Through-thickness permeability of woven fabric under increasing air pressure: Theoretical framework and simulation

Many technical applications of woven fabric are subject to increasing high pressure from air transport through the fabric. The through-thickness permeability (TP) of woven materials exhibits a dynamic response to increased air pressure. This paper presents an analytical model for predicting the steady TP of woven fabric. The approach was based on Darcy’s law and the Poiseuille equation, using the flow boundary of an idealized plain-weave unit cell. The unit cell model consists of a gradual converging-diverging (GCD) duct with a rectangular cross-section. Further, the dynamic TP of the GCD duct was established analytically as a function of increasing pressure, which correlates to the separation of air flow from the GCD duct wall. Air flow separation from the duct wall led to a quadratic relationship between the increasing pressure and air flow velocities. This dynamic TP and air flow nonlinearity were simulated numerically in the computational fluid dynamics solver CFX. Five GCD ducts under increasing air pressure were analyzed numerically and analytically. The comparison showed good agreement between the proposed analytical model and the CFD simulation, with a maximum error up to 12%. A sensitivity study showed that an increase in porosity or a decrease in the thickness of weave materials could result in a larger dynamic TP value.