Computation of Far-Field Sound Generation in a Fluid-Structure Interaction Problem

Abstract

The problem of generation of sound in moving media has become an important problem in recent years. Accordingly, in this paper we examine the inviscid flow past a bump on a plane wall in which vorticity disturbances initially placed upstream convect downstream and interact with the bump. The physical situation of interest is that of a flow in which vortices are formed far upstream and then impinge on a surface protrusion. The bump in the wall is assumed to be cylindrical in shape and mounted on a mechanical spring. It may undergo nonlinear transverse oscillations as a result of the unsteady loading caused by the vortices. The flow field and the structure are then fully coupled and solutions for the vortex paths and consequent structure position must be obtained interactively and numerically at each time step. The relevant acoustic variables such as pressure, and potential may then be obtained in the limit as the Mach number M → 0 by asymptotic methods for any number of vortices. An acoustic point dipole is generated by impingement of an isolated vortex on the structure but a much more complicated behavior of the acoustic pressure is generated for more complex vortex arrays. Results for a single vortex and two vortices are presented.