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Experimental study on heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts
Accepted Manuscript Research Paper Experimental study on Heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts Yan He, Li Liu, Pengxiao Li, Lianxiang Ma PII: DOI: Reference:
S1359-4311(17)35445-5 https://doi.org/10.1016/j.applthermaleng.2017.12.029 ATE 11550
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
22 August 2017 22 November 2017 7 December 2017
Please cite this article as: Y. He, L. Liu, P. Li, L. Ma, Experimental study on Heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts, Applied Thermal Engineering (2017), doi: https:// doi.org/10.1016/j.applthermaleng.2017.12.029
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Experimental study on Heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts Yan He1*, Li Liu1, Pengxiao Li2, Lianxiang Ma1* 1. School of Mechanical Engineering, Qingdao University of Science & Technology, Qingdao, China 2. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, Chinau
Abstract This study experimentally investigates the heat transfer and friction factor (f) characteristics of a tube fitted with cross hollow twisted tape inserts of hollow widths of 6, 8 and 10 mm under uniform heat flux. Experimental data of a plain tube are compared to the standard correlations for validation. Results show that the Nusselt number (Nu) and f decrease and then increase as the hollow width increases from 6 mm to 10 mm. Nu and f for the 6 mm hollow width increase by 93%–120% and 883%–1042%, respectively, in comparison with those of the plain tube. The performance evaluation criterion(PEC) varies from 0.87 to 0.98 under a Reynolds number of 5600–18000. Correlations based on the experimental data are established to predict Nu and f under turbulent flow. These parameters match the experimental data well within 3.6% (Nu) and 2.3% (f). Key words: cross hollow twisted tape inserts; hollow width; turbulent flow; heat transfer enhancement 1. Introduction Industrial development has led to the need for efficient heat exchangers and their application to actual projects. Many active and passive techniques are used to improve the performance of heat exchangers. Such turbulators as small pipes [1, 2], drainage inserts [3], twisted tapes [4, 5] and vortex generators [6, 7, 8] are easy to use and effectively enhance heat transfer. These devices can improve the heat transfer coefficient considerably but usually with increased pressure drop. Dewan [9] summarised studies about twisted tape and wire coil inserts and concluded that twisted tape inserts are efficient under laminar flow and wire coils are efficient under turbulent flow. Liu [10] reviewed numerous inserts and implied that shape optimisation should be considered in insert design to reduce drag. Hasanpour [11] reviewed the development of twisted tapes and confirmed their effectiveness. Many studies [4, 5] have proposed mechanisms to enhance the heat transfer of twisted tapes, including the use of spiral steam lines. (1) The use of spiral steam lines means achieving a long flow path, which can increase heat transfer. (2) Swirls can be generated to increase the turbulence of the flow boundary layer. (3) The swirls enhance the mixing of fluids in the near-wall and central regions. The heat transfer and friction factor (f) characteristics of enhanced tubes fitted with twisted tapes have been studied by past experimental and numerical investigations. Sicashanmugam [10] experimentally studied helical screw tape inserts under laminar flow. The same author [13, 14]
experimentally investigated the heat transfer and f characteristics of a tube fitted with regularly spaced helical screw tape inserts under laminar and turbulent flow conditions. Zhang [15] numerically studied the heat transfer performance of tubes fitted with helical screw tapes without core rod inserts and found that the thermal performance factor varied from 1.58 to 2.35. Meanwhile, He [16] investigated the heat transfer enhancement of tubes fitted with multiple regularly spaced twisted tapes in the same manner. The results showed that the model varied from 1.64 to 2.46, which was better than those in prior studies. Bhuiya et al. [17] assessed the performance of a tube fitted with double counter twisted tape inserts and derived an empirical correlation in the function of the twisted ratio, the Reynolds number (Re) and the Prandtl number (Pr) for predicting the Nusselt number (Nu) and f. For improved heat transfer coefficient, Guo [18] proposed a model with cross twisted tape inserts. He concluded that wide cross twisted tapes had better heat transfer coefficient under laminar flow, whereas narrow twisted tapes had better heat transfer coefficient than other inserts under turbulent flow. According to them, compound heat transfer enhancement technologies can also improve heat transfer performance. A tube fitted with a conical ring combined with twisted tape was experimentally studied by Promvonge [19]. The conventional heat transfer enhancement approach commonly aims to enhance heat transfer, which is often accompanied by a significant increase in flow resistance. To reveal the physical mechanism for convective heat transfer, Guo et al. [20] proposed the field synergy principle, which Liu et al. [21, 22, 23] developed into the physical quantity synergy principle. Their study suggested that convective heat transfer performance depends on the synergetic relation among the velocity, heat flux and pressure fields. Many numerical and experimental investigations have been conducted to verify the applicability of the field synergy principle in the design of units with good performance and low-flow-resistance heat transfer [25-30]. According to entrance theory, a flow field structure with a multi-longitudinal vortex has comprehensive optimisation performance that features high heat transfer efficiency and low flow resistance [31-35]. Recently, certain optimised structures have been designed for twisted tapes to improve strengthening performance without risking a large pressure drop, which is commonly caused by inserts. Murugesan [36, 37] studied heat transfer and pressure drop characteristics in a tube fitted with V- and square-cut twisted tapes under turbulent flow. The results showed that both twisted tapes offered better heat transfer enhancement than plain twisted tape. Eiamsa-ard et al. [38] reported performance indexes of a heat exchanger tube fitted with alternating clockwise and counter-clockwise twisted tapes. The experimental results implied that the heat rate, f and enhancement index of the new inserts were higher than those of typical twisted tapes. Meanwhile, the serrated tapes in the study of Eiamsa-ard et al. [39] provided a heat transfer rate that was 72.2% and 27% better than that of plain tube and typical twisted tape, respectively. The thermal performance factor implied that the serrated tape was better than the typical twisted tape. Eiamsa-ard et al. [40] designed a wing part at the age of twisted tape to enhance the degree of turbulence near the tube wall, and the experimental results showed that the delta-winglet twisted tape provided better heat transfer performance than the typical twisted tape. Guo [41] optimised the upwind area of conical strip inserts; the results implied that reducing the upwind area of the insert could reduce the pressure drop considerably but with a slight decrease in the heat transfer coefficient. Many similar optimised designs have been proposed for the twisted tape, such as perforated [42] and center-cleared twisted tapes [43]. The numerical simulation revealed that the center-cleared twisted tape had a good overall heat transfer performance. Rahimi [44] compared the
thermal-hydraulic performances of tubes fitted with perforated, notched and jagged twisted tapes and found that the jagged twisted tape had the best heat transfer performance due to the high turbulence intensity of the fluid close to the tube wall. A prior numerical simulation on the cross hollow twisted tape [45] showed that a tube fitted with cross twisted tape had good heat transfer performance under laminar flow. The cross twisted tape could generate intense swirling flow, and the hollow part played a significant role in decreasing pressure drop. The present paper experimentally investigates the heat transfer and f characteristics of a tube fitted with cross hollow twisted tape inserts with different hollow widths under turbulent flow. 2. Experimental set-up The experimental set-up used for the study consists of a Roots blower, flow meter, inlet section, test section, outlet section and the data acquisition system (Fig. 1). The inlet, test and outlet sections have the same dimensions: 18 mm inner diameter (D i) and 20 mm outer diameter (Do); they are made of stainless steel tube. The inlet section, which is 1500 mm long, is set to eliminate the entrance effect. The outlet section, which is 500 mm long, is used for outlet stability. The test section, which is 300 mm long, is wound with a nichrome heating wire that is set with small ceramic protection tubes. Then, three layers of asbestos tapes and insulation cotton tapes with 50 mm thickness are wound over the heating wire in sequence to reduce heat loss. Over the insulation layer, an auxiliary heating wire is wound over the insulation layer also to reduce radial heat loss; another insulation layer is wound on the surface. Heat flux can be controlled by setting the voltage applied to the heating wires using a voltage regulator. The inlet, test and outlet sections are connected by flanges, in-between which rubber and bakelite gaskets are placed to minimise axial heat loss. Five T-type thermocouples are uniformly arranged on the outside wall of the test to measure the wall temperature. Two groups of T-type thermocouples (one before and another after the test section) are placed to measure the air temperature at the inlet and outlet. The pressure drop in the test section is measured by a pressure transmitter. Temperatures, pressures, flow rate, voltage and current are recorded using a data logger.
Fig. 1. Diagram of experimental set-up
3. Cross hollow twisted tape inserts
The geometry information of the cross hollow twisted tapes is shown in Fig. 2. The twist ratio (y/W) of the tape is set as 3, and its length is the same as that of the test section. Central and lateral support structures are arranged for every 360° twisted pitch along the tape to connect its parts and affix it to the tube wall. The thickness of the support structures is 1 mm. The axial length of the lateral support structure is 2 mm, and the radial height (H) is 1 mm. A ring-shaped gasket is designed at the inlet of the tape and clipped inside the flange at the beginning of the test section to prevent axial movement of the tape. The outer and inner diameters of the gasket are 38 and 18 mm, which are the same as those of the rubber gasket sand bakelite gaskets and the test tube, respectively. 3D printing technology is a feasible means of manufacturing the models given the complex structure of cross hollow twisted tapes. A previous work [29] implied that these tapes may have an optimised hollow width (C) of 8 mm under laminar flow. Therefore, 6, 8 and 10 mm are selected as the hollow widths (C) of the cross hollow twisted tapes in the present study.
Fig. 2. Geometry of cross hollow twisted tapes with different hollow widths
4. Experimental procedure The flow rate to the test section is regulated by the inverter connected to the Roots blower and the bypass valve. The excess flow rate is discharged by the bypass valve, and the flow rate to the test section is discharged to the environment by the outlet section. Re varies from 5600 to 18000. The voltage of the heating wire is set to adjust the constant heat flux that we need. The related temperatures, pressure drop, flow rate, voltage and electric current are recorded by the data logger after the test section reaches steady state (The fluctuation range of temperatures should be less than 0.2 ℃.). A total of 4 h is needed from start to stability under turbulent flow. An average of approximately 600 sets of data are processed to minimise the measurement error of system. After the completion of a set of experiments, the flow rate and the electrical heat flux are adjusted to start the next set of experiments. In general, steady state is reached again after 2 h. 5. Data processing The data reduction of the measured results is summarised in this section. The heat transfer rate of air in the test section is calculated as
QQv CP （Ta,o Ta,i）. The electrical heat flux is expressed as
(1)
Qe IV .
(2)
The average value of heat transfer rate obtained by heat supplied by the electric heating wire and that absorbed by the air in the test section is determined for the calculation of internal convective heat transfer coefficient. The average heat transfer rate is determined using
Qa
Q Qe . 2
(3)
The heat transfer coefficient (h) is determined as
h
Qa , Di L (Tw,i,m Ta,m )
(4)
where the average temperature of the inner tube wall ( Tw ,i ,m ) can be calculated as
Q ln( Do / Di ) . Tw,i ,m Tw,o,m a 2wL
(5)
Therefore, Nu can be expressed by
Nu
hDi . a
(6)
f is given by
f
p . 1 L 2 U （ ） 2 Di
(7)
To evaluate the comprehensive enhancement of heat transfer, the formula of performance evaluation criterion (PEC) is proposed as [46] PEC
Nu/ Nu0 . ( f / f0 )1/3
According to the Coleman and Steele method [47] and the ANSI/ASME standard uncertainties of Re, Nu and f are calculated as follows:
Re Re
Nu Nu
f f
[(
[(
[(
2 U 2 Di 2 2 0.5 ) ( ) ( ) ( ) ] , U Di
h 2 Di 2 a 2 0.5 and ) ( ) ( ) ] h Di a
p 2 2 U 2 Di 2 L 2 0.5 ) ( ) (2 ) ( ) ( ) ] . p U Di L
(8) [48]
, the
(9)
(10)
(11)
The maximum uncertainties are calculated to be 2.3%, 4.7% and 5.2% for Re, Nu and f, respectively.
6. Results and discussion In this section, the results obtained with the tube fitted with cross hollow twisted tape inserts are depicted in the form of Nu or f versus Re. The trends of Nu/Nu0 or f/f0 versus Re are also analysed. PEC is used to evaluate the comprehensive performance of the inserts. The tapes have three different hollow widths of 6, 8 and 10 mm, and Re varies from 5600 to 18000. Moreover, the heat transfer coefficient and f of the plain tube are validated with the results obtained from the relevant correlations. 6.1. Validation of plain tube As shown in Fig. 3, the Nu and f obtained from the present experiments are compared with data obtained from the Gnielinski and Blasius equations for heat transfer and friction factor of the plain tube, respectively. The empirical correlation of Gnielinski is expressed as Nu 0.0214(Re0.8 100) Pr 0.4[1( D / L)2/3](T /T )0.45 . 0 i a,m w,i,m
(12)
The empirical correlation of Blasius is expressed as
f 0.3164/Re0.25 .
(13)
Overall, the results agree within 10% and 5% deviations with the Gnielinski and Blasius equations, respectively. This analysis shows the reliability of the experimental system. The correlations derived from the present data for the Nu and f are as follows:
Nu= 0.08938Re0.6485Pr 0.32 ,
(14)
f 0.246Re0.221.
(15)
Fig. 3. Verification of plain tube: (a) Nusselt number (Nu) (b) friction factor (f).
6.2. Effect of hollow width on heat transfer characteristics After the validation of plain tube, the cross hollow twisted tapes of different hollow widths are inserted into the test section for experiments. Figure 4(a) shows the variation in Nu versus Re for the different hollow widths (C = 6, 8 and 10 mm). The heat transfer rate increases with Re for all tapes. As a prior investigation [45] showed, the cross hollow twisted tape can generate substantial swirls in the tube. Thus, the trend of Nu can be explained by the fact that strong turbulence is caused to the flow near the tube wall by swirls as Re increases. These intensive swirls promote the mixing of fluid in the near-wall and central regions. Fig. 4(b) implies that heat transfer is better with the tube fitted with cross hollow twisted tape inserts than with the plain tube. Moreover, the tapes with 8 and 6 mm hollow widths provide the worst and best heat transfer performances, respectively. The Nu ratio (Nu/Nu0) of the tape with 6 mm hollow width is 3.8%–5.7% higher than that of the tape with 8 mm hollow width. A previous numerical work [43, 45] implied that the mechanism of heat transfer enhancement with cross hollow and center-cleared twisted tapes consists of two parts. (1) The swirls generated by the tape can enhance heat transfer, and the degree of enhancement depends on the upwind area of the tape. The enhancement is weakened as the hollow width increases because of the weakened swirls. (2) The irregular disturbance caused by the hollow part is enhanced as the hollow width increases. Fig. 5 shows that the space (S) between parts of the tape in the core region enlarges as the hollow width increases. The enlarged space allows the fluid in the core and near-wall regions to mix evenly under the influence of irregular disturbance and swirls, thereby enhancing heat transfer. The influences of
the two factors are merged under turbulent flow conditions. Thus, heat transfer capability decreases and then increases as the hollow width increases from 6 mm to 10 mm. According to the experimental data shown in Fig. 4(b), the Nu values of the tube fitted with cross hollow twisted tape inserts are 84%–120% higher than those of the plain tube.
Fig. 4. Variation in Nu or Nu ratio (Nu/Nu0) with Reynolds number (Re) for tube fitted with cross hollow twisted tape: (a) Nu (b) Nu/Nu0.
Fig. 5.Space (S) between parts of cross twisted tape in core region
6.3. Effect of hollow width on friction factor The f and f ratio of the tube fitted with cross hollow twisted tapes are shown in Fig. 6(a) and 6(b), respectively. The f of the tube fitted with tapes decreases as Re increases. This finding implies that cross hollow twisted tapes can cause additional pressure drop, leading to a higher
friction factor compared to the plain tube. The contact between the large upwind area of the twisted tape and air, long flow path and strong turbulence to the boundary layer caused by intensive swirls are the main causes of the change in resistance. The figure also shows that the hollow width plays an important role in influencing f. The tapes with 6 and 8 mm hollow widths obtains the highest and lowest f, respectively. A previous work [27] concluded that the following two explanations are the main factors that affect f. (1) The small upwind area of cross hollow twisted tape achieves small pressure loss as the hollow width increases. Meanwhile, turbulence is reduced by the weakened swirls. (2) As mentioned in Section 6.2, the large space (S) between parts of cross hollow twisted tape in the core region promotes an even mixing of the fluid in the core and near-wall regions. Consequently, f increases due to this irregular mixing. The importance of these two factors varies by Re. The experimental data show that f decreases and then increases as the hollow width of the tapes increases, as shown in Fig. 6(a). Considering heat resistance and price, the present work uses nylon for the cross hollow twisted tapes in the experiments. However, the surface of nylon is not as smooth as that of metal. Furthermore, the central support structure that connects parts of the tape may cause considerable turbulence in the core region under turbulent flow. Consequently, the variation in friction factor with hollow width under turbulent flow in the current experiment is different from that under laminar flow in a previous work [27]. However, the hollow part can be applied to reduce the additional pressure drop caused by inserts. Over the range investigated, the f of the tape with 8 mm hollow width is 17.9%–20.9% smaller than that with 6 mm hollow width.
Fig. 6. Variation in friction factor (f) or f ratio (f/f0) with Reynolds number (Re) for tube fitted with cross hollow twisted tape: (a) f (b) f/f0.
6.4. Comprehensive performance evaluation PEC is defined by Eq. (8). Figure 7 shows the variation in PEC with Re for the tube fitted with cross hollow twisted tape inserts. Overall, PEC varies from 0.87 to 0.98, which indicates that the tube fitted with cross hollow twisted tape inserts may not achieve the expected energy saving under turbulent flow. However, the tube with tape inserts is advantageous in terms of energy saving when Re is low. In comparison with a previous numerical simulation under laminar flow [27] , the tube fitted with cross twisted tape in the current study is more advantageous. The f is slightly larger than expected because the twisted tapes are made of nylon, which influences PEC. Therefore, PEC may be improved if smooth materials, such as metals, are used to manufacture the inserts.
Fig. 7. Variation in performance evaluation criterion (PEC) with Re for tube fitted with cross hollow twisted tape.
6.5. Correlations for Nusselt number and friction factor The hollow width (C) is converted to dimensionless parameters (c) as follows: c = C/W. The correlations of Re, hollow ratio (c) and Pr for Nu and f are obtained as follows:
Nu = 0.3415Re0.5911Pr0.32(0.9058c3+0.5439c2-1.345c+1.271) ,
(16)
f 9.348Re-0.3959(5.53c3+2.578c2-7.307c+3.499) .
(17)
Fig. 8(a) and 8(b) show the comparison of data obtained from the experiments and the correlations for Nu and f, respectively. The values calculated from the correlations agree with the experimental data within 3.6% (Nu) and 2.3% (f). They are in good agreement with each other. The reason for this error can be attributed to the turbulent fluctuation firstly. There are still a bit axial heat loss in the flanges. And the surface of the cross hollow twisted tapes in the experiment is rougher than metal.
Fig. 8. Comparison of experimental data and correlations for (a) Nu and (b) f.
7. Conclusion Experimental data about the heat transfer and f characteristics of a tube fitted with cross hollow twisted tapes with hollow widths of 6, 8 and 10 mm are presented in this investigation. The conclusions of this work are as follows. (1) The mechanism of heat transfer enhancement for cross hollow twisted tapes is complicated. Under turbulent flow conditions, the heat transfer coefficient and f reach their maximum values with the twisted tape with 6 mm hollow width and their minimum values with 8 mm hollow width. (2) The tube with cross hollow twisted tape inserts obtains better heat transfer enhancement under laminar flow than under turbulent flow. (3) The hollow part is a feasible structure for reducing the additional pressure drop caused by inserts and helpful in designing inserts that are advantageous in terms of energy saving. Acknowledgement
This work is financially supported by the National Natural Science Foundation of China (No. 51376069) and National key research and development program sub-project of China (No. 2017YFB0602901-4)
Nomenclature y 180° twist pitch of the twisted tape, mm W Width of the twisted tape, mm y/W Twist ratio Di Inner diameter of the tube, mm Do Outer diameter of the tube, mm L Length of the test tube, mm C Hollow width of the cross hollow twisted tape, mm H Radial height of the lateral support structure, mm Q Heat transfer rate of air in the test section, W Qv Flow rate of the test section, m3/s Qe Electrical heat flux, W Qa Average heat transfer rate, W
Density of air, kg / m
Cp
Specific heat at constant pressure of air, J / kg K
Ta,o Ta,i I V
Outlet bulk temperature of air, K Inlet bulk temperature of air, K Current output from the voltage regulator, A Voltage output from the voltage regulator, V
h
Heat transfer coefficient, W/m K
Tw,i,m Ta,m Tw,o,m
Average outer wall temperature of the test section, K Bulk average air temperature, K Average inner wall temperature of the test section, K
w
Thermal conductivity of stainless steel, W / m K
a
Thermal conductivity of air, W / m K
Dynamic viscosity of air, kg / m s
U
Bulk average velocity of air, m/s
p
Pressure drop of air, Pa
Nu Nu0 f f0
Nusselt number of the tube fitted with cross hollow twisted tape Nusselt number of the plain tube Friction factor of the tube fitted with cross hollow twisted tape Friction factor of the plain tube
3
2
Re Pr S c
Reynolds number Prandtl number Space between parts of cross twisted tape in the core region, mm Hollow ratio
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[34] Jia H, Liu W, Liu ZC, Enhancing convective heat transfer based on minimum power consumption principle, Chemical Engineering Science, 2012, 69:225-230 [35] Wang J, Liu W, Liu Z. The application of exergy destruction minimization in convective heat transfer optimization[J]. Applied Thermal Engineering, 2015, 88: 384-390 [36] P. Murugesan, K.Mayilsamy, S. Suresh, P.S.S. Srinivasan, Heat transfer and pressure drop characteristics in a circular tube fitted with and without V-cut twisted tape insert. International Communications in Heat and Mass Transfer, 2011, 38: 329 - 334. [37] P. Murugesan, K.Mayilsamy, S. Suresh, Turbulent heat transfer and pressure drop in tube fitted with square-cut twisted tape. Chinese Journal of Chemical Engineering, 2010, 18(4): 609 - 617. [38] S. Eiamsa-ard, P. Promvonge, Performance assessment in a heat exchanger tube with alternate clockwise and counter-clockwise twisted-tape inserts. International Journal of Heat and Mass Transfer, 2010, 53: 1364 - 1372. [39] S. Eiamsa-ard, P. Promvonge, Thermal characteristics in round tube fitted with serrated twisted tape. Applied Thermal Engineering, 2010, 30: 1673 - 1682. [40] S. Eiamsa-ard, K. Wongcharee, P. Eiamsa-ard, C. Thianpong, Heat transfer enhancement in a tube using delta-winglet twisted tape inserts, Applied Thermal Engineering, 2010, 30: 310 318. [41] J. Guo, Y.X. Yan, W. Liu, F.M. Jiang, A.W. Fan, Effects of upwind area of tube inserts on heat transfer and flow resistance characteristics of turbulent flow. Experimental Thermal and Fluid Science, 2013, 48: 147 - 155. [42] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Saha, M.T. Islam, Heat transfer and friction factor characteristics in turbulent flow through a tube fitted with perforated twisted tape inserts, International Communications in Heat and Mass Transfer, 2013, 46: 49 - 57. [43] J. Guo, A.W. Fan, X.Y. Zhang, W. Liu, A numerical study on heat transfer and friction factor characteristics of laminar flow in a circular tube fitted with center-cleared twisted tape. International Journal of Thermal Sciences, 2011, 50(7): 1263 - 1270. [44] M. Rahimi, S.R. Shabanian, A.A. Alsairafi, Experimental and CFD studies on heat transfer and friction factor characteristics of a tube equipped with modified twisted tape inserts. Chemical Engineering and Processing:Process Intensification, 2009, 48: 762 - 770. [45] P.X. Li, Z.C. Liu, W. Liu, G. Chen, Numerical study on heat transfer enhancement characteristics of tube inserted with centrally hollow narrow twisted tapes. International Journal of Heat and Mass Transfer, 2015, 88: 481 - 491. [46] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, International Journal of Heat and Mass Transfer, 1981, 24: 715 - 726. [47] H.W. Coleman, W.G. Steele, Experimental and Uncertainty Analysis for Engineers, Wiley, New York, 1989. [48] ANSI/ASME, Measurement Uncertainty, PTC 19.1-1985, 1986.
Highlights Mechanism of heat transfer enhancement for cross hollow twisted tapes is experimentally investigated. Tube fitted with cross hollow twisted tape inserts obtains better HTE in laminar flow than in turbulent flow. Hollow part is a feasible structure to reduce the extra pressure drop obtained.
S1359-4311(17)35445-5 https://doi.org/10.1016/j.applthermaleng.2017.12.029 ATE 11550
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Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
22 August 2017 22 November 2017 7 December 2017
Please cite this article as: Y. He, L. Liu, P. Li, L. Ma, Experimental study on Heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts, Applied Thermal Engineering (2017), doi: https:// doi.org/10.1016/j.applthermaleng.2017.12.029
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Experimental study on Heat transfer enhancement characteristics of tube with cross hollow twisted tape inserts Yan He1*, Li Liu1, Pengxiao Li2, Lianxiang Ma1* 1. School of Mechanical Engineering, Qingdao University of Science & Technology, Qingdao, China 2. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, Chinau
Abstract This study experimentally investigates the heat transfer and friction factor (f) characteristics of a tube fitted with cross hollow twisted tape inserts of hollow widths of 6, 8 and 10 mm under uniform heat flux. Experimental data of a plain tube are compared to the standard correlations for validation. Results show that the Nusselt number (Nu) and f decrease and then increase as the hollow width increases from 6 mm to 10 mm. Nu and f for the 6 mm hollow width increase by 93%–120% and 883%–1042%, respectively, in comparison with those of the plain tube. The performance evaluation criterion(PEC) varies from 0.87 to 0.98 under a Reynolds number of 5600–18000. Correlations based on the experimental data are established to predict Nu and f under turbulent flow. These parameters match the experimental data well within 3.6% (Nu) and 2.3% (f). Key words: cross hollow twisted tape inserts; hollow width; turbulent flow; heat transfer enhancement 1. Introduction Industrial development has led to the need for efficient heat exchangers and their application to actual projects. Many active and passive techniques are used to improve the performance of heat exchangers. Such turbulators as small pipes [1, 2], drainage inserts [3], twisted tapes [4, 5] and vortex generators [6, 7, 8] are easy to use and effectively enhance heat transfer. These devices can improve the heat transfer coefficient considerably but usually with increased pressure drop. Dewan [9] summarised studies about twisted tape and wire coil inserts and concluded that twisted tape inserts are efficient under laminar flow and wire coils are efficient under turbulent flow. Liu [10] reviewed numerous inserts and implied that shape optimisation should be considered in insert design to reduce drag. Hasanpour [11] reviewed the development of twisted tapes and confirmed their effectiveness. Many studies [4, 5] have proposed mechanisms to enhance the heat transfer of twisted tapes, including the use of spiral steam lines. (1) The use of spiral steam lines means achieving a long flow path, which can increase heat transfer. (2) Swirls can be generated to increase the turbulence of the flow boundary layer. (3) The swirls enhance the mixing of fluids in the near-wall and central regions. The heat transfer and friction factor (f) characteristics of enhanced tubes fitted with twisted tapes have been studied by past experimental and numerical investigations. Sicashanmugam [10] experimentally studied helical screw tape inserts under laminar flow. The same author [13, 14]
experimentally investigated the heat transfer and f characteristics of a tube fitted with regularly spaced helical screw tape inserts under laminar and turbulent flow conditions. Zhang [15] numerically studied the heat transfer performance of tubes fitted with helical screw tapes without core rod inserts and found that the thermal performance factor varied from 1.58 to 2.35. Meanwhile, He [16] investigated the heat transfer enhancement of tubes fitted with multiple regularly spaced twisted tapes in the same manner. The results showed that the model varied from 1.64 to 2.46, which was better than those in prior studies. Bhuiya et al. [17] assessed the performance of a tube fitted with double counter twisted tape inserts and derived an empirical correlation in the function of the twisted ratio, the Reynolds number (Re) and the Prandtl number (Pr) for predicting the Nusselt number (Nu) and f. For improved heat transfer coefficient, Guo [18] proposed a model with cross twisted tape inserts. He concluded that wide cross twisted tapes had better heat transfer coefficient under laminar flow, whereas narrow twisted tapes had better heat transfer coefficient than other inserts under turbulent flow. According to them, compound heat transfer enhancement technologies can also improve heat transfer performance. A tube fitted with a conical ring combined with twisted tape was experimentally studied by Promvonge [19]. The conventional heat transfer enhancement approach commonly aims to enhance heat transfer, which is often accompanied by a significant increase in flow resistance. To reveal the physical mechanism for convective heat transfer, Guo et al. [20] proposed the field synergy principle, which Liu et al. [21, 22, 23] developed into the physical quantity synergy principle. Their study suggested that convective heat transfer performance depends on the synergetic relation among the velocity, heat flux and pressure fields. Many numerical and experimental investigations have been conducted to verify the applicability of the field synergy principle in the design of units with good performance and low-flow-resistance heat transfer [25-30]. According to entrance theory, a flow field structure with a multi-longitudinal vortex has comprehensive optimisation performance that features high heat transfer efficiency and low flow resistance [31-35]. Recently, certain optimised structures have been designed for twisted tapes to improve strengthening performance without risking a large pressure drop, which is commonly caused by inserts. Murugesan [36, 37] studied heat transfer and pressure drop characteristics in a tube fitted with V- and square-cut twisted tapes under turbulent flow. The results showed that both twisted tapes offered better heat transfer enhancement than plain twisted tape. Eiamsa-ard et al. [38] reported performance indexes of a heat exchanger tube fitted with alternating clockwise and counter-clockwise twisted tapes. The experimental results implied that the heat rate, f and enhancement index of the new inserts were higher than those of typical twisted tapes. Meanwhile, the serrated tapes in the study of Eiamsa-ard et al. [39] provided a heat transfer rate that was 72.2% and 27% better than that of plain tube and typical twisted tape, respectively. The thermal performance factor implied that the serrated tape was better than the typical twisted tape. Eiamsa-ard et al. [40] designed a wing part at the age of twisted tape to enhance the degree of turbulence near the tube wall, and the experimental results showed that the delta-winglet twisted tape provided better heat transfer performance than the typical twisted tape. Guo [41] optimised the upwind area of conical strip inserts; the results implied that reducing the upwind area of the insert could reduce the pressure drop considerably but with a slight decrease in the heat transfer coefficient. Many similar optimised designs have been proposed for the twisted tape, such as perforated [42] and center-cleared twisted tapes [43]. The numerical simulation revealed that the center-cleared twisted tape had a good overall heat transfer performance. Rahimi [44] compared the
thermal-hydraulic performances of tubes fitted with perforated, notched and jagged twisted tapes and found that the jagged twisted tape had the best heat transfer performance due to the high turbulence intensity of the fluid close to the tube wall. A prior numerical simulation on the cross hollow twisted tape [45] showed that a tube fitted with cross twisted tape had good heat transfer performance under laminar flow. The cross twisted tape could generate intense swirling flow, and the hollow part played a significant role in decreasing pressure drop. The present paper experimentally investigates the heat transfer and f characteristics of a tube fitted with cross hollow twisted tape inserts with different hollow widths under turbulent flow. 2. Experimental set-up The experimental set-up used for the study consists of a Roots blower, flow meter, inlet section, test section, outlet section and the data acquisition system (Fig. 1). The inlet, test and outlet sections have the same dimensions: 18 mm inner diameter (D i) and 20 mm outer diameter (Do); they are made of stainless steel tube. The inlet section, which is 1500 mm long, is set to eliminate the entrance effect. The outlet section, which is 500 mm long, is used for outlet stability. The test section, which is 300 mm long, is wound with a nichrome heating wire that is set with small ceramic protection tubes. Then, three layers of asbestos tapes and insulation cotton tapes with 50 mm thickness are wound over the heating wire in sequence to reduce heat loss. Over the insulation layer, an auxiliary heating wire is wound over the insulation layer also to reduce radial heat loss; another insulation layer is wound on the surface. Heat flux can be controlled by setting the voltage applied to the heating wires using a voltage regulator. The inlet, test and outlet sections are connected by flanges, in-between which rubber and bakelite gaskets are placed to minimise axial heat loss. Five T-type thermocouples are uniformly arranged on the outside wall of the test to measure the wall temperature. Two groups of T-type thermocouples (one before and another after the test section) are placed to measure the air temperature at the inlet and outlet. The pressure drop in the test section is measured by a pressure transmitter. Temperatures, pressures, flow rate, voltage and current are recorded using a data logger.
Fig. 1. Diagram of experimental set-up
3. Cross hollow twisted tape inserts
The geometry information of the cross hollow twisted tapes is shown in Fig. 2. The twist ratio (y/W) of the tape is set as 3, and its length is the same as that of the test section. Central and lateral support structures are arranged for every 360° twisted pitch along the tape to connect its parts and affix it to the tube wall. The thickness of the support structures is 1 mm. The axial length of the lateral support structure is 2 mm, and the radial height (H) is 1 mm. A ring-shaped gasket is designed at the inlet of the tape and clipped inside the flange at the beginning of the test section to prevent axial movement of the tape. The outer and inner diameters of the gasket are 38 and 18 mm, which are the same as those of the rubber gasket sand bakelite gaskets and the test tube, respectively. 3D printing technology is a feasible means of manufacturing the models given the complex structure of cross hollow twisted tapes. A previous work [29] implied that these tapes may have an optimised hollow width (C) of 8 mm under laminar flow. Therefore, 6, 8 and 10 mm are selected as the hollow widths (C) of the cross hollow twisted tapes in the present study.
Fig. 2. Geometry of cross hollow twisted tapes with different hollow widths
4. Experimental procedure The flow rate to the test section is regulated by the inverter connected to the Roots blower and the bypass valve. The excess flow rate is discharged by the bypass valve, and the flow rate to the test section is discharged to the environment by the outlet section. Re varies from 5600 to 18000. The voltage of the heating wire is set to adjust the constant heat flux that we need. The related temperatures, pressure drop, flow rate, voltage and electric current are recorded by the data logger after the test section reaches steady state (The fluctuation range of temperatures should be less than 0.2 ℃.). A total of 4 h is needed from start to stability under turbulent flow. An average of approximately 600 sets of data are processed to minimise the measurement error of system. After the completion of a set of experiments, the flow rate and the electrical heat flux are adjusted to start the next set of experiments. In general, steady state is reached again after 2 h. 5. Data processing The data reduction of the measured results is summarised in this section. The heat transfer rate of air in the test section is calculated as
QQv CP （Ta,o Ta,i）. The electrical heat flux is expressed as
(1)
Qe IV .
(2)
The average value of heat transfer rate obtained by heat supplied by the electric heating wire and that absorbed by the air in the test section is determined for the calculation of internal convective heat transfer coefficient. The average heat transfer rate is determined using
Qa
Q Qe . 2
(3)
The heat transfer coefficient (h) is determined as
h
Qa , Di L (Tw,i,m Ta,m )
(4)
where the average temperature of the inner tube wall ( Tw ,i ,m ) can be calculated as
Q ln( Do / Di ) . Tw,i ,m Tw,o,m a 2wL
(5)
Therefore, Nu can be expressed by
Nu
hDi . a
(6)
f is given by
f
p . 1 L 2 U （ ） 2 Di
(7)
To evaluate the comprehensive enhancement of heat transfer, the formula of performance evaluation criterion (PEC) is proposed as [46] PEC
Nu/ Nu0 . ( f / f0 )1/3
According to the Coleman and Steele method [47] and the ANSI/ASME standard uncertainties of Re, Nu and f are calculated as follows:
Re Re
Nu Nu
f f
[(
[(
[(
2 U 2 Di 2 2 0.5 ) ( ) ( ) ( ) ] , U Di
h 2 Di 2 a 2 0.5 and ) ( ) ( ) ] h Di a
p 2 2 U 2 Di 2 L 2 0.5 ) ( ) (2 ) ( ) ( ) ] . p U Di L
(8) [48]
, the
(9)
(10)
(11)
The maximum uncertainties are calculated to be 2.3%, 4.7% and 5.2% for Re, Nu and f, respectively.
6. Results and discussion In this section, the results obtained with the tube fitted with cross hollow twisted tape inserts are depicted in the form of Nu or f versus Re. The trends of Nu/Nu0 or f/f0 versus Re are also analysed. PEC is used to evaluate the comprehensive performance of the inserts. The tapes have three different hollow widths of 6, 8 and 10 mm, and Re varies from 5600 to 18000. Moreover, the heat transfer coefficient and f of the plain tube are validated with the results obtained from the relevant correlations. 6.1. Validation of plain tube As shown in Fig. 3, the Nu and f obtained from the present experiments are compared with data obtained from the Gnielinski and Blasius equations for heat transfer and friction factor of the plain tube, respectively. The empirical correlation of Gnielinski is expressed as Nu 0.0214(Re0.8 100) Pr 0.4[1( D / L)2/3](T /T )0.45 . 0 i a,m w,i,m
(12)
The empirical correlation of Blasius is expressed as
f 0.3164/Re0.25 .
(13)
Overall, the results agree within 10% and 5% deviations with the Gnielinski and Blasius equations, respectively. This analysis shows the reliability of the experimental system. The correlations derived from the present data for the Nu and f are as follows:
Nu= 0.08938Re0.6485Pr 0.32 ,
(14)
f 0.246Re0.221.
(15)
Fig. 3. Verification of plain tube: (a) Nusselt number (Nu) (b) friction factor (f).
6.2. Effect of hollow width on heat transfer characteristics After the validation of plain tube, the cross hollow twisted tapes of different hollow widths are inserted into the test section for experiments. Figure 4(a) shows the variation in Nu versus Re for the different hollow widths (C = 6, 8 and 10 mm). The heat transfer rate increases with Re for all tapes. As a prior investigation [45] showed, the cross hollow twisted tape can generate substantial swirls in the tube. Thus, the trend of Nu can be explained by the fact that strong turbulence is caused to the flow near the tube wall by swirls as Re increases. These intensive swirls promote the mixing of fluid in the near-wall and central regions. Fig. 4(b) implies that heat transfer is better with the tube fitted with cross hollow twisted tape inserts than with the plain tube. Moreover, the tapes with 8 and 6 mm hollow widths provide the worst and best heat transfer performances, respectively. The Nu ratio (Nu/Nu0) of the tape with 6 mm hollow width is 3.8%–5.7% higher than that of the tape with 8 mm hollow width. A previous numerical work [43, 45] implied that the mechanism of heat transfer enhancement with cross hollow and center-cleared twisted tapes consists of two parts. (1) The swirls generated by the tape can enhance heat transfer, and the degree of enhancement depends on the upwind area of the tape. The enhancement is weakened as the hollow width increases because of the weakened swirls. (2) The irregular disturbance caused by the hollow part is enhanced as the hollow width increases. Fig. 5 shows that the space (S) between parts of the tape in the core region enlarges as the hollow width increases. The enlarged space allows the fluid in the core and near-wall regions to mix evenly under the influence of irregular disturbance and swirls, thereby enhancing heat transfer. The influences of
the two factors are merged under turbulent flow conditions. Thus, heat transfer capability decreases and then increases as the hollow width increases from 6 mm to 10 mm. According to the experimental data shown in Fig. 4(b), the Nu values of the tube fitted with cross hollow twisted tape inserts are 84%–120% higher than those of the plain tube.
Fig. 4. Variation in Nu or Nu ratio (Nu/Nu0) with Reynolds number (Re) for tube fitted with cross hollow twisted tape: (a) Nu (b) Nu/Nu0.
Fig. 5.Space (S) between parts of cross twisted tape in core region
6.3. Effect of hollow width on friction factor The f and f ratio of the tube fitted with cross hollow twisted tapes are shown in Fig. 6(a) and 6(b), respectively. The f of the tube fitted with tapes decreases as Re increases. This finding implies that cross hollow twisted tapes can cause additional pressure drop, leading to a higher
friction factor compared to the plain tube. The contact between the large upwind area of the twisted tape and air, long flow path and strong turbulence to the boundary layer caused by intensive swirls are the main causes of the change in resistance. The figure also shows that the hollow width plays an important role in influencing f. The tapes with 6 and 8 mm hollow widths obtains the highest and lowest f, respectively. A previous work [27] concluded that the following two explanations are the main factors that affect f. (1) The small upwind area of cross hollow twisted tape achieves small pressure loss as the hollow width increases. Meanwhile, turbulence is reduced by the weakened swirls. (2) As mentioned in Section 6.2, the large space (S) between parts of cross hollow twisted tape in the core region promotes an even mixing of the fluid in the core and near-wall regions. Consequently, f increases due to this irregular mixing. The importance of these two factors varies by Re. The experimental data show that f decreases and then increases as the hollow width of the tapes increases, as shown in Fig. 6(a). Considering heat resistance and price, the present work uses nylon for the cross hollow twisted tapes in the experiments. However, the surface of nylon is not as smooth as that of metal. Furthermore, the central support structure that connects parts of the tape may cause considerable turbulence in the core region under turbulent flow. Consequently, the variation in friction factor with hollow width under turbulent flow in the current experiment is different from that under laminar flow in a previous work [27]. However, the hollow part can be applied to reduce the additional pressure drop caused by inserts. Over the range investigated, the f of the tape with 8 mm hollow width is 17.9%–20.9% smaller than that with 6 mm hollow width.
Fig. 6. Variation in friction factor (f) or f ratio (f/f0) with Reynolds number (Re) for tube fitted with cross hollow twisted tape: (a) f (b) f/f0.
6.4. Comprehensive performance evaluation PEC is defined by Eq. (8). Figure 7 shows the variation in PEC with Re for the tube fitted with cross hollow twisted tape inserts. Overall, PEC varies from 0.87 to 0.98, which indicates that the tube fitted with cross hollow twisted tape inserts may not achieve the expected energy saving under turbulent flow. However, the tube with tape inserts is advantageous in terms of energy saving when Re is low. In comparison with a previous numerical simulation under laminar flow [27] , the tube fitted with cross twisted tape in the current study is more advantageous. The f is slightly larger than expected because the twisted tapes are made of nylon, which influences PEC. Therefore, PEC may be improved if smooth materials, such as metals, are used to manufacture the inserts.
Fig. 7. Variation in performance evaluation criterion (PEC) with Re for tube fitted with cross hollow twisted tape.
6.5. Correlations for Nusselt number and friction factor The hollow width (C) is converted to dimensionless parameters (c) as follows: c = C/W. The correlations of Re, hollow ratio (c) and Pr for Nu and f are obtained as follows:
Nu = 0.3415Re0.5911Pr0.32(0.9058c3+0.5439c2-1.345c+1.271) ,
(16)
f 9.348Re-0.3959(5.53c3+2.578c2-7.307c+3.499) .
(17)
Fig. 8(a) and 8(b) show the comparison of data obtained from the experiments and the correlations for Nu and f, respectively. The values calculated from the correlations agree with the experimental data within 3.6% (Nu) and 2.3% (f). They are in good agreement with each other. The reason for this error can be attributed to the turbulent fluctuation firstly. There are still a bit axial heat loss in the flanges. And the surface of the cross hollow twisted tapes in the experiment is rougher than metal.
Fig. 8. Comparison of experimental data and correlations for (a) Nu and (b) f.
7. Conclusion Experimental data about the heat transfer and f characteristics of a tube fitted with cross hollow twisted tapes with hollow widths of 6, 8 and 10 mm are presented in this investigation. The conclusions of this work are as follows. (1) The mechanism of heat transfer enhancement for cross hollow twisted tapes is complicated. Under turbulent flow conditions, the heat transfer coefficient and f reach their maximum values with the twisted tape with 6 mm hollow width and their minimum values with 8 mm hollow width. (2) The tube with cross hollow twisted tape inserts obtains better heat transfer enhancement under laminar flow than under turbulent flow. (3) The hollow part is a feasible structure for reducing the additional pressure drop caused by inserts and helpful in designing inserts that are advantageous in terms of energy saving. Acknowledgement
This work is financially supported by the National Natural Science Foundation of China (No. 51376069) and National key research and development program sub-project of China (No. 2017YFB0602901-4)
Nomenclature y 180° twist pitch of the twisted tape, mm W Width of the twisted tape, mm y/W Twist ratio Di Inner diameter of the tube, mm Do Outer diameter of the tube, mm L Length of the test tube, mm C Hollow width of the cross hollow twisted tape, mm H Radial height of the lateral support structure, mm Q Heat transfer rate of air in the test section, W Qv Flow rate of the test section, m3/s Qe Electrical heat flux, W Qa Average heat transfer rate, W
Density of air, kg / m
Cp
Specific heat at constant pressure of air, J / kg K
Ta,o Ta,i I V
Outlet bulk temperature of air, K Inlet bulk temperature of air, K Current output from the voltage regulator, A Voltage output from the voltage regulator, V
h
Heat transfer coefficient, W/m K
Tw,i,m Ta,m Tw,o,m
Average outer wall temperature of the test section, K Bulk average air temperature, K Average inner wall temperature of the test section, K
w
Thermal conductivity of stainless steel, W / m K
a
Thermal conductivity of air, W / m K
Dynamic viscosity of air, kg / m s
U
Bulk average velocity of air, m/s
p
Pressure drop of air, Pa
Nu Nu0 f f0
Nusselt number of the tube fitted with cross hollow twisted tape Nusselt number of the plain tube Friction factor of the tube fitted with cross hollow twisted tape Friction factor of the plain tube
3
2
Re Pr S c
Reynolds number Prandtl number Space between parts of cross twisted tape in the core region, mm Hollow ratio
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Highlights Mechanism of heat transfer enhancement for cross hollow twisted tapes is experimentally investigated. Tube fitted with cross hollow twisted tape inserts obtains better HTE in laminar flow than in turbulent flow. Hollow part is a feasible structure to reduce the extra pressure drop obtained.