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Air Permeability of Woven Fabrics

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Air Permeability of Woven Fabrics Volume 5, Issue 2, Summer2006 Air Permeability of Woven Fabrics R. Tugrul OGULATA Cukurova University Engineering and Architecture Faculty, Adana-Turkey ABSTRACT Air permeability is an important property for wovens and it depends on many parameters of the fabric. Thus, a theoretical determination is highly complex and difficult in relating the parameters to the air permeability. Therefore, establish of the air permeability is usually made experimentally. In th is study, it has been attempted to establish a simple theoretical model for the air permeability of woven fabrics. For the purpose, a capillary model of porous systems on D’Arcy’s law was used, and theoretical values were investigated. Keywords: Air permeability, woven, fabric structure, warp and weft yarn. Introduction a textile fabric plays a major role in a variety of consumer and industrial applications, The air permeability is a very important including apparel comfort, flammability, factor in the performance of some textile thermal insulation efficiency, barrier fabric materials. Especially, it is taken into performance, and the precision of filter consideration for clothing, parachutes sails, media [2]. vacuum cleaners, fabric for air bags and industrial filter fabrics. The air permeability The void volume in woven textile fabrics is mainly dependent upon the fabric’s causes air permeability. The air permeability weight and construction (thickness and of a textile fabric is determined by the rate porosity). of air flow through a material under a differential pressure between the two fabric Woven fabrics are produced by interlacing surfaces [3]. The prescribed pressure warp and weft yarns. The warp lies along differential is 10 mm of water [4,5]. the length of the fabric whereas the weft (or filling) lies across the width. Every warp The air permeability of a fabric is influenced yarn is separated from all the others. Thus, by several factors: the type of fabric the warp consists of a multitude of separate structure, the design of a woven, the number yarns fed to the weaving apparatus. On the of warp and weft yarns per centimeter (or other hand, the weft yarn is usually laid into inch), the amount of twist in yarns, the size the fabric, one length at a time [1]. of the yarns and the type of yarn structure [6]. Therefore, establishing a more complex There are voids between weft and warp theory expressing the air permeability yarns in the fabric. The void volume within related to all fabric parameters will bring out Article Designation: Refereed 1 JTATM Volume 5, Issue 2,Summer 2006 difficulties. To simplify the case and close to volume of fabric. The porous are by voids the aim, some important parameters such as between weft and warp yarns in the the pore in the fabric were taken into fabrics. The air passes through the pores account in calculation the air permeability. from the surface of the fabric. Three factors are mainly considered related to the pores in the fabrics. Cross-sectional The air permeability is defined as the area of each pore, depth of each pore or the volume of air in milliliters which is thickness of the fabric and the number of passed in one second through 100 s mm2 pores per unit area or the number of warp of the fabric at a pressure difference of 10 and weft threads per unit area. mm head of water [5]. So, in this study, these parameters are A woven fabric structure (plain woven) considered to develop a simple theoretical is shown in figure 1 and the cross- approach for the air permeability, examining sectional fabric structure is shown in a plain woven fabric, non-manufactured but figure 2. During the transport of the air imagined, i.e. assuming that the warp yarn through the porous of woven fabrics part count and density are Nm20 and 20 ends/cm of the energy of the air is used to respectively varying the weft yarn count. overcome the friction of the fluid on the The results of model applications based on fabric and the rest to surmount the inertia the assumed parameters of the imagined forces. When the size of the pores fabric are given and discussed in the end of decreases, the fluid friction of the fabric the paper. increases [7]. Determination of air permeability 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 Ac dwe b dwa a Figure 1. Plain woven fabric structure Article Designation: Refereed 2 JTATM Volume 5, Issue 2,Summer 2006 h weft thread warp thread Figure 2. Cross-sectional fabric structure The dependence of the friction coefficient of the fabric is related to the friction f on the Reynolds Number Re for laminar factor f by the following expression [9]. and turbulent flow is described by the Blasius equation [8]; h U 2 DP = f ? m (4) d 2 f = l.Re -n (1) h where h is the thickness of the fabric, r where l is the coefficient of laminar or is the air density. For simple woven turbulent flow, n is a coefficient structures, h depends on the structure indicating the flow regime. phase d<h<2d (Figure 2, It is accepted dwa=dwe=d) [7]. In this study, it is taken Laminar flow: l = 64, n=1 h=1,5.d . As known, the length of air flow Turbulent flow : l = 0.3164, n=0.25 paths through a fabric is effected upon air permeability. The type of flow depends on Reynolds number. The Reynolds number represents The woven fabric is porous structure. For the ratio of inertia force to viscous force. this reason, the air velocity in pores This result implies that viscous forces are must be taken into consideration [7], dominant for small Reynolds numbers and inertia forces are dominant for large Reynolds numbers [8]. The Reynolds U = Um e (5) number is used as the criterion for determining the change from laminar to where Um is the air velocity through turbulent flow. pores, e is rate of void area. Porosity of a fabric is defined by the ratio of free space U .d to fiber in a given volume of fabric [10]. Re = m h (2) It may be written as; n e = m. Ac Af (6) Where Um is the mean flow velocity, dh is the hydraulic diameter. The hydraulic diameter is defined by [8], where Af is the surface area of the fabric, m is the number of pores in the unit fabric determined by the warp and weft d 4.A P (3) h = c densities as; where A is the cross-sectional area of a c m = m .m (7) pore (figure 1) and P is the wetted wa we perimeter of a pore. The pressure drop of the flow through a duct over the thickness Article Designation: Refereed 3 JTATM Volume 5, Issue 2,Summer 2006 where mwe is the number of weft and mwa L a = - d (12) is the number of warp in the unit fabric. m wa wa The air velocity through pores of the L (13) fabric has not usually a high value. b = - d we m we Therefore, the fluid flow in the pores is laminar flow. For non circular ducts, the A a.b (14) turbulent flow occurs for Re>2300. For c = this reason, the mean air velocity through one pore can be rewritten from equation P = 2(a + b) (15) (1) and (4) as: where dwa is diameter of warp threads and 2 U = (d 32.h.h) .?P (8) dwe is diameter of weft threads. m h The flow rate of the air for the fabric with As known, the yarns in the structure of porous material Q becomes fabric have not a smooth surface and a solid construction. There are a lot of emptiness in the yarns. Hence the cross- Q = m.A c .U (9) sectional area of the pore is increased almost 25%. The cross-sectional area of a pore is given by [8] Results and Discussions p.d 2 In this study, the theoretical model can be A = h (10) c 4 used to calculate the air permeability of woven fabrics. The construction factors and finishing techniques affects the air Thus, equation (9) can be rewritten as; permeability. It is influenced by several m 4 factors such as the type of fabric Q = .(p.dh /128.?.h) (11) e structure, the design fabric density, the amount of twist in yarns, the size of the Here the hydraulic diameter of a pore yarns, the type of yarn structure, the size (dh) is calculated by eq. (3). Hence, it of the interstices in the fabric and etc. [6]. needs the determined cross-sectional area and perimeter of a pore. The values of Ac The theoretical results are given in and P can be determined as follows (see figures 3-5. The specific gravity value also figure 1) [11]. used was 1.5 gr/cm3 for cotton [12], and dynamic viscosity of the air value taken 18.10-6 Pa.s [13] in the theoretical calculations. Article Designation: Refereed 4 JTATM Volume 5, Issue 2,Summer 2006 140 /s] 2 120 Weft No(Nm) /cm 3 100 20 [cm 30 80 40 60 50 60 40 20 Air permeability 0 20 22 24 26 28 30 32 34 36 38 40 Number of weft yarns per cm Figure 3a. The variations of the air permeability of the woven with the number of weft yarns per centimeter for different weft number (Warp no: 20 Nm, Number of warp yarns per cm:20).
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