Flow across structured fiber bundles: a dimensionless correlation

Abstract

We present a computational analysis of viscous flow across unidirectional arrays of fiber bundles using the boundary element method (BEM). We consider hexagonal arrays of fiber bundles in which the individual filaments are packed in hexagonal or square arrangements. Up to 300 individual filaments are included in each simulation. These are simple but not trivial models for dual porosity fibrous media (such as the preforms used in composites manufacturing or fiber bundles used in hollow membrane oxygenators) characterized by different inter- and intra-tow porosities. The way these porosities interact to determine the hydraulic permeability of such media is not well understood. Numerical solution of the flow problem yields the flowrate through the unit cell, from which the hydraulic permeability ( K p) of the dual porosity medium is computed. Through a large number of simulations we determine K p for a range of inter- and intra-tow porosities and for a range of fiber sizes. A semi-empirical correlation is proposed which collapses all the numerical data (a total of 380 data points) on a single curve, for both, hexagonal and square intra-tow fiber arrangements. This correlation allows prediction of the permeability of hexagonal arrays of fiber bundles from a knowledge of their inter- and intra-tow porosities, the type of intra-tow packing and the size (or number) of the intra-tow filaments.