A high-porosity limit for the transition from conductive to convective burning in gas-permeable explosives

The experimentally known phenomenon of an abrupt transition from slow conductive to fast convective (penetrative) burning in a confined gas-permeable explosive is discussed. A simple model, involving only the most essential physical ingredients, is formulated and analyzed. In addition to commonly utilized assumptions of the solid-gas thermal equilibrium, validity of Darcy's law, immobility of the solid phase, and one-step Arrhenius kinetics, the model employs the distinguished limit combining high-porosity with high solid/gas density ratio, resulting in conservation of enthalpy, advantageous for theoretical analysis. A good qualitative agreement between theoretical and experimental dependencies is obtained. The transition is triggered by a localized 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 exceeds a certain critical level. In line with observations the critical overpressure increases with diminishing permeability.