Boundary element simulation of void formation in fibrous reinforcements based on the Stokes–Darcy formulation

The Boundary Element Method (BEM) is applied for the solution of the problem of void formation in fibrous reinforcements used in composite materials. Stokes and Darcy formulations for the channel and porous medium are considered, including three main differences with most of the previous models reported in the literature that deal with this type of problem: the consideration of the general form of the Beavers–Joseph slip condition instead of the Saffman simplification, the calculation of the flow direction-dependent capillary pressure in the porous medium without experimental factors and the consideration of the surface traction effects in the channel fluid front. An analytical solution of a simple problem is presented to assess the accuracy and convergence of the BEM solution, obtaining good agreement between the results.In order to evaluate the main differences between the Stokes–Darcy formulation and a dual-scale permeability Darcy approach, a problem of constant pressure filling is considered, showing significant differences in the evolution of the flow field as: filling times, shape of the moving fluid front and size and shape of the formed voids.Finally, several simulations at constant flow rate are carried out to analyze the influence of the capillary number, tow porosity, width of transverse tow, fluid penetrability and RUC porosity on the size, shape and location of the void. In general, the void size and shape are influenced by the considered parameters, but the void location is not.