Influence of combustion parameters on instability in solid propellant motors. I - Development of model and linear analysis.

A model is developed for the unsteady-state combustion of a solid propellant subject to acoustic pressure oscillations in the intermediate frequency range. The solution for perturbations is obtained and arranged in a matrix form which can be conveniently altered to accommodate model modifications. The acoustic admittance calculated from the model is found to depend strongly on only four parameters, the activation energies of a surface reaction and the flame reaction, the order of the flame reaction, and the surface temperature. A relationship is found between the frequency at which the maximum in the acoustic admittance occurs and the surface temperature and the surface activation energy.