Fast subsonic combustion as a free-interface problem

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 draginduced 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 (Tb) as occurs in deflagrative combustion. The evaluatedD(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. Premixed gas combustion is the combustion of gaseous reactants which are perfectly mixed prior to ignition. The most distinctive feature of premixed combustion is its ability to assume the form of a self-sustained reaction wave propagating subsonically or supersonically at a well-defined speed. Apart from their technological relevance, combustion waves constitute a truly fascinating dynamical system, displaying an amazingly rich variety of phenomena such as non-uniqueness of possible propagation regimes, their birth (ignition) and destruction (extinction), chaotic self-motion and fractal-like growth, various hysteretic transitions, etc. One of the most effective practices in the theoretical exploration of combustion waves is their description in terms of a free-interface problem where the reaction zone is considered as infinitely thin compared to the other length-scales involved. The current study is concerned with the formulation and analysis of a free-interface problem associated with the recently identified new mode of subsonic combustion arising in hydraulically resisted flows (e.g. porous beds), and where the combustion wave is driven by the drag-induced diffusion of pressure, rather than thermal diffusivity as occurs in conventional unconfined flames. In the simplest case (the so-called small-heat release approximation) the emerging free-interface problem is described by a single filtration equation (Sec. 6), = r 2 ,