Subsonic #ows over Helmholtz resonators often cause strong periodic pressure #uctuations inside the resonators over a range of outer #ow velocities. The #ow-excitation mechanism is known to be governed by both the shedding of discrete vortices within the shear layer over the ori"ce and the acoustic response of the cavity. This self-sustained oscillation phenomenon is often analyzed by using a feedback loop model where the #ow 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 #ow 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 #uctuations to be predicted for a range of #ow velocities. In addition, the extended Nyquist stability criterion was used to estimate the onset and the termination velocities of the "rst two modes of the shear layer #ow 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.
2002 Elsevier Science Ltd.