This paper develops a semi-empirical acoustic impedance model of circular perforates under a low-Mach-number (Formula: see text) grazing air flow. The formulation combines a no-flow impedance, appropriate to the high–Strouhal-number (Formula: see text) regime, and a with-flow impedance given by the low-Strouhal-number asymptotic limit of the proposed linear theory. The model accounts for viscous losses, shear-flow effects, coupling between adjacent orifices, porous media via complex effective densities, and acoustic nonlinearities at high sound-pressure levels (SPLs). Realistic shear-layer convection is represented by an empirical phase-speed factor Formula: see text, whose real and imaginary parts primarily affect the acoustic resistance and reactance, respectively. Validation against published experimental datasets (Formula: see text, Formula: see text, and Formula: see text) indicates that, for air-backed configurations, Formula: see text. with Formula: see text, whereas for porous-backed configurations, we adopt Formula: see text and neglect Formula: see text. Overall, the model shows good agreement with experiments and robustness across representative operating conditions. As a limitation, the model does not capture certain behaviors that may arise at moderate Formula: see text (e.g., negative resistance and coupling between grazing flow and acoustic nonlinearity), which lie beyond the present scope.
Meng et al. (Mon,) studied this question.