SIMULATION OF HEAT TRANSFER THROUGH WOVEN FABRICS BASED ON THE FABRIC GEOMETRY MODEL

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1 SIMULATION OF HEAT TRANSFER THROUGH WOVEN FABRICS BASED ON THE FABRIC GEOMETRY MODEL Zhenron Zhen a,b*, Nannan Zhan a and Xiaomin Zhao a,* a Collee o Tetiles, Tianjin Polytechnic University, Tianjin, , China; b Key Laboratory o Advanced Tetile Composites o Ministry o Education, Tianjin, , China * Correspondin author, tianjinzhenzr@163.com; te_zhao@163.com Numerical simulation is a rapid, eective and low cost method to predict the heat transer perormance o abrics. However, in previous research abrics are usually assumed to be a uniorm plate. Here, eometry models o 5/3 satin weave, double plain weave and double twill lass iber abrics have been established based on the abric thickness, yarn path and yarn cross-section shape. In the abric unit, air occupies 60% to 80% by volume o the abric unit. Thereore, the air in the abric unit should be considered in the numerical simulation by inite element analysis. In this work, the abric unit cells consisted o a yarn domain and an air domain. Based on the abric unit cell model, the inite element method was used to predict the heat transer throuh abrics. The numerical temperature data are very close to the eperiment data or lass iber abrics. Prediction results show that the temperature o 5/3 satin abrics increase more rapidly than the double layer abrics, and the heatin rate o double twill abric is lower than that or the double plain weave abric, and they coincide well with the eperiment data. Key Words: Fabric eometry model, heat transer, inite element method 1. Introduction Glass iber abrics have characteristics o sotness, liht weiht, hih intensity, non-combustion, thermal insulation, chemical stability and can be easily shaped. They have an important application in the ield o acility protection [1,]. To develop a thermal protective abric, the current methods are eperimental, the processin o which includes desin o the abric, weavin and testin at hih temperatures. This method has lots o problems, such as lon processin time, hih cost, hih enery consumption and production o umes. The numerical simulation o the heat transer throuh abrics can provide the theoretical basis or the desin and application o the thermal protective abric. It can be widely used in the desin o thermal abrics or ireihters, welder, hot pipelines, oil reinin equipment and so on. Many researchers have tried dierent techniques to predict the thermal property o woven abric. Fan used the inite control volume method to predict heat transer throuh ibrous assemblies incorporatin relective interlayers [3,4]. Sun studied heat transer throuh layers o tetiles usin the inite element method [5]. Gon established the one-dimensional abric heat transer model, and Ansys sotware was used to simulate and orecast the time o the second-deree burn injury o abric samples [6]. Wan [7-9] proposed a much more eicient thermal lattice Boltzmann alorithm to predict the eective thermal conductivity o various materials, such as comple multiphase materials, 1

2 composites and ibrous materials. They ound it was useul or desin and optimization o new materials, beyond just predictin and analyzin the eistin ones. Chen [10] used the inite element simulation to predict the response o dierent layers o abric to investiate the ballistic perormance o hybrid abric panels. Min [11] investiated the eects o layerin sequence on the thermal response o multilayer ibrous materials under unsteady-state cases. It ound that the abric in contact with the hot heat source was the key layer to aectin the system s thermal response. Woven abrics are classiied into weave or structure accordin to the style in which warp and wet cross each other. The teture o abric has a siniicant eect on properties such as thermal insulation, mechanical behavior and moisture permeability [1]. Some o the popular patterns or enineerin purposes are plain, twill and satin weave [13]. Thermal behaviors o the abric chane i any o the weave patterns varies. Fabrics are hihly porous materials consistin mainly o solid iber and air void spaces. The porosity o most abrics ranes rom 60% to 80% [14-15]. The eective thermal conductivity o the abric with dierent iber ractions was calculated by Muhammad ORS [16]. A CAD system or clothin thermal unctional desin and simulation was developed by Li Yi [17]. Durin the process o CAD system established, the porosity o the abric was considered. Thereore, the air in the abric unit should be considered in the numerical simulation. In this paper, the lass iber yarns were used to weave abrics. A sinle yarn is made up o 1800 continuous ilament ibers. The lass iber yarn count is 80te and turns per cm. In order to smoothly create the abric eometry model, the whole yarn is assumed as a pillar and the twist o yarn is not considered in the modelin process. Three structures o abrics, 5/3 satin (1EPcm, 10PPcm), double plain (0EPcm, 10PPcm) and double twill (0EPcm, 10PPcm), were woven and used to model and simulate. Durin the abric eometry is modeled, the actual cross-sectional shape o the yarn, the rotation and delection o yarns due to side-crimp orces are all considered. In this work, abric eometry models have been established and the inite element method was used to predict the heat transer throuh abrics. The abric eometry unit includes the yarn domain and the air domain, as shown in i. 1. Net, the heat transer throuh the lass iber abrics have been investiated based on the abric eometry model. The ront aces o the abrics were ablated usin an alcohol blast burner at 900, the veriication eperiment was done in the ume hood, so a convective heat transer coeicient 15 W/(m C) was deined on the back ace o the abric (shown in i. 1). This research aims to identiy and evaluate the heat transer throuh abrics, includin details o temperature chanes o the abric throuh time, the temperature distribution at the cross-section o the abric, the ambient temperature and the eects o abric structure on the heat transer properties. Furthermore, the eperiments are used to validate the numerical simulation results.. Methodoloy.1 Geometrical modelin Fabric eometric structures are determined mainly by the central paths and cross-sectional shapes o their constituent yarns. TeGen is an automated modellin approach[18]. It can easily describe the shape o yarn cross-section, yarn path and the yarn interweavin [19]..1.1 Yarn path representation

3 The path o a yarn can be considered as a one dimensional line representin the yarn s center-line in three dimensional space. The yarn path can be deined as its position in 3D space as a unction o distance alon the yarn. To obtain an accurate yarn path or woven abrics, it is suicient to speciy one or two master nodes per crossover as lon as the interpolation unction is suitable. The most eneral orm o yarn path is represented by a polynomial spline S( (Bezier, natural or periodic cubic) [0]: S0( i t0t t1 S1( i t1t t Eq. (1) S(.. Sk( i tkttk 1 where t i values S are called control nodes (knots). The vector S=(S,S 1,..., S k- ) is called a knot vector or the spline, shown in i...1. Yarn cross-section shape The cross-section is deined as the D shape o the yarn. Circular shape is one o the commonly used eometry models or yarn cross-section. However, the yarns are delected duo to side crimp orces in the weavin process, enerally yarn cross-sections are not circular [0]. Ellipse, power ellipse and lenticular shapes are other three types o eometry models or yarn cross-section. (1) Ellipse It is a derivative o circular shape, and its equation is deined as [0]: w C( cos( 0 t1 Eq. () h C( y sin(t ) 0 t1 Yarn width (w) and heiht (h) were measured as the maimum distance between the yarn edes alon the major and minor aes respectively. As shown in i. 3, yarn width is the distance o line AB, and yarn heiht is the distance o line CD. C( represents the knots o the ellipse. C( and C(y are the X and Y coordinates o the knots respectively. I the distance o AB is equal to that o CD, the cross-section shape o yarn is a circle. () Power ellipse The power ellipse is a sliht modiication to the elliptical cross-section where the y-coordinate is assined a power n to make the section resemble a rectanle with rounded edes when n < 1 or a shape similar to a lenticular cross-section when n > 1. The power ellipse is deined as [0]: 3

4 C( C( y cos(t ) 0 t 1 h n (sin(t )) i 0 t 0.5 h n ( sin(t )) i 0.5 t1 Eq. (3) (3) Lenticular The lenticular cross-section is the intersection o two circles o radii r 1 and r each oset vertically by distances O 1 and O respectively. The parameters r 1, r, O 1 and O can be calculated rom the desired width w, heiht h and distortion distance d o the lenticular section [0]. ( h d) r1 ; r 4( h d) ( h d) ; O 4( h d) 1 h r1 ; O r ; Eq. (4) h Thereore, the lenticular section is described as ollows [0]: r1 sin C( rsin i 0 t 0.5 ; i 0.5 t 1 r1 cos o1 C( y r cos o i i 0 t t 1 Eq. (5) Where [19]: 1 (1 4sin ( ) r1 1 ( 3 4sin ( ) r i 0 t 0.5 i 0.5 t1 Eq. (6).1.3 Weave pattern Woven abrics are prepared by an interlacin arranement between the warp and wet yarns. The weave pattern can be epressed by a D binary matri; 0 and 1 are used to represent the yarn interpenetrations. 0 means the wet yarn over the warp yarn, and 1 means the warp yarn over the wet yarn. Fi. 4 shows a binary array or a plain weave. For 3D weave patterns, since yarns interlace throuh multiple layers, the D matri method is limited. 3D abric is deined by the centerlines o the yarn paths in 3D space with superimposed cross sections. The control nodes alon a yarn path are created around a yarn circumerence at interlacin points. These nodes help avoid yarn intersections and capture local waviness. Since an automated enerator or 3D abric has been written by Python script in TeGen, the eometry models o orthoonal and anle inter-lock abrics can be automatically enerated. Some parameters, such as number o layers, yarn spacin (the distance rom the ede o one yarn to the correspondin ede o an adjacent yarn), cross sections o wet, warp and binder yarns, are required..1.4 Geometric measurements Fabric thickness was tested usin YG141D diital abric thickness aue under area o pressin oot o 5 cm, pressin weiht 0 CN/cm. The morpholoy o the satin weave and double plain weave abrics was obtained by USB liht microscopy (0X-400X, Dino-Lite, Taiwan, China). The 4

5 morpholoy o the double twill weave abric was obtained by SEM (TM1000, Hitachi, Japan). The cross-sectional imaes o the yarn were analyzed by imaej sotware. The parameters (yarn spacin, width and heiht, cross-section shape) were measured and their values are shown in tab. 1. They were then used to create the unit cell eometries. Note that yarn spacin is the distance rom the ede o one yarn to the correspondin ede o an adjacent yarn.. Numerical solution with inite element method..1 Heat transer equation Heat transer throuh a abric system is a comple process, involvin conduction, convection and radiation processes. Considerin the abric thickness dimension is much smaller than the dimensions o abric width and lenth, it is reasonable to assume the heat transer throuh a abric is a one-dimensional phenomenon. In this work, it is assumed that the thermal properties o abrics and temperature o heat source were constant, the abric boundary was adiabatic, and only conduction and convection heat transers are considered and the radiative heat transer is neliible. Accordin to Fourier s law, Newton's law o coolin and enery conservation, the total heat lu is described as: dt() Q total - A (T ) d Ah T Eq. (7) where -λa(dt()/d) stands or the conduction heat lu, λ is the conductivity (Wm -1 K -1 ), A is heat lu area(m ), T is the temperature( K), (m) represents the direction o heat transer. Ah(T Г -T ) stands or the convection heat lu, h is the ilm coeicient (Wm - K -1 ), T Г is the out surace temperature o the abric (K), and T is the temperature o the ambient atmosphere (K). At the transient-heat condition, conduction heat transer throuh the abric in the thickness direction o the tetile assembly is epressed by Eq. (8) [1-3]: T t T c Eq. (8) where T, t, λ, c and ρ are temperature (K), time (s), conductivity (Wm -1 K -1 ), speciic heat (JK -1 K -1 ) and mass density (Km -3 ), and (m) represents the direction o heat transer. Since the abrics consist o ibers and air, the abric and air domains are deined respectively, total conductive heat transer area is divided into two parts, heat transer throuh the zones o yarns and that o the air aps. So it is reasonable that the physical parameters such as the thermal conductivity, mass density and speciic heat o abrics ( λ, ρ and c ) and air ( λ, ρ and c ) are assined respectively. φ is the heat transer area raction o yarn, and 1-φ is the heat transer area raction o air ap, which can be accurately obtained rom the eometry model in Ansys. Hence, the transient-heat transer o conduction heat is described as: T t T ( 1-) T c c Eq. (9) Convection involves the transer o heat enery in the air by movement o currents rom hih temperature abric to the surroundins. When cold air moves past a warm abric, it sweeps away warm air adjacent to the abric and replaces it with cold air. Studies showed that there is no convection inside clothin insulation even with a very low density [4]. Hence, the convective heat transer is considered only at the outer surace o the abric. In the heat transer analysis by Ansys sotware, the 5

6 convective heat transer will be set as a boundary condition. Substitutin Eq. (9) into Eq. (7), we readily obtain the heat transer equation at the transient-heat condition, shown in Eq. (10). T t T ( 1-) T c c T T - h( ) Eq. (10).. Mesh eneration and boundary conditions The abric models were converted to Ansys workbench. Material properties were set as described in tab..the speciic heat and thermal conductivity o the abrics were measured at 0 ºC by the Hot Disk Thermal Constant Analyzer (TPS500, Sweden). Here, the thermal conductivity o the abric was tested in the thickness direction o the abric. Ten-node linear tetrahedral elements (SOLID 87) were used to mesh the unit cell, and the element ede lenth was all assined as 0. mm. The automatic mesh eneration was perormed directly in these models. There were 3833 elements and nodes or the 5/3 satin abric model, 8009 elements and nodes or the double plain weave abric model, and elements and nodes or the double twill weave abric model. The meshed unit cells o double plain weave abric are shown in i. 5. Initial temperatures o abric and environment are assined as C. A temperature o 900 C was loaded on the back ace o the lass iber abric. The assumption is made that the eperiment was done in the ume hood and the heat transer between air and abric is orced convection. The coeicient o convection heat transer between air and abric is 15 W/(m C)...3 Numerical solution The inite element method is used to compute the numerical solution o this interative heat transer mode. A positive inteer N is selected. 0 1 N is a discretization o abric thickness and i 1, i indicates the ith control volume (shown in i. 1). The rid points 1,,, N are located at the centers o control volumes, i.e. i ( i- i) /., 0 N 1 are the two boundary points (they represent the points at the ace and back side o the abric respectively). The distance between rid points is denoted by i i i 1. Denote T i T( i ), i 0,1,, N 1. I the value o temperature T 0 is obtained, the conductive heat and the total heat low can be calculated by Eq. (10). Hence, the value o temperature T N 1 can be calculated...4 Veriication o the model Eperiments have been carried out to validate the numerical simulation results. An illustration o the eperimental process is shown in i. 6. An asbestos auze was placed above the lame, and a circle o radius 3 cm was cut out in its center. Then the abric was placed on the asbestos auze. The ront ace o the abric was ablated usin an alcohol blast burner at 900 ºC, and a convective heat transer coeicient 15 W/(m C) was deined or the back ace o the abric. An inrared thermocouple (Raytek, American) was used to measure the variation o the temperature o the back ace o the abric durin the heatin process. The lower temperature o the abric at the same time represents improved heat resistance. 6

7 3. Results and Discussion 3.1 Geometry models The abric unit cell is described as the smallest unit o abric structure. To simpliy the abric, the unit cells o abrics are used or investiation by thermal transer analysis. With the measured eometric dimension, the unit cells o lass iber abrics were created by usin TeGen, and they are presented in is Fi. 7(a) is the liht microscopic imae o 5/3 satin abric, and i. 7(b) shows its eometric model. The yarn paths o this abric use the Bezier splines, and the weave pattern o the warp and wet yarns are the same as the real abric. In is. 7(c) and 7(d), the elliptical cross-sections are iven to the warp yarn and wet yarn respectively. Double layer abric consists o two layers, which are woven one above the other. The enerated model o double plain weave is shown in i. 8. Ellipse cross-sections were assined to the warp yarn and wet yarn. Fi. 9 shows the eometry model o the double twill weave abric. Compared with i. 8(c) and i. 8(d), the non-symmetrical structure o the twill weave ives bendin and contact orces causin the yarns to rotate and delect. As shown in i. 9(c), the let yarns are rotated by 10º and the riht yarns are rotated by -10º. 3. Simulation results and discussion The simulation results o thermal distributions in the double plain abric ater 10 seconds are shown in i. 10. Fi. 10 (a) shows the abric unit cell with the air domain, and the top ace represents the heated ace, which is subjected to a constant heat lu. The abric cross-section shows the temperature radually decreasin rom the heated side o the abric to the opposite side. Fi. 10 (b) shows the abric only, where the air domain has been hidden. It is shown that the closer the abric is to the heat source, the hiher its temperature is. Fi. 10(c) shows the heat distribution or the air domain, where the abric part has been hidden. The eperimental temperatures o Nodes on the abrics were compared with the numerical values rom the inite element model. The results are shown in i. 11. Fi. 11(a) shows that the temperature in Node 1 o the satin abric; the eperimental temperature o the back ace o the abric rises rapidly, it reached 483 ºC in 5 seconds, then the temperature tends to stabilize. The numerical temperature data are very close to the eperiment data, it indicates that the inite element model is able to predict the heat transer property o the abric. Fi. 11(b) shows that the eperimental temperature o double plain weave rises to 307 ºC in 11 seconds and 453 ºC in 0 seconds; the numerical temperature was slihtly hiher than that or the eperiment data. Fi. 11(c) shows that the eperimental temperature o the double twill abric reached 99ºC in 11 seconds and radually reached 439 ºC in 0 seconds, and the numerical temperature was slihtly lower than that or the eperiment data. Correlation coeicients have been calculated or the eperiment and numerical data or the satin weave, double plain and double twill weave abrics, they were 0.995, and respectively. The averae relative deviations at Node1, Node and Node 3 were 8.1 %, 5.6 % and 8 % respectively. The thermophysical parameters o the abric and air used in the simulation are the values measured at the standard temperature and humidity, which are constant in the heat transer simulation process. However, the thermal conductivity, speciic heat and density o the abric and air chane with the temperature increasin. It is necessary to urther measure the thermophysical parameters at dierent temperatures, then the accuracy o the simulation will be 7

8 improved. The heat transer properties o the satin abric, the double plain weave and double twill abrics were numerical and compared in i. 11(d). It clearly shows that the temperature o the satin abric increases more rapidly than the others, and the heatin rate o the double twill abric is lower than that or the double plain abric. This is because the satin abric is a sinle layer abric, and the abric thickness is less than the double layer abric. The double layer abrics have more yarns to deend the heat lu, and they can hold more still air within the abric. Thereore, the double layer abrics have better thermal resistance. Compared with the double plain weave, the double twill abric has less interlacin in the same area; it has more space to accommodate the still air, hence the temperature is lower ater the same heatin time. In i. 11(d), the numerical models were successully used to predict the heat transer property o abric, and the numerical results have ecellent correlation with the eperiment data. 4. Conclusion The numerical simulation is a rapid, eective and low cost method to predict the heat transer property o abric. Normally, abrics have been assumed to be a uniorm plate. Woven abrics are comprised o yarns, which are woven in one o several dierent patterns. Besides ibers and yarns in the abric unit, lots o air holes eist and air occupies 60% to 80% by volume o the abric unit. Thereore, the air in the abric unit should be considered in the numerical simulation by inite element analysis. In this work, abric eometry models have been established and the inite element method was used to predict the heat transer throuh abrics. The ollowin conclusions can be made: (1) based on the abric thickness, yarn path and yarn cross-section shape, the eometry models o 5/3 satin, double plain and double twill lass iber abrics have been established. The abric unit cells consist o a yarn domain and an air domain, and the abric eometry models are very close to the real abrics. () the numerical temperatures are very close to the eperimental temperatures or the lass iber abrics, it indicated that the inite element model is able to predict the heat transer property o the abric. (3) the temperature o the 5/3 satin abric increases more rapidly than the double layer abrics, and the heatin rate o the double twill abric is lower than that or the double plain weave abric. Acknowledment This work was supported by the National Natural Science Foundation o China under Grant 51061, Natural Science Foundation o Tianjin under Grant 13JCQNJC03000 and Technical Guidance Project o China National Tetile and Apparel Council under Grant Reerences [1] Aloni, J., et al., Current Emerin Techniques to Impart Flame Retardancy to Fabrics: An overview, Polym. Derad. Stab., 106(014),pp [] Poon, C.K., et al., Eects o TiO and Curin Temperatures on Flame Retardant Finishin o Cotton,Carbohydr. Polym., 11(015),pp [3] Wan, X., et al., Heat Transer Throuh Fibrous Assemblies Incorporatin Relective Interlayers, Int. J. Heat Mass Trans., 55 (01),pp [4] Fan, J.T., et al., Modelin Heat and Moisture Transer Throuh Fibrous Insulation with Phase Chane 8

9 and Mobile Condensates, Int. J. Heat Mass Trans., 45 (00), pp [5] Sun,Y., et al., Study o Heat Transer Throuh Layers o Tetiles Usin Finite Element Method, Int. J. Cloth. Sci. and Tech., (010),pp [6] Gon, Y. R., et al., Numerical Simulation on Thermal Protection Properties o Tetile Materials, Journal o Donhua University (Natural Science),36 (010), pp [7] Wan, M.R., et al., Lattice Boltzmann Modelin o the Eective Thermal Conductivity or Fibrous Materials, Int. J. Therm. Sci., 46(007), pp [8] Wan, M.R., et al., Predictions o Eective Physical Properties o Comple Multiphase Materials, Mater. Sci. En. R, 63 (008), pp.1-30 [9] Wan, M.R., et al., Thermal Conductivity Enhancement o Carbon Fiber Composites, Appl. Therm. En., 9(009), pp [10] Chen, X.G., et al., Numerical and Eperimental Investiations into Ballistic Perormance o Hybrid Fabric Panels, Composites Part B, 58(014), pp.35-4 [11] Tian, M.W., et al., Eects o Layerin Sequence on Thermal Response o Multilayer Fibrous Materials: Unsteady-state Cases, Therm Fluid Sci., 41(01), pp [1] Cao, J., et al., Characterization o Mechanical Behavior o Woven Fabrics: Eperimental Methods and Benchmark Results, Composites Part A, 13(008), pp [13] Suppakul, P., et al., The Eect o Weave Pattern on the Mode-I Interlaminar Fracture Enery o E-lass Vinyl Ester Composites, Compos. Sci. Technol., 6(00), pp [14] Wan, T., et al., Introduction to the Thermal and Humid Comort and Evaluation Method, China Fiber Inspection, (015), pp [15] Zhan, C., Thermal Comort and Climate in Clothin, Journal o Wu Han University o Science and Enineerin, 18(005), pp. 4-7 [16] Muhammad, O.R.S., et al., Finite Element Analysis o Thermal Conductivity and Thermal Resistance Behavior o Woven Fabric,Comput. Mater. Sci., 75(013), pp [17] Li, Y., et al., P-Smart A Virtual System or Clothin Thermal Functional Desin, Computer-Aided Desin, 38(006), pp [18] Lin, H., et al., Finite Element Modellin o Fabric Compression, Modellin Simul. Mater. Sci. En., 16(008), pp.1-16 [19] Won, C.C., et al., Comparisons o Novel and Eicient Approaches or Permeability Prediction Based on the Fabric Architecture, Composites Part A 37(006), pp [0] Sherburn, M., Geometric and Mechanical Modellin o Tetiles. Ph.D. Thesis, University o Nottinham, UK, 007 [1] Farnworth, B., Mechanisms o Heat Transer Throuh Clothin Insulation, Tetile Res.J., 53(1983), pp []Yan, S.M., et al., Heat Transer, Hiher Education Press, Beijin, China,1999 [3] Incropera, F.P., et al., Fundamentals o Heat Transer, 5th ed., Wiley Somerset, NJ, 00 [4] Peirce, F.T., et al., The Transmission o Heat Throuh Tetile Fabrics, Part II, J. Tet. Inst., 37(1946), pp