Cross flow hydrodynamics in regular and random fiber bundles in the Darcyan and non-Darcyan regimes

Computational results are presented for cross flow past straight parallel fiber bundles. Different configurations are compared: regular square lattices of circular or elliptic fibers, and random distributions of circular fibers. For these latter, two alternative algorithms for the generation of random clusters, a "static" one and a "dynamic" one, are shown to be equivalent. CFD simulations are conducted for different directions and amplitudes of the driving pressure gradient, yielding Reynolds numbers in both the Darcyan (linear) and non-Darcyan (inertial) regimes, and corresponding permeability polar charts are built. The results depict a complex scenario, which includes isotropic, orthotropic and general anisotropic behaviors. A systematic classification is proposed, distinguishing between configurations that are isotropic for Re -> 0 and become anisotropic only when nonlinear resistance terms become significant (regular lattices of circular fibers), and configurations that are already anisotropic (in particular, orthotropic) for Re -> 0 (regular lattices of elliptic fibers, random clusters of circular fibers).