Modelling wave dispersion in fluid saturating periodic scaffolds

TL;DR

This paper develops effective models and dispersion equations for acoustic waves in fluid-saturated periodic porous structures, accounting for advection and microstructure effects, with numerical validation showing anisotropic wave behavior.

Contribution

It introduces a combined homogenization and Floquet-Bloch approach that accounts for advection in porous media, providing new insights into wave dispersion.

Findings

Advection causes anisotropy in wave dispersion.

Microstructure size influences wave behavior.

Homogenized models accurately predict dispersion characteristics.

Abstract

Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem imposed in a bounded medium, 2) harmonic acoustic waves are studied in an infinite medium using the Floquet-Bloch (FB) wave decomposition. In contrast with usual simplifications, the advection phenomenon of the Navier-Stokes equations is accounted for. For this, an acoustic approximation is applied to linearize the advection term. The homogenization results are based the periodic unfolding method combined with the asymptotic expansion technique providing a straight upscaling procedure which leads to the macroscopic model defined in terms of the effective model parameters. These are computed using the characteristic responses of the porous microstructure. Using the FB theory, we derive dispersion equations for the scaffolds saturated by the inviscid, or the viscous, barotropic fluids, whereby the advection due to a permanent flow in the porous structures is respected. A computational study is performed for the numerical models obtained using the finite element discretization. For the FB methods-based dispersion analysis, quadratic eigenvalue problems must be solved. The numerical examples show influences of the microstructure size and of the advection generating an anisotropy of the acoustic waves dispersion.