Air Permeability of Woven Fabrics

Volume 5, Issue 2, Summer2006

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

A c

dwe

dwa a

Figure 1. Plain woven fabric structure

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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

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.

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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).

/s] 2 40 Weft No (Nm) /cm 3 35 20

[cm 30

30 25 40 20 50 15 60 10 5 Air permeability 0 20 22 24 26 28 30 32 34 36 38 40

Number of weft yarns per cm

Figure 3b. 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: 30).

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/s] 7 Weft No (Nm) 2

/cm 6 20 3 5 30 [cm 4 40 50 3 60 2 1

Air 0 20 22 24 26 28 30 32 34 36 38 40 Number of weft yarns per cm

Figure 3c. 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:40).

Number of

100 warp yarns /s]

2 90 per cm

/cm 80 3 20 70 [cm

25 60 50 30 40 35 30 40 20 10 Air permeability 0 20 22 24 26 28 30 32 34 36 38 40 Number of weft yarns per cm

Figure 4a. The variations of the air permeability of the woven with the number of weft yarns per centimeter for different warp number (Warp no: 20 Nm, Weft no: 20 Nm).

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120

/s] Number of 2 warp yarns

/cm 100 3 per cm [cm 80 20 25 60 30 40 35 40 20

Air permeability 0 20 22 24 26 28 30 32 34 36 38 40 Number of weft yarns per cm

Figure 4b. The variations of the air permeability of the woven with the number of weft yarns per centimeter for different warp number (Warp no: 20 Nm, Weft no: 30 Nm).

/s] 70 Number of 2 warp yarns

/cm 60 3 per cm [cm 50 20 40 25 30 30 35 20 40 10

Air permeability 0 20 30 40 50 60 Weft number

Figure 5a. The variation of the air permeability of the woven with the weft number for different the number of warp yarns per centimeter (Warp no: 20 Nm, Number of weft yarns per cm: 30).

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80 Number of

warp yarns /s] 2 70 per cm /cm 3 60 20

[cm 50 25 40 30 35 30 40 20 10 Air permeability 0 20 30 40 50 60 Warp number

Figure 5b. The variation of the air permeability of the woven with the warp number for different the number of the warp yarns per centimeter (Weft no: 20 Nm, Number of weft yarns per cm: 30).

100

/s] Number of

2 90 warp yarns

/cm 80 3 per cm 70

[cm 20 60 50 25 40 30 30 35 20 40 10

Air permeability 0 0,12 0,15 0,17 0,2 0,23 0,26 0,28 0,31 0,33 0,36 0,39 Porosity rate

Figure 5c. The variation of the air permeability of the woven with the porosity rate for different the number of the warp yarns per centimeter (Warp no: 20 Nm, Weft no: 20 Nm).

The variations of the air permeability of centimeter (warp density) results a tightly the woven with the number of filling (or woven structure. So it is thought that the weft) yarns per centimeter (weft density) air permeability of the woven is reduced. for different filling number are shown in figures 3a,b,c. It can be seen that, when The variations of the air permeability of the number of filling yarns per centimeter the woven with the number of filling increases, the air permeability of the yarns per centimeter for different warp woven decreases. The higher the values number are shown in figures 4a,b. As of filling number cause decreases the air seen the figures, the air permeability of permeability of the woven. As known, the woven decrease with an increase for increasing number of warp yarn per the number of filling yarns per

Article Designation: Refereed 8 JTATM Volume 5, Issue 2,Summer 2006 centimeter. Also the increase in the L width and length of fabric [m] number of warp yarns per centimeter m number of pores per squrae leads to a decrease for the air mwa number of warp per centimeter permeability. An increase for the number mwe number of weft per centimeter of warp and weft yarns per centimeter n coefficient indicating the flow decrease the porous rate. This decreases regime [-] the air permeability. P wetted perimeter of a pore [m] Re Reynolds number [-] Figure 5a shows the variation of the air Q total flow rate of the air [m3/s] permeability with the filling number for U air flow velocity [m/s] different. As seen, the air permeability Um air mean flow velocity [m/s] increases with an increase in the filling l the coefficient of laminar and number. It is also decreased with the turbulent flow higher the values of the number of filling r air density [kg/m3] yarns per centimeter. e rate of void area [-] n kinematic viscosity of the air [m2/s] Figure 5b shows the variation of air h dynamic viscosity of the air [Pa.s] permeability with the warp number (warp D P Pressure drop [Pa] count) for different the number of the warp yarns per centimeter (warp density). Refe re nces As seen in the figure, the increase in the warp number increases the air permeability of the woven. Also the [1] Lord P.R. and Mohamed M.H., higher the values of the number of the Weaving: Conversion of yarn to warp yarns per centimeter cause decrease fabric, Merrow Publishing Co. Ltd. the air permeability. England, 1973.

The permeability and porosity are [2] Epps H.H. and Leonas K.K., The strongly related to each other. If a fabric relationship between porosity and air has very high porosity, it can be assumed permeability of woven textile fabrics, that it is permeable. A fabric with zero Journal of testing and evaluation, porosity can be assumed to have a zero JTEVA, Vol. 25, No.1, 108-113, permeability in theory [10]. The variation January 1997. of the air permeability with the porosity rate for different the number of the warp [3] Epps H.H., Prediction of single -layer yarns per centimeter is shown in figure fabric air permeability by statistical 5c. It is seen that the air permeability of modeling, Journal of testing and the woven increases with the porosity evaluation JTEVA, Vol. 24, No.1, rate. On the other hand, the increase in 26-31, January 1986. the number of warp yarns per centimeter leads to an decrease the air permeability [4] Method of determining the air of the woven. permeability of textile fabrics TS- 391, Turkish Standards, Turkish Nomenclature Standards Institution (TSE)-Turkey,

2 April 1974. Ac cross-sectional area of a pore [m ] 2 Af surface area of the fabric [m ] [5] Saville B.P., Physical testing of d yarn diameter [m] textiles, The Textile Institute, dh hydraulic diameter of a pore [m] Woodhead publishing limited, dwa diameter of warp thread [m] Cambridge-England, 2003. dwe diameter of weft thread [m] f friction coefficient [-] h thickness of fabric [m] Article Designation: Refereed 9 JTATM Volume 5, Issue 2,Summer 2006

[6] Joseph M.L., Introductory textile [10] Dunn M.W., Biotextiles:Fluid flow science, Fifth edition CBS College modeling, publishing, USA, 1986. http://fiberarchitects.com/biomedical/ fluids.html , 2005. [7] Kulichenko A.V. and Langenhova L.V., The resistance to flow [11] Ogulata R.T. and Koç E., A Theoretical transmission of porous materials, J. Model for Air Permeability of Woven Text. Inst. Vol.83, No.1, 127-132, Fabrics, A.M.S.E., Association for The 1992. Advancement of Modeling & Simulation Techniques in Enterprises, [8] Bayazitoglu Y. And Özisik M.N., Vol. 70, No: 8, 39-48, 2001. Elements of heat transfer, McGraw- Hill Book Company, [12] Morton W.E. and Hearle J.W.S., 1988. Physical properties of textile fibres, The Textile Institute, Manchester , [9] Holman J.P., Heat transfer, Seventh 1986. edition, McGraw-Hill Book Company, 1982. [13] Gebhart B., Heat conduction and mass diffusion, McGraw-Hill Book Company, 1993.

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