Linear Stability of the Activation-Energy-Asymptotics Reactive-Layer Structure: I. Liñán’s Premixed-Flame Regime

Abstract

ABSTRACT Overall linear instability characteristics of an asymptotically thin reactive layer in a flame are investigated, particularly for Liñán’s premixed-flame regime of activation-energy asymptotics. The reactive-layer instability analysis, formulated with the characteristic length and timescales of the inner reaction zone, is carried out not only by a numerical method but also by an asymptotic method, with the small expansion parameter obeying the distinguished limit of and , where , , and denote the downstream heat-loss factor, the Zel’dovich number, and the Lewis number, respectively. The asymptotic analysis yields an explicit dispersion relation, which is comprised of three distinct destabilizing or stabilizing contributions: (i) the reaction sensitivity associated with the downstream heat-loss effect, (ii) the reaction sensitivity associated with the preferential diffusion effect, and (iii) the diffusive relaxation. Three instability modes, namely cellular instability, planar instability, and pulsating instability, are found to be similar to the conventional diffusional-thermal instability. Consequently, the reactive-layer instability is seen to be good enough to serve as a general baseline for diffusional-thermal instability, despite lacking the detailed instability characterization in the proximity of , the corrections for which can be achieved by the conventional diffusional-thermal instability analysis within the NEF (nearly-equidiffusional flame) limit.