Analytical determination of viscous permeability of hybrid fibrous reinforcements

Transverse and longitudinal permeability for hybrid fibrous porous media were determined by solving Stokes and Darcy–Weisbach equations, respectively. A rectangular representative unit hybrid-cell with two sizes of fibre was used for solving one dimensional fluid flow to obtain velocity profile, flux, pressure drop and finally permeability. Both models were validated by using analytical models for permeability in symmetric cells reported in literature. Numerical simulations were performed using computational fluid dynamics to assess the permeability behaviour of several hybrid cells. Interesting results were found for several fibre radii ratios where the permeability changes differently for transverse and longitudinal models, so this model is based on fibre spacing and the change in diameter. It is notorious that for low porosity values and low fibre radii ratios, the transverse permeability decreases with respect to the constant fibre radii cell. It can be concluded that the permeability only depends on geometric variables, and the hybrid effect is more relevant in the permeability for porosities lower than 0.65.