Parallel flow through ordered fibers: An analytical approach

In this study, fully developed flow parallel to ordered fibers 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 arrangements over the entire range of porosity and the results are compared with the proposed solutions. The developed solutions are successfully verified through comparison with 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 geometrical arrangements; on the other hand, for lower porosities the hexagonal arrangement provides lower pressure drop, as expected.