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

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 𝑃 𝑒. 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.