How to Predict the Sound Spectrum of a Helmholtz Resonator under Grazing Turbulent Flow
* Presenting author
Perforated linings backed by arrays of Helmholtz resonators are well-established as silencers of tonal noise in turbulent flow. Areas of application are automotive engines or jet engines. Typically, these devices operate at subsonic and low-frequency conditions. I.e. the Strouhal number is smaller than the cutoff-frequency of the cavity.We exploit the confined range of operation to tune a spectral impedance model for a single Helmholtz resonator. The model consists of three parts: First, a characterization of the turbulent boundary layer using the Chase model of wall pressure fluctuations; second, a filter function of the rectangular opening; third, a cavity’s impedance function describing the resonances of the shear layer and the depth/base modes of the cavity. The model will be contrasted with a Direct-Numerical-Simulation and with an experiment.Based on the model predictions are made: Without flow, the resistance is always positive. With flow the Helmholtz resonator can act both as a silencer or as an amplifier: At low frequency, the shear layer absorbs acoustic energy; on the contrary at higher frequencies tones occur. The resistance of an opening is increased with the flow velocity. However, this is counteracted by an increase of acoustic source terms of the turbulent boundary layer.