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Heat transfer enhancement in double-pipe heat exchanger by means of rotor-assembled strands
Chemical Engineering and Processing 60 (2012) 26–33
Contents lists available at SciVerse ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Heat transfer enhancement in double-pipe heat exchanger by means of rotor-assembled strands Zhen Zhang, Yumei Ding, Changfeng Guan, Hua Yan ∗ , Weimin Yang State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 15 November 2011 Received in revised form 1 May 2012 Accepted 16 June 2012 Available online 26 June 2012 Keywords: Heat transfer enhancement Rotor-assembled strand Thermal performance factor Empirical correlation
a b s t r a c t Thermo-hydraulic characteristics of turbulent flow in plain tube equipped with rotor-assembled strands of different geometries and leads were reported, ahead of which an experiment considering a smooth tube had been conducted to calibrate the experimental system and data reduction method. The effects of rotor lead on heat transfer and friction characteristics were emphasized consequently. Experimental results revealed that rotor-assembled strands of different geometries employed improved heat transfer significantly with Nusselt number increased by 71.5–123.1% and friction factor increased by 37.4–74.8% compared with plain tube. There into, the helical blade rotor brought the most augmentation of heat transfer, while the blade-discreted rotor caused the largest friction loss. Generally considering, helical blade rotor with ladders offered first-class performance sequentially followed by helical blade rotor and blade-discreted rotor. For helical blade rotor with ladders, Nusselt number and friction factor both increased with the decrease of rotor lead. The best thermal performance factor was achieved when helical blade rotor with ladders was manufactured with certain parameters (rotor diameter is 22 mm, rotor lead is 150 mm). At last, the correlations of experimental results were presented based on thorough multivariate linear normal regression method. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Shell-and-tube heat exchangers are widely used in electric power generation, petrochemical industry and metallurgical industry. It is important to achieve more efficient technologies for shell-and-tube heat exchangers in order to increase their heat transfer efficiency at present. The technique of improving the performance of heat transfer system is referred to as heat transfer augmentation or intensification. Heat transfer enhancement technology has been developed and widely applied to heat exchanger applications. There are three different approaches to enhance tubeside convective heat transfer, namely inserted devices, internal fins and integral roughness. Insert devices involve various geometric forms which are inserted in a smooth tube. Researchers have been doing lots of valuable work on heat transfer enhancement and online automatic cleaning, most of which focused on tube inserts. García et al. [1] carried out an experimental research on a round tube fitted with helical wire coils in order to characterize its thermo-hydraulic behavior in laminar, transition and turbulent flow, which showed wire coil inserts offered best performance
∗ Corresponding author. Tel.: +86 10 64434734; fax: +86 10 64434734. E-mail address: [email protected] (H. Yan). 0255-2701/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cep.2012.06.003
within the transition region. Sibel et al. [2] launched experimental studies on the optimum values of the design parameters in a tube with equilateral triangular cross-sectioned coiled wire inserts. The effects of the ratio of the distance between the coiled wire and test tube wall to tube diameter, pitch ratio, ratio of the side length of equilateral triangle to tube diameter and Reynolds number on heat transfer and pressure drop were also investigated by using Taguchi method. To study flow visualization of tubes assembled with wire coils, Garcia [3] observed several flow patterns in laminar and transition regimes, and the experiment accurately established the transitional Reynolds number to the turbulence. Naphon and Suchana [4] performed investigations on heat transfer characteristics and pressure drop of the horizontal concentric tube with twisted wires brush inserts. Effect of twisted wires density, inlet fluid temperature and relevant parameters on heat transfer characteristics and pressure drop were taken into consideration. The results showed that twisted wires brush insert had an significant effect on heat transfer enhancement. Jaisankar et al. [5] carried out an experimental investigation on the thermo-hydraulic performance of full length twist tape, twist tape fitted with rod and spacer in thermosyphon solar water heater system, which revealed that the overall performance of the twist tape fitted with rod was better than that of the twist tape fitted with spacer. Murugesan et al. [6] investigated the influence of V-cut twisted tape insert on heat transfer, friction factor and thermal performance factor
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Nomenclature Ai Ao C1 C2 Cp,i Cp,o di do dr de De f hi ho K l mi mo Nu p Pr Qi Qo Qave Re Rw T u X Y
internal surface area of inner tube based on di (m2 ) external surface area of inner tube based on do (m2 ) coefficient for annular side heat transfer correlation, dimensionless constant for annular side heat transfer correlation (m2 K W−1 ) tube side specific heat (J kg−1 K−1 ) annular side specific heat (J kg−1 K−1 ) inside diameter of inner tube (m) outside diameter of inner tube (m) diameter of rotors (m) hydraulic diameter of tube side (m) hydraulic diameter of annular side (m) friction factor, dimensionless tube side heat transfer coefficient based on Ai (W m−2 K−1 ) annular side heat transfer coefficient based on Ao (W m−2 K−1 ) overall heat transfer coefficient based on outside tube area Ao (W m−2 K−1 ) length of tube side (m) tube side mass flow rate (kg/s) annular side mass flow rate (kg/s) Nusselt number, dimensionless lead of rotors (m) Prandtl number, dimensionless tube side heat transfer rate (W) annular side heat transfer rate (W) average heat transfer rate (W) Reynolds number, dimensionless tube wall thermal resistance (K W−1 ) temperature (◦ C) mean velocity components (ms−1 ) Wilson plot function (K m2 W−1 ) Wilson plot function or total thermal resistance (K m2 W−1 )
Greek symbols P pressure drop (Pa) Tm logarithmic mean temperature difference (K) thermal conductivity (W m−1 K−1 ) tube side water density (kg/m3 ) thermal performance factor Subscripts f fluid i inner inlet in o outer outlet out pre predicted rotor r exp experimental w wall
characteristics in a circular tube. The obtained results showed that the average Nusselt number and friction factor in the tube with V-cut twisted tape increased with decreasing twist ratios, width ratios and increasing depth ratios. Wongcharee and Eiamsaard [7] experimentally studied the thermo-hydraulic characteristics of the circular tubes equipped with alternate clockwise and counterclockwise twisted-tapes (TA). The experimental results revealed
27
that Nusselt number, friction factor and thermal performance factor associated with TA were higher than those associated with twisted tape (TT). Among the tapes examined, the one with the smallest twist ratio of y/W = 3 was found to be most efficient for heat transfer enhancement. Besides experimental investigations, Park and Chang [8] performed an analysis on the two-phase flow in a helical wire inserted tube. The simulation results showed that both in the bubbly flow and annular flow regions, the effects of pitch length on swirl flow generation and pressure drop were more significant than those of the wire diameters. In small diameter tubes, pitch length was a more dominant factor than wire diameter for the design of the swirl flow generator. Guo et al. [9] carried out numerical simulation study on heat transfer and fluid flow characteristics of the tubes fitted with helical screw-tape inserts from the viewpoint of field synergy principle, which revealed that the novel helical inserts with right and left twists alternately yielded better heat transfer performance than the helical inserts. Wang et al. [10] numerically optimized regularly spaced short-length twisted tape in a circular tube for turbulent heat transfer with free space ratio, twist ratio and rotated angle as configuration parameters. The computational results indicated that the larger rotated angle was, the higher heat transfer value and the greater flow resistance could be achieved, whereas the smaller twist ratio resulted in better heat transfer performance. Bali [11] and Ayhan [12] did some experimental and numerical investigations on the decaying swirl flow induced by a propeller-type swirl generator in a circular tube. Rahimi et al. [13] have done experimental and computational fluid dynamics (CFD) studies on wire coils inserted in a proton exchange membrane fuel cell. The experimental results clearly revealed that the proton exchange membrane fuel cell inserted with wire coils increased the generated power density by 41% due to tangential flow close to the gas diffusion layer. CFD study was also carried out so as to explain and analyze the observed results. Cui and Tian [14] carried out three-dimensional numerical simulations and experiments to study the heat transfer characteristics and pressure drop of air flow in a circular tube with Edgefold-Twisted Tape (ETT) inserts and Spiral-Twisted-Tape (STT) inserts of the same twist ratio. Within the studied Reynolds number range, the Nusselt number of the tube with ETT inserts was found to be 3.9–9.2% higher than that of the tube with STT inserts, and the friction factor of the tube with ETT inserts was 8.7–74% higher than that of STT inserts. As one kind of tube inserts, rotor-assembled strand first proposed by Yang et al. [15] consists of four basic elements, which are rotors, steel wire, banking pins and fixed mounts as shown in Fig. 1. Rotors are the functional elements, which can rotate under certain mass flow rate to obtain heat transfer enhancement and online automatic cleaning. Xie et al. [16] carried out experimental studies on pressure drop and heat transfer in a rotor-assembled strands inserted tube with water as the working fluid. The measured data revealed that rotorassembled strand could significantly increase the Nusselt number and overall heat transfer coefficient within experimental Reynolds number range. Li et al. [17] performed commercial tests for smooth tubes inserted with rotors-assembled strands and compared the results with those of non-inserted tubes on condensers in electric power plant using water as working fluid, the single-phase pressure drop and heat transfer were also measured. Zhang et al. [18] experimentally studied thermo-hydraulic characteristics of turbulent flow in the circular tubes equipped with rotor-assembled strands of different diameters and leads. The experimental results showed that the heat transfer and friction factor increased with the growing diameter and decreasing lead of rotor-assembled strands. Recently, three new kinds of rotor structures are developed, and the aim of this article is to experimentally compare the heat transfer and flow friction characteristics of the tube fitted
28
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Fig. 1. Schematic diagram of rotor-assembled strand device for heat transfer enhancement. 1 – fixed mount, 2 – rotor, 3 – banking pin, 4 – tube, 5 – steel wire.
deionized water. The tube side inlet temperature was set to be 18 ◦ C while the annular side inlet temperature was set to be 56 ◦ C. The experiments were conducted by first changing the annulus side flow rate with the tube side flow rate fixed at its maximum and then changing the tube side flow rate with the annular side flow rate fixed at its maximum. 2.2. Data reduction The data reduction of the measured results is summarized in the following procedures. The tube side heat transfer coefficient is calculated by subtracting the annular side convective thermal resistance and the tube wall conduction resistance from the total thermal resistance instead of directly applying the Wilson plot method, which could result in relatively large errors. 1 1 1 = − − Rw KAo hi Ai ho Ao
Fig. 2. Experimental system. 1. Cold water tank, 2. hot water tank, 3. test tube, 4. test section, 5. electromagnetic flowmeter, 6. differential pressure transducer, 7. computer and data acquisition system and 8. refrigerator.
with rotor-assembled strands with these different structure forms. Meanwhile, the effects of the rotor lead on heat transfer, friction factor and thermal performance factor are also studied with Reynolds number ranging from 16,800 to 40,400. 2. Experiments 2.1. Experimental system The experimental system shown in Fig. 2 included cold medium loop, hot medium loop, test section and measuring control system. The experiments were arranged with counter flow of hot water in the annulus and cold water in the test tube. The outer tube had an internal diameter of 50 mm while the inner tube had an internal diameter of 24 mm and an external diameter of 25 mm. The external surface of outer tube was insulated in order to minimize heat loss to surroundings. The effective heat transfer length of the test section was 2000 mm. The rotor-assembled strands with different geometries were inserted inside the inner tubes separately. The geometrical configurations of blade-discreted rotor, helical blade rotor and helical blade rotor with ladders employed in the experiments were shown in Fig. 3, where dr was rotor diameter, p was rotor lead which meant the axial length per twist. Meanwhile, helical blade rotors with ladders of different leads are namely 22–100, 22–150 and 22–200, where 22–100 meant dr = 22 mm and p = 100 mm. The inlet and outlet temperatures of the fluid in the tube and annulus were measured by Resistance Thermometer Detector (RTD). The pressure drop in the tube was measured by a differential pressure transducer with a full range of 80 kPa. Electro-magnetic flowmeters were used to measure the tube side and annular side flow rate. The working fluid for the heat transfer experiments was
(1)
where K is the overall heat transfer coefficient based on the external surface area of innertube. K can be determined from K=
Qave Tm Ao
(2)
where the average heat transfer rate, Qave , is determined from the tube side and annular side as follows: Qave =
Qi + Qo 2
(3)
The tube side and annular side data are used to calculate Qi and Qo , respectively. Qi = mi Cp,i (Ti,out − Ti,in )
(4)
Qo = mo Cp,o (To,in − To,out )
(5)
In the experiments, the heat equilibrium test showed that the heat received by the cold water (Qi ), was within 5% lower than the heat supplied by the hot water (Qo ), this is due to the heat leak from the tube wall:
Qo − Qi Q × 100% < 5%
(6)
o
Rw is the inner tube wall thermal resistance defined as follows: Rw =
ln(do /di ) 2w l
(7)
The logarithmic mean temperature difference is defined as: Tm =
(To,in − Ti,out ) − (To,out − Ti,in ) ln[(To,in − Ti,out )/(To,out − Ti,in )]
(8)
The annular side heat transfer coefficient ho is obtained by using the Wilson plot technique by changing the annular side flow rate with the tube side flow rate fixed at its maximum in order to minimize the tube side convective thermal resistance. The annular side heat transfer coefficient is in the form of: ho = C1
o 0.8 0.4 Re Pr o De o
(9)
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
29
Fig. 3. Rotor-assembled strands with different geometries (dr = 22 mm, p = 200 mm). (a) Blade-discreted rotor, (b) helical blade rotor and (c) helical blade rotor with ladders.
Since the tube side convective thermal resistance and the tube wall thermal resistance are constant for a constant tube side flow rate, the Wilson plot technique for the annular side heat transfer coefficient can be rewritten as: 1 1 1 + C2 = 0.4 K C1 (o /De )Re0.8 o Pr o
Ao hi Ai
1 X + C2 C1
(11)
(13)
2pde lu2
(14)
where p is the pressure drop across the test section and u is mean water velocity of the tube side, de is tube side hydraulic diameter. The thermal performance factor () is defined by [19,20] =
Nur /Nu0 (fr /f0 )
1/3
Uncertainty
◦
0.09 C
0.06 C
mi
mo
P
0.2%
0.1%
0.8%
The measurement uncertainties are listed in Table 1. The derived uncertainty is calculated from
n ∂ ln ϕ 2 ϕ 2 = (xi ) ∂xi
i=1
(12)
The friction factor is evaluated by: f =
T ◦
ϕ
0.4 where X = 1/((o /De )Re0.8 o Pr o ); Y = 1/K.C1 can be calculated from the slope of the Wilson plot line. After C1 is determined for the annular side heat transfer correlation, the tube side flow rate was changed while keeping the annular side flow rate at its maximum to minimize the annular side convective thermal resistance. And then the tube side heat transfer coefficient hi can be obtained, thus the tube side average Nusselt number can be calculated from
hd Nui = i i i
T
2.3. Experimental uncertainties
Eq. (10) can be rewritten in a linear form as: Y=
Variable
(10)
where C1 is the coefficient in Eq. (9) and C2 is the sum of the inner tube wall thermal resistance and the annular side convective thermal resistance: C2 = Rw Ao +
Table 1 Measurement uncertainties.
(15)
where Nur is the Nusselt number of the tube with rotors, Nu0 is the Nusselt number of the plain tube, fr is the friction factor of the tube with rotors, and f0 is the friction factor of the plain tube.
(16)
where ϕ is the derived parameter and x1 , x2 , . . ., xn are the measured variables. For the tube inserted with rotor-assembled strand, the relative uncertainty of the tube side Nusselt number is 2.1–3.5% for Reynolds numbers of 16,800–40,400 with water as the working fluid while the friction factor uncertainty is between 1.3–4.2%. The experimental results are reproducible within these uncertainty ranges. 3. Results and discussion 3.1. Verification of plain tube Preliminary experiments have been carried out on a plain tube to check the facility performance and verify the measuring uncertainties. Experimental results were compared with the empirical correlations for Nusselt number and friction factor, respectively. The measured Nusselt numbers were compared directly with the empirical correlation proposed by Gnielinski [21]: Nu =
(f/8)(Re − 1000)Pr f
1 + 12.7
2/3
f/8(Pr f
− 1)
(17)
The measured friction factors were compared directly with the Filonenko Equation: f = (1.82l gRe − 1.64)−2
(18)
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Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Fig. 5. Nusselt number of rotor-assembled strands with different geometries.
these rotor-assembled strands of different geometries shown in Fig. 5. The effect of rotor lead on the Nusselt number of the tube fitted with helical blade rotor with ladders was shown in Fig. 6. The figure showed that Nusselt number decreased with the increase of rotor lead, which could be explained by the fact that the behavior of flow inside the tube inserted with helical blade rotor with ladders was affected by the increase of lead. The smaller the rotor lead was, the more significantly the rotors were twisted, which greatly changed the flow direction and then caused increase in turbulence intensity of the flow in the plain tube assembled with helical blade rotor with ladders. The helical blade rotor with ladders of 22–100 generated around 2.3% and 4.36% higher average Nusselt number than those of 22–150 and 22–200, respectively. 3.3. Results of friction factor (f) Fig. 4. Comparison of measured data with empirical correlations in plain tube. (a) Nusselt number and (b) friction factor.
The comparison results of experimental results and empirical correlation results for Nusselt number and friction factor were shown in Fig. 4a and b, respectively. And the Nusselt numbers of plain tube were found to agree within 3.27% with the previous Eq. (17) approximately, while experimental friction factor results were found to agree within 8.73% with the previous Eq. (18).
Fig. 7 showed the relation of friction factor with Reynolds number of plain tube and the tube fitted with different kinds of rotor-assembled strands. It could be seen from the figure that the friction factor decreased with the increase of Reynolds number. Meanwhile, due to the driving force of rotor rotation, the friction factor obtained from the tube with rotor-assembled strands
3.2. Results of average Nusselt number (Nu) Fig. 5 showed the comparison of Nusselt number among the plain tube and the tube fitted with different kinds of rotorassembled strands in turbulent regime. In the figure, the Nusselt number increased with the increasing tube-side Reynolds number. Meanwhile, under the same Reynolds number, the Nusselt number obtained from the tube with rotor-assembled strands was 71.5–123.1% higher than that obtained from tube without rotor-assembled strands across the range of Reynolds number. Due to the tangential and radial velocity component, the mixing of fluid at the wall region and fluid at the core region, induced by the generated centrifugal force had significant ability to enhance heat transfer. It was also found that the heat transfer augmentation of helical blade rotor was the best among
Fig. 6. Nusselt number of helical blade rotor with ladders of different leads.
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Fig. 7. Friction factor of rotor-assembled strands with different geometries.
was 37.4–74.8% higher than that obtained from tube without rotor-assembled strands across the range of Reynolds number. For rotor-assembled strands of different geometries, the friction factor of blade-discreted rotor was the highest among these rotor-assembled strands shown in Fig. 7, which revealed that the influence of ladders on friction factor was significant. The effect of rotor lead on the friction factor of the tube fitted with helical blade rotor with ladders was shown in Fig. 8. This figure showed that friction factor decreased with the increase of rotor lead, which meant that helical blade rotor with ladders of 22–100 generated around 28.5% and 33.1% higher average friction factor than those of 22–150 and 22–200, respectively. As indicated in reference [22], the rotating speed increased with the decrease of rotor lead. Therefore, helical blade rotor with ladders of 22–100 rotated faster than others, which resulted in more energy loss. 3.4. Results of thermal performance factor () The thermal performance factor (), indicating the practical benefit of the rotor-assembled strands usage, was obtained from Eq. (15), in which Nusselt number and friction factor in the tube with and without rotor-assembled strands were simultaneously determined at the same pumping power. Fig. 9 showed variation of thermal performance factor with Reynolds number for rotorassembled strands of different geometries. As seen from Fig. 9,
Fig. 8. Friction factor of helical blade rotor with ladders of different leads.
31
Fig. 9. Thermal performance factor of rotor-assembled strands with different geometries.
the thermal performance factor tended to decrease with the rise of Reynolds number for all cases. Among rotor-assembled strands of different geometries, helical blade rotor with ladders offered the best performance followed by helical blade rotor and then blade-discreted rotor. This revealed the advantage of the ladders on rotor-assembled strands in the viewpoint of energy saving. The effect of rotor lead on thermal performance factor of helical blade rotor with ladders was shown in Fig. 10. Comparative data revealed that the thermal performance factor increased with decreasing Reynolds number and varied from 1.776 to 1.956 for 22–150, 1.769 to 1.928 for 22–200 and 1.707 to 1.817 for 22–100 under the experimental conditions. From the above analysis, it was concluded that the tube fitted with helical blade rotor with ladders of 22–150 had the best performance and generated the highest heat transfer enhancement at the same pumping power for the entire range studied, which meant the thermal performance factor could not always increase with increasing lead, but had a maximum value at a certain lead. 3.5. Correlation of the results The predicted data of the Nu and f calculated from Table 2 were plotted against experimental data of the Nu and f in Figs. 11 and 12,
Fig. 10. Thermal performance factor of helical blade rotors with ladders of different leads.
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Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Table 2 Correlations of experimental results. Rotors
Nu
f
Blade-discreted rotor Helical blade rotor
Nu = 0.05Re0.75709 Pr0.60207 Nu = 0.005Re0.70125 Pr2.17539
f = 0.4073Re−0.22307 f = 0.3548Re−0.21198
Helical blade rotor with ladders
Nu = 0.02Re0.76621 Pr 1.1385
600 550 500
Nupre
400 350 300
300
350
400
450
500
550
Blade-discreted rotor Helical blade rotor Helical blade rotor with ladders (22-200) Helical blade rotor with ladders (22-150) Helical blade rotor with ladders (22-100)
fpre
0.044
0.040
0.036
0.036
0.040
0.044
di
0.048
The authors are grateful to the National Nature Science Foundation of Beijing (No. 3102023) and National Science and Technology Support Plan Project (No. 2011BAA04B02) for the financial assistance for this study. References
0.048
0.032 0.032
p −0.42388
Acknowledgments
Fig. 11. Comparison between predicted and experimental Nusselt number.
0.052
f = 0.2638Re−0.15885
600
Nuexp
0.056
di
(2) Among rotor-assembled strands of different geometries, the heat transfer enhancement of helical blade rotor was the best; the friction factor of blade-discreted rotor was the highest among these rotor-assembled strands; helical blade rotor with ladders offered the best overall performance followed by helical blade rotor and then blade-discreted rotor. For helical blade rotors with ladders of different leads, Nusselt number and friction factor increased with the decrease of rotor lead; the thermal performance factor of 22–150 was the best one in these rotor-assembled strands employed in the experiment. (3) Based on thorough multivariate linear normal regression method, the Nusselt number and friction factor correlations of all rotor-assembled strands employed in the experiment were established; the correlated results were in good agreement with experimental results.
Blade-discreted rotor Helical blade rotor Helical blade rotor with ladders (22-200) Helical blade rotor with ladders (22-150) Helical blade rotor with ladders (22-100)
450
250 250
p −0.0686
0.052
0.056
fexp Fig. 12. Comparison between predicted and experimental friction factor.
respectively. As shown in these figures, the maximum deviation between the experimental and predicted data were ±1.7% and ±6.5%, respectively. 4. Conclusions The experimental work has been carried out in order to study the heat transfer rate (Nu), friction factor (f) and thermal performance factor () of smooth tube fitted with rotor-assembled strands of different geometries. Meanwhile, the influence of rotor lead on heat transfer enhancement was also investigated. The comparison conclusions have been drawn as follows: (1) Rotor-assembled strands significantly improved heat transfer with the Nusselt number increased by 71.5–123.1% and friction factor increased by 37.4–74.8% over plain tube within the experimental Reynolds number range.
[1] A. García, P.G. Vicente, A. Viedma, Experimental study of heat transfer enhancement with wire coil inserts in laminar-transition-turbulent regimes at different Prandtl numbers, International Journal of Heat and Mass Transfer 48 (2005) 4640–4651. [2] G. Sibel, M. Eyuphan, S. Ercan, O. Veysel, A. Taguchi approach for optimization of design parameters in a tube with coiled wire inserts, Applied Thermal Engineering 31 (2011) 2568–2577. [3] A. García, J.P. Solano, P.G. Vicente, A. Viedma, Flow pattern assessment in tubes with wire coil inserts in laminar and transition regimes, International Journal of Heat Fluid Flow 28 (2007) 516–525. [4] P. Naphon, T. Suchana, Heat transfer enhancement and pressure drop of the horizontal concentric tube with twisted wires brush inserts, International Communications in Heat and Mass Transfer 38 (2011) 236–241. [5] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes, Applied Thermal Engineering 29 (2009) 1224–1231. [6] 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 38 (2011) 329–334. [7] K. Wongcharee, S. Eiamsaard, Friction and heat transfer characteristics of laminar swirl flow through the round tubes inserted with alternate clockwise and counter-clockwise twisted-tapes, International Communications in Heat and Mass Transfer 38 (2011) 348–352. [8] Y. Park, S.H. Chang, Swirl flow analysis in a helical wire inserted tube using CFD code, Nuclear Engineering and Design 240 (2010) 3405–3412. [9] J.F. Guo, M.T. Xu, L. Cheng, Numerical investigations of circular tube fitted with helical screw-tape inserts from the viewpoint of field synergy principle, Chemical Engineering and Processing 49 (2010) 410–417. [10] Y.J. Wang, M.L. Hou, X.H. Deng, L. Li, C. Huang, H.Y. Huang, G.F. Zhang, C.H. Chen, W.J. Huang, Configuration optimization of regularly spaced short-length twisted tape in a circular tube to enhance turbulent heat transfer using CFD modeling, Applied Thermal Engineering 31 (2011) 1141–1149. [11] T. Bali, Modelling of heat transfer and fluid flow for decaying swirl flow in a circular pipe, International Communications in Heat and Mass Transfer 25 (1998) 349–358. [12] T. Bali, T. Ayhan, Experimental investigation of propeller type swirl generator for a circular pipe flow, International Communications in Heat and Mass Transfer 26 (1999) 13–22. [13] M. Rahimi, B. Aghel, A.A. Alsairafi, Experimental and CFD studies on using coil wire insert in a proton exchange membrane fuel cell, Chemical Engineering and Processing 49 (2010) 689–696.
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33 [14] Y.Z. Cui, M.C. Tian, Three-dimensional numerical simulation of thermalhydraulic performance of a circular tube with edgefold-twisted-tape inserts, Journal of Hydrodynamics 22 (2010) 662–670. [15] W.M. Yang, Y.M. Ding, L.B. Geng, W. Huang, Rotor-assembled automatic cleaning and heat transfer enhancement device, CN Patent 200520127121.9 (2005); assigned to Huang Wei and Beijing University of Chemical Technology. [16] P.C. Xie, F.X. Li, Y.M. Ding, H. Yan, C.F. Guan, W.M. Yang, Experimental study of heat transfer enhancement and friction loss induced by inserted rotorassembled strand (I) water, Chinese Journal of Chemical Engineering 16 (2008) 849–855. [17] F.X. Li, Y.M. Ding, C.F. Guan, P.C. Xie, H. Yan, W.M. Yang, Laboratory investigation and commercial test for rotors-assembled strand applied in smooth tube, Experimental Thermal and Fluid Science 33 (2008) 1–9.
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[18] Z. Zhang, W.M. Yang, C.F. Guan, Y.M. Ding, F.X. Li, H. Yan, Heat transfer and friction characteristics of turbulent flow through plain tube inserted with rotorassembled strands, Experimental Thermal and Fluid Science 38 (2012) 33–39. [19] S. Eiamsaard, 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 53 (2010) 1364–1372. [20] P. Bharadwaj, A.D. Khondge, A.W. Date, Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert, International Journal of Heat and Mass Transfer 52 (2009) 1938–1944. [21] V. Gnielinski, New equation for heat and mass transfer in turbulent pipe and channel flows, International Chemical Engineering 16 (1976) 359–368. [22] F.X. Li, Investigation of Heat Transfer Enhancement and Structure Modification of Tube Side Assembled Rotors for Heat Exchangers, Beijing University of Chemical Technology, Beijing, 2009.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Heat transfer enhancement in double-pipe heat exchanger by means of rotor-assembled strands Zhen Zhang, Yumei Ding, Changfeng Guan, Hua Yan ∗ , Weimin Yang State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 15 November 2011 Received in revised form 1 May 2012 Accepted 16 June 2012 Available online 26 June 2012 Keywords: Heat transfer enhancement Rotor-assembled strand Thermal performance factor Empirical correlation
a b s t r a c t Thermo-hydraulic characteristics of turbulent flow in plain tube equipped with rotor-assembled strands of different geometries and leads were reported, ahead of which an experiment considering a smooth tube had been conducted to calibrate the experimental system and data reduction method. The effects of rotor lead on heat transfer and friction characteristics were emphasized consequently. Experimental results revealed that rotor-assembled strands of different geometries employed improved heat transfer significantly with Nusselt number increased by 71.5–123.1% and friction factor increased by 37.4–74.8% compared with plain tube. There into, the helical blade rotor brought the most augmentation of heat transfer, while the blade-discreted rotor caused the largest friction loss. Generally considering, helical blade rotor with ladders offered first-class performance sequentially followed by helical blade rotor and blade-discreted rotor. For helical blade rotor with ladders, Nusselt number and friction factor both increased with the decrease of rotor lead. The best thermal performance factor was achieved when helical blade rotor with ladders was manufactured with certain parameters (rotor diameter is 22 mm, rotor lead is 150 mm). At last, the correlations of experimental results were presented based on thorough multivariate linear normal regression method. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Shell-and-tube heat exchangers are widely used in electric power generation, petrochemical industry and metallurgical industry. It is important to achieve more efficient technologies for shell-and-tube heat exchangers in order to increase their heat transfer efficiency at present. The technique of improving the performance of heat transfer system is referred to as heat transfer augmentation or intensification. Heat transfer enhancement technology has been developed and widely applied to heat exchanger applications. There are three different approaches to enhance tubeside convective heat transfer, namely inserted devices, internal fins and integral roughness. Insert devices involve various geometric forms which are inserted in a smooth tube. Researchers have been doing lots of valuable work on heat transfer enhancement and online automatic cleaning, most of which focused on tube inserts. García et al. [1] carried out an experimental research on a round tube fitted with helical wire coils in order to characterize its thermo-hydraulic behavior in laminar, transition and turbulent flow, which showed wire coil inserts offered best performance
∗ Corresponding author. Tel.: +86 10 64434734; fax: +86 10 64434734. E-mail address: [email protected] (H. Yan). 0255-2701/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cep.2012.06.003
within the transition region. Sibel et al. [2] launched experimental studies on the optimum values of the design parameters in a tube with equilateral triangular cross-sectioned coiled wire inserts. The effects of the ratio of the distance between the coiled wire and test tube wall to tube diameter, pitch ratio, ratio of the side length of equilateral triangle to tube diameter and Reynolds number on heat transfer and pressure drop were also investigated by using Taguchi method. To study flow visualization of tubes assembled with wire coils, Garcia [3] observed several flow patterns in laminar and transition regimes, and the experiment accurately established the transitional Reynolds number to the turbulence. Naphon and Suchana [4] performed investigations on heat transfer characteristics and pressure drop of the horizontal concentric tube with twisted wires brush inserts. Effect of twisted wires density, inlet fluid temperature and relevant parameters on heat transfer characteristics and pressure drop were taken into consideration. The results showed that twisted wires brush insert had an significant effect on heat transfer enhancement. Jaisankar et al. [5] carried out an experimental investigation on the thermo-hydraulic performance of full length twist tape, twist tape fitted with rod and spacer in thermosyphon solar water heater system, which revealed that the overall performance of the twist tape fitted with rod was better than that of the twist tape fitted with spacer. Murugesan et al. [6] investigated the influence of V-cut twisted tape insert on heat transfer, friction factor and thermal performance factor
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Nomenclature Ai Ao C1 C2 Cp,i Cp,o di do dr de De f hi ho K l mi mo Nu p Pr Qi Qo Qave Re Rw T u X Y
internal surface area of inner tube based on di (m2 ) external surface area of inner tube based on do (m2 ) coefficient for annular side heat transfer correlation, dimensionless constant for annular side heat transfer correlation (m2 K W−1 ) tube side specific heat (J kg−1 K−1 ) annular side specific heat (J kg−1 K−1 ) inside diameter of inner tube (m) outside diameter of inner tube (m) diameter of rotors (m) hydraulic diameter of tube side (m) hydraulic diameter of annular side (m) friction factor, dimensionless tube side heat transfer coefficient based on Ai (W m−2 K−1 ) annular side heat transfer coefficient based on Ao (W m−2 K−1 ) overall heat transfer coefficient based on outside tube area Ao (W m−2 K−1 ) length of tube side (m) tube side mass flow rate (kg/s) annular side mass flow rate (kg/s) Nusselt number, dimensionless lead of rotors (m) Prandtl number, dimensionless tube side heat transfer rate (W) annular side heat transfer rate (W) average heat transfer rate (W) Reynolds number, dimensionless tube wall thermal resistance (K W−1 ) temperature (◦ C) mean velocity components (ms−1 ) Wilson plot function (K m2 W−1 ) Wilson plot function or total thermal resistance (K m2 W−1 )
Greek symbols P pressure drop (Pa) Tm logarithmic mean temperature difference (K) thermal conductivity (W m−1 K−1 ) tube side water density (kg/m3 ) thermal performance factor Subscripts f fluid i inner inlet in o outer outlet out pre predicted rotor r exp experimental w wall
characteristics in a circular tube. The obtained results showed that the average Nusselt number and friction factor in the tube with V-cut twisted tape increased with decreasing twist ratios, width ratios and increasing depth ratios. Wongcharee and Eiamsaard [7] experimentally studied the thermo-hydraulic characteristics of the circular tubes equipped with alternate clockwise and counterclockwise twisted-tapes (TA). The experimental results revealed
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that Nusselt number, friction factor and thermal performance factor associated with TA were higher than those associated with twisted tape (TT). Among the tapes examined, the one with the smallest twist ratio of y/W = 3 was found to be most efficient for heat transfer enhancement. Besides experimental investigations, Park and Chang [8] performed an analysis on the two-phase flow in a helical wire inserted tube. The simulation results showed that both in the bubbly flow and annular flow regions, the effects of pitch length on swirl flow generation and pressure drop were more significant than those of the wire diameters. In small diameter tubes, pitch length was a more dominant factor than wire diameter for the design of the swirl flow generator. Guo et al. [9] carried out numerical simulation study on heat transfer and fluid flow characteristics of the tubes fitted with helical screw-tape inserts from the viewpoint of field synergy principle, which revealed that the novel helical inserts with right and left twists alternately yielded better heat transfer performance than the helical inserts. Wang et al. [10] numerically optimized regularly spaced short-length twisted tape in a circular tube for turbulent heat transfer with free space ratio, twist ratio and rotated angle as configuration parameters. The computational results indicated that the larger rotated angle was, the higher heat transfer value and the greater flow resistance could be achieved, whereas the smaller twist ratio resulted in better heat transfer performance. Bali [11] and Ayhan [12] did some experimental and numerical investigations on the decaying swirl flow induced by a propeller-type swirl generator in a circular tube. Rahimi et al. [13] have done experimental and computational fluid dynamics (CFD) studies on wire coils inserted in a proton exchange membrane fuel cell. The experimental results clearly revealed that the proton exchange membrane fuel cell inserted with wire coils increased the generated power density by 41% due to tangential flow close to the gas diffusion layer. CFD study was also carried out so as to explain and analyze the observed results. Cui and Tian [14] carried out three-dimensional numerical simulations and experiments to study the heat transfer characteristics and pressure drop of air flow in a circular tube with Edgefold-Twisted Tape (ETT) inserts and Spiral-Twisted-Tape (STT) inserts of the same twist ratio. Within the studied Reynolds number range, the Nusselt number of the tube with ETT inserts was found to be 3.9–9.2% higher than that of the tube with STT inserts, and the friction factor of the tube with ETT inserts was 8.7–74% higher than that of STT inserts. As one kind of tube inserts, rotor-assembled strand first proposed by Yang et al. [15] consists of four basic elements, which are rotors, steel wire, banking pins and fixed mounts as shown in Fig. 1. Rotors are the functional elements, which can rotate under certain mass flow rate to obtain heat transfer enhancement and online automatic cleaning. Xie et al. [16] carried out experimental studies on pressure drop and heat transfer in a rotor-assembled strands inserted tube with water as the working fluid. The measured data revealed that rotorassembled strand could significantly increase the Nusselt number and overall heat transfer coefficient within experimental Reynolds number range. Li et al. [17] performed commercial tests for smooth tubes inserted with rotors-assembled strands and compared the results with those of non-inserted tubes on condensers in electric power plant using water as working fluid, the single-phase pressure drop and heat transfer were also measured. Zhang et al. [18] experimentally studied thermo-hydraulic characteristics of turbulent flow in the circular tubes equipped with rotor-assembled strands of different diameters and leads. The experimental results showed that the heat transfer and friction factor increased with the growing diameter and decreasing lead of rotor-assembled strands. Recently, three new kinds of rotor structures are developed, and the aim of this article is to experimentally compare the heat transfer and flow friction characteristics of the tube fitted
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Fig. 1. Schematic diagram of rotor-assembled strand device for heat transfer enhancement. 1 – fixed mount, 2 – rotor, 3 – banking pin, 4 – tube, 5 – steel wire.
deionized water. The tube side inlet temperature was set to be 18 ◦ C while the annular side inlet temperature was set to be 56 ◦ C. The experiments were conducted by first changing the annulus side flow rate with the tube side flow rate fixed at its maximum and then changing the tube side flow rate with the annular side flow rate fixed at its maximum. 2.2. Data reduction The data reduction of the measured results is summarized in the following procedures. The tube side heat transfer coefficient is calculated by subtracting the annular side convective thermal resistance and the tube wall conduction resistance from the total thermal resistance instead of directly applying the Wilson plot method, which could result in relatively large errors. 1 1 1 = − − Rw KAo hi Ai ho Ao
Fig. 2. Experimental system. 1. Cold water tank, 2. hot water tank, 3. test tube, 4. test section, 5. electromagnetic flowmeter, 6. differential pressure transducer, 7. computer and data acquisition system and 8. refrigerator.
with rotor-assembled strands with these different structure forms. Meanwhile, the effects of the rotor lead on heat transfer, friction factor and thermal performance factor are also studied with Reynolds number ranging from 16,800 to 40,400. 2. Experiments 2.1. Experimental system The experimental system shown in Fig. 2 included cold medium loop, hot medium loop, test section and measuring control system. The experiments were arranged with counter flow of hot water in the annulus and cold water in the test tube. The outer tube had an internal diameter of 50 mm while the inner tube had an internal diameter of 24 mm and an external diameter of 25 mm. The external surface of outer tube was insulated in order to minimize heat loss to surroundings. The effective heat transfer length of the test section was 2000 mm. The rotor-assembled strands with different geometries were inserted inside the inner tubes separately. The geometrical configurations of blade-discreted rotor, helical blade rotor and helical blade rotor with ladders employed in the experiments were shown in Fig. 3, where dr was rotor diameter, p was rotor lead which meant the axial length per twist. Meanwhile, helical blade rotors with ladders of different leads are namely 22–100, 22–150 and 22–200, where 22–100 meant dr = 22 mm and p = 100 mm. The inlet and outlet temperatures of the fluid in the tube and annulus were measured by Resistance Thermometer Detector (RTD). The pressure drop in the tube was measured by a differential pressure transducer with a full range of 80 kPa. Electro-magnetic flowmeters were used to measure the tube side and annular side flow rate. The working fluid for the heat transfer experiments was
(1)
where K is the overall heat transfer coefficient based on the external surface area of innertube. K can be determined from K=
Qave Tm Ao
(2)
where the average heat transfer rate, Qave , is determined from the tube side and annular side as follows: Qave =
Qi + Qo 2
(3)
The tube side and annular side data are used to calculate Qi and Qo , respectively. Qi = mi Cp,i (Ti,out − Ti,in )
(4)
Qo = mo Cp,o (To,in − To,out )
(5)
In the experiments, the heat equilibrium test showed that the heat received by the cold water (Qi ), was within 5% lower than the heat supplied by the hot water (Qo ), this is due to the heat leak from the tube wall:
Qo − Qi Q × 100% < 5%
(6)
o
Rw is the inner tube wall thermal resistance defined as follows: Rw =
ln(do /di ) 2w l
(7)
The logarithmic mean temperature difference is defined as: Tm =
(To,in − Ti,out ) − (To,out − Ti,in ) ln[(To,in − Ti,out )/(To,out − Ti,in )]
(8)
The annular side heat transfer coefficient ho is obtained by using the Wilson plot technique by changing the annular side flow rate with the tube side flow rate fixed at its maximum in order to minimize the tube side convective thermal resistance. The annular side heat transfer coefficient is in the form of: ho = C1
o 0.8 0.4 Re Pr o De o
(9)
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
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Fig. 3. Rotor-assembled strands with different geometries (dr = 22 mm, p = 200 mm). (a) Blade-discreted rotor, (b) helical blade rotor and (c) helical blade rotor with ladders.
Since the tube side convective thermal resistance and the tube wall thermal resistance are constant for a constant tube side flow rate, the Wilson plot technique for the annular side heat transfer coefficient can be rewritten as: 1 1 1 + C2 = 0.4 K C1 (o /De )Re0.8 o Pr o
Ao hi Ai
1 X + C2 C1
(11)
(13)
2pde lu2
(14)
where p is the pressure drop across the test section and u is mean water velocity of the tube side, de is tube side hydraulic diameter. The thermal performance factor () is defined by [19,20] =
Nur /Nu0 (fr /f0 )
1/3
Uncertainty
◦
0.09 C
0.06 C
mi
mo
P
0.2%
0.1%
0.8%
The measurement uncertainties are listed in Table 1. The derived uncertainty is calculated from
n ∂ ln ϕ 2 ϕ 2 = (xi ) ∂xi
i=1
(12)
The friction factor is evaluated by: f =
T ◦
ϕ
0.4 where X = 1/((o /De )Re0.8 o Pr o ); Y = 1/K.C1 can be calculated from the slope of the Wilson plot line. After C1 is determined for the annular side heat transfer correlation, the tube side flow rate was changed while keeping the annular side flow rate at its maximum to minimize the annular side convective thermal resistance. And then the tube side heat transfer coefficient hi can be obtained, thus the tube side average Nusselt number can be calculated from
hd Nui = i i i
T
2.3. Experimental uncertainties
Eq. (10) can be rewritten in a linear form as: Y=
Variable
(10)
where C1 is the coefficient in Eq. (9) and C2 is the sum of the inner tube wall thermal resistance and the annular side convective thermal resistance: C2 = Rw Ao +
Table 1 Measurement uncertainties.
(15)
where Nur is the Nusselt number of the tube with rotors, Nu0 is the Nusselt number of the plain tube, fr is the friction factor of the tube with rotors, and f0 is the friction factor of the plain tube.
(16)
where ϕ is the derived parameter and x1 , x2 , . . ., xn are the measured variables. For the tube inserted with rotor-assembled strand, the relative uncertainty of the tube side Nusselt number is 2.1–3.5% for Reynolds numbers of 16,800–40,400 with water as the working fluid while the friction factor uncertainty is between 1.3–4.2%. The experimental results are reproducible within these uncertainty ranges. 3. Results and discussion 3.1. Verification of plain tube Preliminary experiments have been carried out on a plain tube to check the facility performance and verify the measuring uncertainties. Experimental results were compared with the empirical correlations for Nusselt number and friction factor, respectively. The measured Nusselt numbers were compared directly with the empirical correlation proposed by Gnielinski [21]: Nu =
(f/8)(Re − 1000)Pr f
1 + 12.7
2/3
f/8(Pr f
− 1)
(17)
The measured friction factors were compared directly with the Filonenko Equation: f = (1.82l gRe − 1.64)−2
(18)
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Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Fig. 5. Nusselt number of rotor-assembled strands with different geometries.
these rotor-assembled strands of different geometries shown in Fig. 5. The effect of rotor lead on the Nusselt number of the tube fitted with helical blade rotor with ladders was shown in Fig. 6. The figure showed that Nusselt number decreased with the increase of rotor lead, which could be explained by the fact that the behavior of flow inside the tube inserted with helical blade rotor with ladders was affected by the increase of lead. The smaller the rotor lead was, the more significantly the rotors were twisted, which greatly changed the flow direction and then caused increase in turbulence intensity of the flow in the plain tube assembled with helical blade rotor with ladders. The helical blade rotor with ladders of 22–100 generated around 2.3% and 4.36% higher average Nusselt number than those of 22–150 and 22–200, respectively. 3.3. Results of friction factor (f) Fig. 4. Comparison of measured data with empirical correlations in plain tube. (a) Nusselt number and (b) friction factor.
The comparison results of experimental results and empirical correlation results for Nusselt number and friction factor were shown in Fig. 4a and b, respectively. And the Nusselt numbers of plain tube were found to agree within 3.27% with the previous Eq. (17) approximately, while experimental friction factor results were found to agree within 8.73% with the previous Eq. (18).
Fig. 7 showed the relation of friction factor with Reynolds number of plain tube and the tube fitted with different kinds of rotor-assembled strands. It could be seen from the figure that the friction factor decreased with the increase of Reynolds number. Meanwhile, due to the driving force of rotor rotation, the friction factor obtained from the tube with rotor-assembled strands
3.2. Results of average Nusselt number (Nu) Fig. 5 showed the comparison of Nusselt number among the plain tube and the tube fitted with different kinds of rotorassembled strands in turbulent regime. In the figure, the Nusselt number increased with the increasing tube-side Reynolds number. Meanwhile, under the same Reynolds number, the Nusselt number obtained from the tube with rotor-assembled strands was 71.5–123.1% higher than that obtained from tube without rotor-assembled strands across the range of Reynolds number. Due to the tangential and radial velocity component, the mixing of fluid at the wall region and fluid at the core region, induced by the generated centrifugal force had significant ability to enhance heat transfer. It was also found that the heat transfer augmentation of helical blade rotor was the best among
Fig. 6. Nusselt number of helical blade rotor with ladders of different leads.
Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Fig. 7. Friction factor of rotor-assembled strands with different geometries.
was 37.4–74.8% higher than that obtained from tube without rotor-assembled strands across the range of Reynolds number. For rotor-assembled strands of different geometries, the friction factor of blade-discreted rotor was the highest among these rotor-assembled strands shown in Fig. 7, which revealed that the influence of ladders on friction factor was significant. The effect of rotor lead on the friction factor of the tube fitted with helical blade rotor with ladders was shown in Fig. 8. This figure showed that friction factor decreased with the increase of rotor lead, which meant that helical blade rotor with ladders of 22–100 generated around 28.5% and 33.1% higher average friction factor than those of 22–150 and 22–200, respectively. As indicated in reference [22], the rotating speed increased with the decrease of rotor lead. Therefore, helical blade rotor with ladders of 22–100 rotated faster than others, which resulted in more energy loss. 3.4. Results of thermal performance factor () The thermal performance factor (), indicating the practical benefit of the rotor-assembled strands usage, was obtained from Eq. (15), in which Nusselt number and friction factor in the tube with and without rotor-assembled strands were simultaneously determined at the same pumping power. Fig. 9 showed variation of thermal performance factor with Reynolds number for rotorassembled strands of different geometries. As seen from Fig. 9,
Fig. 8. Friction factor of helical blade rotor with ladders of different leads.
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Fig. 9. Thermal performance factor of rotor-assembled strands with different geometries.
the thermal performance factor tended to decrease with the rise of Reynolds number for all cases. Among rotor-assembled strands of different geometries, helical blade rotor with ladders offered the best performance followed by helical blade rotor and then blade-discreted rotor. This revealed the advantage of the ladders on rotor-assembled strands in the viewpoint of energy saving. The effect of rotor lead on thermal performance factor of helical blade rotor with ladders was shown in Fig. 10. Comparative data revealed that the thermal performance factor increased with decreasing Reynolds number and varied from 1.776 to 1.956 for 22–150, 1.769 to 1.928 for 22–200 and 1.707 to 1.817 for 22–100 under the experimental conditions. From the above analysis, it was concluded that the tube fitted with helical blade rotor with ladders of 22–150 had the best performance and generated the highest heat transfer enhancement at the same pumping power for the entire range studied, which meant the thermal performance factor could not always increase with increasing lead, but had a maximum value at a certain lead. 3.5. Correlation of the results The predicted data of the Nu and f calculated from Table 2 were plotted against experimental data of the Nu and f in Figs. 11 and 12,
Fig. 10. Thermal performance factor of helical blade rotors with ladders of different leads.
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Z. Zhang et al. / Chemical Engineering and Processing 60 (2012) 26–33
Table 2 Correlations of experimental results. Rotors
Nu
f
Blade-discreted rotor Helical blade rotor
Nu = 0.05Re0.75709 Pr0.60207 Nu = 0.005Re0.70125 Pr2.17539
f = 0.4073Re−0.22307 f = 0.3548Re−0.21198
Helical blade rotor with ladders
Nu = 0.02Re0.76621 Pr 1.1385
600 550 500
Nupre
400 350 300
300
350
400
450
500
550
Blade-discreted rotor Helical blade rotor Helical blade rotor with ladders (22-200) Helical blade rotor with ladders (22-150) Helical blade rotor with ladders (22-100)
fpre
0.044
0.040
0.036
0.036
0.040
0.044
di
0.048
The authors are grateful to the National Nature Science Foundation of Beijing (No. 3102023) and National Science and Technology Support Plan Project (No. 2011BAA04B02) for the financial assistance for this study. References
0.048
0.032 0.032
p −0.42388
Acknowledgments
Fig. 11. Comparison between predicted and experimental Nusselt number.
0.052
f = 0.2638Re−0.15885
600
Nuexp
0.056
di
(2) Among rotor-assembled strands of different geometries, the heat transfer enhancement of helical blade rotor was the best; the friction factor of blade-discreted rotor was the highest among these rotor-assembled strands; helical blade rotor with ladders offered the best overall performance followed by helical blade rotor and then blade-discreted rotor. For helical blade rotors with ladders of different leads, Nusselt number and friction factor increased with the decrease of rotor lead; the thermal performance factor of 22–150 was the best one in these rotor-assembled strands employed in the experiment. (3) Based on thorough multivariate linear normal regression method, the Nusselt number and friction factor correlations of all rotor-assembled strands employed in the experiment were established; the correlated results were in good agreement with experimental results.
Blade-discreted rotor Helical blade rotor Helical blade rotor with ladders (22-200) Helical blade rotor with ladders (22-150) Helical blade rotor with ladders (22-100)
450
250 250
p −0.0686
0.052
0.056
fexp Fig. 12. Comparison between predicted and experimental friction factor.
respectively. As shown in these figures, the maximum deviation between the experimental and predicted data were ±1.7% and ±6.5%, respectively. 4. Conclusions The experimental work has been carried out in order to study the heat transfer rate (Nu), friction factor (f) and thermal performance factor () of smooth tube fitted with rotor-assembled strands of different geometries. Meanwhile, the influence of rotor lead on heat transfer enhancement was also investigated. The comparison conclusions have been drawn as follows: (1) Rotor-assembled strands significantly improved heat transfer with the Nusselt number increased by 71.5–123.1% and friction factor increased by 37.4–74.8% over plain tube within the experimental Reynolds number range.
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