Low–frequency instability of solid rocket motors. Influence of the Mache effect and charge geometry

Nonacoustic (low–frequency) instability of combustion of a solid propellant in a jet motor is considered. A model of unsteady combustion in motors with channel charges is proposed. The model takes into account the change in the temperature distribution in combustion products induced by the change in the gas pressure (Mache effect). The unsteady gas–release rate and the temperature of combustion products are determined on the basis of the Zel'dovich phenomenological approach, taking into account the change in the propellant–surface temperature (Novozhilov model) and the flame temperature (Gostintsev–Sukhanov model). The dependence of the stability limit of the solid rocket motor (SRM) on the charge–channel length and pre–nozzle volume of the motor chamber is determined. It is shown that the Mache effect leads to a significant constriction (by a factor of 1.5 to 2) of the range of stable combustion parameters in the SRM. It is found that an SRM with a channel charge has a narrower range of stability in terms of the Zel'dovich parameter $k$ than an SRM with a butt–end charge and an identical combustion–chamber volume. For channel charges, the stability limit depends mainly on the volume of the pre–nozzle part of the combustion chamber.