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.

The aero-acoustic resonance behavior of partially covered slender cavities

“…Vortex roll-up occurs midway across the opening during the maximum outflow phase. This phase-averaged shear layer pattern is corresponding to the observations by Ma et al (2009). The generated vortex is convected downstream and impinges on the downstream edge, where the vortex gets partly entrapped into the cavity.…”

Numerical investigation of a honeycomb liner grazed by laminar and turbulent boundary layers

“…Ozalp, Pinarbasi & Rockwell (2003) studied the self-excited oscillations of a turbulent boundary layer along a perforated plate closed by a cavity using particle image velocimetry (PIV). Ma, Slaboch & Morris (2009) also investigated the detailed fluid dynamic characteristics of a flow-excited Helmholtz resonator using PIV and proposed a predictive methodology for the corresponding measurements. Marx & Aurégan (2013) performed linear stability normal mode analysis of a lined wall with flow and the effect of viscous dissipation while Fischer, Bake & Bassetti (2013) performed a comparison between the PIV and computational aeroacoustic results in the vicinity of an acoustic liner, with phase-locked results, with encouraging agreement between a linearized boundary condition and the experimental data.…”

Resonant mode characterisation of a cylindrical Helmholtz cavity excited by a shear layer

“…Rossiter's equation for the shear layer excitation frequency, however, has been used by many authors to accurately model other feedback mechanisms. 11,32 This equation is given as…”

“…For the low subsonic speeds considered here, a ¼ 0 was found to be appropriate, and has been used by other authors, 11,33,34 who argued that there is no need to consider a phase delay when the convection speed is much less than the speed of sound. The typical value of j ¼ 0.5 is the average of the free stream speed and the flow in the cavity, and does not include effects of the boundary layer which acts to retard the apparent free stream velocity.…”

“…A range of convection speed coefficients are to be found in the literature. 2,11,32 A value of j ¼ 0.42 has been used here as a best fit to the measured data.…”