Effects of vorticity on rocket combustion stability

Combustion stability computations are currently based on an irrotational model that allows slip flow at the burning surface. However, the no-slip boundary condition must be satisfied when gas motions are parallel to the combustion zone. Then waves of vorticity are created that distort the acoustic wave structure and modify the fluctuating normal velocity component upon which system stability is so strongly dependent. This flow problem is solved here in analytical form to bring the physical details into focus. Crocco's theorem shows that the creation of vorticity is due primarily to the axial unsteady pressure gradient across mean flow streamlines at the surface. Hence, there is a transfer of energy from the pressure oscillations (acoustic field) to the rotational waves (vorticity field). It is in this interaction that the incoming flow acquires the axial motion of the acoustic wave. Stability calculations based on this model yield the three-dimensional form of Culick's one-dimensional flow-turning correction and clarify its origin. However, continuity at the burning surface requires a correction to the radial velocity fluctuations. Incorporation of this new driving effect leads to a motor system that is significantly less stable than in the classical prediction (Standard Stability Prediction Program) for some configurations.