Diffusional/Thermal Instability of a Solid Propellant Flame

The stability of a gas flame attached to a deflagrating solid propellant is investigated through an asymptotic analysis in the limit of large gas-phase activation energy. Since the diffusional/thermal model for solid propellant combustion employed relaxes the usual assumptions of gas-phase quasisteadiness and quasiplanarity, the overall stability of the deflagration is determined by both the stability of condensed-phase pyrolysis and the stability of the gas flame. For relatively large flame standoff distances, the latter dominates, and a parameter regime is identified that allows the derivation of a dispersion relation by formal asymptotic matching techniques. The results show how the neutral stability boundaries for a freely propagating flame, which is obtained in an appropriate limit, are modified for a solid propellant flame. In particular, the cellular instability is suppressed by the proximity of the solid/gas interface for sufficiently small disturbance wavenumbers, but the pulsating instability is usually enhanced by the proximity of the interface. In addition, the neutral stability boundaries possess features, such as relative maxima and multiple branches, which are not present in the corresponding stability boundaries for the freely propagating flame.