Influence of combustion parameters on instability in solid propellant motors. II - Nonlinear analysis.

The analysis of an unsteady-state model for the combustion of a solid propellant is extended to include the nonlinearities of the second order. The second order response in burning velocity is found to have a constant and a second harmonic frequency component. For all values of the frequency and parameters of interest, the former component is found to represent a relatively small decrease in the mean burning rate during oscillatory combustion. The nonlinear system behavior is dominated by only two nonlinearities: one between the burning rate and the flame temperature in the heat convected out of the flame and the other between the pressure and the flame temperature in the flame burning rate expression.