Nonlinear Dynamics and Pattern Formation in Combustion

Northwestern University, Evanston IL

Investigators

Abstract

NSF Award Abstract - DMS-0072491 Mathematical Sciences: Nonlinear Dynamics and Pattern Formation in Combustion Abstract 0072491 Matkowsky This research involves a synergism of analytical and numerical studies of problems in combustion and flame propagation. This approach is highly successful in elucidating behavior of solutions to the highly nonlinear systems of partial differential equations under study. Interest centers on problems exhibiting complex spatio-temporal dynamics in gaseous combustion as well as in solid fuel combustion and in heterogeneous combustion (solid plus gas), which arise in the self-propagating high-temperature synthesis process for advanced materials. The goal of the research is to describe transitions to, and the structure of, complex solution behavior. The project addresses gaseous combustion problems in the areas of flames with sequential reactions and flames in gas filled tubes. These systems exhibit transitions to states with greater degrees of spatio-temporal complexity as parameters are varied. The project also analyzes problems in solid fuel combustion, in which high temperature combustion waves, referred to as solid flames, are used to synthesize advanced materials. Research centers on the areas of solid flames and filtration combustion, which involves heterogeneous combustion, with reaction between gas and solid phases. The analytical studies are based on bifurcation and nonlinear stability theories, which employ asymptotic analysis and singular perturbation theory in the neighborhood of bifurcation or other transition points to yield a local description of the solution. An adaptive pseudo-spectral method is employed for large scale scientific computations, with which the local description is globally extended. The solutions exhibit layers, localized regions in which the solution varies rapidly. The adaptive pseudo-spectral method successfully meets the challenge of accurately and efficiently resolving such layer type behavior. This project is concerned with understanding processes that occur in energy conversion and materials synthesis, two areas of national importance. The research in energy conversion is focused on flame structure and dynamics, which involve interactions among many physical mechanisms. To determine cause and effect relations among the various mechanisms, this work explores parameter dependencies. The research in materials synthesis studies the use of combustion waves to produce materials having desired properties, for example, extreme hardness or imperviousness to temperature extremes. In this innovative technological process, which appears to enjoy advantages over conventional technology, the combustion wave propagates through the sample, converting an unreacted solid powder mixture to solid product. When so synthesized, materials can have superior properties.