Effect of grazing flow on the acoustic impedance of Helmholtz resonators consisting of single and clustered orifices

A semiempirical fluid mechanical model is presented which predicts impedance of a Helmholtz resonator consisting of a single cavity-backed orifice as a function of grazing flow speed, boundary-layer thickness, incident sound amplitude and frequency, and resonator geometry. The incident and cavity sound fields are connected in terms of an orifice discharge coefficient. The effect of multiple orifices was studied experimentally. Interaction between orifices is important only for orifices aligned parallel to the grazing flow. Resistance was virtually independent of both orifice relative spacing and number. Reactance was found to be quite dependent upon orifice spacing but insensitive to the number of orifices.