Influence of porosity and two-phase flow on diffusional thermal instability of a deflagrating energetic material

The combustion of condensed materials is known to admit diffusional/thermal instabilities that can lead to various oscillatory modes of burning. In the present work, asymptotic analyses are developed for nonsteady multiphase deflagration of porous energetic solids, such as degraded nitramine propellants, that experience significant gas flow in the solid preheat region and are characterized by the presence of exothermic reactions in a bubbling melt layer at their surfaces. Relative motion between the gas and condensed phases is taken into account in both regions, and the derived asymptotic model is analyzed to obtain an explicit solution for steady, planar deflagration and a dispersion relation describing its linear stability. The latter determines a pulsating neutral stability boundary in the nondimensional activation energy-disturbance wavenumber plane beyond which nonsteady, nonplanar solutions are anticipated. Focusing on the realistic limit of small ratios of gas-phase to condensed-phase density and thermal conductivity, it is shown that the effect of a nonzero porosity alpha(s) of the unburned solid material is generally destabilizing, by an amount proportional to alpha(s)(1 - alpha(s))(-1), relative to the nonporous case. This effect arises both from the lower combustion temperature of the porous energetic material anc: from the gas-phase diffusion of heat from the reaction zone towards the porous preheat region. These results therefore suggest that degraded propellants, which exhibit greater porosity than their undamaged counterparts, may be especially prone to nonsteady deflagration.