Flow-resonant sound interaction in a duct containing a plate, II: Square leading edge

The interaction between flow and flow-induced acoustic resonances near rigid plates with square leading edges located in a hard-walled duct is described. These plates generate β-mode acoustic resonances over several discrete ranges of flow velocity. A potential flow model for a plate with a square leading edge is developed and the acoustic power generated by vortices, which grow and shed from the leading edge, is calculated as they move through the resonant acoustic field. Vortices grow rapidly during the first half cycle and the vortex growth rate is quantified by using a Kutta condition. This model indicates that a major phase-dependent sound soccurs when a vortex passes the trailing edge of the plate. It is the remoteness of this source from the site at the leading edge where the sound affects the flow which makes possible the discrete resonance ranges.