Permeability calculations in three-dimensional isotropic and oriented fiber networks

Abstract

Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today's high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%-15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

“…Note that another definition of the fiber orientation tensor was proposed by Stylianopoulos et al, 31 in which the fiber lengths l i and the total length of fibers l tot are also considered. The trace of X ½ is always equal to 1.…”

Investigation of transport property of fibrous media: 3D virtual modeling and permeability calculation

“…Structural features involving curvature and aspect ratio of fibers on the permeability were also determined. The virtual geometric models [6,7], however, were constructed without sufficient verification by comparing to the real structures. Recently, X-ray tomography has rapidly developed and has been widely applied to material science, especially in the non-destructive reconstruction of porous materials, such as granular materials [8], metal foams [9], and fiber materials [10].…”

“…Stylianopoluos et al [6] used finite-element simulation to study permeability in fibrous material with isotropic and oriented fiber arrangements. Specifically, aligned networks were generated by selecting directional vectors from an anisotropic distribution and the impact of porosity on permeability was discussed.…”

A multi-scale model for simulating liquid-hair interactions

“…This leads to an assumption of a body of hair as a porous medium, which has also been adopted by the previous hair-fluid coupling models in graphics. Stylianopoulos et al [2008] performed direct simulations of fluid flowing through submerged fiber assemblies in order to derive an empirical coarse-scale drag/permeability model depending on fiber volume fraction, radius, and orientation. We adopt this drag model in our work.…”

“…Both depend on the specific submerged structure through the angle ϑ between the hair direction and the direction of relative velocity δu (x )/∥δu (x )∥. We adopt an empirical drag force model [Stylianopoulos et al 2008] which emerged from a study of the permeability of oriented fiber networks. Experiments have shown that the longitudinal drag d ∥ (along the hair direction) is different from the perpendicular drag d ⊥ (normal to the hair direction).…”