This research applies mathematical methods for partial differential equations to analysis of the structure and stability of combustion processes in real combustible mixtures. Diffusion flames, premixed flames and detonations are addressed in different parts of the research. Rate parameters for elementary chemical steps are evaluated from the 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, leading to rate-ratio asymptotics. 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 methods typically lead to formulas for the quantities of interest, such as burning velocities, ignition or extinction strain rates, and critical conditions for stability, 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 and stability is developed, the essential aspects of the combustion processes are identified, and nonessential complications that play no significant role are eliminated. This type of approach has now been completed for methane and hydrogen combustion, for example, yielding good four-step and two-step memchanisms, respectively. The new research will address higher hydrocarbon combustion, higher alcohol combustion, and production of oxides of nitrogen in flames, as well as intrinsic detonation stability and influences of strain on flames. Special attention will be paid to the derivation of useful reduced kinetic schemes and to their influences on flame and detonation. In addition, reduced chemistry for describing influences of halogens as inhibitors or extinction promoters in hydrogen flames will be addressed. The results constribute to our knowledge of mechanisms of flame propagation, flame structure, flame and detonation instabilities, and ignition and extinction.
