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Experimental investigation of turbulent heat transfer by counter and co-swirling flow in a flat tube fitted with twin twisted tapes
International Communications in Heat and Mass Transfer 75 (2016) 295–302
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Experimental investigation of turbulent heat transfer by counter and co-swirling flow in a flat tube fitted with twin twisted tapes☆ M.Kh. Abdolbaqi a, W.H. Azmi a,b,⁎, Rizalman Mamat a,b, N.M.Z.N. Mohamed a,b, G. Najafi c a b c
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Automotive Engineering Centre, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Tarbiat Modares University, Jalale-E-Aleahmad Highway, Tehran, Iran
a r t i c l e
i n f o
Available online 29 April 2016 Keywords: Heat transfer coefficient Friction factor Twin twisted tape Flat tube
a b s t r a c t The use of inserts has gained extensive attention due to their role in improving the efficiency of thermal systems. In this study, an experimental investigation was conducted to explore the effect of twin counter and co-twisted tapes on heat transfer rate (Nu), friction factor (f) and thermal enhancement index (η). The twin counter twisted tapes (CTT) and twin co-twisted tapes (CoTT) were used as swirl flow generators in a test section. The tests were conducted using the CTT and CoTT with three different twist ratios (H/D) = 5, 10 and 15) for Reynolds numbers range between 7200 and 32,400 under uniform heat flux conditions. The results show that Nusselt number (Nu), friction factor (f) and thermal enhancement index (η) increase with decreasing twist ratio (H/D) and the CTT is more efficient than the CoTT for heat transfer enhancement. Within the scope of this study, heat transfer rates in the flat tube fitted with the CTT are around 22.5% and 61% higher than those with the CoTT and plain flat tube, respectively. The maximum thermal enhancement index (η) obtained at the constant flow rate by the CTT with H/D = 5, 10 and 15, are 1.58, 1.44 and 1.15 respectively, while those obtained using the CoTT with the same range of H/D are 1.43, 1.19 and 1.04, respectively. Furthermore, the empirical correlations of the heat transfer (Nu), friction factor (f) and thermal enhancement index (η) are also reported. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction In the last decade, as energy costs have escalated rapidly, there has been a tremendous need for producing more efficient heat exchanger equipments. Several techniques have been promoted to enhance heat transfer rates, which consequently decreases the size and cost of equipment, especially, the heat exchangers. The thermal performance of tubes can be improved by two different heat transfer enhancement techniques; the active and passive method. The active technique requires external power to enable the wanted flow modification for increasing heat transfer such as electrostatic fields, mechanical aids, jet impingement, suction, injection, surface vibration, and fluid vibration. Whereas, the passive method uses rough surfaces, treated surfaces, extended surfaces, displaced enhancement devices, surface tension device, coiled tube and swirl flow devices and does not need external power [1]. Various active and passive techniques for the augmentation of heat transfer have been suggested by Ahuja [2] and Bergles [3]. These
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (M.K. Abdolbaqi), [email protected] (W.H. Azmi), [email protected] (R. Mamat), [email protected] (N.M.Z.N. Mohamed), g.najafi@modares.ac (G. Najafi).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.04.021 0735-1933/© 2016 Elsevier Ltd. All rights reserved.
techniques have been used to enhance heat transfer in many applications such as chemical reactors, nuclear reactors and general heat exchangers. Several studies have been carried out to investigate the influence of fluctuation generators (turbulent promoters) with different geometries on thermal behaviours in the heat exchanger, for example winglet or fins [4,5], dimpled or grooved tubes [6,7], wire coils [8,9], twisted-tapes [10–14], and combined turbulators [15,16]. The technique of generating swirl flow by insertion of a twisted tape is considered as one of the most favourable passive techniques due to the low cost of the tape and ease of use in the existing system [17]. The influence of twisted tapes has been extensively investigated experimentally and numerically [18–26]. The use of a twisted tape leads to the decrease in thermal boundary layer thickness, leading to increased convective heat transfer [27–29]. As a result of that, the pumping power in the process may increase dramatically. Ultimately, the pumping cost becomes higher. Therefore, the design of twisted tapes with proper geometry is essential to achieve a desired heat transfer rate with economic pumping power in an existing heat exchanger. After the accomplishment of using twisted tape successfully for heat transfer augmentation, which was considered rare was described by Whitham [30], further enhancements of thermal performance for tubes with assorted geometries of twisted tape inserts have been achieved. Kidd [31] and Klepper [32] concluded that the short length twisted tapes were more efficient than the full length twisted
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Nomenclature A B As Cp D IDh ODh f h H H/D I L Nu P Pr ΔP Q Re t T U V V
flat tube width, m flat tube height, m heat transfer surface area, m2 specific heat at constant pressure, J kg−1 K−1 tape width, m inside hydraulic diameter of the test tube, m outside hydraulic diameter of the test tube, m friction factor = ΔP/((L/Dh)(ρU2/2)) heat transfer coefficient, Wm−2 K−1 tape pitch length, m twist ratio current, A length of the test section, m Nusselt number = hDh/k pressure of flow in tube, Pa Prandtl number = μCp/k pressure drop, Pa heat transfer rate, W Reynolds number = ρUDh/μ thickness of the test tube, m temperature, °C average axial flow velocity, m s−1 voltage, V volume flow rate, m3 s−1
Greek letters δ tape thickness, m ρ fluid density, kg m−3 μ fluid dynamic viscosity, kg s−1 m−3 η thermal enhancement index Subscripts b bulk h hydraulic diameter e plain flat tube pp pumping power s swirl generator Abbreviations CTT twin counter twisted tapes CoTT twin co-twisted tapes
tapes for use in gas cooled nuclear reactors. Moreover, several experimental studies of heat transfer enhancement by means of regularly spaced twisted tapes were described by several researchers such as Saha et al. [33], Dasmahapatra and Raja Rao [27] and Eiamsa-ard et al. [12]. In another paper, Date and Gaitonde [34] developed correlations for predicting characteristics of a laminar flow in a tube fitted with regularly spaced twisted tape elements. Chang et al. [29] studied comparative thermal performance in round tubes fitted with single, twin and triple twisted tapes in the range of 3000 b Re b 14 , 000. The results showed that the tubes fitted with twin and triple twisted tapes could offer higher values of heat transfer augmentation with similar levels of performance factor in comparison with the tube fitted with single twisted tape. Bharadwaj et al. [35] investigated the heat transfer performance and pressure drop in a spirally grooved tube fitted with twisted tape under laminar and turbulent flows. In their finding, the direction of twist to grooved surface (clockwise and anticlockwise) affected the thermo-hydraulic characteristics. The effect of twin-counter and co-twisted tapes on heat transfer, friction factor and thermal enhancement index were investigated experimentally by
Eiamsa-ard et al. [17]. They found that the twin counter twisted tapes were more efficient than the twin co-twisted tapes for the heat transfer enhancement. It appears from the aforementioned investigations that numerous studies have been focused on the use of single, double and triple twisted tapes in circular tubes with similar tape-twist direction, apart from the modified twisted-tapes. However, no attempt was made to investigate the use of twin twisted tapes in a flat tube with various forms of counter and co-twist arrangements and different twisted ratios. Therefore, this study aims to investigate experimentally the effect of using twin-twisted tapes on heat transfer enhancement and friction factor in a flat tube with two different direction of counter-twisted tape (CTT) and co-twisted tape (CoTT) as well as three twisted ratios (H/D) of 5, 10 and 15. In addition, the working fluid used was distilled water with a wide range of Reynolds numbers in fully developed turbulent flow. The results obtained by the use of twin twisted tapes in a flat tube were compared with those of the plain flat tube. 2. Twisted tape and flat tube Twin twisted tapes are made of aluminium sheets and have a tape width (D) of 8 mm, tape thickness (δ) of 0.5 mm and tape length (L) of 1500 mm. Both twin-counter and co-twisted tapes were prepared with three different twist ratios, H/D = 5, 10 and 15 where the twist ratio is defined as twist length (180°/twist length) to tape width (D). The comparison of geometric details of the twin-counter and cotwisted tapes (counter and co-swirl tapes) and plain flat tube is shown in Fig. 1. The tape with 0.5 mm thickness was chosen because the thinner tape is easier to twist during the twisting process. In addition, it is also to avoid extra friction in the system that might be caused by a thicker tape. To produce the twisted tape at a specific twist ratio, one end of a straight tape was clamped while another end was carefully twisted to ensure a desired twist length. Both tapes for the twin cotwisted tapes (CoTT) were well aligned and positioned to be twisted in the same direction in order to generate identical direction swirl called co-swirl flow as presented in Fig. 1. Furthermore, two tapes for the twin counter twisted tapes (CTT) were aligned to be twisted in opposite directions to produce counter-swirl flow. 3. Experimental setup The experimental setup was integrated with a circulating pump, flow meter, heater, control panel, thermocouples, pressure transducer, chiller, collecting tank, and the test section. The heaters were enclosed with an aluminium flat tube along its length of 1500 mm, inner hydraulic diameter of 12.5 mm (IDh), outside hydraulic diameter of 14.8 mm (ODh) and wall thickness of 1 mm (t) which constitutes the test section. The total length of fluid flow in the tube was approximately 4.0 m, which ensures turbulent flow conditions at the entry of the test section. The schematic diagram of the experimental setup is shown in Fig. 2. A 1.0 hp (hp) pump connected to a collecting tank of 0.03 m3 capacity was used to circulate the working fluid through the test section. The outer diameter of the test section was wrapped with two nichrome heaters each of 1000 W rating. The heat loss to the surroundings was minimized by enclosing the tube with ceramic fibre insulation. Eight K-type thermocouples were fixed at different locations; six were fixed to the surface of the tube wall at an equal distance from the inlet and the other two were inserted to measure the inlet and outlet temperature of the working fluid. The thermocouples were calibrated before the tests were undertaken and had a maximum accuracy of 0.1 °C. A digital flow meter was connected between the pump and the inlet of the test section that detect flow rates in the range of 4 to 18 l per minute (LPM) with accuracy of 0.1 LPM. A chiller of 2.8 kW rating was located between the test section and the collecting tank. A constant input power of 900 W was supplied to the heater while the chiller was adjusted to obtain a fluid bulk temperature of 30 °C with a deviation of
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297
Fig. 1. Geometries of different type of twisted tape inserts with theorized flow patterns.
± 0.5 °C at all flow rates and fluids. A pressure transducer connected across the test section recorded the pressure drop with an accuracy of 0.5 Pa. The sensor was calibrated using a pressure calibration unit. A data logger recorded the surface and fluid temperatures every five seconds to determine the steady state nature of the experiment. At steady state condition, the temperatures, the flow rate and the power input to the heater were recorded. Experiments were undertaken to determine the pressure drop and heat transfer coefficients at various flow rates. The flow rate, the
pressure drop across the length of the tube, the temperatures of the fluid at the inlet and outlet, and the surface temperatures are recorded under steady state conditions. The experimental values of the friction factor and heat transfer coefficients were evaluated using the Darcy pressure drop and Newton's law of cooling equations, respectively. The reliability and accuracy of the setup were ensured by comparing the experimental values of the plain tube with the equation in literature. Based on the reliability of the present data, experiments were undertaken with twin co-twisted tape and counter twisted tape for different
Fig. 2. Schematic diagram of the experimental heat transfer setup.
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twist ratios of 5, 10 and 15 at various flow rates. The uncertainties in the measurement of physical quantities were estimated following the procedure given by Beckwith et al. [36]. The range of uncertainties is summarized and presented in Table 1. Furthermore the instrumentation error was estimated to be less than 0.91%.
Nusselt number and friction factor from the experiment were verified with the correlations recommended by Dittus–Boelter [37] and Blasius [38] represented by Eqs. (8) and (9) respectively. Nu ¼ 0:023Re0:8 Pr0:4
ð8Þ
4. Heat transfer and friction factor
f ¼ 0:3164Re−0:25
ð9Þ
The heat transfer coefficient was estimated from the electrical energy supplied as the losses were negligible. The following relations were used in the present analysis.
5. Results and discussion
Q ¼V I h exp ¼
ð1Þ
Q As ðT s −T b Þ
ð2Þ
where Tb = (Ti − To)/2As = [(π× B) + 2 × (A − B)]× L. In the experimental results, the average Nusselt number is defined as follows,
Nu exp ¼
h exp Dh : kw
ð3Þ
The friction factor for the tube with or without twisted tape can be calculated using pressure loss, Δp across the test length, L, using the following equations: f ¼
1 Δp Dh : 2 L ρV 2
ð4Þ
The flat tube hydraulic diameter is defined by " Dh ¼ 4
# 2 πd þ ðA−BÞ B 4
π B þ 2 ðA−BÞ
:
ð5Þ
Reynolds number, Prandtl number and all of the thermo-physical properties of the fluid were calculated on the basis of water properties corresponding to the bulk fluid temperature (Tb). The Reynolds number based on the total flow rate at the inlet of the test section is expressed as: Re ¼
ρVIDh μ
ð6Þ
Pr ¼
μC p : k
ð7Þ
It is necessary to validate the present plain tube data of the Nusselt number and friction factor in a fully developed straight/axial flow with the previously published correlations. In the present study, the
The experimental values of the heat transfer coefficients and friction factors as well as the thermal enhancement index in a flat tube fitted with twin counter twisted tape and twin co-twisted tape for counter swirl flow and co-swirl flow respectively are presented in Figs. 5 to 12. The experiments were accomplished using twin twisted tapes for three different twist ratios, H/D = 5, 10 and 15, in the range of Reynolds number between 7200 and 32,400. The results obtained for the plain flat tube were used as a reference for the performance evaluation of the twin twisted tapes. 5.1. Validation test The validation of the Nusselt number (Nu) and friction factor (f) of the plain flat tube was evaluated by comparing the experimental data with the previous correlations shown in Eqs. (8) [37] and (9) [38] under similar circumstances. Hence, the plain tube data acts as a qualification for the facility and the procedure utilized over the scope of the Reynolds number studied. The outcomes illustrated in Figs. 3 and 4, detected that the data for existing plain flat tube were in good accordance with the preceding reports for both the Nusselt number (Nu) and the friction factor (f) correlations. As observed, the present experimental Nusselt number data were in good agreement with the Dittus–Boelter correlation in Eq. (8) with an average deviation of ± 0.8%, while the average definite percentage deviations of experimental friction factor data was ± 1.2% compared with the Blasius correlation in Eq. (9). The empirical correlations of the Nusselt number and friction factor for the present plain flat tube can be described as follows: Nu ¼ 0:029Re0:78 Pr0:4
ð10Þ
f ¼ 0:345Re−0:26 :
ð11Þ
5.2. Effect of twin counter and co-twisted tape inserts In the present experimental study, the influence of the twin counter twisted tapes, CTT and the twin co-twisted tapes, CoTT inserted in the flat tube on the heat transfer rate are clarified in Fig. 5. The heat transfer rates in the flat tube fitted with the CTT were conspicuously higher than those in the tubes fitted with the CoTT for all ranges of the Reynolds numbers studied. From the figure, it was also found that the effect of
Table 1 Summary of uncertainty analysis. No.
Variables
1
Reynolds number, Re
2
Heat flux, q
3
Heat transfer coefficient, h
4
Nusselt number, Nu
5
Friction factor, f
Uncertainty correlations rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U Re Re Uq q Uh h
U
U
2
U
2
¼ ð ρρ Þ þ ð V Þ þ ð μμ Þ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi UV 2 UI 2 ¼ ðVÞ þðIÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼
U Nu Nu Uf f
2
U
2
0.17
2
U
ð qq Þ þ ððTðTw−TbÞ Þ w −T b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Uh 2 Uk 2 ¼ ðhÞ þðkÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼
U
2
U
2
U
Δp ð Δp Þ þ ð ρρ Þ þ ð V Þ
V
Uncertainty values 0.154–0.29
2
0.40–0.41 0.90–0.91 0.15–0.55
M.K. Abdolbaqi et al. / International Communications in Heat and Mass Transfer 75 (2016) 295–302
250 Water o Tb= 30 C
500 Dittus-Boelter [37] Plain flat tube
Plain flat tube CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
400
Nusselt number, Nu
Nusselt Number, Nu
200
150
100
50
300
200
100
0 0
0
5000 10000 15000 20000 25000 30000 35000 40000
0
Reynolds number, Re
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 3. Confirmatory test of empty tube of Nusselt number.
the CTT on the heat transfer rate was stronger at a higher Reynolds number. Over the range considered, the heat transfer rates in the tubes fitted with CTT were, respectively, 22.5% and 61% higher than those in the tubes equipped with the CoTT and the empty tube. Fig. 6 presents the friction factor in the corresponding tubes. Basically, the friction factor decreases with increasing Reynolds number. At the same Reynolds number, the friction factors in the tube fitted with the CTT were higher than those in the tubes fitted with the CoTT and the plain flat tube. It is believed that in the case of the co-swirl twisted tapes, the unidirectional swirl motion is induced in the main flow while the counter-swirl twisted tapes produce swirls in the reverse direction which increases the whirl velocities of the fluid inside the tube. The secondary flow is created by the counter-swirl motion which leads to higher turbulence intensity and better fluid mixing. 5.3. Effect of twist ratio The effect of twist ratios (H/D = 5, 10 and 15) on the heat transfer rate in the tubes fitted with CTT and CoTT is demonstrated in Fig. 5. From the experimental results, it can be observed that the heat transfer enhancement increase as twist ratio decreases. Generally, the smaller twist ratio generates stronger swirl intensity, leading to more efficient interruption of boundary layers along the flow path. Hence, heat can
Fig. 5. Variations of Nusselt number with Reynolds number for various twisted tape inserts.
be transferred efficiently over the thin boundary layer. Moreover, the residence time of the flow increases with increasing swirl flow intensity [12]. This extends the duration of heat transfer between the working fluid and heat source (tube wall). For all the conditions studied, the CTT and CoTT with the smallest twist ratio (H/D = 5) provided the heat transfer rates around 39 to 43% and 47.5 to 61% higher than those in the tubes with larger twist ratios and the empty tube, respectively. As seen in Fig. 6, the friction factor tends to increase with decreasing twist ratio. This is in the same trend found for the Nusselt number. This can be explained by the fact that the use of a twisted tape with a smaller twist ratio leads to higher viscous loss near the tube wall regions caused by a stronger swirl flow. Over the range studied, the friction factors for the tube fitted with CTT with H/D = 5, 10, and 15, are, respectively 16 and 53%, times of those in tubes fitted with the CoTT and in the plain flat tube. Nusselt number and friction factor enhancement ratios with respect to the Reynolds number for different types of twisted tape inserts are presented in Figs. 7 and 8, respectively. Fig. 7 shows that the Nusselt number enhancement ratio decreased with an increase of Reynolds number in all types and the twisted ratio of twisted tapes, which shows that the system should be operated in the range of lower Reynolds number to obtain better heat transfer rates. The Nusselt number 0.200
0.06 Blasius [38] Plain flat tube
Plain flat tube CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
0.175
0.05
0.150 Friction factor, f
0.04 Friction factor, f
299
0.03
0.02
0.125 0.100 0.075 0.050
0.01
0.025 0.000
0.00 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re Fig. 4. Confirmatory test of empty tube of friction factor.
0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 6. Variations of friction factor with Reynolds number for various twisted tape inserts.
300
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4.0
600 CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
Plain flat tube CTT CoTT
500 Nusselt number, Nu (Predicted)
Nusselt number ratio, Nus/Nue
3.5
+15%
-15%
400
300
200
100
0
5000 10000 15000 20000 25000 30000 35000 40000
0
100
Reynolds number, Re Fig. 7. Variation of Nusselt number enhancement ratio with respect to Reynolds number for different types of twisted tape inserts.
200 300 400 500 Nusselt number, Nu (Experimental)
600
Fig. 9. Validation of empirical correlations for Nusselt number.
For the tube fitted with the CoTT: enhancement ratios lie between 1.24 to 2.52 and 1.1 to 2.27 for flat tubes having twin co-swirl twisted tapes twin counter twisted tapes (CTT) and twin co-twisted tapes (CoTT), respectively, while the twist ratio is kept as 5. The friction factor enhancement ratios are found to be in the range of 1.38 to 4.85 and 1.25 to 4.07 for the aforementioned geometries of inserts. In the present investigation, the tests were made in a uniform heat flux tube with water as working fluid and the correlation comparisons between the present data with those calculated by the present correlations for Nusselt number and friction factor are portrayed in Figs. 9 and 10. Evidently, the majority of the heat transfer data falls within ±15% for the present correlations of Eqs. (12) and (14). Eqs. (13) and (15) provided the correlative results of the friction factor with maximum discrepancies of ± 10% with the experimental measurements. For the tube fitted with the CTT:
Nu ¼ 0:209Re0:72 Pr0:4 ðH=DÞ−0:45
ð14Þ
f ¼ 66:7Re−0:6 ðH=DÞ−0:54 :
ð15Þ
6. Thermal enhancement index
Nu ¼ 0:268Re0:7 Pr0:4 ðH=DÞ−0:4
ð12Þ
In order to evaluate the thermal enhancement index of the flat tubes fitted with the CTT and the CoTT, the equal pumping power comparison was performed [39–41]. Performance evaluation was determined to assess the benefits of using the CTT and the CoTT in terms of enhancement index at the same pumping power. The thermal performance factors of the flat tubes fitted with twin twisted tapes were assessed under constant pumping conditions. The constant pumping power conditions can be described as:
f ¼ 24:96Re−0:59 ðH=DÞ0:1 :
ð13Þ
• • V ΔP ¼ V ΔP : e
ð16Þ
s
6
Friction factor ratio, fs /fe
5
4
3
2
1
0.200 0.175
Friction factor, f (Predicted)
CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
Plain flat tube CTT CoTT
+10%
0.150
-10% 0.125 0.100 0.075 0.050 0.025
0 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
0.000
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 Friction factor, f (Experimental)
Fig. 8. Variation of friction factor enhancement ratio with respect to Reynolds number for different types of twisted tape inserts.
Fig. 10. Validation of empirical correlations for friction factor.
M.K. Abdolbaqi et al. / International Communications in Heat and Mass Transfer 75 (2016) 295–302
Under these criteria, the correlation between friction and Reynolds number can be expressed as:
f Re3
e
¼ f Re3
ð17Þ
s
1=3
Res ¼ Ree ð f e =f s Þ
:
The thermal performance factor, η can be assessed based on the power consumption per unit mass of fluid. It is also defined as the ratio between the heat transfer coefficient for the tube with heat transfer promoter (hs) and the value for the plain tube (he) at similar pumping power. η¼
−1=3 hs Nus Nus fs ¼ ¼ he pp Nue pp Nue fe
ð18Þ
Where the Nusselt number for tube with twisted tape inserts are represented as (Nus) and plain flat tube as (Nue) while the friction factor for tubes with twisted tape inserts are represented as (fs) and plain flat tubes as (fe). Applying Eqs. (11), (13), (15) and (17), the Reynolds number for the tube fitted with twisted tape (Res) can be expressed as the function of the Reynolds number of the empty tube (Ree): For the tube fitted with the CTT: Res ¼ 0:118Ree 1:14 ðH=DÞ0:2 :
ð19Þ
For the tube fitted with the CoTT: Res ¼ 0:185Ree 1:106 ðH=DÞ0:18 :
ð20Þ
The thermal enhancement index for the tube fitted with the CTT or CoTT can be obtained by the combination of Eqs. (10), (12), (14), (18), (19) and (20), as follows: For the tube fitted with the CTT: η ¼ 1:5Res 0:035 ðH=DÞ−0:223 :
ð21Þ
For the tube fitted with the CoTT: η ¼ 1:876Res 0:014 ðH=DÞ−0:266 :
ð22Þ
The effect of various twin twisted tapes at different twist ratios (H/D) on the thermal enhancement index in Reynolds number in the
301
range of 7200 and 32,400 has been clarified in Fig. 11. The comparative data revealed that the thermal enhancement index increases with decreasing Reynolds number. In addition, the thermal enhancement indexes were varied between 1.17 and 2.52 for the CTT and 1.07 and 2.26 for the CoTT, depending on the Reynolds number and the twist ratio (H/D). For the CTT, the mean enhancement index for the smallest twist ratio (H/D = 5) was, respectively, 7.8%, and 20.2% higher than those for H/D = 10 and 15. The above data suggest that the highest enhancement index can be obtained at the lowest twist ratio (H/D), and relatively low Reynolds number. It is noteworthy that the enhancement indices in the tube fitted with the CTT were around 22.5% higher than those in the tube fitted with the CoTT. In addition the majority of the thermal enhancement index data fell within ±10% for the present correlations of Eqs. (21) and (22) with the experimental measurements as illustrated in Fig. 12.
7. Conclusions The present paper shows the feasibility of convection heat transfer enhancement by inserting the CTT (counter-swirl flow generators) and the CoTT (co-swirl flow generators) for turbulent flow with a uniform heat flux. Heat transfer coefficient and friction factor were determined experimentally for the tubes fitted with the CTT and CoTT using water as the working fluid with Reynolds number ranging from 7200 and 32,400. Based on the obtained results, it was found that the heat transfer, friction factor, and thermal enhancement index increased as the twist ratio (H/D) decreases. In addition, the Nusselt number increases with increasing Reynolds number while the opposite trends were found for the friction factor and the thermal enhancement index. The CTT (counter-swirl tapes) can enhance heat transfer more efficiently than the CoTT (co-swirl tapes). The quantitative results showed that, heat transfer rates for the CTT were around 22.5% higher than those for the CoTT and 61% higher than those for the empty tubes. The maximum thermal enhancement index (η) obtained at the constant pumping power using the CTT with H/D = 5, was 2.52, while that obtained using the CoTT with the same range of H/D was 2.26. The achieved results indicated that the modified swirl flow (counter-swirl flow) generated by the CTT is a promising approach for heat transfer enhancement. The empirical correlations developed in the present work, provided the correlative results of the Nusselt number and friction factor. The maximum discrepancies between the correlative results and experimental results for Nusselt number and friction factor and thermal enhancement index were found to be ±15%, ±10% and ±10%, respectively.
2.0
Thermal enhancement index,
1.6
(Predicted)
1.8 Thermal enhancement index,
2.5
CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
1.4
1.2
1.0
0.8 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 11. Variations of thermal enhancement index with Reynolds number for various twisted tape inserts.
CTT CoTT
+10%
2.0 -10% 1.5
1.0
0.5
0.0 0.0
0.5 1.0 1.5 2.0 Thermal enhancement index, (Experimental)
Fig. 12. Validation of empirical correlations for thermal enhancement index.
2.5
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Acknowledgements The authors are grateful to the Universiti Malaysia Pahang (UMP) and Automotive Engineering Centre (AEC) for financial supports given under RDU1403153 and RDU151411 (RAGS/1/2015/TK0/UMP/03/2). References [1] A. Bergles, The implications and challenges of enhanced heat transfer for the chemical process industries, Chem. Eng. Res. Des. 79 (4) (2001) 437–444. [2] A.S. Ahuja, Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results, J. Appl. Phys. 46 (8) (1975) 3408–3416. [3] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rohsenow, J.P. Hartnett, E.N. Ganic (Eds.), Handbook of Heat Transfer Applications, McGraw-Hill, New York 1985, pp. 31–380. [4] P. Promvonge, S. Skullong, S. Kwankaomeng, C. Thiangpong, Heat transfer in square duct fitted diagonally with angle-finned tape—Part 1: Experimental study, Int. Commun. Heat Mass Transfer 39 (5) (2012) 617–624. [5] S. Skullong, P. Promvonge, Experimental investigation on turbulent convection in solar air heater channel fitted with delta winglet vortex generator, Chin. J. Chem. Eng. 22 (1) (2014) 1–10. [6] K. Bilen, M. Cetin, H. Gul, T. Balta, The investigation of groove geometry effect on heat transfer for internally grooved tubes, Appl. Therm. Eng. 29 (4) (2009) 753–761. [7] Y. Wang, Y.-L. He, Y.-G. Lei, J. Zhang, Heat transfer and hydrodynamics analysis of a novel dimpled tube, Exp. Thermal Fluid Sci. 34 (8) (2010) 1273–1281. [8] S. Gunes, V. Ozceyhan, O. Buyukalaca, Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts, Exp. Thermal Fluid Sci. 34 (6) (2010) 684–691. [9] P. Promvonge, Thermal performance in circular tube fitted with coiled square wires, Energy Convers. Manag. 49 (5) (2008) 980–987. [10] W.H. Azmi, K. Sharma, P. Sarma, R. Mamat, S. Anuar, Comparison of convective heat transfer coefficient and friction factor of TiO2 nanofluid flow in a tube with twisted tape inserts, Int. J. Therm. Sci. 81 (2014) 84–93. [11] W.H. Azmi, K. Sharma, P. Sarma, R. Mamat, S. Anuar, L.S. Sundar, Numerical validation of experimental heat transfer coefficient with SiO2 nanofluid flowing in a tube with twisted tape inserts, Appl. Therm. Eng. 73 (1) (2014) 296–306. [12] S. Eiamsa-ard, C. Thianpong, P. Promvonge, Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements, Int. Commun. Heat Mass Transfer 33 (10) (2006) 1225–1233. [13] S.W. Chang, Y.J. Jan, J.S. Liou, Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape, Int. J. Therm. Sci. 46 (5) (2007) 506–518. [14] S.W. Chang, T.L. Yang, J.S. Liou, Heat transfer and pressure drop in tube with broken twisted tape insert, Exp. Thermal Fluid Sci. 32 (2) (2007) 489–501. [15] S. Eiamsa-Ard, P. Nivesrangsan, S. Chokphoemphun, P. Promvonge, Influence of combined non-uniform wire coil and twisted tape inserts on thermal performance characteristics, Int. Commun. Heat Mass Transfer 37 (7) (2010) 850–856. [16] P. Promvonge, Thermal augmentation in circular tube with twisted tape and wire coil turbulators, Energy Convers. Manag. 49 (11) (2008) 2949–2955. [17] S. Eiamsa-Ard, C. Thianpong, P. Eiamsa-Ard, Turbulent heat transfer enhancement by counter/co-swirling flow in a tube fitted with twin twisted tapes, Exp. Thermal Fluid Sci. 34 (1) (2010) 53–62. [18] K. Wongcharee, S. Eiamsa-ard, Enhancement of heat transfer using CuO/water nanofluid and twisted tape with alternate axis, Int. Commun. Heat Mass Transfer 38 (6) (2011) 742–748. [19] K. Wongcharee, S. Eiamsa-ard, Heat transfer enhancement by using CuO/water nanofluid in corrugated tube equipped with twisted tape, Int. Commun. Heat Mass Transfer 39 (2) (2012) 251–257.
[20] S. Eiamsa-ard, P. Seemawute, Decaying swirl flow in round tubes with short-length twisted tapes, Int. Commun. Heat Mass Transfer 39 (5) (2012) 649–656. [21] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Shahabuddin, M. Saha, L.A. Memon, Thermal characteristics in a heat exchanger tube fitted with triple twisted tape inserts, Int. Commun. Heat Mass Transfer 48 (2013) 124–132. [22] M.T. Naik, G.R. Janardana, L.S. Sundar, Experimental investigation of heat transfer and friction factor with water–propylene glycol based CuO nanofluid in a tube with twisted tape inserts, Int. Commun. Heat Mass Transfer 46 (2013) 13–21. [23] 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, Int. Commun. Heat Mass Transfer 46 (2013) 49–57. [24] K. Nanan, K. Yongsiri, K. Wongcharee, C. Thianpong, S. Eiamsa-ard, Heat transfer enhancement by helically twisted tapes inducing co- and counter-swirl flows, Int. Commun. Heat Mass Transfer 46 (2013) 67–73. [25] V. Mokkapati, C.-S. Lin, Numerical study of an exhaust heat recovery system using corrugated tube heat exchanger with twisted tape inserts, Int. Commun. Heat Mass Transfer 57 (2014) 53–64. [26] P. Promvonge, S. Suwannapan, M. Pimsarn, C. Thianpong, Experimental study on heat transfer in square duct with combined twisted-tape and winglet vortex generators, Int. Commun. Heat Mass Transfer 59 (2014) 158–165. [27] J. Dasmahapatra, M. Raja Rao, ‘Laminar flow heat transfer to generalized power law fluids inside circular tubes fitted with regularly spaced twisted tape elements for uniform wall temperature condition, Heat Transfer Div. HTD 174 (1991) 51–58. [28] S. Al-Fahed, L. Chamra, W. Chakroun, Pressure drop and heat transfer comparison for both microfin tube and twisted-tape inserts in laminar flow, Exp. Thermal Fluid Sci. 18 (4) (1998) 323–333. [29] S.W. Chang, K.-W. Yu, M.H. Lu, Heat transfers in tubes fitted with single, twin, and triple twisted tapes, Exp. Heat Transfer 18 (4) (2005) 279–294. [30] J. Whitham, The effects of retarders in fire tubes of steam boilers, Str. Railw. J. 12 (6) (1896) 374. [31] G.J. Kidd, Heat transfer and pressure drop for nitrogen flowing in tubes containing twisted tapes, AICHE J. 15 (4) (1969) 581–585. [32] O. Klepper, Heat Transfer Performance of Short Twisted Tapes, National Lab., Tenn., Oak Ridge, 1972. [33] S. Saha, U. Gaitonde, A. Date, Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Sci. 2 (3) (1989) 310–322. [34] A. Date, U. Gaitonde, Development of correlations for predicting characteristics of laminar flow in a tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Sci. 3 (4) (1990) 373–382. [35] P. Bharadwaj, A. Khondge, A. Date, Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert, Int. J. Heat Mass Transf. 52 (7) (2009) 1938–1944. [36] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements, Pearson Prentice Hall, Upper Saddle River, NJ, 2007. [37] F.W. Dittus, L.M.K. Boelter, Heat Transfer in Automobile Radiators of the Tubular Type, vol. 2University of California Publications on Engineering, 1930 443–461. [38] F.P. Incropera, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 2011. [39] R.L. Webb, N.-H. Kim, Principle of Enhanced Heat Transfer, Taylor Francis, New York, NY, USA, 1994. [40] K. Yakut, B. Sahin, S. Canbazoglu, Performance and flow-induced vibration characteristics for conical-ring turbulators, Appl. Energy 79 (1) (2004) 65–76. [41] K. Bilen, U. Akyol, S. Yapici, Heat transfer and friction correlations and thermal performance analysis for a finned surface, Energy Convers. Manag. 42 (9) (2001) 1071–1083.
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International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental investigation of turbulent heat transfer by counter and co-swirling flow in a flat tube fitted with twin twisted tapes☆ M.Kh. Abdolbaqi a, W.H. Azmi a,b,⁎, Rizalman Mamat a,b, N.M.Z.N. Mohamed a,b, G. Najafi c a b c
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Automotive Engineering Centre, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Tarbiat Modares University, Jalale-E-Aleahmad Highway, Tehran, Iran
a r t i c l e
i n f o
Available online 29 April 2016 Keywords: Heat transfer coefficient Friction factor Twin twisted tape Flat tube
a b s t r a c t The use of inserts has gained extensive attention due to their role in improving the efficiency of thermal systems. In this study, an experimental investigation was conducted to explore the effect of twin counter and co-twisted tapes on heat transfer rate (Nu), friction factor (f) and thermal enhancement index (η). The twin counter twisted tapes (CTT) and twin co-twisted tapes (CoTT) were used as swirl flow generators in a test section. The tests were conducted using the CTT and CoTT with three different twist ratios (H/D) = 5, 10 and 15) for Reynolds numbers range between 7200 and 32,400 under uniform heat flux conditions. The results show that Nusselt number (Nu), friction factor (f) and thermal enhancement index (η) increase with decreasing twist ratio (H/D) and the CTT is more efficient than the CoTT for heat transfer enhancement. Within the scope of this study, heat transfer rates in the flat tube fitted with the CTT are around 22.5% and 61% higher than those with the CoTT and plain flat tube, respectively. The maximum thermal enhancement index (η) obtained at the constant flow rate by the CTT with H/D = 5, 10 and 15, are 1.58, 1.44 and 1.15 respectively, while those obtained using the CoTT with the same range of H/D are 1.43, 1.19 and 1.04, respectively. Furthermore, the empirical correlations of the heat transfer (Nu), friction factor (f) and thermal enhancement index (η) are also reported. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction In the last decade, as energy costs have escalated rapidly, there has been a tremendous need for producing more efficient heat exchanger equipments. Several techniques have been promoted to enhance heat transfer rates, which consequently decreases the size and cost of equipment, especially, the heat exchangers. The thermal performance of tubes can be improved by two different heat transfer enhancement techniques; the active and passive method. The active technique requires external power to enable the wanted flow modification for increasing heat transfer such as electrostatic fields, mechanical aids, jet impingement, suction, injection, surface vibration, and fluid vibration. Whereas, the passive method uses rough surfaces, treated surfaces, extended surfaces, displaced enhancement devices, surface tension device, coiled tube and swirl flow devices and does not need external power [1]. Various active and passive techniques for the augmentation of heat transfer have been suggested by Ahuja [2] and Bergles [3]. These
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (M.K. Abdolbaqi), [email protected] (W.H. Azmi), [email protected] (R. Mamat), [email protected] (N.M.Z.N. Mohamed), g.najafi@modares.ac (G. Najafi).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.04.021 0735-1933/© 2016 Elsevier Ltd. All rights reserved.
techniques have been used to enhance heat transfer in many applications such as chemical reactors, nuclear reactors and general heat exchangers. Several studies have been carried out to investigate the influence of fluctuation generators (turbulent promoters) with different geometries on thermal behaviours in the heat exchanger, for example winglet or fins [4,5], dimpled or grooved tubes [6,7], wire coils [8,9], twisted-tapes [10–14], and combined turbulators [15,16]. The technique of generating swirl flow by insertion of a twisted tape is considered as one of the most favourable passive techniques due to the low cost of the tape and ease of use in the existing system [17]. The influence of twisted tapes has been extensively investigated experimentally and numerically [18–26]. The use of a twisted tape leads to the decrease in thermal boundary layer thickness, leading to increased convective heat transfer [27–29]. As a result of that, the pumping power in the process may increase dramatically. Ultimately, the pumping cost becomes higher. Therefore, the design of twisted tapes with proper geometry is essential to achieve a desired heat transfer rate with economic pumping power in an existing heat exchanger. After the accomplishment of using twisted tape successfully for heat transfer augmentation, which was considered rare was described by Whitham [30], further enhancements of thermal performance for tubes with assorted geometries of twisted tape inserts have been achieved. Kidd [31] and Klepper [32] concluded that the short length twisted tapes were more efficient than the full length twisted
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Nomenclature A B As Cp D IDh ODh f h H H/D I L Nu P Pr ΔP Q Re t T U V V
flat tube width, m flat tube height, m heat transfer surface area, m2 specific heat at constant pressure, J kg−1 K−1 tape width, m inside hydraulic diameter of the test tube, m outside hydraulic diameter of the test tube, m friction factor = ΔP/((L/Dh)(ρU2/2)) heat transfer coefficient, Wm−2 K−1 tape pitch length, m twist ratio current, A length of the test section, m Nusselt number = hDh/k pressure of flow in tube, Pa Prandtl number = μCp/k pressure drop, Pa heat transfer rate, W Reynolds number = ρUDh/μ thickness of the test tube, m temperature, °C average axial flow velocity, m s−1 voltage, V volume flow rate, m3 s−1
Greek letters δ tape thickness, m ρ fluid density, kg m−3 μ fluid dynamic viscosity, kg s−1 m−3 η thermal enhancement index Subscripts b bulk h hydraulic diameter e plain flat tube pp pumping power s swirl generator Abbreviations CTT twin counter twisted tapes CoTT twin co-twisted tapes
tapes for use in gas cooled nuclear reactors. Moreover, several experimental studies of heat transfer enhancement by means of regularly spaced twisted tapes were described by several researchers such as Saha et al. [33], Dasmahapatra and Raja Rao [27] and Eiamsa-ard et al. [12]. In another paper, Date and Gaitonde [34] developed correlations for predicting characteristics of a laminar flow in a tube fitted with regularly spaced twisted tape elements. Chang et al. [29] studied comparative thermal performance in round tubes fitted with single, twin and triple twisted tapes in the range of 3000 b Re b 14 , 000. The results showed that the tubes fitted with twin and triple twisted tapes could offer higher values of heat transfer augmentation with similar levels of performance factor in comparison with the tube fitted with single twisted tape. Bharadwaj et al. [35] investigated the heat transfer performance and pressure drop in a spirally grooved tube fitted with twisted tape under laminar and turbulent flows. In their finding, the direction of twist to grooved surface (clockwise and anticlockwise) affected the thermo-hydraulic characteristics. The effect of twin-counter and co-twisted tapes on heat transfer, friction factor and thermal enhancement index were investigated experimentally by
Eiamsa-ard et al. [17]. They found that the twin counter twisted tapes were more efficient than the twin co-twisted tapes for the heat transfer enhancement. It appears from the aforementioned investigations that numerous studies have been focused on the use of single, double and triple twisted tapes in circular tubes with similar tape-twist direction, apart from the modified twisted-tapes. However, no attempt was made to investigate the use of twin twisted tapes in a flat tube with various forms of counter and co-twist arrangements and different twisted ratios. Therefore, this study aims to investigate experimentally the effect of using twin-twisted tapes on heat transfer enhancement and friction factor in a flat tube with two different direction of counter-twisted tape (CTT) and co-twisted tape (CoTT) as well as three twisted ratios (H/D) of 5, 10 and 15. In addition, the working fluid used was distilled water with a wide range of Reynolds numbers in fully developed turbulent flow. The results obtained by the use of twin twisted tapes in a flat tube were compared with those of the plain flat tube. 2. Twisted tape and flat tube Twin twisted tapes are made of aluminium sheets and have a tape width (D) of 8 mm, tape thickness (δ) of 0.5 mm and tape length (L) of 1500 mm. Both twin-counter and co-twisted tapes were prepared with three different twist ratios, H/D = 5, 10 and 15 where the twist ratio is defined as twist length (180°/twist length) to tape width (D). The comparison of geometric details of the twin-counter and cotwisted tapes (counter and co-swirl tapes) and plain flat tube is shown in Fig. 1. The tape with 0.5 mm thickness was chosen because the thinner tape is easier to twist during the twisting process. In addition, it is also to avoid extra friction in the system that might be caused by a thicker tape. To produce the twisted tape at a specific twist ratio, one end of a straight tape was clamped while another end was carefully twisted to ensure a desired twist length. Both tapes for the twin cotwisted tapes (CoTT) were well aligned and positioned to be twisted in the same direction in order to generate identical direction swirl called co-swirl flow as presented in Fig. 1. Furthermore, two tapes for the twin counter twisted tapes (CTT) were aligned to be twisted in opposite directions to produce counter-swirl flow. 3. Experimental setup The experimental setup was integrated with a circulating pump, flow meter, heater, control panel, thermocouples, pressure transducer, chiller, collecting tank, and the test section. The heaters were enclosed with an aluminium flat tube along its length of 1500 mm, inner hydraulic diameter of 12.5 mm (IDh), outside hydraulic diameter of 14.8 mm (ODh) and wall thickness of 1 mm (t) which constitutes the test section. The total length of fluid flow in the tube was approximately 4.0 m, which ensures turbulent flow conditions at the entry of the test section. The schematic diagram of the experimental setup is shown in Fig. 2. A 1.0 hp (hp) pump connected to a collecting tank of 0.03 m3 capacity was used to circulate the working fluid through the test section. The outer diameter of the test section was wrapped with two nichrome heaters each of 1000 W rating. The heat loss to the surroundings was minimized by enclosing the tube with ceramic fibre insulation. Eight K-type thermocouples were fixed at different locations; six were fixed to the surface of the tube wall at an equal distance from the inlet and the other two were inserted to measure the inlet and outlet temperature of the working fluid. The thermocouples were calibrated before the tests were undertaken and had a maximum accuracy of 0.1 °C. A digital flow meter was connected between the pump and the inlet of the test section that detect flow rates in the range of 4 to 18 l per minute (LPM) with accuracy of 0.1 LPM. A chiller of 2.8 kW rating was located between the test section and the collecting tank. A constant input power of 900 W was supplied to the heater while the chiller was adjusted to obtain a fluid bulk temperature of 30 °C with a deviation of
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297
Fig. 1. Geometries of different type of twisted tape inserts with theorized flow patterns.
± 0.5 °C at all flow rates and fluids. A pressure transducer connected across the test section recorded the pressure drop with an accuracy of 0.5 Pa. The sensor was calibrated using a pressure calibration unit. A data logger recorded the surface and fluid temperatures every five seconds to determine the steady state nature of the experiment. At steady state condition, the temperatures, the flow rate and the power input to the heater were recorded. Experiments were undertaken to determine the pressure drop and heat transfer coefficients at various flow rates. The flow rate, the
pressure drop across the length of the tube, the temperatures of the fluid at the inlet and outlet, and the surface temperatures are recorded under steady state conditions. The experimental values of the friction factor and heat transfer coefficients were evaluated using the Darcy pressure drop and Newton's law of cooling equations, respectively. The reliability and accuracy of the setup were ensured by comparing the experimental values of the plain tube with the equation in literature. Based on the reliability of the present data, experiments were undertaken with twin co-twisted tape and counter twisted tape for different
Fig. 2. Schematic diagram of the experimental heat transfer setup.
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twist ratios of 5, 10 and 15 at various flow rates. The uncertainties in the measurement of physical quantities were estimated following the procedure given by Beckwith et al. [36]. The range of uncertainties is summarized and presented in Table 1. Furthermore the instrumentation error was estimated to be less than 0.91%.
Nusselt number and friction factor from the experiment were verified with the correlations recommended by Dittus–Boelter [37] and Blasius [38] represented by Eqs. (8) and (9) respectively. Nu ¼ 0:023Re0:8 Pr0:4
ð8Þ
4. Heat transfer and friction factor
f ¼ 0:3164Re−0:25
ð9Þ
The heat transfer coefficient was estimated from the electrical energy supplied as the losses were negligible. The following relations were used in the present analysis.
5. Results and discussion
Q ¼V I h exp ¼
ð1Þ
Q As ðT s −T b Þ
ð2Þ
where Tb = (Ti − To)/2As = [(π× B) + 2 × (A − B)]× L. In the experimental results, the average Nusselt number is defined as follows,
Nu exp ¼
h exp Dh : kw
ð3Þ
The friction factor for the tube with or without twisted tape can be calculated using pressure loss, Δp across the test length, L, using the following equations: f ¼
1 Δp Dh : 2 L ρV 2
ð4Þ
The flat tube hydraulic diameter is defined by " Dh ¼ 4
# 2 πd þ ðA−BÞ B 4
π B þ 2 ðA−BÞ
:
ð5Þ
Reynolds number, Prandtl number and all of the thermo-physical properties of the fluid were calculated on the basis of water properties corresponding to the bulk fluid temperature (Tb). The Reynolds number based on the total flow rate at the inlet of the test section is expressed as: Re ¼
ρVIDh μ
ð6Þ
Pr ¼
μC p : k
ð7Þ
It is necessary to validate the present plain tube data of the Nusselt number and friction factor in a fully developed straight/axial flow with the previously published correlations. In the present study, the
The experimental values of the heat transfer coefficients and friction factors as well as the thermal enhancement index in a flat tube fitted with twin counter twisted tape and twin co-twisted tape for counter swirl flow and co-swirl flow respectively are presented in Figs. 5 to 12. The experiments were accomplished using twin twisted tapes for three different twist ratios, H/D = 5, 10 and 15, in the range of Reynolds number between 7200 and 32,400. The results obtained for the plain flat tube were used as a reference for the performance evaluation of the twin twisted tapes. 5.1. Validation test The validation of the Nusselt number (Nu) and friction factor (f) of the plain flat tube was evaluated by comparing the experimental data with the previous correlations shown in Eqs. (8) [37] and (9) [38] under similar circumstances. Hence, the plain tube data acts as a qualification for the facility and the procedure utilized over the scope of the Reynolds number studied. The outcomes illustrated in Figs. 3 and 4, detected that the data for existing plain flat tube were in good accordance with the preceding reports for both the Nusselt number (Nu) and the friction factor (f) correlations. As observed, the present experimental Nusselt number data were in good agreement with the Dittus–Boelter correlation in Eq. (8) with an average deviation of ± 0.8%, while the average definite percentage deviations of experimental friction factor data was ± 1.2% compared with the Blasius correlation in Eq. (9). The empirical correlations of the Nusselt number and friction factor for the present plain flat tube can be described as follows: Nu ¼ 0:029Re0:78 Pr0:4
ð10Þ
f ¼ 0:345Re−0:26 :
ð11Þ
5.2. Effect of twin counter and co-twisted tape inserts In the present experimental study, the influence of the twin counter twisted tapes, CTT and the twin co-twisted tapes, CoTT inserted in the flat tube on the heat transfer rate are clarified in Fig. 5. The heat transfer rates in the flat tube fitted with the CTT were conspicuously higher than those in the tubes fitted with the CoTT for all ranges of the Reynolds numbers studied. From the figure, it was also found that the effect of
Table 1 Summary of uncertainty analysis. No.
Variables
1
Reynolds number, Re
2
Heat flux, q
3
Heat transfer coefficient, h
4
Nusselt number, Nu
5
Friction factor, f
Uncertainty correlations rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U Re Re Uq q Uh h
U
U
2
U
2
¼ ð ρρ Þ þ ð V Þ þ ð μμ Þ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi UV 2 UI 2 ¼ ðVÞ þðIÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼
U Nu Nu Uf f
2
U
2
0.17
2
U
ð qq Þ þ ððTðTw−TbÞ Þ w −T b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Uh 2 Uk 2 ¼ ðhÞ þðkÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼
U
2
U
2
U
Δp ð Δp Þ þ ð ρρ Þ þ ð V Þ
V
Uncertainty values 0.154–0.29
2
0.40–0.41 0.90–0.91 0.15–0.55
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250 Water o Tb= 30 C
500 Dittus-Boelter [37] Plain flat tube
Plain flat tube CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
400
Nusselt number, Nu
Nusselt Number, Nu
200
150
100
50
300
200
100
0 0
0
5000 10000 15000 20000 25000 30000 35000 40000
0
Reynolds number, Re
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 3. Confirmatory test of empty tube of Nusselt number.
the CTT on the heat transfer rate was stronger at a higher Reynolds number. Over the range considered, the heat transfer rates in the tubes fitted with CTT were, respectively, 22.5% and 61% higher than those in the tubes equipped with the CoTT and the empty tube. Fig. 6 presents the friction factor in the corresponding tubes. Basically, the friction factor decreases with increasing Reynolds number. At the same Reynolds number, the friction factors in the tube fitted with the CTT were higher than those in the tubes fitted with the CoTT and the plain flat tube. It is believed that in the case of the co-swirl twisted tapes, the unidirectional swirl motion is induced in the main flow while the counter-swirl twisted tapes produce swirls in the reverse direction which increases the whirl velocities of the fluid inside the tube. The secondary flow is created by the counter-swirl motion which leads to higher turbulence intensity and better fluid mixing. 5.3. Effect of twist ratio The effect of twist ratios (H/D = 5, 10 and 15) on the heat transfer rate in the tubes fitted with CTT and CoTT is demonstrated in Fig. 5. From the experimental results, it can be observed that the heat transfer enhancement increase as twist ratio decreases. Generally, the smaller twist ratio generates stronger swirl intensity, leading to more efficient interruption of boundary layers along the flow path. Hence, heat can
Fig. 5. Variations of Nusselt number with Reynolds number for various twisted tape inserts.
be transferred efficiently over the thin boundary layer. Moreover, the residence time of the flow increases with increasing swirl flow intensity [12]. This extends the duration of heat transfer between the working fluid and heat source (tube wall). For all the conditions studied, the CTT and CoTT with the smallest twist ratio (H/D = 5) provided the heat transfer rates around 39 to 43% and 47.5 to 61% higher than those in the tubes with larger twist ratios and the empty tube, respectively. As seen in Fig. 6, the friction factor tends to increase with decreasing twist ratio. This is in the same trend found for the Nusselt number. This can be explained by the fact that the use of a twisted tape with a smaller twist ratio leads to higher viscous loss near the tube wall regions caused by a stronger swirl flow. Over the range studied, the friction factors for the tube fitted with CTT with H/D = 5, 10, and 15, are, respectively 16 and 53%, times of those in tubes fitted with the CoTT and in the plain flat tube. Nusselt number and friction factor enhancement ratios with respect to the Reynolds number for different types of twisted tape inserts are presented in Figs. 7 and 8, respectively. Fig. 7 shows that the Nusselt number enhancement ratio decreased with an increase of Reynolds number in all types and the twisted ratio of twisted tapes, which shows that the system should be operated in the range of lower Reynolds number to obtain better heat transfer rates. The Nusselt number 0.200
0.06 Blasius [38] Plain flat tube
Plain flat tube CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
0.175
0.05
0.150 Friction factor, f
0.04 Friction factor, f
299
0.03
0.02
0.125 0.100 0.075 0.050
0.01
0.025 0.000
0.00 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re Fig. 4. Confirmatory test of empty tube of friction factor.
0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 6. Variations of friction factor with Reynolds number for various twisted tape inserts.
300
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4.0
600 CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
Plain flat tube CTT CoTT
500 Nusselt number, Nu (Predicted)
Nusselt number ratio, Nus/Nue
3.5
+15%
-15%
400
300
200
100
0
5000 10000 15000 20000 25000 30000 35000 40000
0
100
Reynolds number, Re Fig. 7. Variation of Nusselt number enhancement ratio with respect to Reynolds number for different types of twisted tape inserts.
200 300 400 500 Nusselt number, Nu (Experimental)
600
Fig. 9. Validation of empirical correlations for Nusselt number.
For the tube fitted with the CoTT: enhancement ratios lie between 1.24 to 2.52 and 1.1 to 2.27 for flat tubes having twin co-swirl twisted tapes twin counter twisted tapes (CTT) and twin co-twisted tapes (CoTT), respectively, while the twist ratio is kept as 5. The friction factor enhancement ratios are found to be in the range of 1.38 to 4.85 and 1.25 to 4.07 for the aforementioned geometries of inserts. In the present investigation, the tests were made in a uniform heat flux tube with water as working fluid and the correlation comparisons between the present data with those calculated by the present correlations for Nusselt number and friction factor are portrayed in Figs. 9 and 10. Evidently, the majority of the heat transfer data falls within ±15% for the present correlations of Eqs. (12) and (14). Eqs. (13) and (15) provided the correlative results of the friction factor with maximum discrepancies of ± 10% with the experimental measurements. For the tube fitted with the CTT:
Nu ¼ 0:209Re0:72 Pr0:4 ðH=DÞ−0:45
ð14Þ
f ¼ 66:7Re−0:6 ðH=DÞ−0:54 :
ð15Þ
6. Thermal enhancement index
Nu ¼ 0:268Re0:7 Pr0:4 ðH=DÞ−0:4
ð12Þ
In order to evaluate the thermal enhancement index of the flat tubes fitted with the CTT and the CoTT, the equal pumping power comparison was performed [39–41]. Performance evaluation was determined to assess the benefits of using the CTT and the CoTT in terms of enhancement index at the same pumping power. The thermal performance factors of the flat tubes fitted with twin twisted tapes were assessed under constant pumping conditions. The constant pumping power conditions can be described as:
f ¼ 24:96Re−0:59 ðH=DÞ0:1 :
ð13Þ
• • V ΔP ¼ V ΔP : e
ð16Þ
s
6
Friction factor ratio, fs /fe
5
4
3
2
1
0.200 0.175
Friction factor, f (Predicted)
CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
Plain flat tube CTT CoTT
+10%
0.150
-10% 0.125 0.100 0.075 0.050 0.025
0 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
0.000
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 Friction factor, f (Experimental)
Fig. 8. Variation of friction factor enhancement ratio with respect to Reynolds number for different types of twisted tape inserts.
Fig. 10. Validation of empirical correlations for friction factor.
M.K. Abdolbaqi et al. / International Communications in Heat and Mass Transfer 75 (2016) 295–302
Under these criteria, the correlation between friction and Reynolds number can be expressed as:
f Re3
e
¼ f Re3
ð17Þ
s
1=3
Res ¼ Ree ð f e =f s Þ
:
The thermal performance factor, η can be assessed based on the power consumption per unit mass of fluid. It is also defined as the ratio between the heat transfer coefficient for the tube with heat transfer promoter (hs) and the value for the plain tube (he) at similar pumping power. η¼
−1=3 hs Nus Nus fs ¼ ¼ he pp Nue pp Nue fe
ð18Þ
Where the Nusselt number for tube with twisted tape inserts are represented as (Nus) and plain flat tube as (Nue) while the friction factor for tubes with twisted tape inserts are represented as (fs) and plain flat tubes as (fe). Applying Eqs. (11), (13), (15) and (17), the Reynolds number for the tube fitted with twisted tape (Res) can be expressed as the function of the Reynolds number of the empty tube (Ree): For the tube fitted with the CTT: Res ¼ 0:118Ree 1:14 ðH=DÞ0:2 :
ð19Þ
For the tube fitted with the CoTT: Res ¼ 0:185Ree 1:106 ðH=DÞ0:18 :
ð20Þ
The thermal enhancement index for the tube fitted with the CTT or CoTT can be obtained by the combination of Eqs. (10), (12), (14), (18), (19) and (20), as follows: For the tube fitted with the CTT: η ¼ 1:5Res 0:035 ðH=DÞ−0:223 :
ð21Þ
For the tube fitted with the CoTT: η ¼ 1:876Res 0:014 ðH=DÞ−0:266 :
ð22Þ
The effect of various twin twisted tapes at different twist ratios (H/D) on the thermal enhancement index in Reynolds number in the
301
range of 7200 and 32,400 has been clarified in Fig. 11. The comparative data revealed that the thermal enhancement index increases with decreasing Reynolds number. In addition, the thermal enhancement indexes were varied between 1.17 and 2.52 for the CTT and 1.07 and 2.26 for the CoTT, depending on the Reynolds number and the twist ratio (H/D). For the CTT, the mean enhancement index for the smallest twist ratio (H/D = 5) was, respectively, 7.8%, and 20.2% higher than those for H/D = 10 and 15. The above data suggest that the highest enhancement index can be obtained at the lowest twist ratio (H/D), and relatively low Reynolds number. It is noteworthy that the enhancement indices in the tube fitted with the CTT were around 22.5% higher than those in the tube fitted with the CoTT. In addition the majority of the thermal enhancement index data fell within ±10% for the present correlations of Eqs. (21) and (22) with the experimental measurements as illustrated in Fig. 12.
7. Conclusions The present paper shows the feasibility of convection heat transfer enhancement by inserting the CTT (counter-swirl flow generators) and the CoTT (co-swirl flow generators) for turbulent flow with a uniform heat flux. Heat transfer coefficient and friction factor were determined experimentally for the tubes fitted with the CTT and CoTT using water as the working fluid with Reynolds number ranging from 7200 and 32,400. Based on the obtained results, it was found that the heat transfer, friction factor, and thermal enhancement index increased as the twist ratio (H/D) decreases. In addition, the Nusselt number increases with increasing Reynolds number while the opposite trends were found for the friction factor and the thermal enhancement index. The CTT (counter-swirl tapes) can enhance heat transfer more efficiently than the CoTT (co-swirl tapes). The quantitative results showed that, heat transfer rates for the CTT were around 22.5% higher than those for the CoTT and 61% higher than those for the empty tubes. The maximum thermal enhancement index (η) obtained at the constant pumping power using the CTT with H/D = 5, was 2.52, while that obtained using the CoTT with the same range of H/D was 2.26. The achieved results indicated that the modified swirl flow (counter-swirl flow) generated by the CTT is a promising approach for heat transfer enhancement. The empirical correlations developed in the present work, provided the correlative results of the Nusselt number and friction factor. The maximum discrepancies between the correlative results and experimental results for Nusselt number and friction factor and thermal enhancement index were found to be ±15%, ±10% and ±10%, respectively.
2.0
Thermal enhancement index,
1.6
(Predicted)
1.8 Thermal enhancement index,
2.5
CTT-5 CTT-10 CTT-15 CoTT-5 CoTT-10 CoTT-15
1.4
1.2
1.0
0.8 0
5000 10000 15000 20000 25000 30000 35000 40000 Reynolds number, Re
Fig. 11. Variations of thermal enhancement index with Reynolds number for various twisted tape inserts.
CTT CoTT
+10%
2.0 -10% 1.5
1.0
0.5
0.0 0.0
0.5 1.0 1.5 2.0 Thermal enhancement index, (Experimental)
Fig. 12. Validation of empirical correlations for thermal enhancement index.
2.5
302
M.K. Abdolbaqi et al. / International Communications in Heat and Mass Transfer 75 (2016) 295–302
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