Stokes capillary driven flows in fibrous media

摘要: Numerical simulation is a crucial asset for high performance composite manufacturing. When a liquid resin infuses reinforcements made of carbon fibres, voids may be created which will affect the final part. Those voids appear due to the competition between capillary effects and viscous effects. This study is part of an industrial chair with, the Hexcel company aiming at modelling and optimising infusion processes for new generation of structural composites. This study will focus on the capillary effects investigated at the fibre scale. The two fluids (airresin) Stokes problem is solved using a finite element method. The fluid problem is solved with linear approximations for both velocity and pressure. Though this approximation does not satisfy the Ladyzenskaia-Babushka-Brezzi stability condition, hence an Algebraic SubGrid Scale method [?] is used to ensure the existence and uniqueness of the solution. Furthermore, the front of resin is followed by a level-set function [?] which is convected by the flow velocity at each increment of the staggered coupled approach.There are three interfaces, first between the fibres and the resin, second between the fibres and the air, and third between the resin and the air. At each interface the jump of the normal stress gives rise to a capillary force substituted into the weak form of the Stokes equations as a Neumann condition. Modifications using the Laplace-Beltrami operator [?] yield a new expression allowing to include the mechanical equilibrium of the triple line into the weak formulation. This method has the advantage to avoid to impose the contact angle, which is not an intrinsic parameter. Besides there are …