Asymptotic Analyses of Flames with Real Chemistry

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This program applies asymptotic methods--parameter expansions for large and small values of parameters appearing in differential equations--to the analysis of structures of flames in real combustible mixtures. Rate parameters for elementary chemical steps are taken from literature on chemical-kinetic experiments, and through nondimensionalization of the conservation equations, appropriate large and small parameters are identified. These parameters typically involve activation energies, leading to activation-energy asymptotics, or ratios of reaction rates of elementary steps, yielding rate-ratio asymptotics. Identification of limiting values of the parameters simplifies the conservation equations and allows solutions to be obtained largely analytically, without resort to numerical integration of the full set of conservation equations. The methods typically lead to formulas for the quantities of interest, such as burning velocities and extinction strain rates, and the formulas usually contain parameters determined by numerical integrations of two-point boundary-value problems for ordinary differential equations. Since these equations are much simpler than the starting equations, full parametric solutions are obtained, rather than solutions restricted to specific conditions. As a consequence, better understanding of flame structure is developed, the essential aspects of the combustion process are identified, and non-essential complications that play no significant role are eliminated. This type of approach has been completed in a previous study for the ozone decomposition flame, for methane flames, and for hydrogen flames, for example, yielding good four-step and two-step mechanisms for the last two flames, respectively. The current program will address higher hydrocarbon flames, hydrogen flames containing halogens, flames involving nitrogen chemistry, and methanol flames, as well as addressing issues of intrinsic stability and influences of strain on flames. Special attention will be paid to the derivation of reduced kinetic schemes of use to the practicing engineer in combustion design applications. In addition, the results will contribute to our general knowledge of mechanisms of flame propagation, flame structure, and extinction.