Cavity Mode Excitation by Vortex Shedding from a Cross-Beam

Abstract

An analysis is made of the tonal acoustic radiation produced by nominally steady, low Mach number flow past a shallow, rectangular wall cavity in the presence of a cross-beam in the flow adjacent to the cavity. At ‘lock-on’ the frequency of vortex shedding from the beam is equal to one of the resonant frequencies of the cavity. The sound produced by this vorticity is augmented by the presence of the cavity and is calculated for the lowest order resonance frequency of the cavity by using a Green's function derived by Howe (International Journal of Aeroacoustics 2, 347 – 365, 2003). Except for beams of very small cross-section, the efficiency of the aeroacoustic coupling between the beam and the cavity depends on the position of the beam above the cavity. Our results indicate that the coupling is strongest when the beam lies above the cavity mouth between the cavity leading edge and the centre of the mouth. The analysis makes use of two alternative models of vortex shedding, involving either an array of discrete, rectilinear vortices or a continuous, time-harmonic vortex sheet in the wake of the beam. At lock-on each of these models supplies essentially identical predictions of the acoustic sound power radiated directly away from the cavity.