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

We consider non-Newtonian flows, like polymer in fusion or in solution, pushed through a thin periodic filter with period and thickness $\varepsilon \ll 1$. Starting from the Stokes system with a nonlinear viscosity obeying Carreau's law (with a high rate viscosity or without it), we study the asymptotic behavior of the flow as $\varepsilon \rightarrow 0$. We obtain the global convergence of the pressure in the whole domain and not separately in the upper part and in the lower part. Numerical tests for various fluids and various filter shapes are comparing results given by the homogenized model with the ones given by the microscopic Carreau--Stokes model.