INFLUENCE OF PRESSURE-DRIVEN GAS PERMEATION ON THE QUASI-STEADY BURNING OF POROUS ENERGETIC MATERIALS

A theoretical two-phase-how analysis is developed to describe the quas i-steady propagation, across a pressure jump, of a multi-phase deflagr ation in confined porous energetic materials. The difference, or overp ressure, between the upstream (unburned) and downstream (burned) gas p ressure leads to a more complex structure than that which is obtained for an unconfined deflagration in which the pressure across the multi- phase flame region is approximately constant. In particular, the struc ture of such a wave is shown by asymptotic methods to consist of a thi n boundary layer characterized by gas permeation into the unburned sol id, followed by a liquid-gas dame region, common to both types of prob lem, in which the melted material is preheated further and ultimately converted to gaseous products. The effect of gas how relative to the c ondensed material is shown to be significant, both in the porous unbur ned solid as well as in the exothermic liquid-gas melt layer, and is, in turn, strongly affected by the overpressure. Indeed, all quantities of interest, including the burn temperature, gas velocity and the pro pagation speed, depend on this pressure difference, leading to a signi ficant enhancement of the burning rate with increasing overpressure. I n the limit that the overpressure becomes small, the pressure gradient is insufficient to drive gas produced in the reaction zone in the ups tream direction, and all gas flow relative to the condensed material i s directed in the downstream direction, as in the case of an unconfine d deflagration. The present analysis is particularly applicable to tho se types of porous energetic solid, such as degraded nitramine propell ants that can experience significant gas how in the solid preheat regi on and which are characterized by the presence of exothermic reactions in a bubbling melt layer at their surfaces.