Modelling of the transition from conductive to convective burning in porous energetic materials

This paper is concerned with a theoretical interpretation of an abrupt shift from the slow conductive to fast convective burning observed in the combustion of gas-permeable explosives under gradual elevation of the ambient pressure. The paper is a revision of our recent communication on the problem, and is based on the amended heat equation, which meets the requirement of the conservation of energy lacking in the previous model. It appears, however, that both formulations lead (in appropriately chosen units) to a largely similar picture of the transition. The transition is triggered by a localised autoignition in the extended resistance-induced preheat zone formed ahead of the advancing deflagration, provided the pressure difference between hot gas products and gases deep inside the pores of the unburned solid exceed a certain critical level. For moderately high activation energies the critical overpressures are comparable to those observed experimentally. In line with observations, the critical overpressure increases with diminishing permeability. The amended formulation implies the possibility of overpressure-driven gasification waves occurring even in the absence of chemical heat release.