Determination of Acoustic Impedance for Helmholtz Resonators Through Incompressible Unsteady Flow Simulations

The present work proposes and assesses a methodology based on incompressible computational fluid dynamics simulations to study the acoustic behavior of Helmholtz resonators under a large range of excitation amplitudes. It constitutes an alternative approach to the more widespread one based on compressible flow simulations to analyze the nonlinear regime of Helmholtz resonators. In the present methodology, the resonator is decomposed into its two main components: an assumed incompressible orifice neck and a compressible backing volume. The transfer impedance of the single orifice is obtained by means of an incompressible solver of the flow equations without turbulence modeling, whereas an analytical model accounts for the compliance of the gas in the backing cavity. The proposed methodology is compared for validation purposes to both numerical results of the full compressible equations and experimental data for the complete resonator at different sound pressure levels. A good agreement between the results of the two numerical approaches could be achieved. Numerical results match also fairly well with experimental data, but a systematic overprediction of the resistance by simulations is observed. Accounting for the presence of microrounded edges, presumably present due to manufacturing processes, allows a better agreement between numerical and experimental results.