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

A continuation of an ignition analysis for porous energetic materials subje cted to a constant energy flux is presented. In the first part (I), the ana lysis was developed for the case of an open-end, semi-infinite material suc h that gas flow, generated by thermal expansion, was directed out of the po rous 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 pertur bation analysis, based on the smallness of the gas-to-solid density ratio a nd the largeness of the activation energy, is utilized to describe the iner t and transition stages leading to thermal runaway. In both cases it is fou nd that the effects of porosity provide a leading-order reduction in the ti me to ignition relative to that for the non-porous problem, arising from th e reduced amount of solid material that must be heated and the difference i n thermal conductivities of the solid and gaseous phases. A correction to t he leading-order ignition-delay time, however, is provided by the convectiv e flow of gas through the solid, and the sign of this correction is shown t o 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 leadin g-order time to ignition. Here, however, it is demonstrated that when the f low of gas is directed into the porous solid, the relative transport effect s associated with the gas flow serve to preheat the material, resulting in a negative correction and hence a decrease in the ignition-delay time.