Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams

Abstract

In this article, the issue of reconstructing an idealized periodic unit cell ͑PUC͒ to represent a porous medium is examined by means of microcomputed tomography ͑ CT͒. Using CT, three-dimensional images of open-cell foam are collected and used to characterize the representative parameters of its cellular morphology. These parameters are used in order to reconstruct the porous medium by means of an idealized PUC: a tetrakaidecahedron with ligaments of triangular cross sections, whose characteristic dimensions have been measured on the CT images. The proposed reconstruction of the idealized PUC is applied to four aluminum foams. The averaged macroscopic properties of the foams ͑open porosity and thermal characteristic length͒ are deduced from their respective PUC model and compared to experimental measurements and literature data. Good correlations are obtained. For each of the foams, this provides a parameterized idealized periodic unit cell on which the partial differential equations governing sound dissipation and propagation in foams can be solved with a view to studying the microphysical basis of the acoustical macrobehavior.

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

“…Thus, it is shown that the materials mainly differ by their cell size and the presence or lack of membranes closing the faces of the cells. As Perrot et al 8 did in the case of open-cell aluminum foams, the microstructure of polyurethane foam is seen as a packing of tetrakaidecahedra cells (see Fig. 2 taken from Ref.…”

“…The main objective here is to determine, for each material, the properties of a representative tetrakaidecahedra unit-cell (also called PUC in Ref. 8) from which the existing scaling laws would be applied.…”

“…A second approach is based on scaling laws that link macroscopic behavior to microstructure from simplified models of the microstructure 7,8 (cell shape) and wave propagation inside this microstructure. 1,9,10 For example, Allard and Atalla 1 give an analytical expression linking the viscous characteristic length K and the fiber diameter of fibrous materials from the case where the velocity of the air is perpendicular to the direction of the fibers.…”

“…1,9,10 For example, Allard and Atalla 1 give an analytical expression linking the viscous characteristic length K and the fiber diameter of fibrous materials from the case where the velocity of the air is perpendicular to the direction of the fibers. From geometrical considerations of an idealized cell which constitute the porous material, Gibson and Ashby 7 give simple analytical expression linking the porosity U and microstructure properties such as strut length l and thickness t. Recently, Perrot et al 8 adapted this expression for open-cell aluminum foams considering an idealized unit-cell with tetrakaidecahedra shape, and in the same way, proposed an expression for the thermal characteristic length K 0 . Finally, by combining some of the expressions previously mentioned, Lind-Nordgren and Göransson 9,10 proposed a scaling law applied to the airflow a)…”

“…8,[11][12][13][14] The idealized periodic unit cell is then reconstructed, using x-ray tomography (l-san) and advanced computational fluid dynamics analysis is performed to derive properties relevant for the acoustic behavior. These methods allow a great understanding of the impact of microstructure on acoustic behavior.…”