STOKES-DARCY FLUID FLOW SIMULATIONS WITHIN 3D INTERLOCK FABRICS WITH CAPILLARY EFFECTS
Topic(s) : Manufacturing
Co-authors :
Morgan CATALDI , Yanneck WIELHORSKI (FRANCE), Nicolas MOULIN (FRANCE), Augustin PARRET-FREAUD , Monica PUCCI (FRANCE), Pierre-Jacques LIOTIER (FRANCE)Abstract :
Resin Transfer Moulding (RTM) is a process widely used in the field of composite material manufacturing. A fibrous 3D interlock preform is firstly compacted to achieve the desired Fibre Volume Fraction (FVF), and is subsequently impregnated with a liquid polymer resin [1]. The multiscale structure of reinforcements involves dual-scale flows of the liquid resin. A comprehensive understanding of these flows, occurring both between and within homogeneous equivalent porous yarns, is required to predict potential impregnation defects.
At the mesoscopic scale, fabric unit cells are described by both yarn morphology and intra-yarn FVF field. This field is then converted into a permeability tensor field, defined through Darcy’s law, characterising the homogeneous equivalent intra-yarn properties [3]. This dual-scale nature significantly impacts saturated fluid flows, thereby influencing the fabric effective permeability. Furthermore, this effect is even more meaningful on unsaturated flows due to capillary phenomena within yarns. Capillary forces are modelled by a capillary pressure, considered as a pressure discontinuity applied to the fluid front in fibrous media [2].
Our aim is to develop a robust numerical framework to simulate fibrous media impregnation at mesoscopic scale. The fluid flow is modelled by Darcy equation within the porous yarns and by Stokes equation between the yarns. A monolithic approach is used to solve the Stokes-Darcy coupled finite element problem with a mixed velocity-pressure formulation stabilized by a variational multiscale method. An accurate description of the resin flow within the homogeneous equivalent porous yarns is required. To achieve this, a locally oriented intra-yarn permeability tensor field varying along yarns [3] and a capillary stress tensor [4] within them at the resin-air interface are added to model stationary and transient double-scale flow in 3D interlock fabrics. A pressure enrichment is introduced at the fluid front, represented by a level set function, in order to capture the pressure discontinuity in Darcy domains [2].
Saturated and unsaturated Stokes-Darcy fluid flow simulations are carried out both to determine the fabric permeability as a function of the global FVF at different compactions and to evaluate the influence of capillary phenomena on the impregnation scenario.
At the mesoscopic scale, fabric unit cells are described by both yarn morphology and intra-yarn FVF field. This field is then converted into a permeability tensor field, defined through Darcy’s law, characterising the homogeneous equivalent intra-yarn properties [3]. This dual-scale nature significantly impacts saturated fluid flows, thereby influencing the fabric effective permeability. Furthermore, this effect is even more meaningful on unsaturated flows due to capillary phenomena within yarns. Capillary forces are modelled by a capillary pressure, considered as a pressure discontinuity applied to the fluid front in fibrous media [2].
Our aim is to develop a robust numerical framework to simulate fibrous media impregnation at mesoscopic scale. The fluid flow is modelled by Darcy equation within the porous yarns and by Stokes equation between the yarns. A monolithic approach is used to solve the Stokes-Darcy coupled finite element problem with a mixed velocity-pressure formulation stabilized by a variational multiscale method. An accurate description of the resin flow within the homogeneous equivalent porous yarns is required. To achieve this, a locally oriented intra-yarn permeability tensor field varying along yarns [3] and a capillary stress tensor [4] within them at the resin-air interface are added to model stationary and transient double-scale flow in 3D interlock fabrics. A pressure enrichment is introduced at the fluid front, represented by a level set function, in order to capture the pressure discontinuity in Darcy domains [2].
Saturated and unsaturated Stokes-Darcy fluid flow simulations are carried out both to determine the fabric permeability as a function of the global FVF at different compactions and to evaluate the influence of capillary phenomena on the impregnation scenario.