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

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 Damköhler 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≪1) to large-scale wide (Da≫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.