation
60(2)
2.2.4 Two-Particle System
62(3)
2.2.5 Rotational and Vibrational Energy
65(3)
2.2.6 Electronic Energy
68(1)
2.3 Atomic Structure
69(4)
2.3.1 Electron Classification
69(1)
2.3.2 Angular Momentum
69(2)
2.3.3 Spectroscopic Term Classification
71(1)
2.3.4 Excited States
72(1)
2.4 Structure of Diatomic Molecules
73(8)
2.4.1 Born-Oppenheimer Approximation
74(3)
2.4.2 Rotational and Vibrational Energy
77(1)
2.4.3 Electronic States
78(3)
2.5 Summary
81(1)
2.6 Problems
82(2)
3 Statistical Mechanics
84(34)
3.1 Introduction
84(1)
3.2 Molecular Statistical Methods
84(6)
3.2.1 Energy Groups
87(3)
3.3 Distribution of Energy States
90(5)
3.3.1 Boltzmann Limit
92(2)
3.3.2 Boltzmann Energy Distribution
94(1)
3.4 Relation to Thermodynamics
95(4)
3.4.1 Boltzmann's Relation
97(1)
3.4.2 Macroscopic Thermodynamic Properties
98(1)
3.5 Partition Functions
99(12)
3.5.1 Translational Energy
99(4)
3.5.2 Internal Structure
103(1)
3.5.3 Monatomic Gas
104(3)
3.5.4 Diatomic Gas
107(4)
3.6 Dissociation--Recombination System
111(3)
3.7 Summary
114(1)
3.8 Problems
114(4)
4 Finite-Rate Processes
118(31)
4.1 Introduction
118(1)
4.2 Equilibrium Processes
119(7)
4.2.1 Vibrational Energy
119(2)
4.2.2 Equilibrium Chemistry
121(3)
4.2.3 Equilibrium Constant
124(1)
4.2.4 Equilibrium Composition
124(2)
4.3 Vibrational Relaxation
126(3)
4.3.1 Vibrational Relaxation Time
127(2)
4.4 Finite-Rate Chemistry
129(15)
4.4.1 Rate Coefficient
133(3)
4.4.2 Effects of Internal Energy
136(2)
4.4.3 Calculation of Dissociation Rates
138(2)
4.4.4 Finite-Rate Relaxation
140(4)
4.5 Summary
144(1)
4.6 Problems
144(5)
Part II Numerical Simulation
5 Relations Between Molecular and Continuum Gas Dynamics
149(34)
5.1 Introduction
149(1)
5.2 The Conservation Equations
150(5)
5.3 Chapman--Enskog Analysis and Transport Properties
155(18)
5.3.1 Analysis for the BGK Equation
156(6)
5.3.2 Analysis for the Boltzmann equation
162(3)
5.3.3 Analysis for Gas Mixtures
165(3)
5.3.4 General Transport Properties of Polyatomic Mixtures
168(5)
5.4 Evaluation of Collision Cross Sections and Transport Properties
173(8)
5.4.1 Collision Cross Sections
173(2)
5.4.2 Hard-Sphere Interactions
175(1)
5.4.3 Inverse Power-Law Interaction's
176(2)
5.4.4 General Interatomic Potentials
178(3)
5.5 Summary
181(2)
6 Direct Simulation Monte Carlo
183(69)
6.1 Introduction
183(5)
6.2 DSMC Basics
188(16)
6.2.1 Fundamentals
188(5)
6.2.2 Particle Movement and Sorting
193(4)
6.2.3 Collision Rate
197(5)
6.2.4 Cell and Particle Properties
202(2)
6.3 Models for Viscosity, Diffusivity, and Thermal Conductivity
204(22)
6.3.1 The Variable Hard-Sphere Model
204(12)
6.3.2 The Variable Soft-Sphere Model
216(2)
6.3.3 Generalized Hard-Sphere, Soft-Sphere, and LJ Models
218(6)
6.3.4 Thermal Conductivity
224(1)
6.3.5 Model Parametrization
225(1)
6.4 Internal Energy Transfer Modeling in DSMC
226(24)
6.4.1 Continuum and Molecular Models
226(2)
6.4.2 Post-collision Energy Redistribution
228(8)
6.4.3 Inelastic Collision Pair Selection Procedures
236(8)
6.4.4 Generalized Post-collision Energy Redistribution
244(6)
6.5 Summary
250(2)
7 Models for Nonequilibrium Thermochemistry
252(59)
7.1 Introduction
252(1)
7.2 Rotational Energy Exchange Models
252(7)
7.2.1 Constant Collision Number
253(1)
7.2.2 The Parker Model
253(1)
7.2.3 Variable Probability Exchange Model of Boyd
254(1)
7.2.4 Nonequilibrium Direction Dependent Model
255(1)
7.2.5 Model Results
256(3)
7.3 Vibrational Energy Exchange Models
259(8)
7.3.1 Constant Collision Number
259(1)
7.3.2 The Millikan-White Model
260(3)
7.3.3 Quantized Treatment for Vibration
263(2)
7.3.4 Model Results
265(2)
7.4 Dissociation Chemical Reactions
267(10)
7.4.1 Total Collision Energy Model
267(6)
7.4.2 Redistribution of Energy Following a Dissociation Reaction
273(3)
7.4.3 Vibrationally Favored Dissociation Model
276(1)
7.5 General Chemical Reactions
277(32)
7.5.1 Reaction Rates and Equilibrium Constant
277(4)
7.5.2 Backward Reaction Rates in DSMC
281(6)
7.5.3 Three-Body Recombination Reactions
287(2)
7.5.4 Post-Reaction Energy Redistribution and General Implementation
289(4)
7.5.5 DSMC Solutions for Reacting Flows
293(16)
7.6 Summary
309(2)
Appendix A Generating Particle Properties 311(12)
Appendix B Collisional Quantities 323(6)
Appendix C Determining Post-Collision Velocities 329(9)
Appendix D Macroscopic Properties 338(8)
Appendix E Common Integrals 346(3)
References 349(8)
Index 357
Iain D. Boyd received a doctorate in aeronautics and astronautics from the University of Southampton. He worked at NASA Ames Research Center and Cornell University, New York, before joining the University of Michigan. He has authored more than 200 journal articles and 300 conference papers. Professor Boyd is a Fellow of the American Physical Society and a Fellow of the American Institute of Aeronautics and Astronautics, from which he also received the 1998 Lawrence Sperry Award. He has served on the editorial boards of Physics of Fluids, the Journal of Spacecraft and Rockets, the Journal of Thermophysics and Heat Transfer, and Physical Review Fluids. Thomas E. Schwartzentruber received his Bachelor's degree in engineering science and his Master's degree in aerospace engineering from the University of Toronto. He then received his doctorate degree in aerospace engineering from the University of Michigan, advised by Professor Iain D. Boyd. For his doctorate work he received the American Institute of Aeronautics and Astronautics Orville and Wilbur Wright graduate award. After joining the faculty in the Aerospace Engineering and Mechanics department at the University of Minnesota, he received a Young Investigator Program Award from the Air Force Office of Scientific Research and the Taylor Career Development Award from the University of Minnesota, where he is currently an associate professor and Russell J. Penrose Faculty Fellow.
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