Mathematical Models of Premixed Flames

DMS 9803614 Mathematical Models of Premixed Flames, John K. Bechtold This work proposes to systmatically derive generalized mathematical models of premixed flame propagation through a variety of flow conditions. Asymptotic methods will be employed to extract reduced models from a complete set of equations governing combustion processes. Of interest will be to account for flow conditions that are characteristic of turbulent flows. Specific models will include the following phenomena: unsteady flame structure, flow fields with concentration and thermal gradients, and multi-component mixtures. These reduced models possess a tremendous advantage over the full set of equations in that they permit direct analysis of salient features characterizing practical combustion systems. Therefore, it is further proposed that these new models will be used to analyze simplified flame-flow configurations that retain some of the essential features of turbulent reacting flows, including unsteadiness and non-uniformities. Most practical combustion systems, including internal combustion engines, rocket engines and incinerators, operate in a turbulent regime. The study of combustion in these environments provides valuable information on such important issues as efficiency and emissions. These systems are very complicated and are governed by huge sets of equations that are too large to be solved even by the most sophisticated numerical techniques. Scientific progress in these directions relies on the development of simplified mathematical models; that is, reduced systems that retain the most essential features of the combustion process, but that permit direct analysis. The work proposed here involves the systematic derivation of flame models to study flame propagation in a wide range of flow conditions, including time-dependent and non-uniform flows. Of particular interest will be to calculate burning rates and to identify conditions for which flames will be extinguished.