Ignition analyses of porous energetic materials

Abstract

the closed-end problem, however, the flow of gas is directed into the solid, thereby preheating the material and producing a negative correction to the ignition time. These relative transport effects associated with the gas flow are absent from the corresponding calculation for the nonporous problem and produce a number of modifications at the next order in the analysis. ; A theory of ignition is presented to analyze the effect of porosity on the time to ignition of a semiinfinite porous energetic solid subjected to a constant energy flux. 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. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive-diffusive layer adjacent to the exposed surface of the material where chemical effects are firstfelt, a some-what thicker transientdiffusive zone, and finally an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with-respect to the densityratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity provide a leading-order reduction in the time to-ignition relative to that for the nonporous 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. It is also found that the convective flow of gas, which stems from the effects of thermal expansion, provides a correction to the leading-order ignition-delay time. Two different problems are considered, corresponding to whether the heated surface of the solid is open or closed. In the open-end problem, the gas flows out of thesolid, thereby removing energy from the system and providing a positive correction to the leading-order ignition-delay time. In *This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 1 ~~