Aerodynamic lift and drag fluctuations of a sphere

Abstract

An experimental and theoretical investigation is made of the unsteady lift and drag exerted on a sphere in a nominally steady, high Reynolds number, incompressible flow. The net force on the sphere has previously been ascribed to fluctuations in the bound vorticity in the meridian plane normal to the force, produced by large-scale coherent structures shed into the wake. A simplified model of vortex shedding is proposed that involves coherent eddies in the form of a succession of randomly orientated vortex rings, interconnected by pairs of oppositely rotating line vortices, and shed at quasi-regular intervals with a Strouhal number ∼ 0.19. The rings are rapidly dissipated by turbulence diffusion, but it is shown that only the nascent vortex ring makes a significant contribution to the surface force, and that the force spectrum at Strouhal numbers exceeding unity is effectively independent of the shape of the fully formed vortex. Predictions of the lift and drag spectra at these frequencies are found to be in good accord with new towing tank measurements presented in this paper.