Vortex driving mechanism in oscillatory rocket flows

Several mechanisms that cause hydrodynamic instability of sheared regions of flow in a rocket chamber to drive acoustical oscillations are integrated into a comprehensive model for the vortex shedding phenomenon in this analysis. The energy method is utilized to enable later extension of the linear theory described in this paper to finite amplitude problems in which nonlinear effects are likely to be dominant. A detailed model of the feedback effect that links the acoustical and vortical fields in the vicinity of the shear layer origin is presented. This is a vital element since it provides the phasing and also the strength of the vortical waves relative to the superposed acoustic field. The most important mechanism involved in the transfer of vortical energy into the acoustic field is the interaction of the vortices with a solid surface of impingement at a suitable distance and location downstream from the shear layer origin. The energy transfer in this case is equivalent to a dipole sound source, and a more efficient mechanism than the volume quadrapole effects that have previously been evaluated. Two useful analytical tools emerge. The first is a simple rule by which designers can make the necessary changes in internal ballistics to eliminate or reduce vortex driven oscillations. The second is a growth rate model that allows a quantitative assessment of vortical interactions and is compatible with the standard acoustic stability assessment procedures in widespread use.