Strongly nonlinear asymptotic model of cellular instabilities in premixed flames with stepwise ignition temperature kinetics

摘要

In this paper we consider ignition-temperature, first-order reaction model ofthermo-diffusive combustion that describes dynamics of thick flames arising ina theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. Theseflames often assume the shape of propagating curved interfaces that correspondto level sets of constant temperature. We derive a fully nonlinear equationthat governs dynamics of these level sets under a single assumption of smallcurvature. We study this equation for various asymptotic parameter regimes anddiscuss the ranges of validity of the corresponding simplified models. Ourtheoretical findings are supported by numerical simulations.