Ignition Processes in Confined Thermal Explosions

Abstract

The induction period of a high activation energy thermal explosion in a confined, rigid, nondiffusing, combustible material is considered. A method-of-lines approach is used to develop numerical solutions for the infinite slab, infinite cylinder and spherical geometries. When the dimensional initial and boundary temperatures are equal, results are obtained for a wide range of supercritical values of the Frank-Kamenetskii parameter S, and for arbitrary values of the ratio of the chemical heat release and the initial internal energy. The time-history of the spatially variable temperature distribution is described. At a common value of S the thermal runaway time is largest for a sphere and smallest for a slab, with the cylindrical system between. The explosion location re is found to move away from the symmetry point when the wall temperature is made sufficiently large compared to the initial temperature. A further increase in the former moves the value of r" toward the hot boundary. The dependence of the explosion time on the incremental difference between the boundary and initial temperatures and on a modified Frank-Kamenetskii parameter is described in detail. The time-history of an off-center explosion is shown to produce precisely the same kind of highly localized hot spot as that found when the temperature difference is zero.