Influence of intra-yarn flows on whole 3D woven fabric numerical permeability: from Stokes to Stokes-Darcy simulations

• Published in: International journal of multiphase flow 2020-08, Vol.129, p.103349, Article 103349
• Main Authors: Geoffre, Aubin, Wielhorski, Yanneck, Moulin, Nicolas, Bruchon, Julien, Drapier, Sylvain, Liotier, Pierre-Jacques
• Format: Article
• Language: English
• Subjects: 3D Angle-interlock fabric; Engineering Sciences; Flow simulation; Materials; Numerical permeability; Stabilised FEM; Stokes-Darcy coupling
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/j.ijmultiphaseflow.2020.103349

•Dual-scale numerical permeability computations of regular arrangements and 3D interlock ply-to-ply unit cell are proposed.•A mixed velocity-pressure finite element formulation with Variational Multi- Scale (VMS) method to solve Stokes and Stokes-Darcy flows is presented.•A continuous description of transition from Stokes-Darcy to Stokes flows, for both ideal packings and realistic 3D structures is established.•An empirical law to link the effective permeability (i.e. the permeability of the whole unit cell) to the intra-yarn permeability will be proposed.•An intra-yarn permeability threshold from which the yarns can be considered as impermeable is highlighted. 2D and 3D numerical permeability of fibrous media are studied based on Stokes and Stokes-Darcy flows simulated by a Finite Element Modelling (FEM). A monolithic approach stabilised by an Algebraic Sub-Grid Scale (ASGS) method and implemented in a FEM software (Z-set) is used. The 2D geometries have been generated according to ideal arrangements and 3D geometry are representative of a highly anisotropic ply-to-ply interlock unit cell. For both geometries, yarns have been first considered as impermeable, and then the same calculations have been conducted with various intra-yarn permeabilities. The main novelty of this work is to address the dual-scale permeability problem with a Stokes-Darcy modelling so as to override numerical strategy robustness issues. An empirical law has been proposed to link the effective permeability to the intra-yarn one : this allows to generalise previously established results to real 3D materials with complex structures. An intra-yarn permeability threshold (asymptotic value) from which yarns can be considered impermeable has also been highlighted. This study underlines the importance of unit cell definition when it comes to computing permeability of 3D structures numerically generated, especially non-periodicity issues. Two methods to decrease the impact of preferential flows are then discussed.