ANALYSIS OF THE PERIODIC PRESSURE FLUCTUATIONS INDUCED BY FLOW OVER A CAVITY

Abstract

Subsonic flows over Helmholtz resonators often cause strong periodic pressure fluctuations inside the resonators over a range of outer flow velocities. The flow-excitation mechanism is known to be governed by both the shedding of discrete vortices within the shear layer over the orifice and the acoustic response of the cavity. This self-sustained oscillation phenomenon is often analyzed by using a feedback loop model where the flow excitation and the acoustic response of the resonator are approximately modelled as a forward gain function and as a backward gain function respectively. In the present work, a similar approach was followed and a new forward gain function was derived based on the concept of “vortex sound” to model the flow excitation. The formulation combined this forward gain function with a backward gain function from previous work, within the framework of the feedback loop analysis. The approximate method allowed the frequency and the relative amplitude of the cavity pressure fluctuations to be predicted for a range of flow velocities. In addition, the extended Nyquist stability criterion was used to estimate the onset and the termination velocities of the first two modes of the shear layer flow oscillations. Experimental data were obtained using a rigid-walled cavity in a low-speed wind tunnel. The results showed that the model predictions were in reasonably good agreement with the experimental data.