A central role in the mechanism of the self-sustained oscillations of the flow about cavity-type bodies is played by the reattachment edge. Experimentally it has been found that periodic pressure pulses generated on this edge are fed back to the origin of the shear layer and cause the production of discrete vortices. The oscillations have been found to be suppressed or attenuated when the edge has the shape of a ramp of small angle, or when it is properly rounded. To clarify the role of the shape of the reattachment edge in the mechanism of the oscillations, a mathematical model is developed for the vortex–edge interaction. In this model the interaction of one discrete vortex, imbedded within a constant-speed parallel flow, with the reattachment edge is studied. Two typical shapes of the reattachment edge are examined; a ramp of variable angle and an ellipse. The main conclusion of the present analysis is the strong dependence of the pressure pulses, that are induced on the surface of the edge, on the specific shape of the edge. The pressure pulses on reattachment edges with shapes that give rise to steady flows have been found to be of insignificant amplitude. On the other hand, when the reattachment edge has a shape that is known to result in oscillating flow, the induced pressure pulses are of very large amplitude. Intermediate values of the pressure are found for configurations known to stabilize partially the flow. The present results indicate that, for the establishment of the oscillation, the feedback force generated by the vortex–edge interaction must have an appropriate value. The feedback force may be eliminated if the shape of the lip of the edge is properly designed.
Simulations of Modal Active Control Applied to the Self-Sustained Oscillations of the Clarinet