Controlling the amount of viscous absorption with clusters of hard cylinders embedded in air

This work presents a comprehensive study of the viscous absorption of clusters made of rigid cylinders embedded in air. The study employs a homogenization theory in which the clusters, with external circular shape, are represented by a single homogeneous viscous cylinder having a frequency dependent effective viscosity while its effective mass density and sound speed only depend on the geometrical parameters of the underlying periodic distribution; i.e., lattice parameter and cylinder diameter. Numerical experiments based on the boundary element method (BEM) show that the absorbance of the actual clusters is well reproduced by the effective viscous cylinders resulting from the homogenization approach. The results indicate that, in the frequency region under study, the absorbing power of the clusters can be tailored by changing the filling fraction of the underlying lattice. A maximum value is obtained for the lattice in which the separation between nearest-neighbors cylinders is about two times the largest thickness of the viscous boundary layer.