Noise Emission Due to Slender Vortex Solid Body Interactions

Abstract

Interactions of a slender vortex ring with and a stationary rigid sphere are analyzed using a 3D, Lagrangian vortex element scheme which discretizes and tracks the filament centerline using smoothed vortex elements. The filament self-induced velocity is obtained from a desingularized Biot-Savart law that reflects the correct asymptotic behavior of the core vorticity distribution. The effect of the sphere is represented in terms of a potential velocity field that is expressed as a line integral along the image of the filament centerline with regular weight functions. It is shown that the acoustic emission due to the interaction between the filament and the sphere essentially consists of dipoles and quadrupoles whose strengths and orientations are determined by the time-evolution of the weighted first and second moments of vorticity, respectively. The scheme is used to analyze the sound generated during the passage of slender vortex rings near a solid sphere.