Abstract
A numerical study of voids formation in dual-scale fibrous reinforcements is presented. Flow fields in channels (Stokes) and tows (Brinkman) are solved via direct Boundary Element Method and Dual Reciprocity Boundary Element Method, respectively. The present approach uses only boundary discretization and Dual Reciprocity domain interpolation, which is advantageous in this type of moving boundary problems and leads to an accurate representation of the moving interfaces. A problem admitting analytical solution, previously solved by domain-meshing techniques, is used to assess the accuracy of the present approach, obtaining satisfactory results. Fillings of Representative Unitary Cells at constant pressure are considered to analyze the influence of capillary ratio, jump stress coefficient and two formulations (Stokes–Brinkman and Stokes–Darcy) on the filling process, void formation and void characterization. Filling times, fluid front shapes, void size and shape, time and space evolution of the saturation, are influenced by these parameters, but voids location is not.
Highlights
In dual-scale fibrous reinforcements used in composites processing, the permeability of the tows is several orders of magnitudes lower than the permeability of the inter-tow channels
In a recent work [23], focusing in the prediction of the effective saturated permeability of dual-scale reinforcements for unidirectional flow, it was found that the type of stress matching condition has a strong influence on the boundary layer thickness in the porous medium, but not on the effective saturated permeability, which is dependent on the pore geometry
Equations (55) and (56) give the analytical solution for the velocity profiles, which is only valid provided that the boundary layer thickness of the Brinkman flow is smaller than the height of the porous medium, in such a way that the solution tends to a Darcy flow in the lower part of the porous medium domain
Summary
In dual-scale fibrous reinforcements used in composites processing, the permeability of the tows is several orders of magnitudes lower than the permeability of the inter-tow channels. In a recent work [23], focusing in the prediction of the effective saturated permeability of dual-scale reinforcements for unidirectional flow (where a value of β = 0.7 was used), it was found that the type of stress matching condition (continuity or jump) has a strong influence on the boundary layer thickness in the porous medium, but not on the effective saturated permeability, which is dependent on the pore geometry. The developed BEM/DR-BEM numerical scheme is used to simulate the simultaneous filling of channels and tows inside the RUC at constant pressure regime with the purpose of analyzing the influence of the stress matching conditions on the void formation at several values of the capillary ratio, Ccap = Pcap,max /Pin, where Pcap,max and Pin stand for the maximum capillary pressure and the inlet pressure, respectively This type of filling problem has been previously considered in the literature using different formulations and numerical techniques.
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