INFLUENCE OF POROSITY AND 2-PHASE FLOW ON DIFFUSIONAL THERMAL-INSTABILITY OF A DEFLAGRATING ENERGETIC MATERIAL

The combustion of condensed materials is known to admit diffusional/th ermal instabilities that can lead to various oscillatory modes of burn ing. In the present work, asymptotic analyses are developed for nonste ady multiphase deflagration of porous energetic solids, such as degrad ed nitramine propellants, that experience significant gas flow in the solid preheat region and are characterized by the presence of exotherm ic reactions in a bubbling melt layer at their surfaces. Relative moti on between the gas and condensed phases is taken into account in both regions, and the derived asymptotic model is analyzed to obtain an exp licit solution for steady, planar deflagration and a dispersion relati on describing its linear stability. The latter determines a pulsating neutral stability boundary in the nondimensional activation energy-dis turbance wavenumber plane beyond which nonsteady, nonplanar solutions are anticipated. Focusing on the realistic limit of small ratios of ga s-phase to condensed-phase density and thermal conductivity, it is sho wn that the effect of a nonzero porosity alpha(s) of the unburned soli d material is generally destabilizing, by an amount proportional to al pha(s)(1 - alpha(s))(-1), relative to the nonporous case. This effect arises both from the lower combustion temperature of the porous energe tic material anc: from the gas-phase diffusion of heat from the reacti on zone towards the porous preheat region. These results therefore sug gest that degraded propellants, which exhibit greater porosity than th eir undamaged counterparts, may be especially prone to nonsteady defla gration.