On the onset condition of fast-time instability in Liñán's premixed-flame regime

Abstract

The fast-time instability of Liñán's premixed-flame regime is revisited in order to resolve the unrealistic result, previously obtained by Peters, that the inner reaction zone becomes unstable under all subadiabatic conditions. The problem is posed as that of finding the stable range of the heat-loss parameter, defined as the ratio of the downstream heat loss to the total chemical energy influx, near the adiabatic condition. Central to the analysis is rescaling near the adiabatic condition by employing a distinguished limit that the heat-loss parameter is of the order of the inverse of the Zel'dovich number, which enables us to take into account the stabilizing effect of the outer diffusive layers on the inner reaction zone. For a general diffusion flamelet model, the critical value of the heat-loss parameter at the neutral-stability condition is obtained to form a bound for the stable subadiabatic range of the heat–loss parameter.