Determination of acoustic impedance for Helmholtz resonators through incompressible unsteady flow simulations

The present study investigates the physics of Helmholtz resonators under a large range of excitation amplitudes through an approach based on incompressible computational fluid dynamics simulations. By doing so, this work proposes and assesses an alternative approach to the more widespread one based on compressible flow simulations to analyze the non-linear regime of Helmholtz resonators. In the present methodology, the resonator is decomposed into its two main components: an assumed incompressible florice 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 SPLs. The agreement between the results of the two numerical approaches is found to be good. Numerical results match also fairly well with experimental data but a systematic over-prediction of the resistance by simulations is observed. The effect of micro-rounded edges, presumably present due to manufacturing processes, was found to be insufficient to explain the discrepancy.