Asymptotic Analysis of Flame Structure with Real Chemistry

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This research applies asymptotic methods, involving expansions for large and small values of parameters appearing in differential equations, to the analysis of structures of flames in real combustible mixtures. Through nondimensionalization of the conservation equations, large and small parameters are identified. These parameters involve activation energies leading to activation-energy asymptotics, magnitudes of reaction rates leading to Damkohler-number asymptotics, and ratios of reaction rates leading to rate- ratio asymptotics. Rate parameters for elementary steps are taken from the literature on reaction rate experiments. The identification of limiting values of the parameters simplifies the conservation equations and enables solutions to be obtained largely analytically without resort to numerical integration of the full set of conservation equations. The research will address structural differences between premixed flames and diffusion flames for hydrocarbon-oxygen-nitrogen systems for systems involving carbon monoxide, hydrogen and oxygen, as well as the intrinsic stability and influences of strain for these flames. Special attention will be paid to the derivation and application of useful reduced schemes for hydrogen-oxygen systems, for systems containing halogens, for higher hydrocarbons, and possibly also for methanol. The methods typically lead to formulas for the quantities of interest, such as burning velocities, and the formulas usually contain parameters determined by numerical integrations of two-point boundary-value problems for ordinary differential equations. Since these differential equations are much simpler than the starting differential equations, full parametric solutions are obtained, rather than solutions restricted to specific conditions. As a consequence, a better understanding of flame structure ensues, the essential aspects of the combustion processes are identified, and inessential complications that play no significant role are eliminated.