INFLUENCE OF WALL THICKNESS ON RAYLEIGH CONDUCTIVITY AND FLOW-INDUCEDAPERTURE TONES

A theoretical investigation is made of the effect of finite wall thick ness on the interaction of a pressure perturbation, produced by sound or large-scale structural vibration, with a wall aperture in the prese nce of a tangential mean how. Previous analyses for a wall of infinite simal thickness (Howe, Scott & Sipcic) indicate that the perturbation is damped during the interaction if the Strouhal number based on apert ure diameter and mean velocity is smalt The damping is caused by the t ransfer of energy to the mean flow via the production of vorticity in the aperture. We show that the damping at low Strouhal numbers is unch anged when the wall has small, but finite, thickness, characteristic o f real structures. However, wall thickness has a substantial influence on flow stability and on the excitation of self-sustained oscillation s of fluid in the aperture. Instabilities exist when the Rayleigh cond uctivity, K-R(omega), of the aperture at frequency omega possesses pol es in the upper omega-plane (an instability frequency being equal to t he real part of omega at a pole); increasing wall thickness exacerbate s the tendency towards instability by causing poles initially in the l ower 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 zer o 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 thi ckness. In both cases the instability frequencies are shown to progres sively decrease as the wall thickness increases, but externally forced motion at low Strouhal numbers is always damped. (C) 1997 Academic Pr ess Limited.