Microstructure-based calculations and experimental results for sound absorbing porous layers of randomly packed rigid spherical beads

Abstract

Acoustics of stiff porous media with open porosity can be very effectively modelled using the so-called Johnson-Champoux-Allard-Pride-Lafarge model for sound absorbing porous media with rigid frame. It is an advanced semi-phenomenological model with eight parameters, namely, the total porosity, the viscous permeability and its thermal analogue, the tortuosity, two characteristic lengths (one specific for viscous forces, the other for thermal effects), and finally, viscous and thermal tortuosities at the frequency limit of 0 Hz. Most of these parameters can be measured directly, however, to this end specific equipment is required different for various parameters. Moreover, some parameters are difficult to determine. This is one of several reasons for the so-called multiscale approach, where the parameters are computed from specific finite-element analyses based on some realistic geometric representations of the actual microstructure of porous material. Such approach is presented and validated for layers made up of loosely packed small identical rigid spheres. The sound absorption of such layers was measured experimentally in the impedance tube using the so-called two-microphone transfer function method. The layers are characterised by open porosity and semi-regular microstructure: the identical spheres are loosely packed by random pouring and mixing under the gravity force inside the impedance tubes of various size. Therefore, the regular sphere packings were used to generate Representative Volume Elements suitable for calculations at the micro-scale level. These packings involve only one, two, or four spheres so that the three-dimensional finite-element calculations specific for viscous, thermal, and tortuous effects are feasible. In the proposed geometric packings, the spheres were slightly shifted in order to achieve the correct value of total porosity which was precisely estimated for the layers tested experimentally. Finally, in this paper some results based on the self-consistent estimates are also provided.