Flow Excited Acoustic Resonance in a Deep Cavity: an Analytical Model

Flow past the opening of a deep cavity can excite and sustain longitudinal acoustic modes resulting in large pressure fluctuations and loud tone generation. An analytic model of the interaction of the free stream with the acoustic flow field using concentrated vortices in the shear layer is proposed. The model includes a computation of the power transferred by the traveling vortices to the acoustic oscillation in the cavity. Experimentally measured values for the vortex convection velocity and phase are used to enable calculation of the ensuing oscillation amplititude and frequency ratio. The radiated acoustic power is calculated using the model and compared to that found from the measured velocity field Agreement between the model and experiments is found to be good for both the single and double vortex modes near resonance and for values of Ur above the single vortex mode. The single vortex mode resonance, the greatest oscillation amplititude, occurs at Ur = 3.2 with only a single vortex in the cavity opening. The double vortex mode resonance occurs at Ur = 15 with two vortices in the cavity opening simultaneously. In between the modes, the predicted power is too sma1l probably resulting from difficulties in computing the generated acoustic power from the measured velocity field in this region.