Theoretical Estimation of Sound Absorption Coefficients for Randomly Packed Spherical Granules Using Single-Clearance Model

This study aims to establish a simple theoretical method for estimating the sound absorption characteristics of randomly packed granular materials. Using insights gained from existing mathematical models for regular packing and methods utilizing CT images, we propose the “single-clearance” model, a theoretical model that estimates the sound absorption coefficient. It calculates the volume of voids and the surface area of spheres in a granular material based on the material particle size and packing density; the volume and surface area are then used to simplify the packing structure of the granular material to a clearance between two planes. The model is then validated by comparing its obtained theoretical sound absorption coefficients with experimental values and theoretical values derived from CT images. In random packing structures with small variations in porosity relative to the direction of sound propagation, the effect of accounting for this variation on the sound absorption coefficient is negligible. In the single-clearance model, the sound absorption coefficient calculated using a packing density of 0.65 for the random packing structure generally agrees with that derived from CT images at all particle sizes. Thus, the sound absorption coefficient can be estimated simply using particle size and packing density.