Prediction and control of the interior pressure fluctuations in a flow -excited Helmholtz resonator

The interior of an open cavity exposed to a grazing flow is known to experience strong periodic pressure oscillations sustained for a wide range of flow velocities. In the first part of the present study, an analytical model is developed to allow predictions of the amplitude and the frequency of the pressure fluctuations induced inside the cavity. The flow-excited cavity system is assumed to be described in the frequency domain by two gain functions, forming a closed-loop. The forward gain function is associated with the excitation mechanism, governed by the shedding of discrete vortices within the shear layer over the orifice. The backward gain function is associated with the acoustic response of the cavity resonator. An original approach is followed to determine the forward gain function, based on the vorticity formulation of the equations of motion (the so-called “vortex sound” theory). The conservation of circulation strength within a control volume delimiting a region over the cavity orifice, where the interactions between the acoustic pulsation and the vortically induced flow are strong, yields a formulation of the forward gain function similar to that proposed in previous work, but laid out on a different theoretical framework. Onset and termination velocities are predicted using a limit cycle stability analysis based on the Nyquist stability criterion. The analytical model is experimentally verified for a range of flow velocities and orifice dimensions. The predictions are found to be in good agreement with experimental observation. In the second part of this study, an oscillated spoiler device is investigated as a novel actuator for the control of flow-excited Helmholtz resonator. Installed at the sensitive region, whose tip is a separation point, the oscillated spoiler is designed to effectively control the phase of the discrete vortex shedding. In order to guarantee robust performance and stability of the controller over a range of free stream flow velocities, non-model based robust feedback technologies are used to design a robust single-input-single-output (SISO) controller. Sound pressure level reductions of more than 20 dB for a wide range of operating conditions are shown to be achievable by the technique