Nonequilibrium Gas Dynamics and Molecular Simulation (Cambridge Aerospace Series, Band 42)

Contents
List of Illustrations
List of Tables
Preface
Acknowledgments
Part I Theory
	1 Kinetic Theory
		1.1 Introduction
		1.2 Fundamental Concepts
			1.2.1 Particle Model
			1.2.2 Macroscopic Quantities from Molecular Behavior
			1.2.3 Molecular Collisions
			1.2.4 Molecular Transport Processes
		1.3 Kinetic Theory Analysis
			1.3.1 Velocity Distribution Function
			1.3.2 The Boltzmann Equation
			1.3.3 The H-Theorem of Boltzmann
			1.3.4 Maxwellian VDF
			1.3.5 Equilibrium Collision Properties
			1.3.6 Free Molecular Flow onto a Surface
			1.3.7 Kinetic-Based Analysis of Nonequilibrium Flow
			1.3.8 Free Molecular Flow Analysis
		1.4 Summary
		1.5 Problems
	2 Quantum Mechanics
		2.1 Introduction
		2.2 Quantum Mechanics
			2.2.1 Heisenberg Uncertainty Principle
			2.2.2 The Schrödinger Equation
			2.2.3 Solutions of the Schrödinger Equation
			2.2.4 Two-Particle System
			2.2.5 Rotational and Vibrational Energy
			2.2.6 Electronic Energy
		2.3 Atomic Structure
			2.3.1 Electron Classification
			2.3.2 Angular Momentum
			2.3.3 Spectroscopic Term Classification
			2.3.4 Excited States
		2.4 Structure of Diatomic Molecules
			2.4.1 Born–Oppenheimer Approximation
			2.4.2 Rotational and Vibrational Energy
			2.4.3 Electronic States
		2.5 Summary
		2.6 Problems
	3 Statistical Mechanics
		3.1 Introduction
		3.2 Molecular Statistical Methods
			3.2.1 Energy Groups
		3.3 Distribution of Energy States
			3.3.1 Boltzmann Limit
			3.3.2 Boltzmann Energy Distribution
		3.4 Relation to Thermodynamics
			3.4.1 Boltzmann’s Relation
			3.4.2 Macroscopic Thermodynamic Properties
		3.5 Partition Functions
			3.5.1 Translational Energy
			3.5.2 Internal Structure
			3.5.3 Monatomic Gas
			3.5.4 Diatomic Gas
		3.6 Dissociation–Recombination System
		3.7 Summary
		3.8 Problems
	4 Finite-Rate Processes
		4.1 Introduction
		4.2 Equilibrium Processes
			4.2.1 Vibrational Energy
			4.2.2 Equilibrium Chemistry
			4.2.3 Equilibrium Constant
			4.2.4 Equilibrium Composition
		4.3 Vibrational Relaxation
			4.3.1 Vibrational Relaxation Time
		4.4 Finite-Rate Chemistry
			4.4.1 Rate Coefficient
			4.4.2 Effects of Internal Energy
			4.4.3 Calculation of Dissociation Rates
			4.4.4 Finite-Rate Relaxation
		4.5 Summary
		4.6 Problems
Part II Numerical Simulation
	5 Relations Between Molecular and Continuum Gas Dynamics
		5.1 Introduction
		5.2 The Conservation Equations
		5.3 Chapman–Enskog Analysis and Transport Properties
			5.3.1 Analysis for the BGK Equation
			5.3.2 Analysis for the Boltzmann equation
			5.3.3 Analysis for Gas Mixtures
			5.3.4 General Transport Properties of Polyatomic Mixtures
		5.4 Evaluation of Collision Cross Sections and Transport Properties
			5.4.1 Collision Cross Sections
			5.4.2 Hard-Sphere Interactions
			5.4.3 Inverse Power-Law Interactions
			5.4.4 General Interatomic Potentials
		5.5 Summary
	6 Direct Simulation Monte Carlo
		6.1 Introduction
		6.2 DSMC Basics
			6.2.1 Fundamentals
			6.2.2 Particle Movement and Sorting
			6.2.3 Collision Rate
			6.2.4 Cell and Particle Properties
		6.3 Models for Viscosity, Diffusivity, and Thermal Conductivity
			6.3.1 The Variable Hard-Sphere Model
			6.3.2 The Variable Soft-Sphere Model
			6.3.3 Generalized Hard-Sphere, Soft-Sphere, and LJ Models
			6.3.4 Thermal Conductivity
			6.3.5 Model Parametrization
		6.4 Internal Energy Transfer Modeling in DSMC
			6.4.1 Continuum and Molecular Models
			6.4.2 Post-collision Energy Redistribution
			6.4.3 Inelastic Collision Pair Selection Procedures
			6.4.4 Generalized Post-collision Energy Redistribution
		6.5 Summary
	7 Models for Nonequilibrium Thermochemistry
		7.1 Introduction
		7.2 Rotational Energy Exchange Models
			7.2.1 Constant Collision Number
			7.2.2 The Parker Model
			7.2.3 Variable Probability Exchange Model of Boyd
			7.2.4 Nonequilibrium Direction Dependent Model
			7.2.5 Model Results
		7.3 Vibrational Energy Exchange Models
			7.3.1 Constant Collision Number
			7.3.2 The Millikan–White Model
			7.3.3 Quantized Treatment for Vibration
			7.3.4 Model Results
		7.4 Dissociation Chemical Reactions
			7.4.1 Total Collision Energy Model
			7.4.2 Redistribution of Energy Following a Dissociation Reaction
			7.4.3 Vibrationally Favored Dissociation Model
		7.5 General Chemical Reactions
			7.5.1 Reaction Rates and Equilibrium Constant
			7.5.2 Backward Reaction Rates in DSMC
			7.5.3 Three-Body Recombination Reactions
			7.5.4 Post-Reaction Energy Redistribution and General Implementation
			7.5.5 DSMC Solutions for Reacting Flows
		7.6 Summary
Appendix A Generating Particle Properties
Appendix B Collisional Quantities
Appendix C Determining Post-Collision Velocities
Appendix D Macroscopic Properties
Appendix E Common Integrals
References
Index