Method of the model equation in the theory of unsteady combustion of a solid propellant

A model equation for the unsteady burning rate of a solid propellant is proposed and justified. In the frequency range of interest for practice, the proposed model agrees with the phenomenological theory of unsteady combustion, but it is even more convenient for applications because it reduces to an ordinary differential equation of the second order with respect to the burning rate. A parametric study of the transitional process in the solid-propellant rocket motor is performed with variations of the nozzle throat area in a wide range of solid propellant parameters. The model predicts oscillatory combustion regimes and propellant extinction in the case of a decrease in pressure. The boundary of stability of the transitional process in the coordinates “sensitivity of the burning rate to changes in pressure–sensitivity of the burning rate to changes in initial temperature”. It is demonstrated that the calculations performed with the use of this model are in qualitative and quantitative agreement with experimental data for a full-scale solidpropellant rocket motor.