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

TL;DR

This paper develops a nonlinear asymptotic model for cellular instabilities in premixed flames with stepwise ignition temperature kinetics, providing insights into flame dynamics and validating results with numerical simulations.

Contribution

It introduces a fully nonlinear equation for flame front dynamics under small curvature assumptions, expanding understanding of thermo-diffusive combustion instabilities.

Findings

Derived a nonlinear equation governing flame front dynamics.

Analyzed the equation across different asymptotic regimes.

Supported theoretical results with numerical simulations.

Abstract

In this paper we consider ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These flames often assume the shape of propagating curved interfaces that correspond to level sets of constant temperature. We derive a fully nonlinear equation that governs dynamics of these level sets under a single assumption of small curvature. We study this equation for various asymptotic parameter regimes and discuss the ranges of validity of the corresponding simplified models. Our theoretical findings are supported by numerical simulations.