Combustion dynamics in steady compressible flows

TL;DR

This paper investigates how reactive fields evolve in steady compressible flows, deriving a critical length scale for flame quenching and providing a numerical approach to analyze the dynamics.

Contribution

The study introduces an efficient numerical method for analyzing combustion in compressible flows and derives an explicit expression for the critical quenching length scale.

Findings

Derived an expression for the critical length scale lc for flame quenching.

Numerical simulations confirm the theoretical predictions.

Connected results to previous studies in different flow settings.

Abstract

We study the evolution of a reactive field advected by a one-dimensional compressible velocity field and subject to an ignition-type nonlinearity. In the limit of small molecular diffusivity the problem can be described by a spatially discretized system, and this allows for an efficient numerical simulation. If the initial field profile is supported in a region of size l < lc one has quenching, i.e., flame extinction, where lc is a characteristic length-scale depending on the system parameters (reacting time, molecular diffusivity and velocity field). We derive an expression for lc in terms of these parameters and relate our results to those obtained by other authors for different flow settings.