Fast subsonic combustion as a free-interface problem

Abstract

The paper is concerned with the recently identified fast, yet subsonic, combustion waves occurring in obstacle-laden (e.g. porous) systems and driven not by thermal diffusivity but rather by the drag-induced diffusion of pressure. In the framework of a quasi-one-dimensional formulation where the impact of obstacles is accounted for through a frictional drag term, an asymptotic expression for the wave propagation velocity $D$ is derived. The propagation velocity is controlled by the temperature $(T_{+})$ at the entrance to the reaction zone rather than at its exit $(T_b)$ as occurs in deflagrative combustion. The evaluated $D(T_{+})$ dependence allows description of the subsonic detonation in terms of a free-interface problem. The latter is found to be dynamically akin to the problem of gasless combustion known for its rich pattern-forming dynamics.