An analytical model for through-thickness permeability of woven fabric

Woven fabric permeability is relevant to many applications, such as airbags, textile composites processing, paper making and air and water filtration. This paper proposes an analytical model to predict through-thickness fabric permeability based on viscous and incompressible Hagen-Poiseuille flow. The flow is modeled through a unit cell of fabric with a smooth fluid channel at the center with slowly varying cross-section. The channel geometry is determined by yarn spacing, yarn cross-section and fabric thickness. The shape of the channel is approximated by a parabolic function. Volumetric flow rate (Q) is formulated as a function of pressure drop and flow channel geometry for woven fabric. The permeability (K) is calculated thereafter according to Darcy's law. The air permeability of nine different fabrics has been measured to verify the analytical model. A sensitivity study was carried out to understand how geometric parameters influence the fabric permeability. The analytical model shows very close agreement with the experimental data: within 5% for most fabrics. The sensitivity study on permeability indicates the importance of flow channel geometry in obtaining accurate predictions.