Stokes-darcy fluid flow simulations within 3d Interlock fabrics with capillary effects
Résumé
Resin Transfer Moulding is a widely used process in composite material manufacturing, involving the
compaction of a fibrous 3D interlock preform to reach the desired Fibre Volume Fraction (FVF),
followed by impregnation with liquid polymer resin. Understanding the dual-scale flows of resin
within and between homogeneous equivalent porous yarns is essential for predicting impregnation
defects. At the mesoscopic scale, fabric unit cells are characterised by yarn morphology and intra-yarn
FVF fields, converted into a permeability tensor field via Darcy’s law. This dual-scale nature
significantly affects saturated and unsaturated fluid flows, especially due to capillary phenomena
within yarns, modelled by a capillary pressure. The aim is to develop a robust numerical framework
for simulating fibrous media impregnation at the mesoscopic scale. Fluid flow is modelled by Darcy's
equation within porous yarns and by Stokes' equation between yarns, employing a monolithic
approach with a mixed velocity-pressure formulation stabilised by a VMS method. Accurate
description of resin flow within porous yarns requires locally oriented intra-yarn permeability tensor
fields and capillary stress tensor at the resin-air interface. Additionally, pressure enrichment is
introduced at the fluid front, represented by a level set function, to capture pressure discontinuity in
Darcy domains. Saturated and unsaturated Stokes-Darcy fluid flow simulations are conducted to
determine fabric permeability as a function of global FVF at different compactions and to evaluate the
influence of capillary phenomena on the impregnation scenario.