On the added mass of a perforated shell, with application to the generation of aerodynamic sound by a perforated trailing edge

Abstract

This paper examines the theory of oscillatory flow through the perforated surface of a rigid shell. The Reynolds number based on the diameter of a typical perforation is sufficiently large that the flow may be assumed to be irrotational. The case in which the surface apertures are small on a scale of the local radius of curvature of the shell is discussed in detail, and a pair of integral equations is derived whose solutions determine the principal properties of the flow, and in particular the fluctuating inertial drag experienced by the shell. These equations are solvable in closed form only for relatively simple shell geometries. Application of the theory is made to the case of a spherical shell, and to the problem of sound generation by turbulence swept past the trailing edge of a perforated aerofoil. Numerical results are presented which support the view that significant reductions in the level of trailing edge noise are possible, and illustrate the dependence of the attenuation on the distribution of perforations.