Parallel Flow in Ordered Fibrous Structures: an Analytical Approach

In this study, fully-developed flow parallel to ordered fibrous structures is investigated analytically. The considered fibrous media are made up of in-line (square), staggered, and hexagonal arrays of cylinders. Starting from the general solution of Poisson’s equation, compact analytical solutions are proposed for both velocity distribution and permeability of the considered structures. In addition, independent numerical simulations are performed for the considered patterns over the entire range of porosity and the results are compared with the proposed solutions. The developed models are successfully verified through comparison with existing experimental data, collected by others, and the present numerical results over a wide range of porosity. The results show that for the ordered arrangements with high porosity, the parallel permeability is independent of the microstructure geometry; on the other hand, for lower porosities the hexagonal arrays results in lower pressure drop, as expected. NOMENCLATURE d = Fiber diameter, m K = Viscous permeability, 2 m * K = Dimensionless viscous permeability, 2 * / d K K = P = Pressure, Pa Q = Volumetric flow rate, s m / 3 0 r = Fiber radius, m S = Distance between adjacent fibers, m D U = Volume-averaged superficial velocity, s m / w = Velocity in z -direction, s m / Greek symbols ε = Porosity μ = Fluid viscosity, 2 / m s N φ = Solid volume fraction, ε φ − =1 ε = Porosity