Theory of thermohydrodynamic instability of the front of filtration combustion of gases

Based on the filtration equations with account of heat transfer in the heating region, the problem of instability of small perturbations of the wave front of filtration combustion of a gas is solved. Expressions for the growth decrement and critical transverse size of a perturbation are obtained. The problem of the wave-front stability is solved with account of the macroscopic redistribution of filtration in the system. The solution includes macroscopic characteristics such as the transverse size, the width of the high-temperature zone, etc. A method is proposed for taking into account the influence of the characteristics of the system on the evolution of perturbations. It is shown that small deformation perturbations of the front always increase to a certain amplitude; their subsequent development – continuation of their growth or stabilization – is determined by the characteristics of the system.