Influence of geometry on acoustic end-corrections of slits in microslit absorbers

The acoustic behavior of individual slits within microslit absorbers (MSAs) is investigated to explore the influence of porosity, edge geometry, slit position, and plate thickness. MSAs are plates with arrays of slit-shaped perforations, with the height of the order of the acoustic viscous boundary layer thickness, for optimized viscous dissipation. Due to hydrodynamic interaction, each slit behaves as confined in a rectangular channel. The flow within the slit is assumed to be incompressible. The viscous dissipation and the inertia are quantified by the resistive and the inertial end-corrections. These are estimated by using analytical results and numerical solutions of the linearized Navier-Stokes equations. Expressions for the end-corrections are provided as functions of the ratio of the slit height to viscous boundary layer thickness (shear number) and of the porosity. The inertial end-correction is sensitive to the far-field behavior of the flow and for low porosities strongly depends on the porosity, unlike for circular perforations. The resistive end-correction is dominated by the edge geometry of the perforation. The relative position of the slit with respect to the wall of the channel is important for distances to the wall on the order of the slit height. The plate thickness does not have a significant effect on the end-corrections.