End correction model for the transfer impedance of microperforated panels using viscothermal wave theory.

Microperforated panels (MPPs) are efficient sound absorbers featuring microperforations with low porosity. Sound absorption occurs inside the perforations and their vicinity as well, which is represented with an end correction in the transfer impedance of the MPPs. Many empirical models for the end correction were derived from experiment or numerical simulation data. In order to validate these models, this paper presents an analytical solution of the end correction for sharp-edged circular perforations using viscothermal wave theory. The perforations are assumed to be periodically distributed and each perforation is associated with a square duct resulting from a periodic spatial partition. The velocity profile and the temperature field in each perforation are derived from the low reduced frequency model, which pose the boundary conditions to determine the modal coefficients of the acoustic, entropy, and viscous waves in the duct. An impedance end correction model is derived from the asymptotic expansion of the modal solution. It improves the conventional model by introducing a static flow resistance term to describe the energy dissipation due to the acoustic flow distortion outside the perforations. Numerical and experimental examples validate that the proposed model offers better prediction for the transfer impedance and the sound absorption of the MPPs.