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Absorption of sound at a slot in a splitter plate in a mean-flow duct

Perforated screens are often deployed to attenuate aerodynamic sound in heat-exchanger cavities and other ducts conveying mean flow. The dissipation is caused by vorticity production in the perforations. This mechanism is investigated theoretically for the case of a thin rigid plate lying along the centreline of a duct and having a single transverse slot, a configuration that is to be studied experimentally at the Institute of Sound and Vibration Research of Southampton University. Time-harmonic acoustic waves are incident on the slot in the presence of equal parallel mean flows on either side of the plate. A linearized theory of unsteady shearing flow over a slot, which incorporates the influence of vorticity ejection into the flow, is used to examine mean-flow/acoustic energy exchanges. According to this theory acoustic energy is absorbed provided that the Strouhal number based on slot width and mean-flow velocity is sufficiently small. At higher frequencies there exists an infinite set of discrete frequency intervals within which there is a net production of acoustic energy at the slot at the expense of the kinetic energy of the mean flow.