THE INFLUENCE OF SHAPE ON THE RAYLEIGH CONDUCTIVITY OF A WALL APERTURE IN THE PRESENCE OF GRAZING FLOW

A numerical investigation of the influence of grazing flow on the Rayl eigh conductivity K-R of an aperture in a thin rigid wall is made. The Mach number is sufficiently small for the local motion near the apert ure to be regarded as incompressible, and the Reynolds number is taken to be large enough for the aperture shear layer to be modelled by a v ortex sheet. The vortex sheet is assumed to be linearly perturbed from its equilibrium position by a small amplitude, time-harmonic pressure , and K-R is determined from the ratio of the resulting aperture volum e flux to the applied pressure. The frequency dependence of K-R is com puted for a variety of aperture shapes for both one-sided and two-side d flows. For apertures of equal maximum streamwise dimension in one-si ded flow, the Strouhal number range within which perturbation energy i s extracted from the mean flow [where Im(K-R) > 0] is found to be effe ctively independent of the aperture shape. The frequency of the first ''operating stage'' of self-sustained (unforced) oscillations of the a perture shear layer lies approximately in the center of this range, an d is the minimum frequency at which narrow band sound is generated by nominally steady flow over the aperture. The numerical predictions are shown to satisfy the reverse how reciprocal theorem, according to whi ch K-R is unchanged when the mean flow directions on both sides of the wall are reversed (when vortex shedding occurs from the ''opposite'' edge of the aperture). (C) 1998 Academic Press Limited.