Flame propagation in a variable–section channel with gas filtration

A one–dimensional unsteady model is proposed, which describes gas–flame propagation in a narrow variable–section channel with a gas counterflow and takes into account heat propagation over the channel walls. The case of the channel cross section changing slowly at a distance of the order of the thermal thickness of the combustion wave is considered. It is shown that various regimes of flame propagation are possible in such a system: a regime of flame propagation with a high velocity (of the order of the burning velocity of the flame), a regime of flame propagation with a low velocity as in the case of filtrational gas combustion in a porous medium, and an intermittent regime of combustion, where the flame has a high velocity in the wide section of the channel and a low velocity in the narrow section. A simple analytical model of flame oscillations in such a system is constructed. The possibility of these oscillations was predicted by numerical simulation results. The simple model considered is an attempt to take into account the large–scale inhomogeneity of the porous medium in simulation of filtrational combustion of gases.