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Analysis of a high temperature heater in a false twist texturing process
Energy Conversion and Management 44 (2003) 2531–2547 www.elsevier.com/locate/enconman
Analysis of a high temperature heater in a false twist texturing process Nurdil Eskin
*
€ . Makina Fak€ultesi, I_ n€on€u Cad. No 81, G€ I_ .T.U um€ ußs suyu, Taksim, 80191 I_ stanbul, Turkey Received 14 September 2002; accepted 26 December 2002
Abstract The production of textured filament yarns by false twist texturing is an important commercial method that requires heating. In this study, the transient two dimensional modeling of the yarn, heated by high temperature heaters in a false twist texturing process was developed in order to investigate the influence of various heating conditions on the yarn temperature distribution and to quantify the relative contribution of thermal radiation to the total heating. The surface temperatures and the residence time of yarns of different diameters were measured and compared with the simulation results. The temperature distribution in the cross-section of the yarns was calculated for various yarn speeds and for different heater temperatures. The temperature difference between the surface and the center of different types of yarns along the heater was found. For a yarn in a heater, energy is transferred from the heater surface to the yarn by both convection and radiation. As the yarn approaches its heat setting temperature, the total heat rate decreases. However, the calculated results show that the relative contribution of radiation increases up to 60% of the total with yarn temperature and diameter. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Transient heating; Convection radiation type heaters; Yarn; Yarn heating
1. Introduction As natural sources decrease, synthetic yarns are becoming more popular as a result of the increase in the need for textile products in the world. Since synthetic yarns do not have the appearance and handling characteristics of natural fibers, certain processes have to be applied to
*
Fax: +90-212-245-0795. E-mail address: [email protected] (N. Eskin).
0196-8904/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0196-8904(03)00014-1
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Nomenclature A C D F1!2 h k L N V q r0 S T t w
area (m2 ) specific heat (J/kg K) linear density (kg/m3 m) view factor heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) heater length (m) inserted twist (turns/m) velocity (m/s) heat flux (W/m2 ) yarn radius (m) distance between surfaces (m) temperature (°C) time (s) tension in twist zone (gf )
Greeks a e U q / r
thermal diffusivity (m2 /s) emissivity packing factor density (kg/m3 ) viewing angle Stefan–Boltzman constant (W/m2 K4 )
Subscripts a air f fiber g glass transition m melting set setting tex texturing
synthetic yarns in order to combine the superior properties of synthetics, like high strength, uniformity and stretch, with the features that are unique to natural fibers. Texturing is one of the processes that give a crimped and bulky structure, a natural appearance, touch, warmth, stretch and bulk. The method mostly used among texturing processes is false twist texturing, which is used in thermoplastic filaments. If a stationary multi-filament yarn is held at both ends and twisted in the center by suitable means, the yarn could have an equal amount of twist on each side. Although the twist on each side is other than zero, the algebraic sum of the twist throughout
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547 Yarn
Spindle
Output rollers
Cooling plate
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Heater
Feed rollers (Delivery mechanism) Air
Air
Fig. 1. A false twist texturing machine.
the yarn is zero. As the false twist device is rotated continuously, a twist forms in the moving yarn passing from the feed rollers to the twister, but it becomes untwisted due to the reverse twisting effect after the twisting zone. For this reason, this process is called false twist texturing (Fig. 1). During this process, a thermoplastic yarn is first highly twisted, next heated to alleviate the stresses resulting from twisting to set the twist into the molecular structure of the filaments and then cooled in a twisted form. After being cooled, the yarn is untwisted by the twist head to give a high torque, high bulk product. Since the filaments and their molecules have already obtained a migrating helical configuration, the physical untwisting of the filaments will not straighten the molecules. The production of textured filament yarns by false twist texturing is an important commercial method due to its higher texturing speeds and convenience. Higher production rates and, hence, higher yarn speeds necessitate the use of longer heaters so as to heat the yarn adequately. The heater and cooler lengths reach 2.5 m, depending on the fineness of the yarn to be textured. Machine producers and users are, thus, faced with considerable problems. The texturing zone needed to be shortened in order to reduce the investment costs, to make the setting-up and operability of these machines easier, to decrease instabilities and to increase the production further. In order to realize this objective, a shortening of the heating zone primarily must be accomplished [1]. High temperature heaters with operating temperatures up to 1100 °C considerably reduce the residence time required to reach the setting temperature of the polymer, which is the temperature above its glass transition temperature and below its melting temperature. At this temperature, the polymer gains its plastic character, and it can be easily deformed. In order to attain this setting temperature throughout the whole heating process, the heater must be designed with optimum dimensions and temperature. Also, at the heater outlet, the yarn temperature distribution should be uniform throughout the yarn crosssection. Therefore, besides the heater characteristics, one of the important parameters, which affect uniform yarn temperature, is the yarn speed. Previous approaches for using shortened heaters were limited to experimental studies [1–4]. Mathematical models were limited to one dimensional steady state analyses in order to support the experimental studies. Wulfhorst et al. developed a one dimensional simulation model of the temperature distribution of yarn at steady state conditions assuming constant thermal properties. In their study, they ignored the radiation heat transfer, assuming its effect to be less than 10% on the yarn heating. Besides that, the longitudinal heat transfer and texturing speed of the yarn was not taken into consideration in the formulation [5,6]. In this study, unsteady two dimensional modelling of the yarn heated by convection–radiation type high temperature heaters in a false twist texturing process is developed, and the parameters affecting the performance of the texturing process are analyzed according to the simulation.
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2. Mathematical analysis In the high temperature heaters, the residence time of the yarn in the heating zone ranges approximately from 0.12 to 0.072 s, depending on the speed of the yarn and the length of the heater. During this short time, the temperature of the yarn has to be raised to the yarn heat setting temperature. The problem is to determine the temperature at all points within the yarn as a function of time when it is suddenly exposed to hot air and infrared radiation. The following assumptions are based on the yarn behavior observed during texturing with high temperature heating [1–3] and the current texturing experiments with convection–radiation heating [4,6,7]: (a) Provided that the amount of twist inserted in a multi-filament yarn is insufficient to cause snarling, the yarn shape approximates to an infinitely long cylinder. Therefore, the yarn can be assumed to be a solid cylinder [7]. (b) Any point in the cross-section of the yarn can be located by the polar coordinates r, h and z. While the yarn is in the heater, it rotates at a high speed (up to 500,000 rpm) due to the twisting by the spindle. In the heater, the yarn is heated by convection from the hot surrounding air. It is also heated by radiation from the surrounding surfaces of the heater. Resulting from these factors, the yarn is heated uniformly all around its circumference, and the temperature would be the same around the circumference at any radius in the cross-section of the yarn. Then, the temperature of the yarn is independent of the coordinate h. (c) The temperature of the heater surface is not constant throughout its length. The measurement of temperature at different points of the heater showed that the temperature profile was parabolic with the peak temperature at the middle of the heater [6]. Therefore, the heater surface temperature profiles used in this study were assumed to be parabolic. These measurements were conducted without yarn passing through. It can be assumed that the latter causes the air to be mixed better within the heater, and then, a more even temperature distribution is available. With the assumptions above, the differential equation describing the yarn temperature is given by: 2 1 o oT oT oT oT r ¼ qC ð1aÞ qCVtex þk k 2 r or or oz oz ot The specification of the inlet yarn temperature as the ambient temperature serves as the initial boundary condition. Hence, T ðr; z; tÞ ¼ T0
at t ¼ 0
ð1bÞ
and the boundary conditions, oT ðr; z; tÞ ¼0 or k
at r ¼ 0
oT ðr; z; tÞ ¼ hðTa T ðr; z; tÞÞ þ q or
oT ¼0 oz
at z ¼ 0 and z ¼ L
ð1cÞ at r ¼ r0
ð1dÞ ð1eÞ
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Here, q represents the incoming energy due to thermal radiation from the heater wall. The net radiative method for enclosures was used to calculate the thermal radiative heat flux to each surface [8]. N N X X dkj 1 ej Fkj qj ¼ Fkj rðTk4 Tj4 Þ e e j j j¼1 j¼1
F12 ¼
1 A1
Z
Z A1
A2
cos /1 cos /2 dA2 dA1 2 pS1!2
The view factors between the exterior ring element of the yarn and the annular elements of the heater were obtained from the literature [9,10]. The problem, Eq. (1) is expressed in dimensionless form as, 2 o2 h 1 oh oh oh 2o h þ u ¼ þ b 2 2 og g og oc oc on
n>0
0
0
ð2aÞ
subject to the following initial and boundary conditions: h ¼ h0
at f ¼ 0
ð2bÞ
oh ¼0 og
at g ¼ 0
ð2cÞ
oh ¼ Biðha hÞ þ # og
at g ¼ 1
ð2dÞ
oh ¼0 oc
and c ¼ 1
ð2eÞ
at
c¼0
where the various dimensionless quantities are defined by: hðg; c; nÞ ¼ T =Tr ; Bi ¼ hr0 =k; n¼
ta=r02 ;
g ¼ r=r0 ;
# ¼ qr0 Tr =k; ha ¼ Ta =Tr ;
c ¼ z=L b ¼ r0 =L
Vtex r02 u¼ aL
ð2fÞ
Here, Tr is the reference temperature, h0 is the dimensionless initial temperature and Bi is the Biot number. The emissivity of the heater is taken to be 0.75, and the emissivity of the yarn is taken to be 0.7 [11]. Natural convection within the heater is in the laminar regime. Based on the maximum temperature difference and a characteristic length equal to the heater height, the Rayleigh number is 2:35 106 , which is below the critical value.
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3. Yarn diameter The dimensions of a yarn are expressed in units of tex or decitex (dtex), which are the mass of the yarn in grams per 1000 m (106 kg/m) or 10,000 m (107 kg/m). This unit (dtex) has replaced the denier, which is expressed as 1 g/9000 m (1:111 107 kg/m). The yarn radius r0 can be calculated by using the yarn linear density D1 (dtex), which can be calculated in terms of the tension in twist zone, w and inserted twist N as follows [3]: 29N 2 105 D1 ¼ D0 1 þ f0:9D0 2ðw 5Þg ð3Þ 2ð60 wÞ where D0 is the linear density (dtex) in the twist zone for zero twist. w D0 ¼ 1:17Dn 1 3:75 208
ð4Þ
Here, Dn is the nominal linear density (dtex) of the supply yarn. The experimental data also showed that the linear density, D on the output roller depends only on the nominal linear density, Dn and twist zone tension, w. w D ¼ 0:93D0 þ 2:0 ¼ 1:0881Dn 1 1:2085 ð5Þ 208 This relation was found to agree with experimental data within 2% [3]. Thus, the radii can be calculated from the definition of linear density, D1 ¼ pr02 1; 000; 000 cm q or
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D1 ðdtexÞ r0 ¼ 103 pq
ð6Þ
where q and r0 are the density (g/cm3 ) and the radius (cm) of the yarn, respectively. 4. Yarn speed In a false twist process, the twist construction causes a decrease in the yarn speed in the twist zone. Because of the construction during the twisting, the speed of the twisted yarn is different from the speed of the untwisted yarn. Accordingly, the yarn speed required for calculating the heating time cannot be obtained by measuring the speed of the top feed rolls, which is the speed of the untwisted yarn. Further, the actual twists per inch of the yarn in the zone is not known due to the distribution of twists from the twisting point (spindle) toward the heating zone. If the product of the linear density and speed of the threadline is D1 Vtex in the speed zone and D V on the output roller since, at equilibrium, the mass flow through the system per unit time is constant: D1 Vtex ¼ D V
ð7Þ
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If L is the length of the heating medium in the twist zone, then the heating time is given by: t ¼
L LD1 ¼ Vtex D V
ð8Þ
Since the yarn through put speed V can be measured on the output roller, the texturing velocity of the yarn in the heater and the contact time can be obtained in terms of the linear density, both in the twist zone and on the output roller.
5. Yarn thermal properties Hearle et al. have reported that highly twisted nylon and polyester yarns with a twist multiplier of more than 70 have a packing factor of the order of 0.75 [12]. The coefficient of thermal conductivity of the yarn was calculated from the following equation [2]. # " U ð9Þ kyarn ¼ ka 1 þ a ð1 UÞ=4 þ ðkf kk aÞ The values of the thermal conductivity of polyester and nylon fibers are kf ¼ 0:1406 (J/m K) and kfiber ¼ 0:2428 (J/m K), respectively. The thermal properties of the yarns used in the calculations are given in Table 1 [13]. This completes the data required for the calculations. Solution of the coupled set of differential Eqs. (1a)–(1e) was obtained using a finite difference scheme. The net radiative heat transfer to each yarn surface element was obtained by simultaneous solution of all the radiative transfer equations. A grid resolution study confirmed the accuracy of results for a 434 32 uniform staggered grid. Convergence of the non-linear equation solution was obtained using a relaxation factor of 0.85. The time step of 0.0005 s was adequate and produced the same results as shorter time steps.
6. Experimental set-up and procedure To compare the experimental values and the predicted values of the surface temperature, the false twist texturing machine at the textile factory in I_ stanbul, which permits mechanical texturing speeds up to 1500 m/min, was used for the study (Fig. 1). Three yarns of polyester fiber were run (Table 2). Table 1 Thermal properties of the yarn in the calculations Yarn type
Tg and Tm (°C)
Density, q (kg/m3 )
Specific heat, C (J/kg K)
Nylon 6.6 Polyester
45 and 260 45 and 215
1040 1030
3307 1883
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Table 2 Yarns used in the experiment Number
Fiber
Denier (dtex)
Yarn diameter (cm)
1 2 3
Polyester Polyester Polyester
70 (63) 100 (90) 185 (167)
0.00859 0.0107 0.01436
In the experiment, the texturing speed was changed between 600 and 1400 m/min in steps of 100 m/min in order to change the yarn residence time in the heater, and the heater temperature was set to a constant value. The Barmag high temperature heater is used in the false twist texturing system. In this type of heater, the yarn is heated based on the convection–radiation principle. The yarn is supported in the heater by the help of ceramic supporting points situated at the entry and exit of the heater. Heater temperatures up to 1100 °C are set with the aid of the temperature controller. The specification of the heater used in these experiments is given in Table 3. The yarn, after being heated in the heater, passes over a cooling plate having a length of 80 cm. Then, the yarn enters the friction discs for insertion of the twist. The actual temperature of the yarn depends on the heater temperature, the residence time of the yarn in the heater and the thermal properties of the yarn. The actual temperature of the yarn at the exit of the heater was measured by the ‘‘fiber tempâ ’’ measuring system by Luxtron-Transmet at the inlet and exit of the heater. The measuring head comprises two sensors. The sensitivity element of its probe was located approximately 1/10 in. from the heater sides. The use of this noncontact type instrument eliminates the error produced by the frictional heat developed between the sensor and the yarn in contact type temperature measuring devices. The temperature measurement is based on heat exchange by convection between the running yarn and the measuring head. The yarn temperature is calculated with the aid of the microprocessor from the relationship between the heat input, heat output and the temperatures of the two measuring sensors. The tolerance of the sensors in the temperature measurements is 2 °C. After calibrating the instrument, the temperature of the yarn was measured at spindle speeds ranging from 100,000 rpm to 500,000 rpm. Five readings were taken at each spindle speed. In these experiments, a coarse yarn with a linear density of 167 dtex was used. These yarns have the longest heating time, and the temperature variation along the yarn cross-section can be no-
Table 3 Heater specifications Heater type
High temperature convection–radiation heater
Heater dimensions Length Width Thickness
1200 mm outer–800 mm inner 330 mm 200 mm
Heater temperature range
200–1100 °C
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ticeable. During the experiments, the heater temperature, yarn inlet and outlet temperatures, ambient air temperature and relative humidity and texturing velocity were measured, and temperatures were monitored throughout the system.
7. Results and discussion To test and validate the formulation presented in this study, the calculated surface temperature of the yarn at the exit of the heater were compared with experimental values at different heater temperatures (Fig. 2). The outputs of the experimental results were taken at 1000 m/min texturing velocity and for 167 dtex (d ¼ 0:01436 cm) polyester (PES) yarn and 600 m/min texturing velocity for 90 dtex (d ¼ 0:0135 cm) nylon 6.6 yarn. The calculated temperature values correspond well with the measured data as is shown in Fig. 2. The maximum difference between the simulated and experimental results is about 5 °C, which corresponds to about 5% deviation from the experimental values. The expected errors are 2% for the temperature measurements and 3% due to the assumption of constant temperature in the heater. For the experiment series, the heater temperature was increased in steps of 100 °C, starting with a temperature of 400 °C. The texturing speed was selected so that the yarn temperature at the
24 0
Calculated, PES Measured, PES
Yarn exit temperature,(˚C)
22 0
Calculated,Nylon 6.6 Measured, Nylon 6.6 [4]
20 0
18 0
16 0
14 0 360
380
40 0
420
440
460
480
50 0
520
Heater Temperature, (˚C)
Fig. 2. Comparison of calculated yarn temperature at the heater exit with experimental values for different heater temperatures.
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15 00
70
(a)
1200
(b)
Tset = 18 0˚C; PES filament 167 dt ex
Tset =195˚C PES 167 dtex Measur ed Vt ex [T hi s st ud y]
Me asur ed t *
Calcu lat ed V t ex
14 00
Calcu lat ed t *
55
12 00 50
Mea sur ed t * [6 ] Mea sur ed Vtex [6 ]
80
600
40
300
11 00 45
40 435
45 0
465
480
495
10 00 510
0 400
600
800
1000
0 1200
Heater Temperature,(˚C)
Heater Temperature, (˚C)
Fig. 3. Variation of texturing velocity with respect to residence time for different heater temperatures.
210 T= 195˚C ; PES set t ing t em per at ur e
18 0
15 0
Yarn temperature (˚C)
Residence time, (msec.)
13 00
900
Calcu lat ed t *
12 0
90
Vt ex = 1200 m/min.
Th= 400 ˚C
60
Th= 600 ˚C Th= 900 ˚C Th= 1000 ˚C
30
Th= 1100˚ C
0
0
25
50
75
100
125
Residence time,(msec)
Fig. 4. Variation of yarn temperature at different heater temperatures.
Texturing Velocity,(m/min.)
Calculat ed,Vt ex
Texturing Velocity,(m/min.)
60
Measu r ed t* [ This St ud y]
120
Me asur ed Vt ex
Residence time, (msec.)
65
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heater outlet was 180 and 195 °C for the polyester yarns. For these experiments, a coarse yarn with a denier of 167 dtex was selected, as this has the longest heating times and the drops in temperature along the yarn cross-section are particularly noticeable in this case. In Fig. 3a and b, the texturing speeds Vtex and the residence time t are shown as a function of the heater temperature for different exit temperatures of the polyester yarn. These measurement values were compared with the calculated values using the simulation program. It is shown that the theoretical considerations correspond very well with the measurements taken. The residence time in the heater falls hyperbolically when the heater temperature rises. This means that at very high heater temperatures, only a few minor shortenings of the heating zone can be achieved. The most effective parameter that increases the heat transfer to the yarn in a convective– radiative heater is the temperature difference between the heater and the yarn. Since the yarn temperature at the exit of the heater is already prescribed, the greater temperature difference can only be attained by increasing the heater temperature. In Fig. 4, the calculated heating curves of the polyester yarn with a fineness of 167 dtex are shown. At low heater temperatures, the yarn temperature approaches the yarn heater temperature asymptotically. As the heater temperature is increased, the flatter part of the heating curve falls away, and it is getting steeper. The result is that considerably lower heating times can be obtained. The fact that the residence time gets smaller with increase in heater temperature shows that shorter heating zones can be achieved at very high heater temperatures. However, the temperature profile throughout the yarn cross-section is an important parameter that affects the crimping and 0
Temperature difference, (˚C)
-1 0
-2 0
Tset = 195 ˚ C 16 7 d t ex PES yar n
Th = 400 ˚ C Th = 500 ˚ C
-3 0
Th = 700 ˚ C Th = 800 ˚ C Th = 900 ˚ C Th = 1000 ˚ C
-40
Th = 1100 ˚ C
0. 00
0.20
0.40
0. 60
0.80
1.00
r/R (-)
Fig. 5. Radial temperature distributions of yarn-simulation results.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547 200
S C
Yarn Temperature,(˚C)
160
120
S C
80
S-surf ace C-cent er
40
Vtex =300 m / m in. Vtex =600m / min. 0 0. 00
0. 20
0.40
0. 60
0. 80
1. 00
Heater length,(m)
Fig. 6. Temperature distribution of the 180 dtex nylon yarn along the heater length. 200
S
160
C S C
Yarn temperature, (˚C)
2542
120
80
Vt ex = 600 m / m in. 40
Vt ex = 1200 m / m in.
0 0. 00
0 .20
0. 40
0 .60
0. 80
1 .00
Heater length, (m)
Fig. 7. Comparison of the surface and the center temperatures of the 63 dtex polyester yarn.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
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dye absorption of the yarn [6,15], so the temperature difference between the center and the surface of the yarn must be taken into consideration. It was possible to calculate the temperature 20 0
S
C
16 0
Yarn temperature, (˚C)
S
C
12 0
80 S-surface C-cent er Vt ex = 600 m/ mi n. Vt ex = 1200 m/ m in.
40
0 0.00
0.20
0.40
0. 60
0. 80
1. 00
Heater length,(m)
Fig. 8. Comparison of the surface and the center temperatures of the 90 dtex polyester yarn.
200
S S
Yarn Temperature (˚C)
150
100
50
Vt ex= 600 m/min. Vt ex= 1200 m/min.
0 0. 00
0. 20
0. 40
0. 60
0. 80
1.00
Heater length(m)
Fig. 9. Comparison of the surface temperatures of the 167 dtex polyester yarn.
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distribution throughout the yarn at the heater exit. The results are shown in Fig. 5. As the heater temperature increases, the temperature difference between the center and the surface of the yarn grows. The maximum temperature difference was found to be 34 °C at a heater temperature of 1100 °C. The temperature distribution along the heater length can be calculated using the simulation program. The calculations have been made for a heater length of 100 cm and heater temperature of 400 °C for two different types of yarn. The temperatures were also calculated along the crosssection of the yarn. Figs. 6–9 show the surface temperature increase of the yarns at the surface and the temperature at the center. It is clear from these figures that the temperature differences between the core and the surface of the yarn decrease with the increase in heater length. The temperature distribution along the heater for different diameters and types of yarns can also be examined from these figures. Polyester yarns were found to be heated faster than nylon yarns because of the lower specific heat of the former. Similarly, coarser yarns, which have larger mass, are heated slowly. Therefore, the rate of increase in the temperature of the yarn decreases with linear density, and also, it is lower for nylon compared to that for polyester. The texturing velocity has an important role in the temperature distribution of the yarn, as it increases the temperature difference across the yarn cross-section increases. In high temperature heaters, perturbations in local air temperature due to flow disturbances may affect the yarn temperature distribution and ultimately the quality of yarn. The radiant heat
600
Tot al heating Therm al radiative heating
Heat Rate(W)
400
200
0
0
10
20
30
40
50
Time (msec)
Fig. 10. Variation of radiative and total heating of a 167 dtex polyester yarn with respect to residence time.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
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70 90 dt ex
Percentage Thermal Radiative Heating (%)
167 dtex 309 dtex
60
50
40
30 0
50
100
150
200
250
Maximum Yarn Temperature,(˚C)
Fig. 11. Percentage of heating due to thermal radiation for various diameter yarns.
transfer, however, is dependent on the steady state temperature of the heater and is less likely to be perturbed. Fig. 10 shows the radiative and total heating of a polyester yarn at 1000 °C heater temperature. The overall trend shows a decrease in both the radiative and convective heat rates as the temperature difference between the yarn and the heater diminishes with time. The peak of the total heating curve is at time zero due to the maximum temperature difference between the heater and the yarn. A simple linearization of the radiative term with respect to temperature difference between the heater and the yarn surface temperature reveals that as the yarn temperature increases, the radiation heat transfer coefficient increases. Since the radiative and convective heat rates are proportional to the yarn surface area, the total heating of the yarn increases with the yarn diameter. However, the resistance for radiative flux from the heater to the yarn increases for coarser yarns. At the same time, the convective flux decreases more rapidly compared to the radiative flux. Therefore, the relative contribution of thermal radiative heating increases with increasing yarn diameter (Fig. 11).
8. Conclusions The temperature distribution of the yarn was solved numerically. From this, the temperature in the cross-section of the yarn and the temperature distribution along the heater can be found.
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The temperature difference across the yarn cross-section at the exit of the heater increases as the heater temperature increases. The maximum temperature difference between the center and the surface of the polyester yarn was calculated to be 34 °C for the 167 dtex polyester yarn at a yarn speed of 1100 m/min. Similarly, the maximum temperature difference between the center and the surface of nylon yarns was calculated to be 11 °C for 600 m/min yarn speed for 180 dtex nylon yarns. Since the linear densities for nylon yarns can be larger, of the order of 450–1800 dtex, when used as carpet yarns, high temperature heaters can cause a higher temperature difference across the yarn crosssection. When a certain temperature difference along the yarn cross-section is reached, a decline in the quality of yarn can be expected [14]. On attaining an average yarn temperature of 195 °C, the temperature difference should not exceed 24 °C at the heater exit. In order to obtain a low radial temperature difference, the heater temperature can be maintained below 900 °C. An almost uniform temperature distribution across the yarn diameter is achieved below this temperature. The yarn temperature distribution and heating time in the heater varies widely depending on the surface temperature of the heater. Heating times from 15 to 125 ms were predicted for the 195 °C setting temperature. This suggests that through the control of the heater temperature, the yarn temperature distribution and heating time can be optimized. In addition, the texturing costs and heat loss to the environment can potentially be reduced for the false twist texturing process. Synthetic yarns, which have higher linear densities, are heated slowly. This is due to the decrease in the ratio of surface area to the mass of the yarn with increase in linear density. Therefore, the rate of increase in the temperature of the yarn decreases with linear density. Also, it is lower for nylon compared to that for polyester. In high temperature heaters, energy is transferred from the heater surface to the yarn by both convection and radiation. As the yarn temperature approaches its heat setting temperature, the total heat rate decreases. However, the calculated results show that the relative contribution of radiation increases up to 60% of the total with yarn temperature and diameter. These results provide a basis for selecting the heater parameters to obtain an optimum temperature distribution across the yarn diameter at the exit of the heater as soon as possible and to minimize the waste of energy.
References [1] Gupta VB, Majumdar A, Seth KK. Structural changes in nylon 6 yarn on heat-setting and friction twisted texturing. Textile Research Journal 1974:539–44. [2] Egambaram T, Afify EM, El-Shiekh A. Heat transfer in false-twist texturing. Textile Research Journal 1974:803– 12. [3] Jones CR, Mason T. Heat transfer in false-twist-bulking process. J Textile Institute 1970;62:147–65. [4] Brooks R. An experimental method for determining the heat transfer coefficient of polymeric fibers and yarns during rapid convective heating. J Textile Institute 1984;6:398–404. [5] Wulfhorst B, Meier K. Simulation der Fadener- w€ armung im Falschdrahttexturierproseß. Melliand Textilberichte 1991;72:695–700. [6] Wulfhorst B, Meier K. Investigations on a short high-temperature heater. Chemiefasern/Textilindustrie 1993;43:40–5.
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[7] Bruske JF. Technologies and Machines for texturing of filament yarns. Chemical Fibers International 1995;45:136– 9. [8] Siegel R, Howell JR. Thermal radiation heat transfer. Taylor & Francis; 1992. [9] Rea SN. Rapid method for determining concentric cylinder radiation view factors. AIAA J 1975;13(8):1112–23. [10] Reid RL, Tennant JS. Annular ring view factors. AIAA J 1973;11(10):1446–8. [11] Sala A. Radiation properties of materials. Elsevier; 1986. [12] Hearle JWS, Grosberg P, Backer S. Structural mechanics of fibers, yarns and fabrics. New York: WileyInterscience; 1970. [13] Warner SB. Fiber science. Prentice Hall; 1995. [14] Dupeuble JC. Texturierung von PA-Garnen auf Texturier-maschinen mit Hochtemperaturheizer. Chemiefasern/ Textilindustrie 1993;(43):831–4. [15] Pal SK, Gandhi RS, Kothari VK. Influence of texturing parameters on structural properties of microfiber polyester yarns. Chemical Fibers International 1995;(45):418–20.
Analysis of a high temperature heater in a false twist texturing process Nurdil Eskin
*
€ . Makina Fak€ultesi, I_ n€on€u Cad. No 81, G€ I_ .T.U um€ ußs suyu, Taksim, 80191 I_ stanbul, Turkey Received 14 September 2002; accepted 26 December 2002
Abstract The production of textured filament yarns by false twist texturing is an important commercial method that requires heating. In this study, the transient two dimensional modeling of the yarn, heated by high temperature heaters in a false twist texturing process was developed in order to investigate the influence of various heating conditions on the yarn temperature distribution and to quantify the relative contribution of thermal radiation to the total heating. The surface temperatures and the residence time of yarns of different diameters were measured and compared with the simulation results. The temperature distribution in the cross-section of the yarns was calculated for various yarn speeds and for different heater temperatures. The temperature difference between the surface and the center of different types of yarns along the heater was found. For a yarn in a heater, energy is transferred from the heater surface to the yarn by both convection and radiation. As the yarn approaches its heat setting temperature, the total heat rate decreases. However, the calculated results show that the relative contribution of radiation increases up to 60% of the total with yarn temperature and diameter. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Transient heating; Convection radiation type heaters; Yarn; Yarn heating
1. Introduction As natural sources decrease, synthetic yarns are becoming more popular as a result of the increase in the need for textile products in the world. Since synthetic yarns do not have the appearance and handling characteristics of natural fibers, certain processes have to be applied to
*
Fax: +90-212-245-0795. E-mail address: [email protected] (N. Eskin).
0196-8904/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0196-8904(03)00014-1
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Nomenclature A C D F1!2 h k L N V q r0 S T t w
area (m2 ) specific heat (J/kg K) linear density (kg/m3 m) view factor heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) heater length (m) inserted twist (turns/m) velocity (m/s) heat flux (W/m2 ) yarn radius (m) distance between surfaces (m) temperature (°C) time (s) tension in twist zone (gf )
Greeks a e U q / r
thermal diffusivity (m2 /s) emissivity packing factor density (kg/m3 ) viewing angle Stefan–Boltzman constant (W/m2 K4 )
Subscripts a air f fiber g glass transition m melting set setting tex texturing
synthetic yarns in order to combine the superior properties of synthetics, like high strength, uniformity and stretch, with the features that are unique to natural fibers. Texturing is one of the processes that give a crimped and bulky structure, a natural appearance, touch, warmth, stretch and bulk. The method mostly used among texturing processes is false twist texturing, which is used in thermoplastic filaments. If a stationary multi-filament yarn is held at both ends and twisted in the center by suitable means, the yarn could have an equal amount of twist on each side. Although the twist on each side is other than zero, the algebraic sum of the twist throughout
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547 Yarn
Spindle
Output rollers
Cooling plate
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Heater
Feed rollers (Delivery mechanism) Air
Air
Fig. 1. A false twist texturing machine.
the yarn is zero. As the false twist device is rotated continuously, a twist forms in the moving yarn passing from the feed rollers to the twister, but it becomes untwisted due to the reverse twisting effect after the twisting zone. For this reason, this process is called false twist texturing (Fig. 1). During this process, a thermoplastic yarn is first highly twisted, next heated to alleviate the stresses resulting from twisting to set the twist into the molecular structure of the filaments and then cooled in a twisted form. After being cooled, the yarn is untwisted by the twist head to give a high torque, high bulk product. Since the filaments and their molecules have already obtained a migrating helical configuration, the physical untwisting of the filaments will not straighten the molecules. The production of textured filament yarns by false twist texturing is an important commercial method due to its higher texturing speeds and convenience. Higher production rates and, hence, higher yarn speeds necessitate the use of longer heaters so as to heat the yarn adequately. The heater and cooler lengths reach 2.5 m, depending on the fineness of the yarn to be textured. Machine producers and users are, thus, faced with considerable problems. The texturing zone needed to be shortened in order to reduce the investment costs, to make the setting-up and operability of these machines easier, to decrease instabilities and to increase the production further. In order to realize this objective, a shortening of the heating zone primarily must be accomplished [1]. High temperature heaters with operating temperatures up to 1100 °C considerably reduce the residence time required to reach the setting temperature of the polymer, which is the temperature above its glass transition temperature and below its melting temperature. At this temperature, the polymer gains its plastic character, and it can be easily deformed. In order to attain this setting temperature throughout the whole heating process, the heater must be designed with optimum dimensions and temperature. Also, at the heater outlet, the yarn temperature distribution should be uniform throughout the yarn crosssection. Therefore, besides the heater characteristics, one of the important parameters, which affect uniform yarn temperature, is the yarn speed. Previous approaches for using shortened heaters were limited to experimental studies [1–4]. Mathematical models were limited to one dimensional steady state analyses in order to support the experimental studies. Wulfhorst et al. developed a one dimensional simulation model of the temperature distribution of yarn at steady state conditions assuming constant thermal properties. In their study, they ignored the radiation heat transfer, assuming its effect to be less than 10% on the yarn heating. Besides that, the longitudinal heat transfer and texturing speed of the yarn was not taken into consideration in the formulation [5,6]. In this study, unsteady two dimensional modelling of the yarn heated by convection–radiation type high temperature heaters in a false twist texturing process is developed, and the parameters affecting the performance of the texturing process are analyzed according to the simulation.
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2. Mathematical analysis In the high temperature heaters, the residence time of the yarn in the heating zone ranges approximately from 0.12 to 0.072 s, depending on the speed of the yarn and the length of the heater. During this short time, the temperature of the yarn has to be raised to the yarn heat setting temperature. The problem is to determine the temperature at all points within the yarn as a function of time when it is suddenly exposed to hot air and infrared radiation. The following assumptions are based on the yarn behavior observed during texturing with high temperature heating [1–3] and the current texturing experiments with convection–radiation heating [4,6,7]: (a) Provided that the amount of twist inserted in a multi-filament yarn is insufficient to cause snarling, the yarn shape approximates to an infinitely long cylinder. Therefore, the yarn can be assumed to be a solid cylinder [7]. (b) Any point in the cross-section of the yarn can be located by the polar coordinates r, h and z. While the yarn is in the heater, it rotates at a high speed (up to 500,000 rpm) due to the twisting by the spindle. In the heater, the yarn is heated by convection from the hot surrounding air. It is also heated by radiation from the surrounding surfaces of the heater. Resulting from these factors, the yarn is heated uniformly all around its circumference, and the temperature would be the same around the circumference at any radius in the cross-section of the yarn. Then, the temperature of the yarn is independent of the coordinate h. (c) The temperature of the heater surface is not constant throughout its length. The measurement of temperature at different points of the heater showed that the temperature profile was parabolic with the peak temperature at the middle of the heater [6]. Therefore, the heater surface temperature profiles used in this study were assumed to be parabolic. These measurements were conducted without yarn passing through. It can be assumed that the latter causes the air to be mixed better within the heater, and then, a more even temperature distribution is available. With the assumptions above, the differential equation describing the yarn temperature is given by: 2 1 o oT oT oT oT r ¼ qC ð1aÞ qCVtex þk k 2 r or or oz oz ot The specification of the inlet yarn temperature as the ambient temperature serves as the initial boundary condition. Hence, T ðr; z; tÞ ¼ T0
at t ¼ 0
ð1bÞ
and the boundary conditions, oT ðr; z; tÞ ¼0 or k
at r ¼ 0
oT ðr; z; tÞ ¼ hðTa T ðr; z; tÞÞ þ q or
oT ¼0 oz
at z ¼ 0 and z ¼ L
ð1cÞ at r ¼ r0
ð1dÞ ð1eÞ
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
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Here, q represents the incoming energy due to thermal radiation from the heater wall. The net radiative method for enclosures was used to calculate the thermal radiative heat flux to each surface [8]. N N X X dkj 1 ej Fkj qj ¼ Fkj rðTk4 Tj4 Þ e e j j j¼1 j¼1
F12 ¼
1 A1
Z
Z A1
A2
cos /1 cos /2 dA2 dA1 2 pS1!2
The view factors between the exterior ring element of the yarn and the annular elements of the heater were obtained from the literature [9,10]. The problem, Eq. (1) is expressed in dimensionless form as, 2 o2 h 1 oh oh oh 2o h þ u ¼ þ b 2 2 og g og oc oc on
n>0
0
0
ð2aÞ
subject to the following initial and boundary conditions: h ¼ h0
at f ¼ 0
ð2bÞ
oh ¼0 og
at g ¼ 0
ð2cÞ
oh ¼ Biðha hÞ þ # og
at g ¼ 1
ð2dÞ
oh ¼0 oc
and c ¼ 1
ð2eÞ
at
c¼0
where the various dimensionless quantities are defined by: hðg; c; nÞ ¼ T =Tr ; Bi ¼ hr0 =k; n¼
ta=r02 ;
g ¼ r=r0 ;
# ¼ qr0 Tr =k; ha ¼ Ta =Tr ;
c ¼ z=L b ¼ r0 =L
Vtex r02 u¼ aL
ð2fÞ
Here, Tr is the reference temperature, h0 is the dimensionless initial temperature and Bi is the Biot number. The emissivity of the heater is taken to be 0.75, and the emissivity of the yarn is taken to be 0.7 [11]. Natural convection within the heater is in the laminar regime. Based on the maximum temperature difference and a characteristic length equal to the heater height, the Rayleigh number is 2:35 106 , which is below the critical value.
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3. Yarn diameter The dimensions of a yarn are expressed in units of tex or decitex (dtex), which are the mass of the yarn in grams per 1000 m (106 kg/m) or 10,000 m (107 kg/m). This unit (dtex) has replaced the denier, which is expressed as 1 g/9000 m (1:111 107 kg/m). The yarn radius r0 can be calculated by using the yarn linear density D1 (dtex), which can be calculated in terms of the tension in twist zone, w and inserted twist N as follows [3]: 29N 2 105 D1 ¼ D0 1 þ f0:9D0 2ðw 5Þg ð3Þ 2ð60 wÞ where D0 is the linear density (dtex) in the twist zone for zero twist. w D0 ¼ 1:17Dn 1 3:75 208
ð4Þ
Here, Dn is the nominal linear density (dtex) of the supply yarn. The experimental data also showed that the linear density, D on the output roller depends only on the nominal linear density, Dn and twist zone tension, w. w D ¼ 0:93D0 þ 2:0 ¼ 1:0881Dn 1 1:2085 ð5Þ 208 This relation was found to agree with experimental data within 2% [3]. Thus, the radii can be calculated from the definition of linear density, D1 ¼ pr02 1; 000; 000 cm q or
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D1 ðdtexÞ r0 ¼ 103 pq
ð6Þ
where q and r0 are the density (g/cm3 ) and the radius (cm) of the yarn, respectively. 4. Yarn speed In a false twist process, the twist construction causes a decrease in the yarn speed in the twist zone. Because of the construction during the twisting, the speed of the twisted yarn is different from the speed of the untwisted yarn. Accordingly, the yarn speed required for calculating the heating time cannot be obtained by measuring the speed of the top feed rolls, which is the speed of the untwisted yarn. Further, the actual twists per inch of the yarn in the zone is not known due to the distribution of twists from the twisting point (spindle) toward the heating zone. If the product of the linear density and speed of the threadline is D1 Vtex in the speed zone and D V on the output roller since, at equilibrium, the mass flow through the system per unit time is constant: D1 Vtex ¼ D V
ð7Þ
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
2537
If L is the length of the heating medium in the twist zone, then the heating time is given by: t ¼
L LD1 ¼ Vtex D V
ð8Þ
Since the yarn through put speed V can be measured on the output roller, the texturing velocity of the yarn in the heater and the contact time can be obtained in terms of the linear density, both in the twist zone and on the output roller.
5. Yarn thermal properties Hearle et al. have reported that highly twisted nylon and polyester yarns with a twist multiplier of more than 70 have a packing factor of the order of 0.75 [12]. The coefficient of thermal conductivity of the yarn was calculated from the following equation [2]. # " U ð9Þ kyarn ¼ ka 1 þ a ð1 UÞ=4 þ ðkf kk aÞ The values of the thermal conductivity of polyester and nylon fibers are kf ¼ 0:1406 (J/m K) and kfiber ¼ 0:2428 (J/m K), respectively. The thermal properties of the yarns used in the calculations are given in Table 1 [13]. This completes the data required for the calculations. Solution of the coupled set of differential Eqs. (1a)–(1e) was obtained using a finite difference scheme. The net radiative heat transfer to each yarn surface element was obtained by simultaneous solution of all the radiative transfer equations. A grid resolution study confirmed the accuracy of results for a 434 32 uniform staggered grid. Convergence of the non-linear equation solution was obtained using a relaxation factor of 0.85. The time step of 0.0005 s was adequate and produced the same results as shorter time steps.
6. Experimental set-up and procedure To compare the experimental values and the predicted values of the surface temperature, the false twist texturing machine at the textile factory in I_ stanbul, which permits mechanical texturing speeds up to 1500 m/min, was used for the study (Fig. 1). Three yarns of polyester fiber were run (Table 2). Table 1 Thermal properties of the yarn in the calculations Yarn type
Tg and Tm (°C)
Density, q (kg/m3 )
Specific heat, C (J/kg K)
Nylon 6.6 Polyester
45 and 260 45 and 215
1040 1030
3307 1883
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Table 2 Yarns used in the experiment Number
Fiber
Denier (dtex)
Yarn diameter (cm)
1 2 3
Polyester Polyester Polyester
70 (63) 100 (90) 185 (167)
0.00859 0.0107 0.01436
In the experiment, the texturing speed was changed between 600 and 1400 m/min in steps of 100 m/min in order to change the yarn residence time in the heater, and the heater temperature was set to a constant value. The Barmag high temperature heater is used in the false twist texturing system. In this type of heater, the yarn is heated based on the convection–radiation principle. The yarn is supported in the heater by the help of ceramic supporting points situated at the entry and exit of the heater. Heater temperatures up to 1100 °C are set with the aid of the temperature controller. The specification of the heater used in these experiments is given in Table 3. The yarn, after being heated in the heater, passes over a cooling plate having a length of 80 cm. Then, the yarn enters the friction discs for insertion of the twist. The actual temperature of the yarn depends on the heater temperature, the residence time of the yarn in the heater and the thermal properties of the yarn. The actual temperature of the yarn at the exit of the heater was measured by the ‘‘fiber tempâ ’’ measuring system by Luxtron-Transmet at the inlet and exit of the heater. The measuring head comprises two sensors. The sensitivity element of its probe was located approximately 1/10 in. from the heater sides. The use of this noncontact type instrument eliminates the error produced by the frictional heat developed between the sensor and the yarn in contact type temperature measuring devices. The temperature measurement is based on heat exchange by convection between the running yarn and the measuring head. The yarn temperature is calculated with the aid of the microprocessor from the relationship between the heat input, heat output and the temperatures of the two measuring sensors. The tolerance of the sensors in the temperature measurements is 2 °C. After calibrating the instrument, the temperature of the yarn was measured at spindle speeds ranging from 100,000 rpm to 500,000 rpm. Five readings were taken at each spindle speed. In these experiments, a coarse yarn with a linear density of 167 dtex was used. These yarns have the longest heating time, and the temperature variation along the yarn cross-section can be no-
Table 3 Heater specifications Heater type
High temperature convection–radiation heater
Heater dimensions Length Width Thickness
1200 mm outer–800 mm inner 330 mm 200 mm
Heater temperature range
200–1100 °C
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
2539
ticeable. During the experiments, the heater temperature, yarn inlet and outlet temperatures, ambient air temperature and relative humidity and texturing velocity were measured, and temperatures were monitored throughout the system.
7. Results and discussion To test and validate the formulation presented in this study, the calculated surface temperature of the yarn at the exit of the heater were compared with experimental values at different heater temperatures (Fig. 2). The outputs of the experimental results were taken at 1000 m/min texturing velocity and for 167 dtex (d ¼ 0:01436 cm) polyester (PES) yarn and 600 m/min texturing velocity for 90 dtex (d ¼ 0:0135 cm) nylon 6.6 yarn. The calculated temperature values correspond well with the measured data as is shown in Fig. 2. The maximum difference between the simulated and experimental results is about 5 °C, which corresponds to about 5% deviation from the experimental values. The expected errors are 2% for the temperature measurements and 3% due to the assumption of constant temperature in the heater. For the experiment series, the heater temperature was increased in steps of 100 °C, starting with a temperature of 400 °C. The texturing speed was selected so that the yarn temperature at the
24 0
Calculated, PES Measured, PES
Yarn exit temperature,(˚C)
22 0
Calculated,Nylon 6.6 Measured, Nylon 6.6 [4]
20 0
18 0
16 0
14 0 360
380
40 0
420
440
460
480
50 0
520
Heater Temperature, (˚C)
Fig. 2. Comparison of calculated yarn temperature at the heater exit with experimental values for different heater temperatures.
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N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547 160
15 00
70
(a)
1200
(b)
Tset = 18 0˚C; PES filament 167 dt ex
Tset =195˚C PES 167 dtex Measur ed Vt ex [T hi s st ud y]
Me asur ed t *
Calcu lat ed V t ex
14 00
Calcu lat ed t *
55
12 00 50
Mea sur ed t * [6 ] Mea sur ed Vtex [6 ]
80
600
40
300
11 00 45
40 435
45 0
465
480
495
10 00 510
0 400
600
800
1000
0 1200
Heater Temperature,(˚C)
Heater Temperature, (˚C)
Fig. 3. Variation of texturing velocity with respect to residence time for different heater temperatures.
210 T= 195˚C ; PES set t ing t em per at ur e
18 0
15 0
Yarn temperature (˚C)
Residence time, (msec.)
13 00
900
Calcu lat ed t *
12 0
90
Vt ex = 1200 m/min.
Th= 400 ˚C
60
Th= 600 ˚C Th= 900 ˚C Th= 1000 ˚C
30
Th= 1100˚ C
0
0
25
50
75
100
125
Residence time,(msec)
Fig. 4. Variation of yarn temperature at different heater temperatures.
Texturing Velocity,(m/min.)
Calculat ed,Vt ex
Texturing Velocity,(m/min.)
60
Measu r ed t* [ This St ud y]
120
Me asur ed Vt ex
Residence time, (msec.)
65
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
2541
heater outlet was 180 and 195 °C for the polyester yarns. For these experiments, a coarse yarn with a denier of 167 dtex was selected, as this has the longest heating times and the drops in temperature along the yarn cross-section are particularly noticeable in this case. In Fig. 3a and b, the texturing speeds Vtex and the residence time t are shown as a function of the heater temperature for different exit temperatures of the polyester yarn. These measurement values were compared with the calculated values using the simulation program. It is shown that the theoretical considerations correspond very well with the measurements taken. The residence time in the heater falls hyperbolically when the heater temperature rises. This means that at very high heater temperatures, only a few minor shortenings of the heating zone can be achieved. The most effective parameter that increases the heat transfer to the yarn in a convective– radiative heater is the temperature difference between the heater and the yarn. Since the yarn temperature at the exit of the heater is already prescribed, the greater temperature difference can only be attained by increasing the heater temperature. In Fig. 4, the calculated heating curves of the polyester yarn with a fineness of 167 dtex are shown. At low heater temperatures, the yarn temperature approaches the yarn heater temperature asymptotically. As the heater temperature is increased, the flatter part of the heating curve falls away, and it is getting steeper. The result is that considerably lower heating times can be obtained. The fact that the residence time gets smaller with increase in heater temperature shows that shorter heating zones can be achieved at very high heater temperatures. However, the temperature profile throughout the yarn cross-section is an important parameter that affects the crimping and 0
Temperature difference, (˚C)
-1 0
-2 0
Tset = 195 ˚ C 16 7 d t ex PES yar n
Th = 400 ˚ C Th = 500 ˚ C
-3 0
Th = 700 ˚ C Th = 800 ˚ C Th = 900 ˚ C Th = 1000 ˚ C
-40
Th = 1100 ˚ C
0. 00
0.20
0.40
0. 60
0.80
1.00
r/R (-)
Fig. 5. Radial temperature distributions of yarn-simulation results.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547 200
S C
Yarn Temperature,(˚C)
160
120
S C
80
S-surf ace C-cent er
40
Vtex =300 m / m in. Vtex =600m / min. 0 0. 00
0. 20
0.40
0. 60
0. 80
1. 00
Heater length,(m)
Fig. 6. Temperature distribution of the 180 dtex nylon yarn along the heater length. 200
S
160
C S C
Yarn temperature, (˚C)
2542
120
80
Vt ex = 600 m / m in. 40
Vt ex = 1200 m / m in.
0 0. 00
0 .20
0. 40
0 .60
0. 80
1 .00
Heater length, (m)
Fig. 7. Comparison of the surface and the center temperatures of the 63 dtex polyester yarn.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
2543
dye absorption of the yarn [6,15], so the temperature difference between the center and the surface of the yarn must be taken into consideration. It was possible to calculate the temperature 20 0
S
C
16 0
Yarn temperature, (˚C)
S
C
12 0
80 S-surface C-cent er Vt ex = 600 m/ mi n. Vt ex = 1200 m/ m in.
40
0 0.00
0.20
0.40
0. 60
0. 80
1. 00
Heater length,(m)
Fig. 8. Comparison of the surface and the center temperatures of the 90 dtex polyester yarn.
200
S S
Yarn Temperature (˚C)
150
100
50
Vt ex= 600 m/min. Vt ex= 1200 m/min.
0 0. 00
0. 20
0. 40
0. 60
0. 80
1.00
Heater length(m)
Fig. 9. Comparison of the surface temperatures of the 167 dtex polyester yarn.
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N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
distribution throughout the yarn at the heater exit. The results are shown in Fig. 5. As the heater temperature increases, the temperature difference between the center and the surface of the yarn grows. The maximum temperature difference was found to be 34 °C at a heater temperature of 1100 °C. The temperature distribution along the heater length can be calculated using the simulation program. The calculations have been made for a heater length of 100 cm and heater temperature of 400 °C for two different types of yarn. The temperatures were also calculated along the crosssection of the yarn. Figs. 6–9 show the surface temperature increase of the yarns at the surface and the temperature at the center. It is clear from these figures that the temperature differences between the core and the surface of the yarn decrease with the increase in heater length. The temperature distribution along the heater for different diameters and types of yarns can also be examined from these figures. Polyester yarns were found to be heated faster than nylon yarns because of the lower specific heat of the former. Similarly, coarser yarns, which have larger mass, are heated slowly. Therefore, the rate of increase in the temperature of the yarn decreases with linear density, and also, it is lower for nylon compared to that for polyester. The texturing velocity has an important role in the temperature distribution of the yarn, as it increases the temperature difference across the yarn cross-section increases. In high temperature heaters, perturbations in local air temperature due to flow disturbances may affect the yarn temperature distribution and ultimately the quality of yarn. The radiant heat
600
Tot al heating Therm al radiative heating
Heat Rate(W)
400
200
0
0
10
20
30
40
50
Time (msec)
Fig. 10. Variation of radiative and total heating of a 167 dtex polyester yarn with respect to residence time.
N. Eskin / Energy Conversion and Management 44 (2003) 2531–2547
2545
70 90 dt ex
Percentage Thermal Radiative Heating (%)
167 dtex 309 dtex
60
50
40
30 0
50
100
150
200
250
Maximum Yarn Temperature,(˚C)
Fig. 11. Percentage of heating due to thermal radiation for various diameter yarns.
transfer, however, is dependent on the steady state temperature of the heater and is less likely to be perturbed. Fig. 10 shows the radiative and total heating of a polyester yarn at 1000 °C heater temperature. The overall trend shows a decrease in both the radiative and convective heat rates as the temperature difference between the yarn and the heater diminishes with time. The peak of the total heating curve is at time zero due to the maximum temperature difference between the heater and the yarn. A simple linearization of the radiative term with respect to temperature difference between the heater and the yarn surface temperature reveals that as the yarn temperature increases, the radiation heat transfer coefficient increases. Since the radiative and convective heat rates are proportional to the yarn surface area, the total heating of the yarn increases with the yarn diameter. However, the resistance for radiative flux from the heater to the yarn increases for coarser yarns. At the same time, the convective flux decreases more rapidly compared to the radiative flux. Therefore, the relative contribution of thermal radiative heating increases with increasing yarn diameter (Fig. 11).
8. Conclusions The temperature distribution of the yarn was solved numerically. From this, the temperature in the cross-section of the yarn and the temperature distribution along the heater can be found.
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The temperature difference across the yarn cross-section at the exit of the heater increases as the heater temperature increases. The maximum temperature difference between the center and the surface of the polyester yarn was calculated to be 34 °C for the 167 dtex polyester yarn at a yarn speed of 1100 m/min. Similarly, the maximum temperature difference between the center and the surface of nylon yarns was calculated to be 11 °C for 600 m/min yarn speed for 180 dtex nylon yarns. Since the linear densities for nylon yarns can be larger, of the order of 450–1800 dtex, when used as carpet yarns, high temperature heaters can cause a higher temperature difference across the yarn crosssection. When a certain temperature difference along the yarn cross-section is reached, a decline in the quality of yarn can be expected [14]. On attaining an average yarn temperature of 195 °C, the temperature difference should not exceed 24 °C at the heater exit. In order to obtain a low radial temperature difference, the heater temperature can be maintained below 900 °C. An almost uniform temperature distribution across the yarn diameter is achieved below this temperature. The yarn temperature distribution and heating time in the heater varies widely depending on the surface temperature of the heater. Heating times from 15 to 125 ms were predicted for the 195 °C setting temperature. This suggests that through the control of the heater temperature, the yarn temperature distribution and heating time can be optimized. In addition, the texturing costs and heat loss to the environment can potentially be reduced for the false twist texturing process. Synthetic yarns, which have higher linear densities, are heated slowly. This is due to the decrease in the ratio of surface area to the mass of the yarn with increase in linear density. Therefore, the rate of increase in the temperature of the yarn decreases with linear density. Also, it is lower for nylon compared to that for polyester. In high temperature heaters, energy is transferred from the heater surface to the yarn by both convection and radiation. As the yarn temperature approaches its heat setting temperature, the total heat rate decreases. However, the calculated results show that the relative contribution of radiation increases up to 60% of the total with yarn temperature and diameter. These results provide a basis for selecting the heater parameters to obtain an optimum temperature distribution across the yarn diameter at the exit of the heater as soon as possible and to minimize the waste of energy.
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