Modelling of the Through-air Bonding Process

Transcription

1 Modelling of the Through-air Bonding Process M. Hossain 1, M. Acar, Ph.D. 2, W. Malalasekera 2 1 School of Engineering, The Robert Gordon University, Aberdeen, UNITED KINDOM 2 Mechanical and Manufacturing Engineering, Loughborough University, Leicestershire, UNITED KINGDOM Correspondence to: Meis Acar, Ph.D. eail:.acar@lboro.ac.uk ABSTRACT A coputational fluid dynaics (CFD) odelling of the through-air bonding process of nonwoven fabric production is reported in this article. In the throughair process, hot air is passed through the fibrous web to heat and elt polyer fibers. Molten polyer subsequently flows to the point of contact between any two fibers to produce a bond. Two different odelling strategies are adapted to produce a coprehensive understanding of the through-air bonding process. In acroscale odelling, a CFD odel is developed treating the whole web as a porous edia in order to investigate the effect of process paraeters. Results reveal that the tie required to heat and elt the fibers decreases with the increasing porosity of the web and the velocity of hot air. The CFD odelling technique is then used to analyze the bonding process at a ore fundaental level by considering the bonding of individual fibers at icroscale. The effects of the fiber diaeter, bonding teperature and contact angle between two fibers on the bonding tie are investigated. Results show that the tie required to bond fibers is weakly related to bonding teperature and fiber diaeter. Fiber orientation angle, on the other hand, has significant effect on the progression of bond foration. INTRODUCTION The Coputational Fluid Dynaics (CFD) technique has becoe a ajor tool for the design and developent of any engineering systes involving fluid flow and heat transfer. It has been extensively used in the field of aerospace, autootive, bioedical, cheical and any other industrial applications. Its use in textile research and developent is however not very coon. There are only very few exaples of such coputational odelling in textile research and developent. Gong et al. [1] developed an experiental process for producing through-air bonded three diensional nonwoven web by applying the CFD technique. Gong et al. [2] in a subsequent article investigated the distribution of velocity, pressure and teperature inside the bonding chaber and optiized the design. Tafreshi and Pourdeyhii [3] and Tafreshi et al. [4] investigated the flow dynaics inside hydroentangling nozzles using CFD odelling. More recently, Hossain et al. [5, 6] reported a CFD odel of the airflow and heat transfer through fibrous webs as well as a siulation of the fiber bonding process. These exaples alone show that the CFD ethod can play a vital role in analyzing and iproving the nonwoven anufacturing processes. Manufacturing of nonwoven fabric begins by laying fibers to for a web. The through-air bonding process, involves passing hot air through an unbonded web to heat and elt the polyer fibers. To create a bond of sufficient strength, the web is kept at an elevated teperature for certain aount of tie, known as the dwell tie. Then, the olten polyer, aided by the reduced viscosity at high teperatures, flows to the contact point of fibers by the surface tension force. Most through-air bonded webs consist of bicoponent sheath-core type polyer fibers, while the core aterial with a higher elting point provides the structural integrity to the web whereas the sheath polyer with a lower elting point enables the bonding of the fibers together at the point of contact. Literature survey reveals that the published work on the through-air bonding process is ostly concerned with the experiental study investigating the effects of process paraeters on the properties of the nonwoven. Randall [7] reported an experiental study of the effects of process variables such as air teperature, air velocity, dwell tie, restraining and carrying esh size on the echanical properties of the through-air bonded nonwovens. Randall [8] also studied the effects of binder type, binder fiber content, web basis-weight on the product properties. Ki et al. [9] investigated experientally the foration of bond and the bonding tie for different fiber diaeters between two fibers laying orthogonal Journal of Engineered Fibers and Fabrics 1

2 to each other. Ki et al. [10] in a follow up article investigated the bond foration and developent between two fibers by using a siple coputational odel and predicted the characteristics shape. However, it failed to predict the bonding tie relationship with the fiber diaeters as observed in the experients. In the present study, the fundaental echanis of bond foration during the through-air bonding process has been investigated in greater detail using the coputational fluid dynaics technique. First a acroscale odel is developed in which the web as a whole is odelled as a porous edia. Then, a icroscale odel is developed to study the bond foration between two contacting fibers. MATHEMATICAL MODEL Macroscale Model A acroscopic forulation based on volue averaging is used in the present study. The averaged ass and oentu equations for a single doain based odel are given by Beckeran [11]: Continuity: Moentu: ( φρ a ) ρ +.( ρ uφ ) = 0 a ρ φu ) ρ ρ u u P 2 ρ μ ρ ρ + ρ ( φ. ) = φ + μ ( φu ) u a a k (1) ( (2) The last ter in the oentu equation is due to Dercy s ter representing the resistance caused by the fibrous web. The value of pereability k is calculated fro a odel given by Mao and Russell [12, 13]. The averaged energy equation for air and the porous atrix can be written as T γ ρ c + ρ c ut ) =.( k T ) ( 1 φ ) ερ Δh a a eff l.( (3) The ean theral capacitance of the ixture, ρ c, is defined as, [ ε ( γρ c + ( 1 γ ) ρ c ) + ( 1 ε ρ c ] ρ c φρ c + ( 1 φ ) ) a a l l s s = (4) c c The effective theral conductivity is given as a voluetric average, [ ε ( γk + ( 1 γ ) k ) + ( 1 k ] k φk + ( 1 φ ) ε ) eff a l s = (5) In addition, the relationship describing elt fraction γ as a function of teperature is given by, 1 if T > T + ΔT γ = 0 if T < T ΔT T T + ΔT if T ΔT < T < T + ΔT 2ΔT c (6) The FLUENT CFD software was used for the solution of the governing continuity and oentu and energy equations. Microscale odeling In icroscale odeling, two-phase Volue of Fluid (VOF) ethod is used for the odelling of the air and olten polyer flows. In the VOF ethod, a single set of oentu equations is shared by phases (here, air and polyer) and volue fraction of each phase is tracked through the coputational doain. Molten polyer flows to the contact point because of the surface tension force. Therefore, the oentu equation contains a source ter representing the surface tension force. The governing equations for the VOF odel are given below: Continuity: ρ +.( ρu ) = 0 Moentu: ρ (8) ( u ) +.( ρuu ) = P +. μ( u + u T ) + S + F (7) Initially, the fibers are in solid state and obviously the velocity is zero. When the fibers are elted by heat transfer fro the flowing hot air, the olten polyer starts to flow. The ter S in equation (8) works as a oentu sink to ensure that the fiber velocities in the initial cold state and then in the olten hot state are correctly represented. The surface tension force in equation (8) is represented by F. The force at the surface is expressed as a volue force and is added to the oentu equation as a source ter. Volue fraction equation: Journal of Engineered Fibers and Fabrics 2

3 To track the interface between phases a volue fraction continuity equation for the secondary phase (fiber) is solved along with the above equations: α q ϖ + u. α q = 0 (9) where subscript q represents each phase coponent Air volue fraction is obtained fro the relation 2 α 1 q =. q= 1 The properties appearing in the transport equations are deterined by the presence of the coponent phases in each control volue. For exaple, the density is considered to be: ρ = 2 q= 1 α q ρ q RESULTS AND DISCUSSION (10) Macroscale analysis of through-air bonding A scheatic drawing of a through-air bonding syste is shown in Figure 1. A nonwoven web is wrapped around a perforated rotating dru, through which the hot air passes radially. To siplify the developent of the odel, the CFD calculation was carried out on a 60 sector of the dru. obtained with a fixed tie step of one icrosecond [5]. The web is assued to be ade of sheath-core type bi-coponent fibers of polyethylene (PE) sheath and polypropylene (PP) core with 68 web thickness. This is a high loft web which represents and extree thickness. The calculations are carried out for the air inlet velocity of 1.5, 2.0, 2.25, 2.5 and 3.0 /s and the web porosity of 0.5, 0.7 and 0.9. Figure 2(a) gives the siulation results of the teperature distribution inside the web and Figure 2(b) shows the corresponding distribution of the elt fraction of fibers. The predicted results are for the porosity 0.9 and air velocity 1.5 /s. The hot air transfers heat to the web as it flows through it. The fiber teperature rapidly increases to the elting point of sheath polyethylene fiber and the fiber starts to elt. The siulation result shows that it takes approxiately 6.6 seconds to heat and elt fibers throughout the web thickness and to reach a steady state condition. Hossain et al. [5] showed that the tie required to elt the fibers through the thickness of the web shows a diinishing linear relationship with the web porosity. This relationship is quite realistic as the increased porosity of the web iplies that there is less volue of fibers within the sae volue of web to be heated and elted. The volue of the hot air flowing through the web increases with the increasing air velocity which in turn leads to higher convective heat transfer rates to the web consequently resulting in a reduced heating and elting tie. Although, the acroscopic odel is very useful in providing inforation related to the heating and elting tie, this odel can not provide inforation regarding the actual bond foration process. A icroscale odel, which considers the bonding process of individual fibers, is reported in the next section. A detailed account of the icro level odelling can be found in Hossain et al. [6]. FIGURE 1. A Scheatic Drawing of the Through-Air Bonding Process The coputational doain is divided into coputational esh with an average grid size of 1 in both the radial and circuferential directions. A unifor inlet velocity and teperature is specified at the inlet boundary. Pressure boundary condition is used at the outlet boundary. The inlet teperature is kept fixed at 140 C. The transient solution is Journal of Engineered Fibers and Fabrics 3

4 FIGURE 2. (a) Contour plot of teperature of web at different tie steps (b) corresponding contour plot of the elt fraction of fibers for a porosity of 0.9 and air velocity of 1.5 /s. Microscale analysis of through-air bonding Stochastic nature of fiber distribution in a web akes it very coplicated and resource intensive to generate a realistic coputational odel for a web specien. Instead, the foration of a single bond between two fibers is investigated in the present study. In the first instance, bonding of two fibers at a contact angle of 90, as shown in Figure 3, is studied at a bonding teperature of 140 C. Then the effects of the air teperature and the fiber diaeter are investigated. Finally, the effect of contact angle between two fibers is investigated. circuferentially to the contact point. As the bond foration progresses, the olten polyethylene begins to flow along the fiber axis towards the intersection, which then continues to flow to the contact point. This causes a reduction in the fiber diaeter in the vicinity of the intersection. The developent of bond foration between two polyethylene sheath/polypropylene core bicoponent fibers is shown in Figure 4 as a function of tie. The olten polyethylene flows to the intersection of two fibers to for a bond. The flow of olten polyer is ainly driven by the surface tension force. In the initial stages of the bond foration, olten polyethylene flows Journal of Engineered Fibers and Fabrics 4

5 FIGURE 3. Coputational doain showing two fibers at 90 contact angle. FIGURE 4. Coputed shape of bond at different ties for the bonding teperature of 140 C. In order to quantify the progress of bonding, a diensionless characteristic bond size is proposed as the ratio of the area of the section of the bond on a plane parallel to the axes of the fibers through their contact point to the cross-sectional area of the fibers. This characteristic bond size provides a quantitative coparison of the bonding. Bonding proceeds at a faster rate at the initial stages. This is because the olten polyer flows rapidly to fill up the narrow gap at the contact point of two fibers driven by the high surface tension force. As the bond grows filling the gap at the contact point between the two fibers, the surface curvature increases, consequently reducing the surface tension, which in turn slows down the rate of the bond developent. Coparison of the bond size developent with tie shows that the air teperature in the range of [ C] and fiber diaeter in the range of [ μ] ade very little effect on the bonding process. Bonding appears to proceed at a slightly faster rate at higher teperatures. Surface tension force and viscosity are the two ost iportant paraeters that control the flow of the olten polyer. When the bonding teperature increases, both viscosity and surface tension force decrease. Overall the reduction of viscosity at higher teperature over copensates the reduction in surface tension force. This results in a sall increase of the bonding rate at higher teperatures. The effect of the fiber diaeter on the bond size developent shows a slight decrease with the increasing fiber diaeter. This is in line with the experiental finding of Ki et al. [9]. Effect of the fiber contact angle The effect of the angle between two fibers on the progression of bonding is also investigated. Figure 5 shows the coputational odel involving two fibers with orientation angle of 10, 20 and 30. Figures 6 and 7 show the progress of bonding for these contact angles at 1 and 5 seconds respectively. The characteristic bond size defined earlier has been used to copare the bond size for different fiber contact angles. Figure 8 shows the developent of the bond size with tie for different contact angles. The effect of the contact angle on the progress of bond developent is found to be significant. FIGURE 5. Coputational doain showing fibers at contact angles of (a) 10 (b) 20 and (c) 30 Journal of Engineered Fibers and Fabrics 5

6 The overlap of the fibers at low fiber contact angles is uch greater than the overlap at high contact angles. The bonding at saller contact angles proceeds at a uch faster rate because the low contact angle causes a greater aount of polyer to flow in the circuferential direction to the contact point due to the greater fiber overlap. This causes a rapid developent of the bond size. As the orientation angle increases this rate becoes slower. At high fiber orientation angles, the initial fiber to fiber overlap is sall and therefore the bond needs to grow with polyer flow not only in the circuferential direction but also in the longitudinal direction which slows down the bond growth rate. These trends are observed in Figure 8. a) (b) (c) FIGURE 6. Progress of bonding after 1 second. The top row shows three-diensional view and the botto row shows cross-sectional view. (a) 10, (b) 20 and (c) 30 contact angle. (a) (b) (c) FIGURE 7. Progress of bonding after 5 seconds. The top row shows three-diensional view and the botto row shows cross-sectional view. (a) 10, (b) 20 and (c) 30 contact angle. Journal of Engineered Fibers and Fabrics 6

7 area between the fibers at low fiber orientation angles. ACKNOWLEDGEMENT The financial support for this research fro the Nonwovens Cooperative Research Center (NCRC), North Carolina State University, Raleigh, is gratefully acknowledged. REFERENCES FIGURE 8. The effect of contact angle at different contact angles on the progression of bonding. CONCLUSION A coputational fluid dynaics study of through-air bonding process of nonwoven fabrics has been presented in this article. The odelling strategy involves acroscale and icroscale odelling to analyze the bonding process. In the acroscale odelling, the web has been treated as a porous edia and the heating and elting tie of fibers within a nonwoven web have been coputed. The relevant operating paraeters such as the effect of air velocity and web porosity on the elting tie of the fibers have been studied. The coputational odel results indicate that the elting tie decreases linearly with the increase of web porosity and decreases nonlinearly with the increase of air velocity. Although the acroscale odel has provided useful inforation, it could not provide inforation regarding the bond foration process. Then, a icroscale odel has been developed to study the foration of bond between two fibers. In the first instant, the effect of bonding tie on the progression of bond between two fibers at 90 contact angle has been studied. The characteristic bond size has been defined and used in analyzing the process. The coputed results show that the foration of bond starts rapidly, but slows down gradually. The effects of teperature and fiber diaeter on the growth of the bond have been shown to be sall. However, the effect of orientation angle between the two fibers on the growth of bond has been observed to be significant. The rate of bonding decreased sharply with the increase of the fiber contact angle. This is attributed to the greater contact [1] Gong, R. H., Fang, C. and Porat, I. Single process production of 3D nonwoven shell structures part 1: web foring syste design using CFD odelling. Int. Nonwovens J., 2000, 9(4), [2] Gong, R. H., Dong, Z. and Porat, I. Single process production of 3D nonwovens shell structures part 2: CFD odelling of theral bonding process. Int. Nonwovens. J., 2001, 10(1), [3] Tafreshi, V. H. and Pourdeyhii, B. Siulating the flow dynaics in hydroentangling nozzles: effect of cone angle and nozzle aspect ratio. Text. Res. J., 2003, 78(3), [4] Tafreshi, V. H., Pourdeyhii, B., Holes, R., and Shiffler, D. Siulating and characterizing water flows inside hydroentangling orifices. Text. Res. J., 2003, 73(3), [5] Hossain, M., Acar, M., and Malalasekera, W., A atheatical odel for airflow and heat transfer through fibrous webs, Proc. IMechE, Part E: J. Process Mechanical Engineering, 2005, 219, N. 4, [6] Hossain, M., Acar, M. and Malalasekera, W., Coputational Analysis of Fiber Bonding in the Through-Air Process, Proceedings of the IMechE, Part E: Journal of Process Mechanical Engineering, Volue 221, No. E2, 2007, pp [7] Randall, K. R. The influence of process variables on the properties of therofusion bonded fabrics. In Proceedings of the Nonwoven Syposiu, TAPPI, [8] Randall, K. R. Through air bonding of nonwoven fabrics. In Proceedings of the 13 th Annual Technical Syposiu Association of the Nonwovens Fabric Industry, Boston, MA, 1985, pp Journal of Engineered Fibers and Fabrics 7

8 [9] Ki, H. S., Ito, H., Kikutani, T. and Okui, N., The theral bonding behavior of polyethylene/poly ethylene terephthalate bicoponent fibers. J. Text. Inst., 1997, 88 (3), [10] Ki, H. S., Ito, H., Kikutani, T. and Okui, N. Coputational analysis on the theral bonding behavior of bicoponent fibers. J. Text. Inst., 1999, 90 (1), [11] Beckerann, C. and Viskanta, R. Natural convection solid/liquid phase change in porous edia. International Journal of Heat and Mass Transfer, 1988, 31(1), [12] Mao, N. and Russell, S.J. Directional pereability in hoogonous nonwoven structures Part 1: The relationship between directional pereability and fiber orientation. Journal of the Textile Institute, part 1, 91(2), [13] Mao, N. and Russell, S.J. Directional pereability in hoogonous nonwoven structures Part 2: pereability in idealized structures. Journal of the Textile Institute, Part 1, 2000, 91(2), NOTATIONS c specific heat [J/kgK] d diaeter of fiber [] f E a activation energy [J/ole] F surface tension force [N/ 3 ] h, H enthalpy [J/kg] k pereability ( 2 ) k effective theral conductivity [W/ 2 K] eff P pressure [N/ 2 ] R universal gas constant [J/kgK] r radius (/s) S source or sink ter [N/ 3 ] S h source or sink ter in the energy equation [W/ 3 ] t tie [s] T teperature [K] u velocity [/s] x, y co-ordinate location Δ h ε heat of elting [J/kg] volue fraction of sheath fiber in the bicoponent fiber μ viscosity [kg/s] ρ density [kg/ 3 ] φ volue fraction of air (porosity) Subscripts a air c core fiber f fiber l sheath fiber in liquid state s sheath fiber in solid state eff effective elting AUTHORS ADDRESSES M. Hossain School of Engineering The Robert Gordon University Schoolhill, Aberdeen, AB10 1FR UNITED KINGDOM M. Acar, Ph.D.; W. Malalasekera Mechanical and Manufacturing Engineering Loughborough University Leicestershire, LE11 3TU UNITED KINGDOM Greek α β γ volue fraction fraction of elt of sheath fiber fraction of elt of sheath fiber Journal of Engineered Fibers and Fabrics 8