Abstract

The viscothermal absorption of a cluster of hard cylinders periodically arranged in air is directly related with the filling fraction of the underlying lattice. In this work, we present a comprehensive study of the viscous absorption of clusters with circular external shape. The study has been performed by using a homogenization theory in which the clusters have been represented by a single fluid-like cylinder with effective parameters. The validity of the homogenization approach has been supported with numerical experiments in which the viscosity of the actual cluster is calculated with an improved version of the boundary element method. The simulations have been performed by embedding the clusters in a multimode impedance tube. For example, for a circular cluster containing 817 hard cylinders distributed in a hexagonal lattice with filling ratio of 0.836, the absorptive factor calculated with the homogenization approach is 41.5%, which underestimates by about 1% the value obtained with the complete cluster.