Acoustic Impedance of Circular Perforates Subjected to Grazing Flow

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.