Effect of a shear flow on the Darrieus-Landau instability in a Hele-Shaw channel

TL;DR

This study investigates how shear flow affects the stability of premixed flames in a Hele-Shaw channel, revealing that shear-induced dispersion can suppress or enhance flame wrinkling depending on propagation direction and mixture properties.

Contribution

It introduces a two-dimensional asymptotic model analyzing the impact of shear flow, anisotropic diffusion, and gravity on flame stability in Hele-Shaw channels, highlighting novel vorticity generation mechanisms.

Findings

Shear flow suppresses Darrieus-Landau instability in streamwise propagation.

Flame stability depends on Lewis number and propagation direction.

Vorticity can be generated by curved flames without gravity, confined to flame zones.

Abstract

The Darrieus--Landau instability of premixed flames propagating in a narrow Hele-Shaw channel in the presence of a strong shear flow is investigated, incorporating also the Rayleigh--Taylor and diffusive-thermal instabilities. The flow induces shear-enhanced diffusion (Taylor dispersion) in the streamwise direction, but not in the spanwise direction and this leads to anisotropic diffusion and flame propagation. To understand how such anisotropies affect flame stability, two important cases are considered. These correspond to initial unperturbed conditions pertaining to a planar flame propagating in the streamwise or spanwise directions. The analysis is based on a two-dimensional model derived by asymptotic methods and solved numerically. These address the influence of the shear-flow strength (or Peclet number $Pe$), preferential diffusion (or Lewis number $Le$) and gravity (or Rayleigh number $Ra$). Dispersion curves characterizing the perturbation growth rate are computed for selected values of $Pe$, $Le$ and $Ra$. Taylor dispersion induced by strong shear flows is found to suppress the Darrieus--Landau instability and to weaken the flame wrinkling when the flame propagates in the streamwise direction. In contrast, when the flame propagates in the spanwise direction, the flame is stabilized in $Le<1$ mixtures, but destabilized in $Le>1$ mixtures. In the latter case, Taylor dispersion coupled with gas expansion facilitates flame wrinkling in an unusual manner. Specifically, stagnation points and counter-rotating vortices are encountered in the flame close to the unburnt gas side. More generally, an original finding is the demonstration that vorticity can be produced by a curved flame in a Hele-Shaw channel even in the absence of gravity, whenever $Pe \neq 0$, and that the vorticity remains confined to the flame preheat and reaction zones.