Fluid mechanics of the flow-excited Helmholtz resonator

Abstract

A flow-excited Helmholtz resonator was investigated experimentally and theoretically. The analysis was focused on a simplified momentum balance integrated over the region of the orifice. The resulting expressions were used to guide an experimental programme designed to obtain measurements of the resonator pressure under flow excitation, as well as the dynamics of the shear layer in the orifice using particle image velocimetry (PIV). The pressure measurements indicated a number of distinctive features as the flow speed varied. The PIV results provided a detailed representation of the shear layer vorticity field, as well as the equivalent hydrodynamic forcing of the resonator. The forcing magnitude was found to be roughly constant over a range of flow speeds. A model was proposed that provides a prediction of the resonator pressure fluctuations based on the thickness of the approach boundary layer, the free stream speed and the acoustic properties of the resonator. The model was shown to provide an accurate representation of the resonating frequency as well as the magnitude of the resonance to within a few decibels.