Stability of homogeneous-solid deflagration with two-phase flow in the reaction zone

Abstract

An asymptotic model is derived for the nonsteady, nonplanar deflagration of energetic solids, such as nitramines, that experience exothermic reactions in liquid layers at their surfaces. The analysis takes into account the role of interphase heat transfer and the relative motion of gas and liquid in the resulting two-phase region at the surface. A basic solution corresponding to steady, planar burning is obtained, and a linear stability yields a neutral stability boundary beyond which the basic solution is unstable to pulsating disturbances. In particular, it is found that stability of the basic solution is lost for sufficiently large values of the activation energy and/or sufficiently small values of the interphase heat transfer parameter. In the combined limit that the latter approaches infinity and a velocity-perturbation parameter, which accounts for two-phase viscous and Marangoni effects, approaches zero, the neutral stability boundary is the same as that encountered for separate-phase solid propellants with an intrusive gas flame.