Stability of quasi-steady deflagrations in confined porous energetic materials

Previous analyses have shown that unconfined deflagrations propagating thro ugh both porous and nonporous energetic materials can exhibit a thermal/dif fusive instability that corresponds to the onset of various oscillatory mod es of combustion. For porous materials, two-phase-flow effects, associated with the motion of the gas products relative to the condensed material, pla y a significant role that can shift stability boundaries with respect to th ose associated with the nonporous problem. In the present work, additional significant effects are shown to be associated with confinement, which prod uces an overpressure in me burned-gas region that leads to reversal of the gas flow and hence partial permeation of the hot gases into the unburned po rous material. This results in a superadiabatic effect that increases the c ombustion temperature and, consequently, the burning rate. Under the assump tion of gas-phase quasi-steadiness. an asymptotic model is presented that f acilitates a perturbation analysis of both the basic solution, correspondin g to a steadily propagating planar combustion wave, and its stability. The neutral stability boundaries collapse to the previous results in the absenc e of confinement, but different trends arising from the presence of the gas -permeation layer are predicted for the confined problem. Whereas two-phase -flow effects are generally destabilizing in the unconfined geometry, the e ffects of increasing overpressure and hence combustion temperature associat ed with confinement are shown to be generally stabilizing with respect to t hermal/diffusive instability, analogous to the effects of decreasing heat l osses on combustion temperature and stability in single-phase deflagrations .