Modeling the structure-permeability relationship for woven fabrics

Xiao, Xueliang (2012) Modeling the structure-permeability relationship for woven fabrics. PhD thesis, University of Nottingham.

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The performance of woven fabric in many technical applications, such as airbags or reinforced composites, relates to fabric through-thickness permeability. A unified analytical model for woven fabric through-thickness permeability is proposed. It involves flow through gaps between yarns and within the yarns in terms of fabric porosity. The yarn permeability is a combination of flow along and transverse to unidirectional fibres. It is a function of fibre radius, fibre volume fraction, fibre array and crimp angle of interwoven yarns. The gap permeability is developed based on viscous and incompressible Hagen-Poiseuille flow in the gaps at low R_e values. The gap is simplified as a smooth fluid channel at the centre with slowly varying circular cross-section. The shape of the channel is approximated by a parabolic function. Volumetric flow rate is formulated as a function of pressure drop and flow channel geometry for the gap. The gap permeability is calculated thereafter according to Darcy’s law.

For a woven fabric subjected to a high pressure load, an energy-based model is developed to predict the fabric out-of-plane deformation using minimum energy theory and an isotropic assumption for woven fabric. The model can predict the fabric maximum displacement and corresponding deflected profile across a diameter given a pressure load. The fabric deflection can be used to obtain the fabric elongation (strain) which results in the change of gap size, yarn width, yarn shape and fabric thickness in loose fabric (clear gaps between yarns) and the change of fibre volume fraction and crimp angle in tight fabric (overlapping yarns). The deformed fabric permeability is calculated by the unified permeability model based on the assumptions of the variation of geometric factors with deformation.

If a woven fabric is subjected to a high decreasing pressure drop by air discharge, the fabric permeability is obtained by fitting pressure history and corresponding flow velocity using the Forchheimer equation. A nonlinear relationship is found between the pressure and velocity where the corresponding permeability is also called the dynamic permeability. The high pressure causes the shape of flow streamlines to vary in the gap between yarns (viewed as a converging-diverging duct). This flow behaviour is modelled by adding a non-Darcy term to Darcy’s law according to continuity theory and the Bernoulli equation. Therefore, a predictive Forchheimer equation is given for flow behaviour in a woven fabric based on the fabric geometry, structure and flow situation.

The developed analytical models were verified by CFD simulations and experiments in this thesis. The comparisons showed good agreements. Sensitivity studies were conducted to understand the effects of geometric factors and mechanical properties on the fabric deformation and permeability. In this thesis, two pieces of equipment in particular were introduced for measuring the fabric dynamic permeability and fabric out-of-plane deformation. The measurements agreed well with their corresponding analytical predictions. Finally, the comparison of fabric deformation and non-Darcy flow showed the importance of fabric deformation in affecting the final fabric permeability.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Long, A.L.
Zeng, X.
Subjects: T Technology > TS Manufactures
Faculties/Schools: UK Campuses > Faculty of Engineering > Department of Mechanical, Materials and Manufacturing Engineering
Item ID: 12895
Depositing User: EP, Services
Date Deposited: 11 Apr 2013 11:02
Last Modified: 13 Oct 2017 20:08

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