Nagnibeda / Kustova Non-Equilibrium Reacting Gas Flows

Kinetic Theory of Transport and Relaxation Processes
1. Auflage 2009
ISBN: 978-3-642-01390-4
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 252 Seiten

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.

Autoren/Hrsg.

Nagnibeda, Ekaterina

Kustova, Elena

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Introduction;12
4;Kinetic Equations and Method of Small Parameter;17
4.1;Energy of Internal Degrees of Freedom: Macroscopic Gas Parameters;17
4.1.1;{\it Rotational and Vibrational Energy of Molecules};17
4.1.2;{\it Distribution Function and Macroscopic Parameters};20
4.1.3;{\it Specific Heats};23
4.2;Kinetic Equations for Distribution Functions in Reacting Gas Mixtures;27
4.3;Small Parameters in Kinetic Equations and the Method of Different Scales;30
4.4;Modification of the Chapman–Enskog Method for Gases with Rapid and Slow Processes;36
5;State-to-State Approach;44
5.1;Zero-Order Distribution Function;44
5.2;Closed Set of Governing Equations;48
5.3;First-Order Distribution Function;50
5.4;Transport Terms;53
5.5;Production Terms;56
6;Multi-Temperature Models in Transport and Relaxation Theory;63
6.1;Generalized Treanor Distribution for a Gas Mixture;64
6.2;Macroscopic Parameters and Specific Heats;70
6.3;Governing Equations in the Multi-Temperature Approach;73
6.4;First-Order Distribution Function;75
6.5;First-Order Transport Terms;80
6.6;Production Terms;83
6.7;Strongly Non-equilibrium Quasi-stationary Distribution in a Pure Gas;88
6.7.1;{\it Zero-Order Distribution Function};88
6.7.2;{\it Equations for Macroscopic Parameters};94
6.7.3;{\it Vibrational Relaxation Time and Specific Heats};95
6.8;Transport Processes in a Gas with Strong Vibrational Excitation;98
6.8.1;{\it First-Order Distribution Function};98
6.8.2;{\it Transport Terms};101
7;One-Temperature Model for Chemically Non-equilibrium Gas Mixtures;104
7.1;Zero-Order Distribution, Macroscopic Parameters and Set of Governing Equations;104
7.2;First-Order Distribution Function: Transport and Production Terms ;109
7.3;Transition to Chemical Equilibrium Regime;113
8;Algorithms for the Calculation of Transport Coefficients ;117
8.1;State-to-State Approach;117
8.1.1;{\it Expansions in the Sonine and Waldmann-Trübenbacher Polynomials};118
8.1.2;{\it Systems of Equations for the Expansion Coefficients};121
8.2;Quasi-stationary Approaches;127
8.2.1;{\it Multi-Temperature Approach};127
8.2.2;{\it One-Temperature Approach};134
8.3;Bracket Integrals;136
8.3.1;{\it State-to-State Approach};137
8.3.2;{\it Multi-Temperature Approach};143
8.3.3;{\it One-Temperature Approach};148
8.4;$\Omega$-Integrals and Relaxation Times;150
8.4.1;{\it $\Omega$-Integrals};151
8.4.2;{\it Relaxation Times};157
8.5;Simplified Formulas for Transport Coefficients in the State-to-State Approach;158
8.6;Transition Between Transport Terms in Different Approaches;164
8.7;A Single-Component Gas: The Generalized Eucken Formula;168
9;Reaction Rate Coefficients;176
9.1;State-to-State Approach: Zero-Order Chapman–Enskog Approximation;177
9.1.1;{\it Rate Coefficients for Vibrational Energy Transitions};178
9.1.2;{\it Dissociation Rate Coefficients};182
9.2;Quasi-stationary Approaches;187
9.3;First-Order Approximation of the Chapman–Enskog Method;193
10;Non-Equilibrium Kinetics and Transport Processes Behind Shock Waves;196
10.1;State-to-State Kinetics in Binary Mixtures with Dissociation and Recombination;196
10.2;Diffusion and Heat Transfer;201
10.3;Vibrational and Chemical Kinetics and Transport Processes in Air Mixtures;203
11;Heat Transfer and Diffusion in a Non-equilibrium Boundary Layer;208
11.1;Equations for a Non-equilibrium Boundary Layer in the State-to-State Approach;209
11.2;A Flow of N_{2}/N Mixture Near the Non-catalytic Surface;213
11.3;A Flow of O_{2}/O Mixture Near the Catalytic Surfaces;217
12;Non-equilibrium Kinetics and Its Influence on the Parameters of Nozzle Flows;226
12.1;Flow Equations, Non-equilibrium Distributions and Macroscopic Parameters;226
12.2;The Influence of Non-equilibrium Kinetics on Gas Dynamics and Transport Processes;233
13;Conclusion;239
14;References;241
15;Index;254