The influence of edge geometry on end-corrections in microslit absorbers

The influence of the edge geometry on the viscous dissipation and inertia in microslit absorbers (MSAs) is investigated. MSAs are plates with arrays of slit-shaped perforations backed by a shallow cavity providing a lightweight solution for acoustic liners. To optimize the viscous dissipation, the slit height and the plate thickness are chosen to be of the order of the acoustic viscous boundary layer thickness i.e. in the submillimeter range. Because of the manufacturing process, for these perforations, the edge shape is not always sharp. The acoustic behavior is investigated assuming a slit in a rectangular confinement channel, given by actual walls or by hydrodynamical interactions due to neighboring slits. The flow within the slit is assumed locally incompressible. Viscous dissipation and inertia of the slit are described in terms of resistive and inertial end-corrections. A combination of analytical models and numerical solutions of the incompressible Linearized Navier-Stokes equations is proposed. The effect of the edge geometry is investigated using potential flow theory combined with a thin viscous boundary layer approximation. The analytical model successfully predicts the end-corrections for rounded edges, up to a radius of curvature of the order of the slit height. From this study it emerges that the inertial end-correction of the slit is a global property sensible to the far-field behavior of the flow and strongly dependent on the porosity, unlike observed for circular perforations. On the contrary, the resistive end-correction is a localized phenomenon, weakly dependent on the porosity and dominated by the edge geometry of the perforation.