Ignition analysis of a porous energetic material: II. Ignition at a closed heated end

A continuation of an ignition analysis for porous energetic materials subjected to a constant energy flux is presented. In the first part (I), the analysis was developed for the case of an open-end, semi-infinite material such that gas flow, generated by thermal expansion, was directed out of the porous solid, thereby removing energy from the system. In the present study, the case of a closed end is considered, and thus the thermally induced gas flow is now directed into the solid. In these studies, an asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. In both cases it is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the non-porous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas through the solid, and the sign of this correction is shown to depend on the direction of the gas flow. Thus, gas flowing out of an open-end solid was shown previously to give a positive correction to the leading-order time to ignition. Here, however, it is demonstrated that when the flow of gas is directed into the porous solid, the relative transport effects associated with the gas flow serve to preheat the material, resulting in a negative correction and hence a decrease in the ignition-delay time.