Semi‐Analytical Formulation of the Effective Permeability of a Dual‐Scale Bi‐Directional Fabric

Modeling flow through dual‐scale bi‐directional (BD) fabric poses significant challenges due to the relatively high permeability inter‐tow gap region adjacent to the low permeability intra‐tow region. Significant work has been done through experiments and modeling (analytical and numerical) to understand the characteristics of dual‐scale flow and permeability estimation of BD fabrics. This study proposes a closed‐form expression for the effective permeability of a BD fabric, which considers tow permeability for both warp and weft directions and inter‐tow gap permeability, as BD fabric architecture parameters, and the length of the partially saturated zone with average weft tow saturation that represents the dual‐scale flow behavior. Tow permeability was independently determined by performing experiments on a single tow, and fabric architecture parameters were determined through scanning electron microscopy. Effective permeability was computed using fabric architecture parameters and dual‐scale flow characteristics through the proposed semi‐analytical model. The comparison of the predicted permeability of the chosen BD fabric with the experimental and numerical results is encouraging. Moreover, the current study found that the average weft tow saturation is 0.41, close to the previously reported value of 0.5.