Nabovati, A,
Llewellin, EW & Sousa, ACM (2009). A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method.
Composites Part A: Applied Science And Manufacturing 40(6-7): 860-869.
Author(s) from Durham
Abstract
Fluid flow analyses for porous media are of great importance in a wide
range of industrial applications including, but not limited to, resin
transfer moulding, filter analysis, transport of underground water and
pollutants, and hydrocarbon recovery. Permeability is perhaps the most
important property that characterizes porous media; however, its
determination for different types of porous media is challenging due
its complex dependence on the pore-level structure of the media. In the
present work, fluid flow in three-dimensional random fibrous media is
simulated using the lattice Boltzmann method. We determine the
permeability of the medium using the Darcy law across a wide range of
void fractions (0.08 <= phi <= 0.99) and find that the values for the
permeability that we obtain are consistent with available experimental
data. We use our numerical data to develop a semi-empirical
constitutive model for the permeability of fibrous media as a function
of their porosity and of the fibre diameter. The model, which is
underpinned by the theoretical analysis of flow through cylinder arrays
presented by [Gebart BR. Permeability of unidirectional reinforcements
for RTM. J Compos Mater 1992: 26(8): 1100-33], gives an excellent fit
to these data across the range of phi. We perform further simulations
to determine the impact of the curvature and aspect ratio of the fibres
on the permeability. We find that curvature has a negligible effect,
and that aspect ratio is only important for fibres with aspect ratio
smaller than 6:1, in which case the permeability increases with
increasing aspect ratio. Finally, we calculate the permeability tensor
for the fibrous media studied and confirm numerically that, for an
isotropic medium, the permeability tensor reduces to a scalar value.
