Three-dimensional diffusive-thermal instability of flames propagating in a plane Poiseuille flow

TL;DR

This study investigates the three-dimensional diffusive-thermal instability of flames in a Poiseuille flow, revealing how parameters like Lewis number, Damköhler number, and flow Peclet number influence flame stability and symmetry in different channel scales.

Contribution

It provides a comprehensive analysis of flame stability in three dimensions, incorporating linear stability eigenvalues and nonlinear simulations across various flow and chemical parameters.

Findings

In narrow channels, flames remain symmetric and shear flow enhances cellular instability.

In large channels, both cellular and oscillatory instabilities persist, with asymmetry more likely when flow opposes flame propagation.

Shear flow effects differ based on Lewis number and channel scale, affecting flame symmetry and oscillations.

Abstract

The three-dimensional diffusive-thermal stability of a two-dimensional flame propagating in a Poiseuille flow is examined. The study explores the effect of three non-dimensional parameters, namely the Lewis number $Le$, the Damk\"ohler number $Da$, and the flow Peclet number $Pe$. Wide ranges of the Lewis number and the flow amplitude are covered, as well as conditions corresponding to small-scale narrow ($Da \ll 1$) to large-scale wide ($Da \gg 1$) channels. The instability experienced by the flame appears as a combination of the traditional diffusive-thermal instability of planar flames and the recently identified instability corresponding to a transition from symmetric to asymmetric flame. The instability regions are identified in the $Le$-$Pe$ plane for selected values of $Da$ by computing the eigenvalues of a linear stability problem. These are complemented by two- and three-dimensional time-dependent simulations describing the full evolution of unstable flames into the non-linear regime. In narrow channels, flames are found to be always symmetric about the mid-plane of the channel. Additionally, in these situations, shear flow-induced Taylor dispersion enhances the cellular instability in $Le<1$ mixtures and suppresses the oscillatory instability in $Le>1$ mixtures. In large-scale channels, however, both the cellular and the oscillatory instabilities are expected to persist. Here, the flame has a stronger propensity to become asymmetric when the mean flow opposes its propagation and when $Le<1$; if the mean flow facilitates the flame propagation, then the flame is likely to remain symmetric about the channel mid-plane. For $Le>1$, both symmetric and asymmetric flames are encountered and are accompanied by temporal oscillations.