The Mathematical Theory of Combustion and Explosions

ISBN-13: 9781461294399 / Angielski / Miękka / 2011 / 597 str.

G. Barenblatt

Opis

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.

Spis treści

1 Introduction. Foundations of the Science of Combustion: Basic Physical Concepts.- 1. Some Results from Chemical Kinetics and Thermochemistry.- Rates of chemical reactions. Reaction rate constants.- Chemical equilibrium. The equilibrium constant.- The heat of reaction.- The molecular energetics of combustion.- The adiabatic combustion temperature.- Complex reactions. The method of quasi-stationary concentrations.- The reaction of hydrogen with chlorine as an example of a nonbranching chain reaction.- The oxidation of nitrogen during combustion. A reversible reaction at variable temperatures.- 2. Self-Accelerating Chemical Reactions and Critical Phenomena — Explosions and Self-Ignition. Semenov’s Theory.- The properties of explosive reactions.- Chain self-ignition. The oxidation of hydrogen.- Thermal self-ignition. Adiabatic thermal explosions.- The Frank-Kamenetskii transformation.- Semenov’s theory of thermal explosions.- The induction period of a thermal explosion.- Interpretation of the theory of thermal explosions on the phase plane.- 3. The Homogeneous Ideally-Mixing Chemical Reactor.- Methods of producting combustion in flows.- Stationary combustion in a homogeneous chemical reactor.- The heat release rate from combustion in an ideally-mixing chemical reactor.- The effect of heat losses.- 4. Laminar Flames.- Chemical reaction waves. Why do they propagate through a fuel mixture.- Chemical transformation in flames.- The similarity of the temperature and concentration distributions in flames.- A formula for the normal propagation velocity of a flame.- Some consequences of the flame velocity formula.- The heat release rate of chemical reactions in flames.- Limits on the propagation of combustion.- Isothermal flames. The decisive role of diffusion of active centers.- Are flames always plane and stationary? Flame stability.- References.- 2 The Time-Independent Theory of Thermal Explosions.- 1. Basic Assumptions of the Theory.- 2. The Conditions for a Thermal Explosion.- Thermal explosions in flat reaction vessels.- Comparison with Semenov’s theory of thermal explosions.- Thermal explosions in cylindrical vessels.- Thermal explosions in spherical vessels.- Thermal explosions with Newtonian heat exchange at the vessel wall.- 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.- References.- 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.- The theory of ignition by a heated plane surface.- Generalization to chemical reaction rates with an arbitrary temperature dependence.- Calculating the ignition conditions in specific instances.- Accounting for reagent consumption near a heated surface.- The effect of surface curvature on the ignition conditions. Cylindrical surfaces.- Ignition of a fuel mixture flowing around a hot object.- 2. The Time-Independent Theory of Ignition by Hot Surfaces as an Intermediate Asymptote of a Time-Dependent Process.- The time evolution of ignition. The transition from a thermal explosion to ignition.- The effect of reagent consumption on nonstationary ignition.- 3. The Initiation of Chemical Reactions by Active Centers.- References.- 4 Laminar Flames.- 1. The Equations of the Theory of Flame Propagation.- Basic ideas and simplifications of the theory.- Propagation of laminar flames at constant velocity. The structure of a flame front; some general properties.- 2. Existence and Uniqueness of the Steady-State Solution of the System of Flame Propagation Equations.- The case Le = 1: the similarity of the temperature and concentration distributions.- Existence of a solution for an arbitrary constant Lewis number.- Uniqueness of the solution for 0 ? Le(z) < 1.- Calculating the flame propagation velocity estimation by the “trial and error” methods.- 3. The velocity and Structure of a Flame Front for Reactions with Large Activation Energies.- The range of variation of the flame propagation velocity.- An asymptotic formula for the flame propagation velocity.- The structure of a laminary flame front.- An appropriate method of deriving a formula for the flame propagation velocity.- Matching asymptotic expansions in the theory of normal flame propagation.- 4. The Spectrum of Flame Propagation Velocities for a Nonzero Reaction Rate near and in the Initial State, The Propagation of Chain Isothermal Flames.- The Kolmogorov-Petrovskii-Piskunov problem.- Summary of results on the existence and uniqueness of solutions to the flame propagation velocity problem.- Flame propagation in a mixture that reacts at the initial temperature.- Spontaneous propagation of chemical reactions. The influence of initial conditions.- 5. Formation of a Stationary Laminar Flame Front.- Review of analytic studies.- Application of numerical methods to the transition to a stationary combustion regime.- Stationary combustion waves as self-similar solutions of the second kind.- 6. The Diffusional-Thermal Stability of Laminar Flames.- One-dimensional stability of flame propagation for Le = 1.- Flame propagation in media with a weakly perturbed initial temperature.- Effects of diffusion and heat conduction on the stability of flames with respect to spatial perturbations.- Diffusional combustion in gaseous mixtures.- 7. Flames in Flows with a Velocity Gradient. Flame “Stretching”.- 8. Self-Igniting Mixtures.- Exothermic chemical reaction regimes in gaseous flows.- Analysis of the limiting cases.- Self-igniting combustion of condensed systems.- References.- 5 Complex and Chain Reactions in Flames.- 1. The Theory of Flames with Multi-step Reactions: Purpose and Methods.- Basic system of equations; assumptions.- An approximate method for calculations involving hot flames with complex and chain reactions.- Application of asymptotic methods to flames with complex structures.- 2. Flames with Unbranched Chain Reactions.- The structure and propagation velocity of flames with unbranched chain reactions involving the combination of two substances.- Calculation of the flame velocity in H2-Cl2 mixtures and comparison with experimental data.- 3. Flames with Branching Chain Reactions.- Properties of flames with branching chain reactions; the simplest chain branching scheme in hot flames.- Flames in hydrogen-oxygen fuel mixtures. Simplest model.- 4. Simple Bulk-Schemes for Multi-step Chemical Reactions in Flames.- Consecutive chemical reactions in flames; “merging,” “control,” and “separation” regimes.- Parallel chemical reactions in flames.- 5. Cool (Isothermal) Flames.- The simplest model of an isothermal flame.- The necessary conditions for existence of an isothermal flame in a multi-component gas mixture. Interaction of chains.- Numerical calculations of the propagation velocity of cool flames in CS2-O2 mixtures and of the critical conditions for propagation; comparison with experiment.- References.- 6 The Gas Dynamics of Combustion.- 1. Motion of Flames in Gas Flows. The Condition for Stationary Combustion.- Propagation of a flame front in a given gas flow field. Huygens’ principle.- The condition for stationary combustion. The Mach angle. The concept of retention points.- The flame on a Bunsen burner.- Propagation of a flame front in a horizontal tube.- Turbulent combustion (general concepts).- Flames as surfaces of gasdynamic discontinuity. Conservation conditions at a flame front. The Hugoniot adiabat.- Inclined plane flame fronts.- Combustion in a fast flow in a tube. Ideal mixing.- Rapid combustion in a tube. Nonuniform flow of combustion products.- Flame fronts as sources of vertical perturbations.- 2. Combustion in Closed Vessels. The Mach Effect.- The difference between combustion at constant volume and combustion at constant pressure. The average temperature and pressure in a closed vessel.- Layered combustion in closed vessels. The Mach effect.- The Mach effect in burned gases. The case of a fuel gas and combustion products with constant and equal adiabatic indices.- The temperature distribution in a spherical vessel with central ignition. Computation of P(t) and rf(t) diagrams.- Experimental manifestations of the Mach effect. Basic approximations of the theory and the conditions for their realization.- Production of nitric oxide during combustion in closed vessels.- 3. Hydrodynamic Instability of Flames.- Statement and solution of Landau’s problem.- Discussion of the results. Physical interpretation of the solution.- Stabilizing effects on plane flame fronts. Markstein’s solution.- The effect of acceleration on the hydrodynamic instability of flames.- The effect of transport processes on the hydro-dynamic instability of flames.- A Laplace transform study of hydrodynamic instability.- The effect of the form of the initial perturbation on the temporal development of hydrodynamic instability. The relationship between Landau’s model and the Laplace transform solution.- Stationary combustion following loss of stability by a plane flame front.- Combustion of liquid explosives. The effect of surface tension on the stability of combustion.- The propagation of spherical flames. Why spherical flames attract the attention of researchers.- Changes in the hydrodynamic stability problem for a spherical flame.- Stability of spherical flames with respect to higher harmonics.- Discussion of the theoretical results and comparison with experimental observations of spherical flames.- 4. Flame Acceleration and Detonation in Tubes.- Experimental observations of detonation onset in tubes.- The breakup of an arbitrary discontinuity in a fuel mixture.- Propagation of a flame from the closed end of a tube. Production of compression waves.- Why a flame develops into a detonation wave. Shchelkin’s explanation.- References.- 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.- References.