Two-scale analysis of the permeability of 3D periodic granular and fibrous media

Abstract

In this paper, a numerical study of slow flow through a filter viewed as a porous medium made of arrays of cubic solid particles or solid fibers of square cross section is considered. A double-scale asymptotic method is used to determine a system of equations that are then solved numerically to calculate the permeability. Simulations are made at the REV scale, and macroscopic properties are deduced. At the microscale, three arrangements (simple cubic, body-centered cubic and face-centered cubic) are analyzed. A parametric study is carried out, for both granular and fibrous cases, showing the porosity evolution with the size ratio between the solid particles and the periodic cell. At the macroscopic scale, the interest of this analysis is to compute the Darcy’s permeability of such arrays as a function of the porosity and the packing characteristics. Results are given over the full porosity range for SC, BCC and FCC arrays. On the other side, the microscopic analysis shows the influence of particle or fiber arrangement and size on the fluid velocity and the pressure field inside the porous structure.

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Notes

  1. 1.

    The dimensional quantities with subscript (r) are the reference ones used to normalize the dimensional Stokes equation.

  2. 2.

    \(\mathbf {v^2}\) is identical to \(\mathbf {v^1}\) by permutation of direction 1 to 2.

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Bourbatache, M.K., Hellou, M. & Lominé, F. Two-scale analysis of the permeability of 3D periodic granular and fibrous media. Acta Mech 230, 3703–3721 (2019). https://doi.org/10.1007/s00707-019-02470-3

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