Instabilities in a combustion model with two free interfaces

TL;DR

This paper analyzes the stability of a combustion model with two free interfaces in a strip, revealing a critical Lewis number below which the planar solution becomes unstable, supported by theoretical and numerical evidence.

Contribution

It introduces a fully nonlinear analysis of a combustion model with two free interfaces and identifies a critical Lewis number for stability in a large-width strip.

Findings

Existence of a critical Lewis number Le_c for stability.

Planar solutions are unstable when Le < Le_c.

Numerical simulations support the theoretical analysis.

Abstract

We study in a strip of $\mathbb R^2$ a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter interface presents an additional difficulty because the non-degeneracy condition is not met. We turn the system to a fully nonlinear problem which is thoroughly investigated. When the width $\ell$ of the strip is sufficiently large, we prove the existence of a critical value $Le_c$ of the Lewis number $Le$, such that the one-dimensional, planar, solution is unstable for $0<Le<Le_c$. Some numerical simulations confirm the analysis.