Study of an Advection-Reaction-Diffusion equation in a compressible flow field

TL;DR

This paper investigates how compressibility affects front propagation in a simplified one-dimensional advection-reaction-diffusion model of combustion, highlighting differences from traditional models and conditions leading to reaction stoppage.

Contribution

It introduces a numerical study of front dynamics in compressible flows, comparing models and analyzing the impact of compressibility on reaction completion.

Findings

Compressibility significantly alters front propagation dynamics.

Certain conditions cause the reaction to stop prematurely.

Differences between models impact predictions of combustion behavior.

Abstract

We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting fluid is a binary mixture of gases. The compressible flow field is given analytically. We analyse the differences between popular models used in fundamental studies of compressible combustion and biological problems. Then, we investigate the effects of compressibility on the front interface dynamics for different reaction types and we characterise the conditions for which the reaction stops before its completion.