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 wit h channel charges is proposed. The model takes into account the change in t he temperature distribution in combustion products induced by the change in the gas pressure (Mache effect). The unsteady gas-release rate and the tem perature of combustion products are determined on the basis of the Zel'dovi ch phenomenological approach, taking into account the change in the propell ant-surface temperature (Novozhilov model) and the flame temperature (Gosti ntsev-Sukhanov model). The dependence of the stability limit of the solid r ocket 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 c ombustion parameters in the SRM. It is found that an SRM with a channel cha rge has a narrower range of stability in terms of the Zelldovich parameter k than an SRM with a butt-end charge and an identical combustion-chamber vo lume. For channel charges, the stability limit depends mainly on the volume of the pre-nozzle part of the combustion chamber.