Theory of Combustion by Analytical Methods for Real Chemistry

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The structure and stability of combustion processes in real mixtures is analyzed using mathematical methods for partial differential equations. Diffusion flames, premixed flames, and detonations are addressed. Through nondimensionalization of the conservation equations, appropriate parameters are identified, typically activation energies or ratios of reaction rates. Asymptotic analysis identifies limiting values and simplifies the conservation equations, enabling solution analytically without resort to numerical integration. Formulas are derived for quantities of interest such as burning velocities, ignition or extinction strain rates, autoignition delay times, and critical conditions for stability. Systems addressed include combustion of higher hydrocarbons and higher alcohols including production of nitrogen oxides, intrinsic detonation stability, and influences of strain on flames. Reduced kinetic schemes are derived and their influences on flame and detonation behaviors are analyzed.