Analysis of transverse flow in aligned fibrous porous media

The permeability of preform materials used in liquid moulding processes such as resin transfer moulding and structural reaction injection moulding is a complex function of weave pattern, packing characteristics, tow structure and intra-tow properties. The development of tools for predicting permeability as a function of these parameters is of great practical importance because such capability would speed process design and optimization, and provide a step towards establishing processing-performance relations. In this study, transverse flow in aligned fibrous porous media has been investigated. A semi-analytical model based on lubrication analysis is derived to predict the effect of tow shape and intra-tow permeability on the overall bed permeability for flow through rectangular arrays of porous elliptical cylinders. The Brinkman equation is used to model flow inside the porous structures, and the Stokes equation to model flow in the open media between the structures. The model predictions are verified by comparing with rigorous finite element calculations. The model shows that the influence of the intra-tow permeability on the overall bed permeability increases with inter-tow packing, and increasing degree of tow ellipticity. The influence is particularly critical for 'stacked' geometries for which previous models predict a zero permeability. A method for predicting intra-tow permeability is also proposed and investigated by comparing the model predictions for overall bed permeability with some experimental data for flow in a model porous medium. The comparison shows that use of the method enables the experimentally measured permeability value to be properly bounded.