Non-Equilibrium Reacting Gas Flows: Kinetic Theory of Transport and Relaxation Processes (Heat and Mass Transfer)

In the present monograph, we develop the kinetic theory of transport phenomena and relaxation processes in the flows of reacting gas mixtures and discuss its applications to strongly non-equilibrium conditions. The main attention is focused on the influence of non-equilibrium kinetics on gas dynamics and transport properties. Closed systems of fluid dynamic equations are derived from the kinetic equations in different approaches. We consider the most accurate approach taking into account the state-to-state kinetics in a flow, as well as simplified multi-temperature and one-temperature models based on quasi-stationary distributions. Within these approaches, we propose the algorithms for the calculation of the transport coefficients and rate coefficients of chemical reactions and energy exchanges in non-equilibrium flows; the developed techniques are based on the fundamental kinetic theory principles. The theory is applied to the modeling of non-equilibrium flows behind strong shock waves, in the boundary layer, and in nozzles. The comparison of the results obtained within the frame of different approaches is presented, the advantages of the new state-to-state kinetic model are discussed, and the limits of validity for simplified models are established. The book can be interesting for scientists and graduate students working on physical gas dynamics, aerothermodynamics, heat and mass transfer, non-equilibrium physical-chemical kinetics, and kinetic theory of gases.;Kinetic Equations and Method of Small Parameter -- State-to-State Approach -- Multi-Temperature Models in Transport and Relaxation Theory -- One-Temperature Model for Chemically Non-equilibrium Gas Mixtures -- Algorithms for the Calculation of Transport Coefficients -- Reaction Rate Coefficients -- Non-equilibrium Kinetics and its Influence on the Transport Processes Behind Strong Shock Waves -- Heat Transfer and Diffusion in a Non-equilibrium Boundary Layer -- Non-equilibrium Kinetics and Its Influence on the Parameters of Nozzle Flows. Subject Title Page 2 Preface 6 Contents 9 Introduction 12 Kinetic Equations and Method of Small Parameter 17 Energy of Internal Degrees of Freedom: Macroscopic Gas Parameters 17 {\it Rotational and Vibrational Energy of Molecules} 17 {\it Distribution Function and Macroscopic Parameters} 20 {\it Specific Heats} 23 Kinetic Equations for Distribution Functions in Reacting Gas Mixtures 27 Small Parameters in Kinetic Equations and the Method of Different Scales 30 Modification of the Chapman–Enskog Method for Gases with Rapid and Slow Processes 36 State-to-State Approach 44 Zero-Order Distribution Function 44 Closed Set of Governing Equations 48 First-Order Distribution Function 50 Transport Terms 53 Production Terms 56 Multi-Temperature Models in Transport and Relaxation Theory 63 Generalized Treanor Distribution for a Gas Mixture 64 Macroscopic Parameters and Specific Heats 70 Governing Equations in the Multi-Temperature Approach 73 First-Order Distribution Function 75 First-Order Transport Terms 80 Production Terms 83 Strongly Non-equilibrium Quasi-stationary Distribution in a Pure Gas 88 {\it Zero-Order Distribution Function} 88 {\it Equations for Macroscopic Parameters} 94 {\it Vibrational Relaxation Time and Specific Heats} 95 Transport Processes in a Gas with Strong Vibrational Excitation 98 {\it First-Order Distribution Function} 98 {\it Transport Terms} 101 One-Temperature Model for Chemically Non-equilibrium Gas Mixtures 104 Zero-Order Distribution, Macroscopic Parameters and Set of Governing Equations 104 First-Order Distribution Function: Transport and Production Terms 109 Transition to Chemical Equilibrium Regime 113 Algorithms for the Calculation of Transport Coefficients 117 State-to-State Approach 117 {\it Expansions in the Sonine and Waldmann-Trübenbacher Polynomials} 118 {\it Systems of Equations for the Expansion Coefficients} 121 Quasi-stationary Approaches 127 {\it Multi-Temperature Approach} 127 {\it One-Temperature Approach} 134 Bracket Integrals 136 {\it State-to-State Approach} 137 {\it Multi-Temperature Approach} 143 {\it One-Temperature Approach} 148 $\Omega$-Integrals and Relaxation Times 150 {\it $\Omega$-Integrals} 151 {\it Relaxation Times} 157 Simplified Formulas for Transport Coefficients in the State-to-State Approach 158 Transition Between Transport Terms in Different Approaches 164 A Single-Component Gas: The Generalized Eucken Formula 168 Reaction Rate Coefficients 176 State-to-State Approach: Zero-Order Chapman–Enskog Approximation 177 {\it Rate Coefficients for Vibrational Energy Transitions} 178 {\it Dissociation Rate Coefficients} 182 Quasi-stationary Approaches 187 First-Order Approximation of the Chapman–Enskog Method 193 Non-Equilibrium Kinetics and Transport Processes Behind Shock Waves 196 State-to-State Kinetics in Binary Mixtures with Dissociation and Recombination 196 Diffusion and Heat Transfer 201 Vibrational and Chemical Kinetics and Transport Processes in Air Mixtures 203 Heat Transfer and Diffusion in a Non-equilibrium Boundary Layer 208 Equations for a Non-equilibrium Boundary Layer in the State-to-State Approach 209 A Flow of N_{2}/N Mixture Near the Non-catalytic Surface 213 A Flow of O_{2}/O Mixture Near the Catalytic Surfaces 217 Non-equilibrium Kinetics and Its Influence on the Parameters of Nozzle Flows 226 Flow Equations, Non-equilibrium Distributions and Macroscopic Parameters 226 The Influence of Non-equilibrium Kinetics on Gas Dynamics and Transport Processes 233 Conclusion 239 References 241 Index 254 "The book can be interesting for scientists and graduate students working on physical gas dynamics, aerothermodynamics, heat and mass transfer, non-equilibrium physical chemical kinetics, and kinetic theory of gases."--Jacket