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Heat transfer and pressure drop correlations for the wavy fin and flat tube heat exchangers
Applied Thermal Engineering 27 (2007) 2066–2073 www.elsevier.com/locate/apthermeng
Heat transfer and pressure drop correlations for the wavy fin and flat tube heat exchangers Dong Junqi a
a,*
, Chen Jiangping a, Chen Zhijiu a, Zhou Yimin b, Zhang Wenfeng
b
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200030, China b Zhejing Yinlun Machine Co. Ltd., Zhejiang 317200, China Received 23 August 2006; accepted 29 November 2006 Available online 12 January 2007
Abstract A total of 11 cross-flow heat exchangers having wavy fin and flat tube were studied experimentally. A series of tests were conducted for air side Reynolds number in the range of 800–6500 with different fin pitches, fin lengths and fin heights, at a constant tube-side water flow rate of 2.5 m3/h. The air side thermal performance data were analyzed using the effectiveness-NTU method. The characteristics of heat transfer and pressure drop for different geometry parameters were reported in terms of Colburn j-factor and Fanning friction factor f, as a function of Re. The effects of fin pitch, fin height and fin length on the performance of heat transfer and pressure drop were examined. The general correlations for j and f factors were derived by multiple linear regression analysis and F test of significance. The correlations for j and f factors can predict 95% of the experimental data within ±10%. 2006 Elsevier Ltd. All rights reserved. Keywords: Flat tube heat exchangers; Performance testing; Wavy fin; Correlation
1. Introduction Extended or finned surfaces are widely used in compact heat exchanger to enhance the heat transfer and reduce the size. Common among these are automobile radiators, charge air coolers, automobile air-conditioning evaporators and condensers to meet the demand for saving energy and resources. In these applications, the heat transfer is normally limited by the thermal resistance on the air side of the heat exchangers. Therefore, various augmented surfaces have been developed to improve air side heat transfer performance. Typical fin geometries are plain fins, wavy fins, offset strip fins, perforated fins and multi-louvered fins, which, besides increasing the surface area density of the exchanger, also improve the convection heat transfer coefficients. Of these, wavy fins are particularly attractive for their simplicity of manufacture and potentials for
*
Corresponding author. Tel.: +86 21 62933242; fax: +86 21 62932601. E-mail address: [email protected] (D. Junqi).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.11.012
enhanced thermal-hydraulic performance. The air side thermal hydraulic performance of wavy fin and round tube heat exchangers have been studied by many researchers [1–4]. However, the study of wavy fin and flat tube heat exchanger is very limited [4]. The air-side thermal hydraulic performance of wavy fin and flat tube heat exchangers depends on the complex geometry of wavy fin such as the corrugation aspect ratio (2A/L), fin spacing ratio (Fp/2A), flow length ratio (Ld/L) and flow cross-section aspect ratio (Fp/Fh) [5]. The surface corrugations of the wavy fins consist of triangular, sinusoidal, and trapezoidal patterns, and the flow behavior has been studied both experimentally and computationally. Asako and Faghri [6] numerically investigated two-dimensional steady laminar flow with Re = 100– 1000, and heat transfer in plate channels with triangularprofiled wall corrugations that are maintained at a uniform temperature. Subsequently, triangular corrugations with round corners were considered [7]. Zhang et al. [5] numerical investigated the effects of wall-corrugation aspect ratios and fin space ratios on the vortex structure and
D. Junqi et al. / Applied Thermal Engineering 27 (2007) 2066–2073
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Nomenclature A 2A Ac Ao Af C C* Cp De d Fh Fp f h hw j k kc ke Ld L l l0 m0 m_ NTU Nu N Pr Dp
area (m2) twice of wavy fin amplitude (mm) minimum free-low area for air side (m2) total air side heat transfer surface area (m2) fin surface area (m2) heat capacity rate (W/k) capacity ratio specific heat at constant pressure (J/kg K) hydraulic diameter of fin entrance (m) hydraulic diameter of tube hole (mm) fin height (mm) fin pitch (mm) fanning friction factor fin heat transfer coefficient of air side (W/m2 K) heat transfer coefficient of water side (W/m2 K) Colburn j factor thermal conductivity (W/(m K)) abrupt contraction pressure-loss coefficient abrupt expansion pressure-loss coefficient wavy fin length (mm) wavy fin wavelength (mm) length of flat tube (mm) Eq. (9), l 0 = Fp h/2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eq. (9), m0 ¼ 2h=k f d mass flow rate (kg/s) number of transfer units Nusselt number number of the experimental data Prandtl number air side pressure drop in inlet and outlet of heat exchanger (Pa)
enhanced heat transfer for low rate with Re = 100–1000. Likewise, Metwally and Manglik [8] have investigated two-dimensional periodically developed laminar flow and heat transfer in sinusoidal wavy channel with different corrugation aspect ratios. More complex three-dimensional, cross-corrugated have also been computationally modeled in a few recent studies [9–11]. Goldstein and Sparrow [12] first studied the corrugated channels with triangular waves used the naphthalene sublimation method. Rush et al. [13] conducted flow visualization test for sinusoidal wavy passages to investigate the local heat transfer and flow behavior of the fluid in the laminar and transitional flow region. Using the visualization methods, they reported that the flow field is characterized as steady and unsteady and the location of the onset of mixing is found to depend on the Reynolds number and channel geometry. In all, it has generally been observed that wall corrugations induce a steady vortex or swirl flow in the trough region of the wavy wall in the low Reynolds number. This results in flow mixing and boundary layer disruption and thinning, thereby significantly enhancing the heat transfer.
Q Qa Qw Re Rew T1 T2 u u1 v d dwall gf ga e s U
average heat transfer rate (W) air side heat transfer rate (W) water side heat transfer rate (W) air side Reynolds number based on fin entrance diameter (u1De/v) water side Reynolds number based on flat tube hole hydraulic diameter inlet temperature (C) outlet temperature (C) air frontal air velocity (m/s) maximum air velocity in the fin (m/s) viscosity (m2/s) fin thickness tube wall thickness fin efficiency air side heat transfer surface effectiveness effectiveness contraction ratio of the fin array j or f factor
Subscripts a air side cor correlation exp experimental f fin Min minimum value Max maximum value w water side wall tube wall
However, there are few researchers carrying out full scale experiments studying the thermal hydraulic performance of wavy fin and flat tube heat exchangers. The earliest experimental data are given in the classical Kays and London [14] sourcebook, though it includes only three types wavy fin. The tests covered a range of Reynolds number from 400 to 8000. And after that, little experimental data of wind tunnel can be found in the public literatures [11]. As for the general correlations for heat transfer and pressure drop of the wavy fins, Jacobi et al. in 2001 [4] reported that it is can not be obtained in the open literatures. General correlations for heat transfer and pressure drop of the wavy fin are not available in the literatures as quoted by Jacobi et al. [4]. Hence, the generation of the correlations for heat transfer and pressure drop for wavy fins is the main objective of the present work. The present study investigates experimentally the thermal hydraulic performance for wavy fin and flat tube heat exchangers with 11 samples. The wavy fins are triangular profile with round corners for different fin pitches, fin heights and fin lengths. The heat transfer coefficients and
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averaged. The air pressure drop across the heat exchangers and the nozzles were, respectively, measured by precision differential pressure transducers, whose accuracies were 0.4% and 0.25%. The model of the two differential pressure transducers are WIDERPLUS-DP and C268, and both of them are mad in China. The air flow measuring station was a multiple nozzle code tester based on the ISO 5167 standard. The hot water flow loop consisted of a storage tank, a 100 kW electric heater, a centrifugal pump, a control unit and a flow meter. The purpose of this loop was to transfer heat to the air flowing through the heat exchangers. The temperature of the hot water in the water tank was measured by pre-calibrated RTDs (Pt-100 X) and was controlled by the temperature controller. Its accuracy was within 0.1 C. After heating the water to the required temperature, the hot water was pumped out of the storage tank, delivered to the heat exchanger and then returned to the storage tank. The water temperatures at the inlet and outlet of the heat exchanger were measured by two per-calibrated RTDs (Pt-100 X) which have an accuracy of 0.1 C.
pressure drop for the heat exchangers with different geometrical configurations are reported in terms of Colburn j factor and Fanning friction factor f, as a function of Reynolds numbers based on the fin entrance hydraulic diameter. The general correlations for j and f factors are developed. 2. Experimental 2.1. Experimental set-up Fig. 1 shows the schematic diagram of the wind tunnel used in the study. Air and hot water were used as working fluids. The main components of the systems were the heat exchangers, water flow loop, air supply, instrumentations and data acquisition systems. The wind tunnel system was designed to suck room air over the finned side of the heat exchangers by a 15 kW centrifugal fan. The speed of the fan could be adjusted by a frequency inverter. The tunnel was a rectangular duct 270 · 220 mm in cross-section. To minimize heat loss to the surroundings, the tunnel surface was insulated with a 10 mm thick glass wool layer. Being supported by stands of perforated steel plate, the tunnel system was kept 75 cm above the floor level of the laboratory. The inlet and exit temperature across the air side of the heat exchangers were measured by two T-type thermocouple meshes. The inlet measuring mesh consists of eight thermocouples while the exit mesh contains sixteen thermocouples. These thermocouples were pre-calibrated which have an accuracy of 0.1 C. The measuring points were located at positions as described in the ASHRAE standard. These data signals were individually recorded and then
18
2.2. Test heat exchangers Figs. 2 and 3 indicate geometrical configuration and terminology of wavy fin and flat tube heat exchangers. The number of the tested wavy fin and flat tube heat exchanger samples is 11. Table 1 shows the specifications of the wavy fins tested in this study. All tested samples core sizes are about 250 · 200 mm due to the different fin height. All tested fins were checked before brazing and overall heat exchangers quality after brazing was excellent.
17
12
14 1
2
3
4
5
6
7
10
8
8 11
15
9
13 Data acquisition system
1, air inlet 2, honey cone straightener 3, T/C inlet temperature measuring station 4, pressure tap (inlet) 5, test unit 6, pressure tap (outlet) 7, T/C outlet temperature measuring station 8, setting means 9, static pressure tap
10, 11, 12, 13, 14, 15, 16, 17, 18,
multiple nozzle plate variable exhaust fan system air outlet difference pressure tap nozzle inlet temperature tap water outlet temperature tap water data acquisition system hot water tank water pump
Fig. 1. Schematic diagram of the wind tunnel test apparatus.
D. Junqi et al. / Applied Thermal Engineering 27 (2007) 2066–2073
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water flow rate. The choice of the water flow rate is based on the principle that the water side thermal resistance is less than 20% and the temperature drop in the tube side is higher than 2.0 C [15]. The water flow rate were maintained at 2.5 m3/h. All the experimental data was obtained on basis of the heat balance which is less than 3%. 2.4. Data reduction Heat transfer rate required for the calculation of air-side heat transfer coefficient can be expressed as
Fig. 2. The wavy fin photo.
Q ¼ ðQw þ Qa Þ=2; Qw ¼ m_ w C pw ðT w1 T w2 Þ;
2.3. Test condition and method The tested wavy fin and flat tube heat exchanger was installed in the test system. In this work, the exchanger height was less than the tunnel dimensions, and the bypass flows were eliminated by a thin layer of foam plastic sandwiched between the heat exchanger core and tunnel edge. Upon completion of the hot water side links, the water tube was completely insulated with a 15 mm thick layer of glass wool. The test was performed in a range of Reynolds number, which is based on hydraulic diameter of fin entrance and maximum air velocity [14], of 800–6500. The inlet water temperature was maintained at 90 C with a constant
Qa ¼ m_ a C pa ðT a2 T a1 Þ:
ð1Þ ð2Þ
Effectiveness-NTU method can be used for obtaining airside heat transfer coefficient. The equation for both fluids unmixed is [15], NTU0:22 ½expðC NTU0:78 Þ 1 ; C C min m_ a C pa e ¼ Q=Qmax ; C ¼ ¼ ; C max m_ w C pw e ¼ 1 exp
ð3Þ ð4Þ
We can obtain overall heat transfer coefficient (UA) for the heat exchangers as UA ¼ ðm_ a C pa ÞNTU:
ð5Þ
Fp
Flat Tube
Fh
Fin A
Fin
Ld
A
Flat Tube
A-A
Fig. 3. Wavy fin and flat tube exchangers.
Table 1 Specification of wavy fin parameters (mm) No.
Fin pitch (Fp)
Fin height (Fh)
Fin length (Ld)
Fin thickness (d)
Wavy amplitude (2A)
Wavelength (L)
1 2 3 4 5 6 7 8 9 10 11
2.0 2.25 2.5 2.0 2.25 2.5 2.0 2.25 2.5 2.0 2.0
8.0 8.0 8.0 8.0 8.0 8.0 7.0 7.0 7.0 8.0 10.0
65.0 65.0 65.0 53.0 53.0 53.0 43.0 43.0 43.0 43.0 43.0
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8
D. Junqi et al. / Applied Thermal Engineering 27 (2007) 2066–2073
The air-side heat transfer coefficient can be obtained from the following equation, assuming zero water side fouling resistance. Due to the contact resistance of the flat tube and fin is a resource of uncertainty, the effect of contact resistance is included in the derived air side resistance ð6Þ
Note that the second term of the right-hand-side of the Eq. (6) indicates the water side thermal resistance and the third term means the tube wall thermal resistance. For water-side heat transfer coefficients, the Gnielinski’s correlation [16,17] for fully developed turbulent flow for the pipe flow is used. That is " 2=3 # d 0:87 0:4 Nuw ¼ 0:012ðRew 280ÞPr 1 þ : ð7Þ l The surface effectiveness and fin efficiency for the dry surface of wavy fins are [17]:
gf ¼
Af ð1 gf Þ; Ao
tanhðm0 l0 Þ ; m 0 l0
sffiffiffiffiffiffiffi 2h 0 m ¼ ; kf d
ð8Þ l ¼ F h =2:
ð9Þ
From the Eqs. (6)–(9), the heat transfer coefficient h can be obtained using the iterative calculation, since the fin efficiency is the function of heat transfer coefficient h. The Colburn j factor is defined as h Pr2=3 ð10Þ j¼ qu1 C p
f
0.12
Fp=2.00mm Ld=65mm Fp=2.25mm Ld=65mm Fp=2.50mm Ld=65mm
0.012
0.08
0.01
The core friction of the heat exchangers was reduced to obtain the Fanning friction factor f. In present study, the pressure drop equation proposed by Kays and London [14], including the entrance and exit pressure losses, was used to evaluate the friction factor. The air is treaded as incompressible fluid, and the density of air is treated as constant according to average air temperature. The simple equation is Ac 2Dp f ¼ kc ke ; ð11Þ qu21 Ao ui D e ð12Þ Re ¼ v
0.008 0.04 0.006
0.004 600
800 1000
2000
4000
6000
8000
Re
Fig. 4. Effect of fin pitch on the j and f factor.
0.014
0.12
Fh=7.0mm Ld=43mm Fh=8.0mm Ld=43mm Fh=10.0mmLd=43mm
0.012
0.08 0.01
j factor
According to the geometry parameters of heat exchanger and the graph given by Kays and London [14], the kc and ke are 0.4 and 0.2. Accounting for all instrument errors, property uncertainties, and geometry tolerances, the uncertainties for the j and f factors are ±9.2% and ±8.1%, respectively [18].
j
0.014
0.008 0.04 0.006
3. Results and discussion 3.1. j and f factors versus Reynolds number 600
The air side heat transfer and friction characteristics of the tested wavy fin and flat tube heat exchangers are pre-
f factor
ga ¼ 1
f factor
1 1 1 dwall ¼ : hga Ao UA hw Aw k wall Awall
sented in terms of the Colburn factor j factor and friction factor f, which are plotted versus the Reynolds number based on the fin entrance hydraulic diameter. Figs. 4–6 illustrates the effects of fin pitch, fin height and fin length on the performance of heat exchangers having different geometry parameters. From these figures, it is observed that the geometry parameters of wavy fins have significant effect on the j factor as a function of Re. Fig. 4 shows that the j and f factors increase with increasing fin pitch at the same Re, in which the wavy have the same fin length of 65.0 mm and fin height of 8.0 mm. The cause of this result from the phenomena is that, when the fin pitch increases, the air flow inside the corrugated flow channel can be mixed better at the same Reynolds number. And this better mixing leads to an increase of the heat transfer coefficient. The explanation can be confirmed by the results of Manglik and Zhang [11] with 3D numerical simulation method for wavy fins. At the same time, the phenomena also result in the pressure drop increase. The behaviors of hydraulic thermal performance with fin pitch are different, compared with the conventional finned tube heat exchangers. Wongwises [3] reported that
j factor
2070
800
2000
4000
6000
Re
Fig. 5. Effect of fin height on the j and f factor.
D. Junqi et al. / Applied Thermal Engineering 27 (2007) 2066–2073
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0.010
j
f
0.012
0.12
Ld=65mm Fh=8.0mm Ld=53mm Fh=8.0mm
0.009
+10%
0.08 0.008
f factor
-10% j cor
j factor
0.009
0.04 0.006
0.007
0.006
0.005
600
800
2000
4000
6000
Re
0.004 0.004
0.005
0.006
0.007
0.008
0.009
0.010
j exp
Fig. 6. Effect of fin length on the j and f factor. 0.08
3.2. Empirical correlations Based on the previous discussion, it is obvious from the test data that no single curve can be expected to describe the complex behaviors about the heat transfer and friction characteristics of the wavy fin. For easier engineer calculation, the empirical correlations for j and f factors were performed by multiple linear regression and F significance test [20] on basis of 154 experimental data with differential wavy fin geometries. The corresponding correlations are given as follows:
+10% 0.07
0.06
-10%
f cor
the fin pitch has no significant effect on the heat transfer and pressure drop characteristics of fined tube heat exchangers. Fig. 5 presents the effect of fin height on j and f factors of wavy fin with fin pitch of 2.0 mm and fin length of 43.0 mm as a function of Re. From Fig. 7, it is interesting to observe that the j factor increase with increasing fin height, while the effects of fin height on the f factor is little. The result is different to the theory that the fin height has little effect on the characteristics of heat transfer which was adopted by many numerical researchers whose numerical model is 2D [5–8]. And the result is similar to that of Manglik and Zhang [11] 3D numerical simulation, who reported that, with increasing flow cross-section aspect ratio, the spatial coverage and strength of the counterrotating vortices are seen to increase, resulting in convective mixing and enhanced heat transfer. From the Fig. 6 can be observed the effects of fin length on the j and f factors against the Re. In the comparison, the wavy fins have the same fin height of 8.0 mm and fin pitch of 2.0 mm. The j and f factors decrease with increasing fin length under the same Re. The reason may be that the effect of fluid entrance is relatively obvious for wavy fin. This result is in accord with the conclusions of Yasar [19], who utilized the numerical simulation and reported that the fluid flow and heat transfer become periodically fully development after 3–5 cycles.
0.05
0.04
0.03 0.03
0.04
0.05
0.06
0.07
0.08
fexp
Fig. 7. Comparison of experimental data and correlation for j and f factor.
Correlation of the heat transfer performance of the wavy fins: 0:1284 0:153 0:326 Fp Ld 0:2309 F p j ¼ 0:0836Re : ð13Þ Fh 2A L Correlation of the frictional performance of the wavy fins 0:3703 0:25 0:1152 Fp Ld 0:309 F p f ¼ 1:16Re : ð14Þ Fh 2A L Fig. 7 shows the comparison of j and f factors of the experimental results with those of the proposed correlations. For the heat transfer and friction f factor correlations, Eqs. (13) and (14) can predict 95% of the experimental data within ±10%. The mean deviations of the correlations Eqs. (13) and (14) are 4.4% and 5.1%, and the average deviations are 0.4% and 0.3%, according to the Eqs. (15) and (16) [21]. ! 1 X /cor /exp Average deviation ¼ 100%; ð15Þ N /exp ! 1 X j/cor /exp j 100%: ð16Þ Mean deviation ¼ N /exp
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0.018
Kays and London 11.44-3/8W Present Correlation 11.44-3/8W Kays and London 11.5-3/8W Present Correlation 11.5-3/8W
j factor
0.015
0.012
0.009
0.006
1000
2000
3000
4000
5000
6000
7000
8000
Re
0.12
Kays and London 11.44-3/8W Present Correlation 11.44-3/8W Kays and London 11.5-3/8W Present Correlation 11.5-3/8W
heat exchangers. The effects of fin pitch, fin height and fin length on the thermal hydraulic performance are examined. On the basis of previous discussions, the following conclusions are made: 1. The j and f factors decrease with increasing Re, in the tested range of Re, Re = 800–6500. And the j and f factors increases with fin space increasing at the same Re; the j factor increases with fin height, while the fin height has little effect on the f factor as a function of Re. 2. Correlations of heat transfer and pressure drop for the wavy fins are developed. The proposed correlations give fairly good predictive ability against the present test data. The mean deviations of the correlations for j and f factors are 4.4% and 5.1%, and the average deviations are 0.4% and 0.3%, respectively. Acknowledgements
0.09
f factor
The authors acknowledge the financial support of Zhejiang Yinlun Machine Co. Ltd. We are grateful to Dr. Niu and Xianhui Zhang for providing the valuable comments. It would not have been possible to carry out this study without their help.
0.06
References
0.03 1000
2000
3000
4000
5000
6000
7000
8000
Re
Fig. 8. Comparison of present correlation and other experiment data.
Fig. 8 presents comparison of present correlation and other experiment data for wavy fin. The Kays and London experiment data is only database for the wavy fin from the public literatures, although it only includes three different wavy fin geometries. The present correlations of j and f factor compared with the experiment data of Kays and London based on two wavy fins, which are named 11.4–3/ 8 W and 11.5–3/8 W [14]. As for the j factors and f factors, compared with experiment data, the average deviation are 22.6% and 11.5%. This indicates that the present correlations predict the values of j and f factors are smaller than those of Kays and London under the same Re. We think the main reasons for the difference are that the profiles of wavy fins are not identical to those of Kays and London. The wavy fins’ profiles in this study are the triangular profiles with round corners, however the Kays and London’s wavy fin profiles are sinusoidal. Another, the fact should not be neglected that the experimental heat exchangers cores manufacture irregularities are not identical due to different manufacture, which also result in the difference. 4. Conclusions The present experimental study reports the air side thermal hydraulic performance of the wavy fin and flat tube
[1] C.C. Wang, W.L. Fu, C.T. Chang, Heat transfer and friction characteristics of typical wavy fin and tube heat exchangers, Exp. Thermal Fluid Sci. 14 (2) (1997) 174–186. [2] C.C. Wang, Y.T. Lin, C.J. Lee, Y.J. Chang, Investigation of wavy fin and tube heat exchangers: a contribution to databank, Exp. Heat Transfer 12 (1999) 73–89. [3] S. Wongwises, Y. Chokeman, Effect of fin pitch and number of tube rows on the air side performance of herringbone wavy fin and tube heat exchangers, Energy Convers. Manage. 46 (2005) 2216–2231. [4] A.M. Jacobi, Y. Park, D. Tafti, X. Zhang, An assessment of the state of the art, and potential design improvement, for flat-tube heat exchangers in air conditioning and refrigeration applications-Phase I, ARTI-21 CR/20020-01, Available to US Department of Energy. [5] J. Zhang, J. Kundu, R.M. Manglik, Effect of fin waviness and spacing on the lateral vortex structure and laminar heat transfer in wavyplate-fin cores, Int. J. Heat Mass Transfer 47 (2004) 1719–1730. [6] Y. Asako, M. Faghri, Finite-volume solutions for laminar flow and heat transfer in a corrugated duct, J. Heat Transfer 109 (3) (1987) 627–634. [7] Y. Asako, H. Nakamura, Heat transfer and pressure drop characteristic in a corrugated duct with rounded corners, Int. J. Heat Mass Transfer 31 (1988) 1237–1245. [8] H.M. Metwally, R.M. Manglik, Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels, Int. J. Heat Mass Transfer 47 (2004) 2283– 2292. [9] D.R. Sawyers, M. Sen, H.C. Chang, Heat transfer enhancement in three-dimensional corrugated channel flow, Int. J. Heat Mass Transfer 41 (1998) 3559–3573. [10] M. Ciafalo, J. Stasiek, M.W. Collins, Investigation of flow and heat transfer in corrugated passages. II. Numerical simulation, Int. J. Heat Mass Transfer 39 (1996) 165–192. [11] R.L. Manglik, J. Zhang, Low Reynolds number forced convection in three-dimensional wavy-plate-fin compact channels: fin density effects, Int. J. Heat Mass Transfer 48 (2005) 1439–1449.
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Heat transfer and pressure drop correlations for the wavy fin and flat tube heat exchangers Dong Junqi a
a,*
, Chen Jiangping a, Chen Zhijiu a, Zhou Yimin b, Zhang Wenfeng
b
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200030, China b Zhejing Yinlun Machine Co. Ltd., Zhejiang 317200, China Received 23 August 2006; accepted 29 November 2006 Available online 12 January 2007
Abstract A total of 11 cross-flow heat exchangers having wavy fin and flat tube were studied experimentally. A series of tests were conducted for air side Reynolds number in the range of 800–6500 with different fin pitches, fin lengths and fin heights, at a constant tube-side water flow rate of 2.5 m3/h. The air side thermal performance data were analyzed using the effectiveness-NTU method. The characteristics of heat transfer and pressure drop for different geometry parameters were reported in terms of Colburn j-factor and Fanning friction factor f, as a function of Re. The effects of fin pitch, fin height and fin length on the performance of heat transfer and pressure drop were examined. The general correlations for j and f factors were derived by multiple linear regression analysis and F test of significance. The correlations for j and f factors can predict 95% of the experimental data within ±10%. 2006 Elsevier Ltd. All rights reserved. Keywords: Flat tube heat exchangers; Performance testing; Wavy fin; Correlation
1. Introduction Extended or finned surfaces are widely used in compact heat exchanger to enhance the heat transfer and reduce the size. Common among these are automobile radiators, charge air coolers, automobile air-conditioning evaporators and condensers to meet the demand for saving energy and resources. In these applications, the heat transfer is normally limited by the thermal resistance on the air side of the heat exchangers. Therefore, various augmented surfaces have been developed to improve air side heat transfer performance. Typical fin geometries are plain fins, wavy fins, offset strip fins, perforated fins and multi-louvered fins, which, besides increasing the surface area density of the exchanger, also improve the convection heat transfer coefficients. Of these, wavy fins are particularly attractive for their simplicity of manufacture and potentials for
*
Corresponding author. Tel.: +86 21 62933242; fax: +86 21 62932601. E-mail address: [email protected] (D. Junqi).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.11.012
enhanced thermal-hydraulic performance. The air side thermal hydraulic performance of wavy fin and round tube heat exchangers have been studied by many researchers [1–4]. However, the study of wavy fin and flat tube heat exchanger is very limited [4]. The air-side thermal hydraulic performance of wavy fin and flat tube heat exchangers depends on the complex geometry of wavy fin such as the corrugation aspect ratio (2A/L), fin spacing ratio (Fp/2A), flow length ratio (Ld/L) and flow cross-section aspect ratio (Fp/Fh) [5]. The surface corrugations of the wavy fins consist of triangular, sinusoidal, and trapezoidal patterns, and the flow behavior has been studied both experimentally and computationally. Asako and Faghri [6] numerically investigated two-dimensional steady laminar flow with Re = 100– 1000, and heat transfer in plate channels with triangularprofiled wall corrugations that are maintained at a uniform temperature. Subsequently, triangular corrugations with round corners were considered [7]. Zhang et al. [5] numerical investigated the effects of wall-corrugation aspect ratios and fin space ratios on the vortex structure and
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Nomenclature A 2A Ac Ao Af C C* Cp De d Fh Fp f h hw j k kc ke Ld L l l0 m0 m_ NTU Nu N Pr Dp
area (m2) twice of wavy fin amplitude (mm) minimum free-low area for air side (m2) total air side heat transfer surface area (m2) fin surface area (m2) heat capacity rate (W/k) capacity ratio specific heat at constant pressure (J/kg K) hydraulic diameter of fin entrance (m) hydraulic diameter of tube hole (mm) fin height (mm) fin pitch (mm) fanning friction factor fin heat transfer coefficient of air side (W/m2 K) heat transfer coefficient of water side (W/m2 K) Colburn j factor thermal conductivity (W/(m K)) abrupt contraction pressure-loss coefficient abrupt expansion pressure-loss coefficient wavy fin length (mm) wavy fin wavelength (mm) length of flat tube (mm) Eq. (9), l 0 = Fp h/2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eq. (9), m0 ¼ 2h=k f d mass flow rate (kg/s) number of transfer units Nusselt number number of the experimental data Prandtl number air side pressure drop in inlet and outlet of heat exchanger (Pa)
enhanced heat transfer for low rate with Re = 100–1000. Likewise, Metwally and Manglik [8] have investigated two-dimensional periodically developed laminar flow and heat transfer in sinusoidal wavy channel with different corrugation aspect ratios. More complex three-dimensional, cross-corrugated have also been computationally modeled in a few recent studies [9–11]. Goldstein and Sparrow [12] first studied the corrugated channels with triangular waves used the naphthalene sublimation method. Rush et al. [13] conducted flow visualization test for sinusoidal wavy passages to investigate the local heat transfer and flow behavior of the fluid in the laminar and transitional flow region. Using the visualization methods, they reported that the flow field is characterized as steady and unsteady and the location of the onset of mixing is found to depend on the Reynolds number and channel geometry. In all, it has generally been observed that wall corrugations induce a steady vortex or swirl flow in the trough region of the wavy wall in the low Reynolds number. This results in flow mixing and boundary layer disruption and thinning, thereby significantly enhancing the heat transfer.
Q Qa Qw Re Rew T1 T2 u u1 v d dwall gf ga e s U
average heat transfer rate (W) air side heat transfer rate (W) water side heat transfer rate (W) air side Reynolds number based on fin entrance diameter (u1De/v) water side Reynolds number based on flat tube hole hydraulic diameter inlet temperature (C) outlet temperature (C) air frontal air velocity (m/s) maximum air velocity in the fin (m/s) viscosity (m2/s) fin thickness tube wall thickness fin efficiency air side heat transfer surface effectiveness effectiveness contraction ratio of the fin array j or f factor
Subscripts a air side cor correlation exp experimental f fin Min minimum value Max maximum value w water side wall tube wall
However, there are few researchers carrying out full scale experiments studying the thermal hydraulic performance of wavy fin and flat tube heat exchangers. The earliest experimental data are given in the classical Kays and London [14] sourcebook, though it includes only three types wavy fin. The tests covered a range of Reynolds number from 400 to 8000. And after that, little experimental data of wind tunnel can be found in the public literatures [11]. As for the general correlations for heat transfer and pressure drop of the wavy fins, Jacobi et al. in 2001 [4] reported that it is can not be obtained in the open literatures. General correlations for heat transfer and pressure drop of the wavy fin are not available in the literatures as quoted by Jacobi et al. [4]. Hence, the generation of the correlations for heat transfer and pressure drop for wavy fins is the main objective of the present work. The present study investigates experimentally the thermal hydraulic performance for wavy fin and flat tube heat exchangers with 11 samples. The wavy fins are triangular profile with round corners for different fin pitches, fin heights and fin lengths. The heat transfer coefficients and
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averaged. The air pressure drop across the heat exchangers and the nozzles were, respectively, measured by precision differential pressure transducers, whose accuracies were 0.4% and 0.25%. The model of the two differential pressure transducers are WIDERPLUS-DP and C268, and both of them are mad in China. The air flow measuring station was a multiple nozzle code tester based on the ISO 5167 standard. The hot water flow loop consisted of a storage tank, a 100 kW electric heater, a centrifugal pump, a control unit and a flow meter. The purpose of this loop was to transfer heat to the air flowing through the heat exchangers. The temperature of the hot water in the water tank was measured by pre-calibrated RTDs (Pt-100 X) and was controlled by the temperature controller. Its accuracy was within 0.1 C. After heating the water to the required temperature, the hot water was pumped out of the storage tank, delivered to the heat exchanger and then returned to the storage tank. The water temperatures at the inlet and outlet of the heat exchanger were measured by two per-calibrated RTDs (Pt-100 X) which have an accuracy of 0.1 C.
pressure drop for the heat exchangers with different geometrical configurations are reported in terms of Colburn j factor and Fanning friction factor f, as a function of Reynolds numbers based on the fin entrance hydraulic diameter. The general correlations for j and f factors are developed. 2. Experimental 2.1. Experimental set-up Fig. 1 shows the schematic diagram of the wind tunnel used in the study. Air and hot water were used as working fluids. The main components of the systems were the heat exchangers, water flow loop, air supply, instrumentations and data acquisition systems. The wind tunnel system was designed to suck room air over the finned side of the heat exchangers by a 15 kW centrifugal fan. The speed of the fan could be adjusted by a frequency inverter. The tunnel was a rectangular duct 270 · 220 mm in cross-section. To minimize heat loss to the surroundings, the tunnel surface was insulated with a 10 mm thick glass wool layer. Being supported by stands of perforated steel plate, the tunnel system was kept 75 cm above the floor level of the laboratory. The inlet and exit temperature across the air side of the heat exchangers were measured by two T-type thermocouple meshes. The inlet measuring mesh consists of eight thermocouples while the exit mesh contains sixteen thermocouples. These thermocouples were pre-calibrated which have an accuracy of 0.1 C. The measuring points were located at positions as described in the ASHRAE standard. These data signals were individually recorded and then
18
2.2. Test heat exchangers Figs. 2 and 3 indicate geometrical configuration and terminology of wavy fin and flat tube heat exchangers. The number of the tested wavy fin and flat tube heat exchanger samples is 11. Table 1 shows the specifications of the wavy fins tested in this study. All tested samples core sizes are about 250 · 200 mm due to the different fin height. All tested fins were checked before brazing and overall heat exchangers quality after brazing was excellent.
17
12
14 1
2
3
4
5
6
7
10
8
8 11
15
9
13 Data acquisition system
1, air inlet 2, honey cone straightener 3, T/C inlet temperature measuring station 4, pressure tap (inlet) 5, test unit 6, pressure tap (outlet) 7, T/C outlet temperature measuring station 8, setting means 9, static pressure tap
10, 11, 12, 13, 14, 15, 16, 17, 18,
multiple nozzle plate variable exhaust fan system air outlet difference pressure tap nozzle inlet temperature tap water outlet temperature tap water data acquisition system hot water tank water pump
Fig. 1. Schematic diagram of the wind tunnel test apparatus.
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water flow rate. The choice of the water flow rate is based on the principle that the water side thermal resistance is less than 20% and the temperature drop in the tube side is higher than 2.0 C [15]. The water flow rate were maintained at 2.5 m3/h. All the experimental data was obtained on basis of the heat balance which is less than 3%. 2.4. Data reduction Heat transfer rate required for the calculation of air-side heat transfer coefficient can be expressed as
Fig. 2. The wavy fin photo.
Q ¼ ðQw þ Qa Þ=2; Qw ¼ m_ w C pw ðT w1 T w2 Þ;
2.3. Test condition and method The tested wavy fin and flat tube heat exchanger was installed in the test system. In this work, the exchanger height was less than the tunnel dimensions, and the bypass flows were eliminated by a thin layer of foam plastic sandwiched between the heat exchanger core and tunnel edge. Upon completion of the hot water side links, the water tube was completely insulated with a 15 mm thick layer of glass wool. The test was performed in a range of Reynolds number, which is based on hydraulic diameter of fin entrance and maximum air velocity [14], of 800–6500. The inlet water temperature was maintained at 90 C with a constant
Qa ¼ m_ a C pa ðT a2 T a1 Þ:
ð1Þ ð2Þ
Effectiveness-NTU method can be used for obtaining airside heat transfer coefficient. The equation for both fluids unmixed is [15], NTU0:22 ½expðC NTU0:78 Þ 1 ; C C min m_ a C pa e ¼ Q=Qmax ; C ¼ ¼ ; C max m_ w C pw e ¼ 1 exp
ð3Þ ð4Þ
We can obtain overall heat transfer coefficient (UA) for the heat exchangers as UA ¼ ðm_ a C pa ÞNTU:
ð5Þ
Fp
Flat Tube
Fh
Fin A
Fin
Ld
A
Flat Tube
A-A
Fig. 3. Wavy fin and flat tube exchangers.
Table 1 Specification of wavy fin parameters (mm) No.
Fin pitch (Fp)
Fin height (Fh)
Fin length (Ld)
Fin thickness (d)
Wavy amplitude (2A)
Wavelength (L)
1 2 3 4 5 6 7 8 9 10 11
2.0 2.25 2.5 2.0 2.25 2.5 2.0 2.25 2.5 2.0 2.0
8.0 8.0 8.0 8.0 8.0 8.0 7.0 7.0 7.0 8.0 10.0
65.0 65.0 65.0 53.0 53.0 53.0 43.0 43.0 43.0 43.0 43.0
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8
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The air-side heat transfer coefficient can be obtained from the following equation, assuming zero water side fouling resistance. Due to the contact resistance of the flat tube and fin is a resource of uncertainty, the effect of contact resistance is included in the derived air side resistance ð6Þ
Note that the second term of the right-hand-side of the Eq. (6) indicates the water side thermal resistance and the third term means the tube wall thermal resistance. For water-side heat transfer coefficients, the Gnielinski’s correlation [16,17] for fully developed turbulent flow for the pipe flow is used. That is " 2=3 # d 0:87 0:4 Nuw ¼ 0:012ðRew 280ÞPr 1 þ : ð7Þ l The surface effectiveness and fin efficiency for the dry surface of wavy fins are [17]:
gf ¼
Af ð1 gf Þ; Ao
tanhðm0 l0 Þ ; m 0 l0
sffiffiffiffiffiffiffi 2h 0 m ¼ ; kf d
ð8Þ l ¼ F h =2:
ð9Þ
From the Eqs. (6)–(9), the heat transfer coefficient h can be obtained using the iterative calculation, since the fin efficiency is the function of heat transfer coefficient h. The Colburn j factor is defined as h Pr2=3 ð10Þ j¼ qu1 C p
f
0.12
Fp=2.00mm Ld=65mm Fp=2.25mm Ld=65mm Fp=2.50mm Ld=65mm
0.012
0.08
0.01
The core friction of the heat exchangers was reduced to obtain the Fanning friction factor f. In present study, the pressure drop equation proposed by Kays and London [14], including the entrance and exit pressure losses, was used to evaluate the friction factor. The air is treaded as incompressible fluid, and the density of air is treated as constant according to average air temperature. The simple equation is Ac 2Dp f ¼ kc ke ; ð11Þ qu21 Ao ui D e ð12Þ Re ¼ v
0.008 0.04 0.006
0.004 600
800 1000
2000
4000
6000
8000
Re
Fig. 4. Effect of fin pitch on the j and f factor.
0.014
0.12
Fh=7.0mm Ld=43mm Fh=8.0mm Ld=43mm Fh=10.0mmLd=43mm
0.012
0.08 0.01
j factor
According to the geometry parameters of heat exchanger and the graph given by Kays and London [14], the kc and ke are 0.4 and 0.2. Accounting for all instrument errors, property uncertainties, and geometry tolerances, the uncertainties for the j and f factors are ±9.2% and ±8.1%, respectively [18].
j
0.014
0.008 0.04 0.006
3. Results and discussion 3.1. j and f factors versus Reynolds number 600
The air side heat transfer and friction characteristics of the tested wavy fin and flat tube heat exchangers are pre-
f factor
ga ¼ 1
f factor
1 1 1 dwall ¼ : hga Ao UA hw Aw k wall Awall
sented in terms of the Colburn factor j factor and friction factor f, which are plotted versus the Reynolds number based on the fin entrance hydraulic diameter. Figs. 4–6 illustrates the effects of fin pitch, fin height and fin length on the performance of heat exchangers having different geometry parameters. From these figures, it is observed that the geometry parameters of wavy fins have significant effect on the j factor as a function of Re. Fig. 4 shows that the j and f factors increase with increasing fin pitch at the same Re, in which the wavy have the same fin length of 65.0 mm and fin height of 8.0 mm. The cause of this result from the phenomena is that, when the fin pitch increases, the air flow inside the corrugated flow channel can be mixed better at the same Reynolds number. And this better mixing leads to an increase of the heat transfer coefficient. The explanation can be confirmed by the results of Manglik and Zhang [11] with 3D numerical simulation method for wavy fins. At the same time, the phenomena also result in the pressure drop increase. The behaviors of hydraulic thermal performance with fin pitch are different, compared with the conventional finned tube heat exchangers. Wongwises [3] reported that
j factor
2070
800
2000
4000
6000
Re
Fig. 5. Effect of fin height on the j and f factor.
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0.010
j
f
0.012
0.12
Ld=65mm Fh=8.0mm Ld=53mm Fh=8.0mm
0.009
+10%
0.08 0.008
f factor
-10% j cor
j factor
0.009
0.04 0.006
0.007
0.006
0.005
600
800
2000
4000
6000
Re
0.004 0.004
0.005
0.006
0.007
0.008
0.009
0.010
j exp
Fig. 6. Effect of fin length on the j and f factor. 0.08
3.2. Empirical correlations Based on the previous discussion, it is obvious from the test data that no single curve can be expected to describe the complex behaviors about the heat transfer and friction characteristics of the wavy fin. For easier engineer calculation, the empirical correlations for j and f factors were performed by multiple linear regression and F significance test [20] on basis of 154 experimental data with differential wavy fin geometries. The corresponding correlations are given as follows:
+10% 0.07
0.06
-10%
f cor
the fin pitch has no significant effect on the heat transfer and pressure drop characteristics of fined tube heat exchangers. Fig. 5 presents the effect of fin height on j and f factors of wavy fin with fin pitch of 2.0 mm and fin length of 43.0 mm as a function of Re. From Fig. 7, it is interesting to observe that the j factor increase with increasing fin height, while the effects of fin height on the f factor is little. The result is different to the theory that the fin height has little effect on the characteristics of heat transfer which was adopted by many numerical researchers whose numerical model is 2D [5–8]. And the result is similar to that of Manglik and Zhang [11] 3D numerical simulation, who reported that, with increasing flow cross-section aspect ratio, the spatial coverage and strength of the counterrotating vortices are seen to increase, resulting in convective mixing and enhanced heat transfer. From the Fig. 6 can be observed the effects of fin length on the j and f factors against the Re. In the comparison, the wavy fins have the same fin height of 8.0 mm and fin pitch of 2.0 mm. The j and f factors decrease with increasing fin length under the same Re. The reason may be that the effect of fluid entrance is relatively obvious for wavy fin. This result is in accord with the conclusions of Yasar [19], who utilized the numerical simulation and reported that the fluid flow and heat transfer become periodically fully development after 3–5 cycles.
0.05
0.04
0.03 0.03
0.04
0.05
0.06
0.07
0.08
fexp
Fig. 7. Comparison of experimental data and correlation for j and f factor.
Correlation of the heat transfer performance of the wavy fins: 0:1284 0:153 0:326 Fp Ld 0:2309 F p j ¼ 0:0836Re : ð13Þ Fh 2A L Correlation of the frictional performance of the wavy fins 0:3703 0:25 0:1152 Fp Ld 0:309 F p f ¼ 1:16Re : ð14Þ Fh 2A L Fig. 7 shows the comparison of j and f factors of the experimental results with those of the proposed correlations. For the heat transfer and friction f factor correlations, Eqs. (13) and (14) can predict 95% of the experimental data within ±10%. The mean deviations of the correlations Eqs. (13) and (14) are 4.4% and 5.1%, and the average deviations are 0.4% and 0.3%, according to the Eqs. (15) and (16) [21]. ! 1 X /cor /exp Average deviation ¼ 100%; ð15Þ N /exp ! 1 X j/cor /exp j 100%: ð16Þ Mean deviation ¼ N /exp
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0.018
Kays and London 11.44-3/8W Present Correlation 11.44-3/8W Kays and London 11.5-3/8W Present Correlation 11.5-3/8W
j factor
0.015
0.012
0.009
0.006
1000
2000
3000
4000
5000
6000
7000
8000
Re
0.12
Kays and London 11.44-3/8W Present Correlation 11.44-3/8W Kays and London 11.5-3/8W Present Correlation 11.5-3/8W
heat exchangers. The effects of fin pitch, fin height and fin length on the thermal hydraulic performance are examined. On the basis of previous discussions, the following conclusions are made: 1. The j and f factors decrease with increasing Re, in the tested range of Re, Re = 800–6500. And the j and f factors increases with fin space increasing at the same Re; the j factor increases with fin height, while the fin height has little effect on the f factor as a function of Re. 2. Correlations of heat transfer and pressure drop for the wavy fins are developed. The proposed correlations give fairly good predictive ability against the present test data. The mean deviations of the correlations for j and f factors are 4.4% and 5.1%, and the average deviations are 0.4% and 0.3%, respectively. Acknowledgements
0.09
f factor
The authors acknowledge the financial support of Zhejiang Yinlun Machine Co. Ltd. We are grateful to Dr. Niu and Xianhui Zhang for providing the valuable comments. It would not have been possible to carry out this study without their help.
0.06
References
0.03 1000
2000
3000
4000
5000
6000
7000
8000
Re
Fig. 8. Comparison of present correlation and other experiment data.
Fig. 8 presents comparison of present correlation and other experiment data for wavy fin. The Kays and London experiment data is only database for the wavy fin from the public literatures, although it only includes three different wavy fin geometries. The present correlations of j and f factor compared with the experiment data of Kays and London based on two wavy fins, which are named 11.4–3/ 8 W and 11.5–3/8 W [14]. As for the j factors and f factors, compared with experiment data, the average deviation are 22.6% and 11.5%. This indicates that the present correlations predict the values of j and f factors are smaller than those of Kays and London under the same Re. We think the main reasons for the difference are that the profiles of wavy fins are not identical to those of Kays and London. The wavy fins’ profiles in this study are the triangular profiles with round corners, however the Kays and London’s wavy fin profiles are sinusoidal. Another, the fact should not be neglected that the experimental heat exchangers cores manufacture irregularities are not identical due to different manufacture, which also result in the difference. 4. Conclusions The present experimental study reports the air side thermal hydraulic performance of the wavy fin and flat tube
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