On the variability of mesoscale permeability of a 2/2 twill carbon fabric induced by variability of the internal geometry

Abstract

This paper incorporates geometric variability in the determination of permeability, using distributions and spatial correlations of yarn spacing, width and thickness and distortions of yarn centrelines. Variability of a 2/2-twill carbon fabric geometry over a region of ten-by-ten unit cells is characterized based on representation of the yarn path deviations using Markov chains and the correlations between the deviations in the neighbouring yarns using Series Expansion approach. The Stokes equation is solved for the generated stochastic unit cells to predict inter-yarn permeability of each unit cell in principal directions. There is a good agreement between the calculated mean permeability and the values in the Permeability Benchmark II. The predictions show permeability varies over the medium as a function of inter-yarn gaps. Permeability variations show a correlation length of circa 20mm, the size of two-unit cells. Permeability values in x direction have no evident correlation with those in y direction.