Linear stability of a plane front in solid combustion at large heat of reaction

Abstract

The existence and linear stability of a uniformly propagating plane front in solid combustion are considered under the assumption of a large heat of reaction, which is of interest in pyrotechnic mixtures. The Zel'dovich number is not necessarily large, and the chemical reaction is not confined to a reaction sheet for typical values of the parameters. Thus the effective calculation of the fronts and the analysis of their stability rely on qualitative methods and on some numerics. It is seen that there is always a minimum burning rate and that the front is stable only if the heat of reaction is sufficiently large. A comparison is made with analytical results obtained from a phenomenological delta-function model.