Co-authors​ :

 Sylvain DRAPIER (FRANCE), Aubin GEOFFRE , Nicolas MOULIN (FRANCE), Julien BRUCHON  

Simulations of the resin flow across fibre arrangements is of prime importance for composite manufacturing simulations, at various scales of observation [1]. Since affordable industrial simulations cannot rely on an explicit description of the whole fibre network, permeabilities (saturated/transient, orthotropic, …), saturation, source/sink terms, and other characteristics are nowadays mandatory to describe upscaled local flows in equivalent homogeneous representations. If such approaches may succeed in some cases, most of the time the gap between models and measurements lead to bring refinements to the permeability that becomes a ‘super-characteristic’, integrating some dependencies upon fibre volume fraction, saturation, fluid velocity, fluid type, fabric architecture, … [1].
Considering the recent capabilities in describing both the local microstructures and the physics in play in transient flows, including surface tension effects, one may aim at upscaling these flows to produce enhanced and potentially stochastic characteristics of the flow where possible, and even more holistic surrogate models to input in adapted simulations tools. Such an approach has been settled at the scale of fibre random packings in our recent work, in both saturated and transient regimes. In [1], starting from high-fidelity stochastic representation of fibre arrangements with variable fibre radii, the saturated flow was averaged [3] from properly defined periodic random cells (Representative Elementary) to yield an explicit stochastic permeability. This permeability was proved to depend equally, and at the first order, on both the fibre volume fraction and the fluid-fibre contact (Fig. 1-a : sat_perm). Its stochastic nature originates from the micro-structure randomness which covers the variation coming from the fiber radius normal distribution. For standard no-slip conditions, this stochastic permeability matches permeabilities proposed in literature [4].
Then transient flows were considered including tension surface effects in the bi-fluid resin-gaz flow [5]. From the velocity and pressure fields computed, saturation was shown to depend only on the capillary number (tensions surface effects over viscous effects) while capillary stress depends on both capillary number and fibre volume fraction. As importantly, characteristic lengths were extracted, with a saturation length of the order of 2-4 fibre mean diameter and characteristic microstructure size of 30-40 fiber mean diameter for a statistical representativity. Eventually, knowing the transient flow configuration and the domain size compared with the saturation and required cell size, one can figure out whether or not a smeared out approach of transient flow in homogeneous equivalent medium can be safely considered (see Fig. 1-b : trans2homog). If not, an approximate of the permeability with a dependency upon saturation may be cast from high-fidelity simulations and used in a Darcy’s like approach.