Air Permeability of Woven Fabrics. R. Tugrul OGULATA Cukurova University Engineering and Architecture Faculty, Adana-Turkey ABSTRACT

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1 Air Pereability of Woven Fabrics R. Tugrul OGULATA Cukurova University Engineering and Architecture Faculty, Adana-Turkey ABSTRACT Volue 5, Issue 2, Suer6 is an iportant property for wovens and it depends on any paraeters of the fabric. Thus, a theoretical deterination is highly coplex and difficult in relating the paraeters to the air pereability. Therefore, establish of the air pereability is usually ade experientally. In this study, it has been attepted to establish a siple theoretical odel for the air pereability of woven fabrics. For the purpose, a capillary odel of porous systes on D Arcy s law was used, and theoretical values were investigated. Keywords:, woven, fabric structure, warp and weft yarn. Introduction The air pereability is a very iportant factor in the perforance of soe textile aterials. Especially, it is taken into consideration for clothing, parachutes sails, vacuu cleaners, fabric for air bags and industrial filter fabrics. The air pereability is ainly dependent upon the fabric s weight and construction (thickness and porosity). Woven fabrics are produced by interlacing warp and weft yarns. The warp lies along the length of the fabric whereas the weft (or filling) lies across the width. Every warp yarn is separated fro all the others. Thus, the warp consists of a ultitude of separate yarns fed to the weaving apparatus. On the other hand, the weft yarn is usually laid into the fabric, one length at a tie [1]. There are voids between weft and warp yarns in the fabric. The void volue within 1 a textile fabric plays a ajor role in a variety of consuer and industrial applications, including apparel cofort, flaability, theral insulation efficiency, barrier fabric perforance, and the precision of filter edia [2]. The void volue in woven textile fabrics causes air pereability. The air pereability of a textile fabric is deterined by the rate of air flow through a aterial under a differential pressure between the two fabric surfaces [3]. The prescribed pressure differential is 1 of water [4,5]. The air pereability of a fabric is influenced by several factors: the type of fabric structure, the design of a woven, the nuber of warp and weft yarns per centieter (or inch), the aount of twist in yarns, the size of the yarns and the type of yarn structure [6]. Therefore, establishing a ore coplex theory expressing the air pereability related to all fabric paraeters will bring out Volue 5, Issue 2,Suer 6

2 difficulties. To siplify the case and close to the ai, soe iportant paraeters such as the pore in the fabric were taken into account in calculation the air pereability. Three factors are ainly considered related to the pores in the fabrics. Cross-sectional area of each pore, depth of each pore or the thickness of the fabric and the nuber of pores per unit area or the nuber of warp and weft threads per unit area. So, in this study, these paraeters are considered to develop a siple theoretical approach for the air pereability, exaining a plain woven fabric, non-anufactured but iagined, i.e. assuing that the warp yarn count and density are N and ends/c respectively varying the weft yarn count. The results of odel applications based on the assued paraeters of the iagined fabric are given and discussed in the end of the paper. volue of fabric. The porous are by voids between weft and warp yarns in the fabrics. The air passes through the pores fro the surface of the fabric. The air pereability is defined as the volue of air in illiliters which is passed in one second through 1 s 2 of the fabric at a pressure difference of 1 head of water [5]. A woven fabric structure (plain woven) is shown in figure 1 and the crosssectional fabric structure is shown in figure 2. During the transport of the air through the porous of woven fabrics part of the energy of the air is used to overcoe the friction of the fluid on the fabric and the rest to surount the inertia forces. When the size of the pores decreases, the fluid friction of the fabric increases [7]. Deterination of air pereability for plain woven The woven textile fabrics have a porous structure. The porosity is defined by the ratio of free space to fiber in a given A c d we b d wa a Figure 1. Plain woven fabric structure 2 Volue 5, Issue 2,Suer 6

3 h weft thread warp thread Figure 2. Cross-sectional fabric structure The dependence of the friction coefficient f on the Reynolds Nuber Re for lainar and turbulent flow is described by the Blasius equation [8]; f n = λ.re (1) where λ is the coefficient of lainar or turbulent flow, n is a coefficient indicating the flow regie. Lainar flow: λ = 64, n=1 Turbulent flow: λ =.3164, n=. The type of flow depends on Reynolds nuber. The Reynolds nuber represents the ratio of inertia force to viscous force. This result iplies that viscous forces are doinant for sall Reynolds nubers and inertia forces are doinant for large Reynolds nubers [8]. The Reynolds nuber is used as the criterion for deterining the change fro lainar to turbulent flow. U.d Re = h (2) ν Where U is the ean flow velocity, d h is the hydraulic diaeter. The hydraulic diaeter is defined by [8], d = h 4.A c P (3) where A c is the cross-sectional area of a pore (figure 1) and P is the wetted perieter of a pore. The pressure drop of the flow through a duct over the thickness 3 of the fabric is related to the friction factor f by the following expression [9]. 2 h U P = f? (4) d 2 h where h is the thickness of the fabric, ρ is the air density. For siple woven structures, h depends on the structure phase d<h<2d (Figure 2, It is accepted d wa =d we =d) [7]. In this study, it is taken h=1,5.d. As known, the length of air flow paths through a fabric is effected upon air pereability. The woven fabric is porous structure. For this reason, the air velocity in pores ust be taken into consideration [7], U = U e (5) where U is the air velocity through pores, ε is rate of void area. Porosity of a fabric is defined by the ratio of free space to fiber in a given volue of fabric [1]. It ay be written as; e =. A c A f (6) where A f is the surface area of the fabric, is the nuber of pores in the unit fabric deterined by the warp and weft densities as; =. (7) wa we Volue 5, Issue 2,Suer 6

4 where we is the nuber of weft and wa is the nuber of warp in the unit fabric. The air velocity through pores of the fabric has not usually a high value. Therefore, the fluid flow in the pores is lainar flow. For non circular ducts, the turbulent flow occurs for Re>2. For this reason, the ean air velocity through one pore can be rewritten fro equation (1) and (4) as: U 2 h = (d 32. η.h).?p (8) The flow rate of the air for the fabric with porous aterial Q becoes Q =.A.U (9) c The cross-sectional area of a pore is given by [8] 2 p.d A = h c 4 (1) Thus, equation (9) can be rewritten as; Q =.(p.d 4 h /128.?.h) (11) e Here the hydraulic diaeter of a pore (d h ) is calculated by eq. (3). Hence, it needs the deterined cross-sectional area and perieter of a pore. The values of A c and P can be deterined as follows (see also figure 1) [11]. L a = d wa (12) wa L b = d we (13) we A c = a.b (14) P = 2(a + b) (15) where d wa is diaeter of warp threads and d we is diaeter of weft threads. As known, the yarns in the structure of fabric have not a sooth surface and a solid construction. There are a lot of eptiness in the yarns. Hence the crosssectional area of the pore is increased alost %. Results and Discussions In this study, the theoretical odel can be used to calculate the air pereability of woven fabrics. The construction factors and finishing techniques affects the air pereability. It is influenced by several factors such as the type of fabric structure, the design fabric density, the aount of twist in yarns, the size of the yarns, the type of yarn structure, the size of the interstices in the fabric and etc. [6]. The theoretical results are given in figures 3-5. The specific gravity value used was 1.5 gr/c 3 for cotton [12], and dynaic viscosity of the air value taken Pa.s [13] in the theoretical calculations. 4 Volue 5, Issue 2,Suer 6

5 Nuber of weft yarns per c Weft No(N) 5 Figure 3a. The variations of the air pereability of the woven with the nuber of weft yarns per centieter for different weft nuber (Warp no: N, Nuber of warp yarns per c:) Nuber of weft yarns per c Weft No (N) 5 Figure 3b. The variations of the air pereability of the woven with the nuber of weft yarns per centieter for different weft nuber (Warp no: N, Nuber of warp yarns per c: ). 5 Volue 5, Issue 2,Suer 6

6 8 Air Nuber of weft yarns per c Weft No (N) 5 Figure 3c. The variations of the air pereability of the woven with the nuber of weft yarns per centieter for different weft nuber (Warp no: N, Nuber of warp yarns per c:) Nuber of weft yarns per c Nuber of warp yarns per c Figure 4a. The variations of the air pereability of the woven with the nuber of weft yarns per centieter for different warp nuber (Warp no: N, Weft no: N). 6 Volue 5, Issue 2,Suer 6

7 Nuber of warp yarns per c Nuber of weft yarns per c Figure 4b. The variations of the air pereability of the woven with the nuber of weft yarns per centieter for different warp nuber (Warp no: N, Weft no: N) Weft nuber Nuber of warp yarns per c Figure 5a. The variation of the air pereability of the woven with the weft nuber for different the nuber of warp yarns per centieter (Warp no: N, Nuber of weft yarns per c: ). 7 Volue 5, Issue 2,Suer 6

8 Warp nuber Nuber of warp yarns per c Figure 5b. The variation of the air pereability of the woven with the warp nuber for different the nuber of the warp yarns per centieter (Weft no: N, Nuber of weft yarns per c: ) ,12,15,17,2,23,26,28,31,33,36,39 Porosity rate Nuber of warp yarns per c Figure 5c. The variation of the air pereability of the woven with the porosity rate for different the nuber of the warp yarns per centieter (Warp no: N, Weft no: N). The variations of the air pereability of the woven with the nuber of filling (or weft) yarns per centieter (weft density) for different filling nuber are shown in figures 3a,b,c. It can be seen that, when the nuber of filling yarns per centieter increases, the air pereability of the woven decreases. The higher the values of filling nuber cause decreases the air pereability of the woven. As known, increasing nuber of warp yarn per 8 centieter (warp density) results a tightly woven structure. So it is thought that the air pereability of the woven is reduced. The variations of the air pereability of the woven with the nuber of filling yarns per centieter for different warp nuber are shown in figures 4a,b. As seen the figures, the air pereability of the woven decrease with an increase for the nuber of filling yarns per Volue 5, Issue 2,Suer 6

9 centieter. Also the increase in the nuber of warp yarns per centieter leads to a decrease for the air pereability. An increase for the nuber of warp and weft yarns per centieter decrease the porous rate. This decreases the air pereability. Figure 5a shows the variation of the air pereability with the filling nuber for different. As seen, the air pereability increases with an increase in the filling nuber. It is also decreased with the higher the values of the nuber of filling yarns per centieter. Figure 5b shows the variation of air pereability with the warp nuber (warp count) for different the nuber of the warp yarns per centieter (warp density). As seen in the figure, the increase in the warp nuber increases the air pereability of the woven. Also the higher the values of the nuber of the warp yarns per centieter cause decrease the air pereability. The pereability and porosity are strongly related to each other. If a fabric has very high porosity, it can be assued that it is pereable. A fabric with zero porosity can be assued to have a zero pereability in theory [1]. The variation of the air pereability with the porosity rate for different the nuber of the warp yarns per centieter is shown in figure 5c. It is seen that the air pereability of the woven increases with the porosity rate. On the other hand, the increase in the nuber of warp yarns per centieter leads to an decrease the air pereability of the woven. Noenclature A c cross-sectional area of a pore [ 2 ] A f surface area of the fabric [ 2 ] d yarn diaeter [] d h hydraulic diaeter of a pore [] d wa diaeter of warp thread [] d we diaeter of weft thread [] f friction coefficient [-] h thickness of fabric [] 9 L width and length of fabric [] nuber of pores per squrae wa nuber of warp per centieter we nuber of weft per centieter n coefficient indicating the flow regie [-] P wetted perieter of a pore [] Re Reynolds nuber [-] Q total flow rate of the air [ 3 /s] U air flow velocity [/s] U air ean flow velocity [/s] λ the coefficient of lainar and turbulent flow ρ air density [kg/ 3 ] ε rate of void area [-] ν kineatic viscosity of the air [ 2 /s] η dynaic viscosity of the air [Pa.s] P Pressure drop [Pa] Refere nces [1] Lord P.R. and Mohaed M.H., Weaving: Conversion of yarn to fabric, Merrow Publishing Co. Ltd. England, [2] Epps H.H. and Leonas K.K., The relationship between porosity and air pereability of woven textile fabrics, Journal of testing and evaluation, JTEVA, Vol., No.1, , January [3] Epps H.H., Prediction of single-layer fabric air pereability by statistical odeling, Journal of testing and evaluation JTEVA, Vol. 24, No.1, 26-31, January [4] Method of deterining the air pereability of textile fabrics TS- 391, Turkish Standards, Turkish Standards Institution (TSE)-Turkey, April [5] Saville B.P., Physical testing of textiles, The Textile Institute, Woodhead publishing liited, Cabridge-England, 3. Volue 5, Issue 2,Suer 6

10 [6] Joseph M.L., Introductory textile science, Fifth edition CBS College publishing, USA, [7] Kulichenko A.V. and Langenhova L.V., The resistance to flow transission of porous aterials, J. Text. Inst. Vol.83, No.1, , [8] Bayazitoglu Y. And Özisik M.N., Eleents of heat transfer, McGraw- Hill Book Copany, [9] Holan J.P., Heat transfer, Seventh edition, McGraw-Hill Book Copany, [1] Dunn M.W., Biotextiles:Fluid flow odeling, fluids.htl, 5. [11] Ogulata R.T. and Koç E., A Theoretical Model for Air Pereability of Woven Fabrics, A.M.S.E., Association for The Advanceent of Modeling & Siulation Techniques in Enterprises, Vol. 7, No: 8, 39-48, 1. [12] Morton W.E. and Hearle J.W.S., Physical properties of textile fibres, The Textile Institute, Manchester, [13] Gebhart B., Heat conduction and ass diffusion, McGraw-Hill Book Copany, Volue 5, Issue 2,Suer 6