Abstract 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.

中文翻译：

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纱线内部流动对整个 3D 机织织物数值渗透率的影响：从斯托克斯到斯托克斯-达西模拟

摘要 基于通过有限元建模 (FEM) 模拟的斯托克斯流和斯托克斯-达西流，研究了纤维介质的 2D 和 3D 数值渗透率。使用由代数子网格尺度 (ASGS) 方法稳定并在 FEM 软件 (Z-set) 中实现的整体方法。2D 几何图形是根据理想排列生成的，3D 几何图形代表高度各向异性的层到层互锁单元。对于这两种几何形状，首先将纱线视为不可渗透的，然后对不同的纱线内渗透率进行了相同的计算。这项工作的主要新颖之处在于使用 Stokes-Darcy 建模解决双尺度渗透率问题，以克服数值策略稳健性问题。已经提出了将有效渗透率与纱线内渗透率联系起来的经验法则：这允许将先前建立的结果推广到具有复杂结构的真实 3D 材料。纱线内部渗透性阈值（渐近值）也已被突出显示，从该阈值可以将纱线视为不可渗透的。这项研究强调了在计算数值生成的 3D 结构的渗透率时，晶胞定义的重要性，尤其是非周期性问题。然后讨论了两种减少优惠流动影响的方法。这项研究强调了在计算数值生成的 3D 结构的渗透率时，晶胞定义的重要性，尤其是非周期性问题。然后讨论了两种减少优惠流动影响的方法。这项研究强调了在计算数值生成的 3D 结构的渗透率时，晶胞定义的重要性，尤其是非周期性问题。然后讨论了两种减少优惠流动影响的方法。