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

✍ Scribed by S.M. GRACE; K.P. HORAN; M.S. HOWE

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 536 KB
• Volume: 12
• Category: Article
• ISSN: 0889-9746
• DOI: 10.1006/jfls.1997.0145

✦ Synopsis

A numerical investigation of the influence of grazing flow on the Rayleigh conductivity K 0 of an aperture in a thin rigid wall is made. The Mach number is sufficiently small for the local motion near the aperture 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 vortex sheet. The vortex sheet is assumed to be linearly perturbed from its equilibrium position by a small amplitude, timeharmonic pressure, and K 0 is determined from the ratio of the resulting aperture volume flux to the applied pressure. The frequency dependence of K 0 is computed for a variety of aperture shapes for both one-sided and two-sided flows. For apertures of equal maximum streamwise dimension in one-sided flow, the Strouhal number range within which perturbation energy is extracted from the mean flow [where Im(K 0 )'0] is found to be effectively independent of the aperture shape. The frequency of the first ''operating stage'' of self-sustained (unforced) oscillations of the aperture shear layer lies approximately in the center of this range, and 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 flow reciprocal theorem, according to which K 0 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).