Virtual density and speed of sound in a fluid-solid mixture wlth periodic structure

Abstract

In a two-phase mixture of solid particles in an inviscid compressible fluid the effective density of the mixture differs from the average density due to relative accelerations between the phases. The effective density directly influences the effective speed of sound. A constructive theory is given to compute density tensors which describe the inertial coupling between the two phases. The theory is based on Hamilton's principle and a general homogcnization method as described in a previous paper. Here we describe a variant of the theory which clarifies the differences between surface and volume averaged velocities. This difference is important in case of two-phase configurations showing a regular periodic pattern like rod bundles in fiuid. Quantitative results are given for rod bundles and partly for spheres in regular square arrangements.