Stability analysis of active control of self-sustained pressure fluctuations due to flow over a cavity

The problem addressed in this paper is the stability analysis of self-sustained pressure fluctuations due to low Mach number turbulent flow over a large shallow cavity in a wing-shaped model. In the studied configuration, sound pressure was generated by the instability of the mixing layer. An original active device, a vibrating surface located at the trailing edge, and an adjustable narrow-band controller were used to control the self-oscillation: to amplify it in an open loop, and to attenuate it in a closed loop. A complete analysis of the system based on the describing function analysis is presented. Experimental data, obtained in an Eiffel-type wind-tunnel compare favorably with the prediction of the model. With the active control, the instability is controlled: the pressure fluctuations measured in the cavity are attenuated to the ground level. Moreover, with the proposed model and the original device, the equivalent volume velocity of the unstable mixing layer and the acoustic feedback gain can be experimentally estimated.