Xueliang Xiao Prof. Andrew Long Dr. Xuesen Zeng Modelling the Structure-Permeability Relationship for Woven Fabrics Division of Materials, Mechanics and Structures Faculty of Engineering

What degree did I do before my PhD? What made I choose this topic? Four years, Bachelor's degree on Textile Science and Engineering(China) Two years, Masters study on Surface Coating and Nano Technique(China) PhD, come to a new field, original topic “Modelling impact performance of wearable airbag for fall protection”. (UK) Where to start? How to start? What methodology? Keywords in the topic? Challenging…… Requirement: Low gas permeability Main jobs on: woven fabric, permeability, fabric structure, analytical modelling 2 Division of Materials, Mechanics and Structures Faculty of Engineering

Summary of main work (discoveries, contributions) during PhD study An analytical static permeability model developed without fitting factor for woven fabric in through-thickness, excellent accuracy! Studied fabric dynamic permeability experimentally, compared it with corresponding fabric static permeability and found their difference; Modelled fabric deformation under high pressure load and its effect on the fabric through-thickness permeability; Studied the nonlinear relationship of pressure and flow velocity when high speed flow through the ‘fabric’ structure; Tried to understand which effect has more contribution on the fabric permeability? fabric deformation or nonlinear flow; 3 Division of Materials, Mechanics and Structures Faculty of Engineering

4 Fabric static through-thickness permeability (unit cell level) ∆P Ohm’s Law K is similar with R Laminar Flow Darcy’s law for low Re values The Forchheimer equation for high Re values Where,Kg ? & Ky ?

5 Previous model The Gebart model The Kulichenko model Current model Yarn permeability Gap permeability Fabric static through-thickness permeability (unit cell level)

6 Yarn permeability model Yarn permeability θ Flow parallel and perpendicular to filaments Fabric static through-thickness permeability (unit cell level) Matrix transpose

7 Fabric static through-thickness permeability (unit cell level) Gap permeability model x y Parabola fitted gap cross section Hagen-Poiseuille flow Gap flow(Gradual converging-diverging flow channel) (straight flow channel)

8 3D woven fabric--- static through-thickness permeability K 1 h1h1 ∆P 1 KiKi hihi ∆P i KnKn hnhn ∆P n ∆P, H μ, v homogenization Real 3D fabric by CT scanning

9 Fabric dynamic through-thickness permeability High initial pressure impact + fabric deformation Transient pressure

10 Fabric deformation under high pressure load Dial gauge Vernier caliper Deformed fabric under high pressure load

11 Fabric deformation under high pressure load r z a’ D:bending rigidity E: Young’s modulus

12 Effect of fabric deformation on its permeability Ly 2a’ Input new predicted geometric parameters into yarn and gap permeability models to get deformed fabric permeability values Assume all yarns have the same ε value

13 Modelling nonlinear flow in gaps of woven fabric Without fabric deformation, both increased pressure and flow velocity display a nonlinear relationship. ∆P V Nonlinear flow based on the Navier-Stokes Equation (body force is 0) x y

14 Modelling nonlinear flow in gaps of woven fabric A1V1P1A1V1P1 A 2 V 2 P 2 BC If C=8, the equation is for a circular tube; If, the equation is for gradual converging-diverging flow channel. The Forchheimer Eq. ABC CFD simulation Forchheimer style Eq. for woven fabric

15 Nonlinear flow model with fabric deformation Fabric U 2 Future research based on current models R d, a d and λ d can be predicted by the deformation model in Chapter 5. 1.To develop rectangular gap permeability model. 2.To study fluid flow in twisted yarns (staple fibres). 3.To simulate flow behaviour in real woven fabric by CFD. 4.To understand why Forchheimer factors varying under high Re values 5.To develop a nonlinear flow model for yarns or tight fabrics.

16 Division of Materials, Mechanics and Structures Faculty of Engineering