INFLUENCE OF WALL THICKNESS ON RAYLEIGH CONDUCTIVITY AND FLOW-INDUCED APERTURE TONES

Abstract

A theoretical investigation is made of the effect of finite wall thickness on the interaction of a pressure perturbation, produced by sound or large-scale structural vibration, with a wall aperture in the presence of a tangential mean flow. Previous analyses for a wall of infinitesimal thickness (Howe, Scott & Sipcic) indicate that the perturbation is damped during the interaction if the Strouhal number based on aperture diameter and mean velocity is small. The damping is caused by the transfer of energy to the mean flow via the production of vorticity in the aperture. We show that the damping at low Strouhal numbers is unchanged when the wall has small, but finite, thickness, characteristic of real structures. However, wall thickness has a substantial influence on flow stability and on the excitation of self-sustained oscillations of fluid in the aperture. Instabilities exist when the Rayleigh conductivity,KR(ο), of the aperture at frequencyοpossesses poles in the upperο-plane (an instability frequency being equal to the real part ofοat a pole); increasing wall thickness exacerbates the tendency towards instability by causing poles initially in the lower half plane to cross the real axis. Detailed results are given for two-sided flow which (for an ideal fluid) is stable for a wall of zero thickness when the flow speed is the same on both sides, and for one-sided flow over an aperture, which is unstable for arbitrary wall thickness. In both cases the instability frequencies are shown to progressively decrease as the wall thickness increases, but externally forced motion at low Strouhal numbers is always damped.