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.