Analytical model for the prediction of pulsations in a cold-gas scale-model of a Solid Rocket Motor

old gas scale model experiments (1/30) demonstrate that coupling of vortex shedding with acoustic standing waves can produce pressure oscillations of the same level as observed in large Solid Rocket Motors. An analytical acoustical energy balance model is proposed in which the system is described as a single mode acoustic resonator and the pulsations are assumed to be purely harmonic. The selected acoustic mode number is an input to the model. Quasi- steady linear models are used to describe losses of acoustic energy by vortex shedding at a thermal inhibitor ring, radiation at the nozzle and friction within the porous injection wall used for gas injection. The sound production is predicted by using a 2-D planar point vortex model combined with the Vortex Sound Theory. The model demonstrates that the sound pro- duction due to interaction of the vortex with the cavity surrounding the integrated nozzle is dominant, explaining previous results of cold gas and hot-gas scale models. The effect of vor- tex ingestion by the nozzle is negligible. Aspects of the nozzle geometry, other than the cavity volume, are not critical. The model predicts pressure pulsations within a factor 2, when the circulation of the vortices is taken one third of the maximum available circulation. This reduc- tion factor of the circulation is assumed to be a consequence of turbulence. The Mach number corresponding to the maximum of pulsation is predicted within 20% in a range comparable to results obtained by axis-symmetrical numerical flow simulations