On the interaction of sound with an annular aperture in a mean flow duct

An analysis is made of long wavelength sound interacting with a thin, rigid disc placed axisymmetrically across a circular cylindrical duct in the presence of a low Mach number mean flow. Vorticity produced at the edge of the disc causes an overall loss of acoustic energy, the effect of which is increased by the flow. Calculations are performed to derive a new analytical representation of the Rayleigh conductivity of the annular aperture between the disc and the duct wall, and a quasi-steady approximation is used to determine the unsteady drag on the disc. The results are used to estimate the corrected form of the conductivity in the presence of flow. This permits the Cummings-Fant 'reduced complexity' equation to be applied to study the absorption of acoustic energy at the disc [A. Cummings, American Institute of Aeronautics and Astronautics Journal 22 (1984) 786-792; G. Fant, Acoustic Theory of Speech Production, The Hague, Mouton, 1960].