Effects of time-varying grain shape on combustion instability of a solid rocket motor

Abstract

A common approach to modeling combustion instability in a rocket propulsion system is to express the pressure oscillation in a combustor as a superposition of acoustic modes with time-varying amplitudes. Here, the tacit assumption is that the acoustic modes themselves remain more or less the same over the entire burning time. However, in the case of a solid rocket motor, the grain shape changes significantly as combustion progresses. This can gradually alter the shapes and frequencies of the acoustic modes, the influence of which on combustion instability has rarely been discussed in the existing literature. In this study, the effects of time-varying grain shape are modeled by introducing a slow time scale associated with the progressive burning of the grain. The resulting model equation accounts for the evolution of acoustic modes as well as their growth/decay in amplitude. Predictions with and without the use of the slow scale are compared with respect to measurements of a static firing test.