Ignition of a Reactive Solid by an Inert Hot Spot

Abstract

case, however, there is a finite amount of energy supplied to the wire and, therefore, ignition will occur or not occur depending on the thermal properties of the materials, amount of energy supplied, wire diameter, and chemical parameters of the condensed phase reaction.A numerical analysis of this problem has been carried out by Goldshleger et al. (1973). An asymptotic analysis for large activation energies was carried out by Berman and Ryazantsev (1976) for the case when the conductivity of the inert body is large enough, so that its temperature can be considered a function of time only, and the density ratio is of order unity, so that when ignition occurs under supercritical conditions only a thin layer has been heated in the reactive material. We consider more general cases including the case when the ratio of thermal diffusivities of the inert and reactive material is not large; our analysis leads to closed-form relations giving the critical hot-spot size, or critical ignition energy, in terms of the physicochemical parameters of the materials.Gap compression has been proposed by Randolph and Simpson (1973) and Randolph (1975), for example, as a mechanism responsible for the accidental ignition of high explosive charges. Accidental ignition occurs, for instance, when an explosive-filled shell explodes prematurely when accelerated during firing or when an encased high explosive charge is subjected to relatively small impacts, e.g., when dropped a few feet. Presumably, in both of these examples ignition was produced by compression heating of gas in voids or cracks due to defective explosive loading. Randolph (1975) considers different pressure rise curves and integrates numerically the equations describing the process. The problem considered in the present work models ignition by gas compression with a step-like pressure rise occurring in a time short compared with the characteristic thermal response time in the reactive solid. II. FormulationWe consider a cylindrical or spherical inert spot of radius a whose temperature T is instantaneously raised at time zero to a value T, higher than the value T 0 of the reactive material. A distributed exothermic reaction of the Arrhenius type takes place in the reactive solid. The energy conservation equation can be written asassuming constant values for the density p, the specific heat c, and heat conductivity k, although not necessarily equal for the inert material, where we shall use the subscript /, and for the reactive medium, subscript 0. In Eq.(1), n = 1 for cylindrical spots and n = 2 for spherical spots. E is the activation energy, and A the pre-exponential factor of the reaction; A =0 in the inert material r<a. At r=a there is a jump in the thermal diffusivity a from its value u, = k,/p,c, in the inert material to the value a 0 = k 0 /p 0 c 0 in the reactive medium.