Quantification of Unidirectional Fiber Bed Permeability

Abstract

A new approach to the closed form quantification of the permeability of a bed of unidirectional fibers is proposed. The methodology is founded on the phase average form of the Navier-Stokes equation and is applied here to low Reynolds number laminar flow of an isotropic non-homogeneous Newtonian fluid through a bed of randomly packed unidirectional fibers. Permeability in both the longitudinal and transverse directions is shown to be a function of fiber volume fraction and fiber diameter only. The results are combined in a flow resistance tensor through which the phase-average Navier-Stokes equation is transformed into a practical tool for the numerical analysis of macroscopic flow in geometrically complex composite moldings. Encouraging agreement between the presented analytical solutions and published experimental results is demonstrated.