The complete prediction of the second order permeability tensor for a three dimensional multi-axial preform is critical if we are to model and design the manufacturing process for composites by considering resin flow through a multi-axial fiber structure. In this study, the in-plane and transverse permeabilities for a woven fabric were predicted numerically by the coupled flow model, which combines microscopic and macroscopic flows. The microscopic and macroscopic flows were calculated by using 3-D CVFEM(control volume finite element method) for micro and macro unit cells. To avoid a checkerboard pressure field and improve the efficiency of numerical computation, a new interpolation function for velocity is proposed on the basis of analytical solutions. The permeability of a plain woven fabric was measured by means of an unidirectional flow experiment and compared with the permeability calculated numerically. Reverse and simple stacking of plain woven fabrics were taken into account and the relationship between the permeability and the structures of the preform such as the fiber volume fraction and stacking order is identified. Unlike other studies, the current study was based on a more realistic three dimensional unit cell. It was observed that in-plane flow is more dominant than transverse flow within the woven perform, and the effect of the stacking order of a multi-layered preform was negligible.
Control volume finite element method for a benchmark validation of a natural convection in a square cavity
