Response of premixed flames to irrotational and vortical velocity fields generated by acoustic perturbations

Abstract

Models based on the linearized G-equation for the response of a premixed flame to acoustic perturbations often rely on a convective velocity model, where a convective wave generates local perturbations of flame shape and surface. The present study scrutinizes the origin and nature of such convective perturbations in flow-flame-acoustic interactions. Given that vortical structures are convected flow features, the study starts from the hypothesis that vorticity shed at the flame anchoring point accounts for the convective nature of flow perturbations. The velocity field induced by an acoustic perturbation is decomposed into irrotational-potential and vortical parts, which are both solved using a Schwarz–Christoffel mapping. The respective effect of each part on the flame response is computed for the case of a slit Bunsen flame by evaluation of the transient response of a linearized G-equation model for the flame dynamics. Any influences of flame front disturbances onto the flow resulting from exothermicity are explicitly excluded from our analysis. It is found that the potential velocity field dominates the flame response, while vortex shedding has only a negligible impact. Based on the observation that the potential part displaces predominantly the flame base, a flame-base-displacement (FBD) model is proposed. Its impulse response is found to compare well with CFD data right after an acoustic velocity perturbation is imposed, but growth of advected flame front perturbations leads to increasing discrepancies for later times and/ or larger confinements. This is attributed to exothermic effects generating vorticity via the Darrieus–Landau mechanism, which was already found to be responsible for convective velocity perturbations in the fresh mixture by previous studies. Since these perturbations are rather an output of flame-flow interactions than a flow-flame model input, it is concluded that modeling approaches that rely on convective velocity perturbations while ignoring exothermic effects misrepresent the causality of flow-flame interactions.