The Mathematical Theory of Combustion and Explosions

vi The amalgamation of individual approaches and results from various schools into a comprehensive scientific theory, which can be generally appreciated throughout the international scientific com­ munity, is oftendifficult and time consuming. We believe that one of the best ways to give a complete and clear presentation of a theoryis to include a review of the developmental history of that theory. We are convinced that explaining a theory in a historical perspectiveis essential for a proper understanding ofits present state and for a sound choice of future developments. So we have endeavored to present a complete picture of investi­ gations performed in both Western and Soviet nations. We understand that Soviet investigations are less familiar to English-speaking readers due to the languagebarrier and the obvious sad circumstances of the interruption of scientific connections before and after World War II, because of this there is an emphasis on Soviet publications in the bibliography. Our attempt to present a comprehensive picture has made our book rather large becauseit has had to include some fundamentals of thermochemistry and kinetics as well as self-ignition and flame propagation invarious conditions. We have also included stability problems in some detail but we have had to leave out the problems of combustion of solid propellants and detonation. We hope that our bookwill be useful to the reader wishing to learn about both the present state of combustion theory and howit originated due to the efforts of many people from different countries. Ya.B.Z.

Table of Contents:
1 Introduction. Foundations of the Science of Combustion: Basic Physical Concepts.- 1. Some Results from Chemical Kinetics and Thermochemistry.- 2. Self-Accelerating Chemical Reactions and Critical Phenomena — Explosions and Self-Ignition. Semenov’s Theory.- 3. The Homogeneous Ideally-Mixing Chemical Reactor.- 4. Laminar Flames.- 2 The Time-Independent Theory of Thermal Explosions.- 1. Basic Assumptions of the Theory.- 2. The Conditions for a Thermal Explosion.- 3. The Stability of the Solutions in the Time-Independent Theory of Thermal Explosions.- 4. Some General Properties of Solutions from the Time-Independent Theory of Thermal Explosions for Vessels of Arbitrary Shape.- 5. Numerical Studies of Thermal Explosions. Experiments.- 6. Application of the Idea of Thermal Explosions to the Mechanics of Polymers.- 3 The Initiation of Chemical Reaction Waves in Fuel Mixtures: Time-Dependent Statements of the Problem.- 1. Ignition of a Fuel Mixture by Heated Surfaces.- 2. The Time-Independent Theory of Ignition by Hot Surfaces as an Intermediate Asymptote of a Time-Dependent Process.- 3. The Initiation of Chemical Reactions by Active Centers.- 4 Laminar Flames.- 1. The Equations of the Theory of Flame Propagation.- 2. Existence and Uniqueness of the Steady-State Solution of the System of Flame Propagation Equations.- 3. The velocity and Structure of a Flame Front for Reactions with Large Activation Energies.- 4. The Spectrum of Flame Propagation Velocities for a Nonzero Reaction Rate near and in the Initial State, The Propagation of Chain Isothermal Flames.- 5. Formation of a Stationary Laminar Flame Front.- 6. The Diffusional-Thermal Stability of Laminar Flames.- 7. Flames in Flows with a Velocity Gradient. Flame “Stretching”.- 8. Self-Igniting Mixtures.- 5 Complexand Chain Reactions in Flames.- 1. The Theory of Flames with Multi-step Reactions: Purpose and Methods.- 2. Flames with Unbranched Chain Reactions.- 3. Flames with Branching Chain Reactions.- 4. Simple Bulk-Schemes for Multi-step Chemical Reactions in Flames.- 5. Cool (Isothermal) Flames.- 6 The Gas Dynamics of Combustion.- 1. Motion of Flames in Gas Flows. The Condition for Stationary Combustion.- 2. Combustion in Closed Vessels. The Mach Effect.- 3. Hydrodynamic Instability of Flames.- 4. Flame Acceleration and Detonation in Tubes.- 7 Diffusional Combustion of Gases.- 1. The General Properties of Diffusion Flames. The Combustion Surface.- 2. The Burke-Schumann Problem.- 3. The Limit of Diffusional Combustion in Unmixed Gases.- 4. Diffusion Flames in Opposed Jets of Oxidant and Fuel.