| We are concerned with the topic of the effect of structure on the hydraulic permeability of structured fibrous media. Such media find extensive applications in the area of composites manufacturing, where a resin is used to infiltrate and consolidate reinforcing mats made of high performance fibers. Knowledge of their permeability is essential for optimal process design. Both analytical and numerical approaches have been used for this purpose. In the latter, the Boundary Element Method (BEM) and the Finite Element Method (FEM) have been utilized to solve the equations of fluid flow in suitable unit cells. In the former, we have developed previously unavailable analytical solutions using the lubrication approximation.; Two different systems, typical for dual porosity structured porous media have been investigated: (i) porous media built up of tows having the same permeability and (ii) media consisting of two different types of tows. Based on the lubrication approximation and an existing permeability analytical model for system (i), a new analytical model for system (ii) was developed. This model was validated with more than 600 numerical simulations, carried out for these two types of systems. Use of dimensionless groups deduced from the above models, resulted in the development of a new empirical model and a master curve for the permeability of media consisting of two different types of tows. Using this, the permeability can be calculated from structural parameters of the intra-tow and inter-tow regions.; Concerning porous systems composed of fibers of two different radii, the permeability has been calculated in both the creeping and the inertial regions. Again, as in the previous study, a large number of simulations (more than 400) has been conducted. The numerical results have been compared to the predictions of the Ergun and the Forchheimer equations. We proposed a modification of the Forchheimer term by which an excellent agreement between numerical results and this model is obtained. Finally, based on the above modification, an explicit model for an apparent permeability that incorporates inertial effects was developed. |
