Instability-induced extinction of diffusion flames established in the stagnant mixing layer

Abstract

Nonlinear dynamics of diffusional-thermal instability in diffusion flames is numerically investigated by employing a diffusion flame established in the stagnant mixing layer as a model. Particular attention is focused on the pulsating-instability regime, which arises for Lewis numbers sufficiently greater than unity. Once the steady flame structure is obtained for a prescribed value of the initial Damköhler number, transient evolution of the flame is calculated after a finite amount of the Damköhler-number perturbation is imposed on the steady flame. Depending on whether the initial Damköhler number is greater than the bifurcation Damköhler number or not, evolution of the transient flame structures can be differently characterized. If the initial Damköhler number is smaller than the bifurcation Damköhler number, pulsating instability can be triggered without any external perturbations, while if the initial Damköhler number is greater than the bifurcation Damköhler number, flame oscillations can be amplified only for the perturbed Damköhler number smaller than the threshold Damköhler number. Therefore, character of the nonlinear instability is subcritical. Once the oscillation amplitudes grow too large, flames are eventually led to extinction. Locus of the threshold Damköhler number is presented, which could be used as a revised extinction criterion for diffusion-flamelet library in the laminar flamelet regime of turbulent combustion.