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In the porous media literature, unidirectional fibrous systems are broadly categorized as ordered or disordered. The former class, easily tractable for analysis purposes but limited in its relation to reality, involves square, hexagonal and various staggered arrays. The latter class involves everything else. While the dimensionless hydraulic permeability of ordered fibrous media is known to be a deterministic function of their porosity φ, the parameters affecting the permeability of disordered fiber arrays are not very well understood. The objective of this study is to computationally investigate flow across many unidirectional arrays of randomly placed fibers and derive a correlation between K and some measure of their microstructure. In the process, we explain the wide scatter in permeability values observed computationally as well as experimentally. This task is achieved using a parallel implementation of the Boundary Element Method (BEM). Over 600 simulations are carried out in twodimensional geometries consisting of 576 fiber cross-sections placed within a square unit cell by a Monte Carlo procedure. The porosity varies from 0.45 to 0.90. The computed permeabilities are compared with earlier theoretical results and experimental data. Analysis of the computational results reveals that the permeability of disordered arrays with φ < 0.7 is reduced as the non-uniformity of the fiber distribution increases. This reduction can be substantial at low porosities. The key finding of this study is a direct correlation between K and the mean nearest inter-fiber spacingδ 1 , the latter depending on the microstructure of the fibrous medium.

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The results of a comprehensive computational evaluation of the Ergun and Forchheimer equations for the permeability of fibrous porous media are reported in this study. Square and hexagonal arrays of uniform fibers have been considered, as well as arrays in which the fiber size is allowed to change in a regular manner, expressed by a size variation parameter (δ). The range of porosity (φ) examined is from 0.30 to 0.60, the Reynolds number ranges between 0 and 160, and the size variation parameter (δ) between 0 (corresponding to the uniform array) and 0.90 (in which case the diameter of the large fibers in the array is 19 times that of the small ones). We obtain computational results for pressure drop and flow rate in a total of 440 cases mapping the (φ,δ,Re) space; these are presented in terms of a friction factor and are compared to the predictions of the Ergun and Forchheimer equations, both widely used models for the permeability of porous media. In the limit of creeping flow (Re&lt;1), the Forchheimer equation is in excellent agreement with the computational results, while the Ergun equation is unable to capture the behavior of fiber arrays in which the flow has a strong contracting/expanding element. The Forchheimer equation, in its original form, is in closer agreement with the computational results. When the Forchheimer term (F) is expressed as a function of porosity, we obtain a modified form of the Forchheimer equation that is in excellent agreement with computational results for the entire range of (φ,δ,Re) examined.

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