RESUMEN

Deflagrations in porous energetic materials are characterized by regions of two-phase flow, where, for sufficiently large flow velocities, temperature-nonequilibration effects can significantly affect the overall burning rate. In the present work, we analyze a two-temperature model of deflagrations in confined porous propellants that exhibit a bubbling melt layer at their surfaces. For appropriately scaled rates of interphase heat transfer, the problem reduces to a nontrivial eigenvalue calculation in the thin reaction region where final conversion of the liquid to gaseous products occurs. For realistically small values of the gas-to-liquid thermal-conductivity ratio, solutions in the reaction zone take on a singular-perturbation character that can be exploited to derive an asymptotic expansion of the burning-rate eigenvalue. The resulting problem requires a rather sophisticated application of techniques in matched asymptotic expansions (asymptotics beyond all orders) stemming from the appearance of an infinite number of logarithmic terms in the asymptotic development that must be summed to arrive at the desired level of approximation. The physical effects of temperature nonequilibrium, which decreases the rate of heat transfer from the reacting liquid phase to the gas-phase products and thus allows a greater amount of thermal energy to remain in the reacting phase, are to increase the burning rate relative to the single-temperature limit and to sharpen the transition from "conductive" to "convective" burning.

RESUMEN

Brailovsky and Sivashinsky have proposed a model for pressure-driven combustion in the form of a degenerate parabolic system for temperature, concentration, and pressure. It is shown that the existence and uniqueness problem for traveling front solutions can be completely solved by exploiting the existing invariants and by phase plane methods. The approach yields exact propagation speeds which are noticeably larger than the approximations obtained so far.