Stability of Quasi-Steady Deflagrations in Confined Porous Energetic Materials

Abstract

Previous analyses have shown that unconfined deflagrations propagating through both porous and nonporous energetic materials can exhibit a thermal/diffusive instability that corresponds to the onset of various oscillatory modes of combustion. For porous materials, two-phase-flow effects, associated with the motion of the gas products relative to the condensed material, playa significant role that can shift stability boundaries with respect to those associated with the nonporous problem. In the present work, additional significant effects are shown to be associated with confinement. which produces an overpressure in the burned-gas region that leads to reversal of the gas flow and hence partial permeation of the hot gases into the unburned porous material. This results in a superadiabatic effect that increases the combustion temperature and consequently, the burning rate. Under the assumption of gas-phase quasi-steadiness, an asymptotic model is presented that facilitates a perturbation analysis of both the basic solution. corresponding to a steadily propagating planar combustion wave, and its stability. The neutral stability boundaries collapse to the previous results in the absence 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 effects of increasing overpressure and hence combustion temperature associated with confinement are shown to be generally stabilizing with respect to thermal/diffusive instability. analogous to the effects of decreasing heat losses on combustion temperature and stability in single-phase deflagrations.