INFLUENCE OF CROSS-SECTIONAL SHAPE ON THE CONDUCTIVITY OF A WALL APERTURE IN MEAN FLOW

An analysis is made of the effect of cross-sectional shape on the moti on induced in a wall aperture by a pressure perturbation in the presen ce of high Reynolds number tangential flow. Previous studies for circu lar and rectangular apertures indicate that there is a transfer of ene rgy from the applied perturbation to the mean flow (via the production of vorticity in the aperture) provided the Stroubal number based on a perture diameter and mean velocity is small. In this paper apertures a re considered whose cross-sections are symmetrically tapered in a dire ction parallel to the mean flow. For highly tapered apertures of trape zoidal cross-section, it is found that low Stroubal number damping is confined to a smaller range of frequencies. Self-sustaining oscillatio ns of the shear layers spanning the aperture can occur at certain disc rete frequencies, which correspond to the real parts of complex eigen frequencies of the aperture motion having positive imaginary parts. Th e eigenfrequencies are poles of the Rayleigh conductivity, and are fou nd to vary in proportion to U/L, where U is mean flow speed and L. is the maximum streamwise length of the aperture, but to be only weakly d ependent on aperture shape. (C) 1997 Academic Press Limited.