Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

Flow through Porous Media: Computation of Permeability of Textile Reinforcements


Dipl.-Math. Margrit Klitz, Dr. Roberto Croce, Prof. Dr. Michael Griebel

Dipl.-Math. Bart Verleye (K.U.-Leuven), Prof. Dr. Dirk Roose (K.U.-Leuven), Prof. Dr. Stepan Lomov (K.U.-Leuven)


Computational Fluid Dynamics (CFD) in porous media has various applications in the evolution of new materials as well as in the improvement of existing materials like foams, filters, ceramics or textiles. In particular, textiles are a very important type of porous media for the paper manufacturing and composites industry. In composite manufacturing one of the key tasks of Computational Fluid Dynamics is the prediction of the textile permeability, for example, in the injection stage of Liquid Composite Moulding. Here, a textile reinforcement is put into a mould for a desired 3D shape and a liquid resin is injected. In this stage an often encountered problem is the non-uniform impregnation of the textile where time and money can be saved by numerical predictions of the permeability.

The calculation of permeability presumes a thorough characterisation of the textile reinforcement, which is provided by the WiseTex software [3] developed at the Katholieke Universiteit Leuven in Belgium. In cooperation with the Composite Materials and the Scientific Computing Research Group in Leuven we are developing a new module for their software package FlowTex for the computation of the permeability of textile reinforcements [1]. This module is based on the freely available flow solver NaSt3DGPF, a CFD package which is developed at the Institute of Numerical Simulation. Results of the permeability predictions can be compared to results obtained by a Lattice Boltzmann model [2] and can be validated by experimental data.

Textile composites are hierarchically structured materials. Therefore, a model for fluid flow in textiles should be able to account for porosity on several length scales of the material. That means, if we want to calculate the permeability on the scale of the composite unit cell (inter-yarn flow), we should be able to decide if the porosity of the yarns is to be taken into consideration (intra-yarn flow).

Hierarchy of Structure and Models of a Textile Composite
Structure Elements Fluid Flow Parameters and Equations
Yarn (tow) Fibres Calculation of permeability $K_{tow}$ if yarns are porous
Fabric (woven, knitted) Yarns  
Composite unit cell Fabric Flow Modelling by Navier-Stokes or Navier-Stokes-Brinkman
    Calculation of the permeability tensor by Darcy's law
Composite part Deformed unit cells Flow of the resin

The above diagrams show the setup if we have to account for intra-yarn porosity. Thus, the flow domain is divided into a fluid part where flow is governed by the Navier-Stokes equations and into a porous part (Brinkman part) where flow is governed by Darcy's equation. In order to avoid interface conditions between these regions flow in the whole domain can be modelled by the Navier-Stokes-Brinkman equation

\begin{displaymath}\frac{\partial u}{\partial t} + (u \cdot \nabla)u - \nu \cdot \Delta u - \nu \cdot K_{tow}^{-1}u = \frac{1}{\rho} \nabla p \end{displaymath}

where $K_{tow}$ denotes the permeability of the yarn, $\nu$ is the fluid viscosity and $\rho$ the fluid density . On the other hand, if intra-yarn porosity is neglected, yarns are merely treated as solid obstacles for the standard Navier-Stokes equations.

In both cases the permeability tensor $K$ of the fabric is calculated via Darcy's law in the composite unit cell

\begin{displaymath}U= - \frac{1}{\nu \rho} K \cdot \nabla P \end{displaymath}

where $U$ and $P$ are the volume averaged fluid velocity and pressure.


Example 1: Permeable Square Array
The above setup shows a parallel array of impermeable tows. And although this setup is not close to actual textile reinforcements, theoretical predictions for the permeability exist which make it an interesting test case. For this porous structure we have validated the Navier-Stokes as well as the Navier-Stokes-Brinkman model: The results of the permeability calculations with Darcy's law coincide well with the theoretical ones. The pictures below show the WiseTex Setup for the Permeable Square Array and a slice through the resulting velocity field in flow direction in a unit cell of the medium.

Example 2: Monofilament Fabric Natte 2115

The Monofilament Fabric is a more realistic structure than the Permeable Square Array. Here, it can be shown that the permeability depends strongly on the nesting of the geometry: The calculated permeability for a single layer of fabric will differ from the permeability of two layers of fabric with various densities of nesting. Below, a maximum nested setup can be seen opposed to a minimum nested setup, which has already been discretised by NaSt3DGP.
In the latter case, there are quite big gaps in the fabric where the fluid is only slightly disturbed by the geometry and which then, of course, leads to an increase in permeability as opposed to maximum nesting.


KU Leuven: Composite Materials group

KULeuven: Scientific Computing Research Group


[1] Verleye B., Klitz M., Croce R., Roose D., Lomov S., Verpoest I., Computation of permeability of textile reinforcements. 17th IMACS World Congress, 2005.
[2] Belov E.B., Lomov S.V., Verpoest I., Peters T., Roose D., Parnas R.S., Hoes K., Sol H., Modelling of permeability of textile reinforcements: lattice Boltzmann method. Composites Science and Technology 2004; 64(7-8):1069-80.
[3] Lomov S.V., Huysmans G., Luo Y., Parnas R.S., Prodromou A., Verpoest I., Phelan F.R., Textile composites: modelling strategies. Composites Part A 2001: 32(10):1379-94.
[4] Griebel M., Dornseifer T., Neunhoeffer T., Numerical Simulation in Fluid Dynamics, a Practical Introduction. SIAM, Philadelphia, 1998.

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