Permeability of textile reinforcements: Simulation, influence of shear and validation B. Verleye a, * , R. Croce b , M. Griebel b , M. Klitz b , S.V. Lomov c , G. Morren d , H. Sol d , I. Verpoest c , D. Roose a a K.U.Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Leuven, Belgium b University Bonn, Institute for Numerical Simulation, Germany c K.U.Leuven, Department of Metallurgy and Materials Engineering, Belgium d Vrije University of Brussel, Department of Mechanics of Materials and Constructions, Belgium article info Article history: Received 29 October 2007 Received in revised form 2 June 2008 Accepted 4 June 2008 Available online 19 June 2008 Keywords: A. Textile composite A. Fabric/textiles B. Multi-scale modelling B. Porosity/voids E. Resin transfer moulding (RTM) abstract The permeability of textile reinforcements is a crucial input for the simulation of the impregnation stage of a composite material fabrication process. In this paper, we present a fast and accurate simulation method for the permeability of a textile reinforcement, based on a finite difference discretisation of the Stokes equations. Results for single layer, multi-layer and sheared models are discussed. The influ- ence of intra-yarn flow and periodic or wall boundary conditions are considered. We compare the numer- ically computed permeability values with experimental data. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The design of a mould for the production of composite parts is still a trial- and error process, or based on accumulated experience. This is however, expensive and waste producing. More and more, the mould filling stage of the resin transfer moulding process is simulated with software tools like PAM-RTM [1] or LIMS [2]. These tools require the input of the permeability of the textile reinforce- ment, not only for the straight textile, but also for the draped tex- tile which is sheared locally. Analytical formulas for the computation of the permeability of porous media such as textiles have been presented by several authors (Table 1). A drawback of analytical formulas, like the ones from Gebart [3], Berdichevski [4] and Phelan [5] is that they are only valid for simplified textile models. Still, these formulas are ap- plied for validation of simulation software and for the computation of the intra-yarn permeability [6]. The permeability can also be determined by numerical simulation of the fluid flow through a textile model and the subsequent use of Darcy’s law. In order to have a fast permeability predicting method, Long et al. reduce the 3D fluid problem to a simplified 2D model [7]. This Grid aver- age approach is well suited for parametric studies, however, it is not clear for which type of textile structures the method gives suf- ficiently accurate predictions of the permeability [8]. Accurate pre- dictions can be obtained by solving the 3D Navier–Stokes or Stokes equations or by solving an equivalent lattice Boltzmann model. Simulation tools based on a lattice Boltzmann model use a regular grid and avoid the difficult mesh generation. However, in order to be useful for parametric studies, the calculation of the permeability must be accurate and fast, which is not the case with the available lattice Boltzmann software [9]. Direct solution of the Navier– Stokes or Stokes equations can be done by a finite element (FE) or finite difference (FD) approach. FE simulation tools which work on a non-structured mesh have the advantage that the geometry can be meshed accurately, but the disadvantage that they are not suited for automatic permeability computations since these solvers require the mesh generation of the fluid region between the yarns of the textile. Authors do not mention problems in that regard, however, we are not aware of publications with results for realistic volume fractions, where the textile model has sharper edges and thus for which the generation of an appropriate mesh is difficult [10–12]. We employ a three-dimensional FD solver: it works on a regular grid but more acceleration techniques for the resulting partial dif- ferential system of equations are available than for the lattice Boltzmann method. For the creation of the textile model, we use the WiseTex software [15–17]. WiseTex implements a generalised description of the internal structure of textile reinforcements on the unit cell level. The WiseTex models are the input for our per- meability predicting software FlowTex. In this paper, we present a mathematical model to predict the permeability and the numerical methods to solve the resulting equations. We validate the results of the simulations with experi- 0266-3538/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2008.06.010 * Corresponding author. Tel.: +32 16 327835; fax: +32 16 327996. E-mail address: bart.verleye@cs.kuleuven.be (B. Verleye). Composites Science and Technology 68 (2008) 2804–2810 Contents lists available at ScienceDirect Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech