LOW STROUHAL NUMBER INSTABILITIES OF FLOW OVER APERTURES AND WALL CAVITIES

A theory is developed to predict the frequency of self-sustained oscil lations of flow over an aperture in a plane wall and over a shallow wa ll cavity. The Mach number is sufficiently small that motion in the ap erture or-cavity may be regarded as incompressible. The shear layer th ickness is small enough to permit it to be modeled by a vortex sheet, which is tal;en to be linearly disturbed from its equilibrium planar f orm. The motion of this sheet is discussed for circular and rectangula r wall apertures. and numerical predictions are given for the Rayleigh conductivity K-R(omega) as a function of the radian frequency omega o f the motion. Instabilities of the aperture flow are determined by pol es of K-R(omega) in the upper complex frequency plane, and it is argue d that the real parts of these complex frequencies correspond to the S trouhal numbers of self-sustained oscillations. An approximate method is given for determining the pole that corresponds to the minimum freq uency, self-sustained oscillation. For incompressible flow there can b e no net volume flux into a shallow wall cavity, and oscillations are in this case related to poles of a frequency-dependent drag coefficien t. The predicted minimum Strouhal number for the cavity is close to me asured values for the first stage of self-sustained oscillations of wa ll apertures and shallow cavities at very low Mach number. (C) 1997 Ac oustical Society of America.