Permeability Estimation with the Method of Cells

Abstract

The Method of Cells (MC) is used to predict the permeability of preforms regardless of their architecture, and to study the effect of disturbances during preform manufacturing on the permeability of the preform. Preforms are made up of bundles of fibers called fiber tows. Different types of preforms can be produced from the same fiber tow. In the MC, a repetitive unit cell is subdivided into subcells in such a way that there is only fiber tow or air in a subcell. The pressure field in each subcell is modeled as a second order polynomial of local coordinates. The coefficients of the polynomial are estimated using a set of equations that include governing equations, boundary conditions, continuity conditions and constitutive equations. Subsequently, the flow field in the subcell is determined. The pressure is averaged at the faces of the unit cell and the pressure gradient is calculated assuming a linear pressure profile across the unit cell in all three dimensions. The velocity is averaged over the unit cell volume. Finally, overall permeability values are estimated using Darcy’s Law. The geometry of the preform varies to some extent due to several effects during production or processing; or there might be some imperfections in the preform, such as improper stitches. The permeability is influenced by both of these disturbances. By varying the properties of the subcells in the model, the effect of these disturbances on the permeability can be evaluated.