Through-thickness permeability prediction of three-dimensional multifilament woven fabrics

Abstract

The lattice Boltzmann method (LBM) is used to investigate the dual-scale problem of fluid flow through three-dimensional multifilament woven fabrics. Such fabrics are characterized by two distinct length scales: the thickness of a single filament and the thickness of a bundle of filaments, known as yarn. The yarn’s thickness is typically two orders of magnitude greater than that of a single filament. The inter-yarn and intra-yarn spaces, through which fluid may flow, are also of two distinct length scales. The direct simulation of fluid flow in multifilament woven fabrics involves the simultaneous resolution of the flow field in the inter-yarn and intra-yarn pores; the LBM is well-suited to modelling such geometrically-complex fluid flow. The methodology is first validated against published analytical results for two-dimensional transverse fluid flow through hexagonal arrays of cylinders; the agreement is excellent. Fluid flow in two-dimensional representations of multifilament woven fabrics is also simulated, and the results are compared against those obtained following Papathanasiou’s approach (2001, Int. J. Multiphase Flow, 27: 1451–1461); the agreement is very good. The model is then used to determine the through-thickness permeability of three-dimensional woven fabrics by direct simulation of the fluid flow. The geometry used for the three-dimensional simulations resembles bi-axial, plain woven fabrics. The inter-yarn porosity (‘weave porosity’, ϕw) and the intra-yarn porosity (‘yarn porosity’, ϕy) are systematically varied in the range 0.3⩽ϕw⩽0.65 and 0⩽ϕy⩽0.80, respectively. These parameters control the weave and yarn permeabilities (Kw and Ky). The influence of these parameters on the effective permeability of the fabric, Kp, is quantified and discussed in terms of the fabric structure. Our results are analyzed following the approach developed by Papathanasiou (2001, Int. J. Multiphase Flow, 27: 1451–1461) for two-dimensional structures. The semi-empirical relationship between the fabric permeability and the weave and yarn permeabilities proposed in that study provides an excellent fit to the data produced by our three-dimensional simulations, with only minor adjustment to the fitting parameters. The parameterized relationship we obtain allows the through-thickness permeability of a three-dimensional woven fabric to be predicted if the weave and yarn permeabilities are known.