Prediction of pulsations in a cold-gas scale-model of a solid rocket motor

In large scale Solid Rocket Motors (SRMs) flow pulsations can be driven by coupling between vortex shedding and acoustic standing waves in the engine. Cold gas scale model experiments (1/30) demonstrate that this process can produce pressure oscillations of the same level as observed in actual full scale engines. Experiments published by Anthoine [Experimental and Numerical Study of Aeroacoustic Phenomena in Large Solid Propellant Boosters, PhD thesis, von Karman Institute For Fluid Dynamics/ ULB, Brussels, Belgium (2000)] indicate that when inhibitor rings are used the pulsation level is proportional to the volume of the cavity around the integrated nozzle as used in the Ariane V boosters. The air flow in the cold gas scale model is supplied through a porous wall. An analytical 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 model cannot predict the acoustic mode which will prevail. The selected mode number is therefore an input to the model. Quasi-steady models are used to describe losses of acoustic energy by: vortex shedding at the inhibitor ring, radiation at the nozzle and friction within the porous injection wall. The sound production is predicted by using the Vortex Sound Theory combined with a simplified flow model. In this flow model the vortical structures are represented by line vortex rings of constant diameter, convected at constant speed. The model assumes the cavity sound production to be dominant, neglecting the e ect of vortex ingestion by the nozzle. The model predicts the observed order of magnitude of the pulsation amplitude. It explains the increase in frequency with increasing Mach number for a specific acoustic mode. The fact that this variation in frequency is predicted within a factor 2 indicates that acoustic losses are reasonably well estimated. This is comparable to results obtained by laminar axis-symmetrical numerical flow simulations available from the literature.