Influence of distributed solid-phase reactions on deflagrations in confined porous propellants

Combustion processes in energetic materials are often modeled by a surface gasification reaction followed by a distributed gaseous flame. However, under confinement, deflagrations in porous or granular propellants are generally accompanied by an increasing pressure difference, or overpressure, between the burned-gas region and the unburned reactants deep within the pores of the material. As the overpressure and/or the solid-phase reaction rate become sufficiently large, the gaseous and solid reaction zones tend to merge into a single multiphase reaction region. Furthermore, in certain parameter regimes, the gas flame penetrates into the porous solid, resulting in subsurface gaseous combustion. When the activation energies of the gaseous and solid-phase reactions are of the same order of magnitude and/or the overpressure becomes significant, gasification reactions may also become active within the solid, thus eliminating a distinct propellant surface and forming a distributed multiphase reaction layer. A large activation-energy analysis of this scenario is presented to study the effects of distributed solid reactions on the deflagration structure and the burning-rate response. The burning-rate eigenvalue is obtained from a numerical solution of the reaction-zone problem, and the results are calculated for various overpressures as well as different gas-to-solid activation-energy and thermal conductivity ratios. It is observed that increasing overpressure results in a more spatially distributed solid-phase reaction and a rapidly increasing flame-propagation speed.