Matalon 9703716 The objectives of the proposed work is to derive and analyze simple mathematical models of reacting flow systems by means of asymptotic and perturbation methods supplemented by numerical computations. The problems that will be addressed are related to phenomena that have been observed experimentally and are not yet completely understood. They fall in two categories: the first class of problems is concerned with premixed flames propagating in tubes, while the second class is concerned with diffusion flames (non-premixed combustion) that result from evaporating liquid fuels. The mathematical formulation of these problems can be reduced to a single, or a couple, of evolution equations that contain the main ingredients of the physical problem and are to be solved numerically. For premixed flames propagating in tubes the evolution equation takes the form of an integro-differential equation that describes the instantaneous shape and location of the flame front. For the burning of liquid films one finds, in general, two equations: one for the dynamics of the interface between the liquid and gas phases, and the other for the diffusion flame sheet which is the interface where the fuel vapor burns with the ambient oxidant. Combustion processes are extremely complicated; they encompass subjects concerned with energy generation and heat transfer, rates and mechanisms of chemical reactions, fluid flow and mass transport. They cover a broad range of important engineering technologies as well as topics of primary societal and environmental concerns. A fundamental way to gain understanding into the complex phenomena that one observe in various combustion systems is through mathematical modeling. This approach enables one to identify the underlying physical mechanisms responsible for the observed phenomenon, to study the interaction between the various physical parameters and to explore whether this interaction leads to the observed behavior. A deep understandin g often leadq to suggestions of new directions for experiments and design. The problems in this study are concerned with premixed flames, relevant to internal combustion engines and aerospace propulsion systems where the fuel and oxidant are intimately mixed prior to ignition, and combustion of liquid fuels, relevant to accidental spillage and fire spread where, under special circumstances, burning may occur with the available ambient oxidant.
