Propagation of a Pulsating Reaction Front in Solid Fuel Combustion

Abstract

We consider a system of reaction diffusion equations which describe gasless combustion of condensed systems. To analytically describe recent experimental results, we show that a solution exhibiting a periodically pulsating, propagating reaction front arises as a Hopf bifurcation from a solution describing a uniformly propagating front. The bifurcation parameter is the product of a nondimensional activation energy and a factor which is a measure of the difference between the nondimensionalized temperatures of unburned propellant and the combustion products. We show that the uniformly propagating plant front is stable for parameter values below the critical value. Above the critical value the plane front becomes unstable and perturbations of the system evolve to the bifurcated state, i.e., to the pulsating propagating state. In our nonlinear analysis we calculate the amplitude, frequency and velocity of the propagating pulsating front. In addition we demonstrate analytically that the mean velocity of the oscillatory front is less than the velocity of the uniformly propagating plane front.