- Email: [email protected]
water–water heat transfer
Energy Conversion and Management 101 (2015) 460–469
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Experimental investigation on performances of trisection helical baffled heat exchangers for oil–water heat transfer Ya-Ping Chen a,⇑, Wei-han Wang b, Jia-Feng Wu a, Cong Dong c a
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China College of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China c School of Mechanical and Automotive Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, China b
a r t i c l e
i n f o
Article history: Received 25 February 2015 Accepted 16 May 2015
Keywords: Heat transfer enhancement Performance experiments Helical baffled heat exchangers Circumferential overlap of baffles Incline angle of baffle
a b s t r a c t The trisection helical baffled shell-and-tube heat exchangers have structural features of more suitable to the equilateral triangular tube layouts and less baffle parts. In particular the circumferential overlap trisection helical baffled shell-and-tube heat exchangers are of anti-shortcut structure that accommodates one row tubes in each circumferential overlapped zone between adjacent baffles for dampening shortcut leakage. The performance tests were conducted on both oil–water and water–water heat transfer in heat exchangers with equilateral triangle tube layout of 16 tubes including five helical baffle schemes with incline angles of 12°, 16°, 20°, 24°, 28° and a segmental baffled one for comparison. The test results show that both the shell side heat transfer coefficient ho and pressure drop Dpo increase but the comprehensive index ho/Dpo decreases with the increase of the mass flow rate of all schemes; and that the shell side heat transfer coefficient, pressure drop and the comprehensive index ho/Dpo decrease with the increase of the baffle incline angle at certain mass flow rate, except that the curves of comprehensive index ho/Dpo of 12° and 16° helical baffle schemes are almost coincide. The average values of shell side heat transfer coefficient, the comprehensive index ho/Dpo of the 12° helical baffled scheme are about 50% higher than those of the segmental one with almost same pressure drop. The correlation equations for shell side Nusselt number and axial Euler number are presented varying with axial Reynolds number, Prandtl number and helical baffle incline angle. Ó 2015 Published by Elsevier Ltd.
1. Introduction The shell-and-tube heat exchangers (STHXs) are widely used in industries such as petroleum refining, chemical engineering, power plants and food processing, and most of them are segmental baffled type. The segmental baffled heat exchangers are mature in design and manufacture, robust and flexible for almost all heat and mass transfer processes; however, they have some drawbacks including stagnant zones, higher pressure drops, and a propensity to induce vibration and fouling. These problems could be ameliorated by replacing segmental baffles with the helical ones. Since Lutcha and Nemcansky [1] proposed the helical baffled heat exchangers (HSTHX) with quadrant sector baffles, many specialists and researchers studied the novel heat exchangers. The mostly investigated items are the optimum incline angle of the sector baffles and the baffle shapes and connection configurations. It is clear that the smaller the incline angle of the sector baffles are, the higher both the heat transfer coefficient and the pressure drop ⇑ Corresponding author. Tel.: +86 (0)13851729402. E-mail address: [email protected] (Y.-P. Chen). http://dx.doi.org/10.1016/j.enconman.2015.05.042 0196-8904/Ó 2015 Published by Elsevier Ltd.
are with increased velocity. Lutcha and Nemcansky [1] indicated that the optimum incline angle of the sector baffles is 40° in the chart of heat transfer coefficient ho versus pressure drop Dpo. However, Jafari Nasr and Shafeghat [2] obtained a fluctuated curve of heat transfer coefficient versus incline angle. Zhang et al. [3] investigated the performance of oil cooler with helical baffles (OCHB) and compared with that of the segmental one (OCSB) with practical size, and also found that the shell side heat transfer coefficients and the shell-side pressure drop of the OCHB are respectively lower than and far lower than those of the OCSB. Zeyninejad et al. [4] presented a site application result of a mid-overlapped helical baffle heat exchanger with 40° incline angled baffles and compared with a segmental one in a petrochemical plant, and the results indicated that the helical one had better comprehensive performance of the shell side heat transfer coefficient per unit pressure drop but its heat transfer coefficient was 15–57% lower than that of the segmental one at same flow rate. As the heat transfer coefficient is of vital importance to an application in fulfilling a certain task, so called optimum baffle incline angle of 40° as universal truth is questionable.
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
461
Nomenclature A cp d, D Eu G h K l Nu p Pr Q T,t Re
area (m2) specific heat (kJ kg1 K1) diameter (m) Euler number flow rate (kg s1) heat transfer coefficient (W m2 K1) overall heat transfer coefficient (W m2 K1) tube length (m) Nusselt number pressure (Pa) Prandtl number transferring heat (kJ) temperature (K, °C) Reynolds number
As the non-continuous helical baffles exhibit shortcut leakage flows at the conjunction of adjacent baffles, it is generally believed as one of major factors hindering heat transfer performance. Many improved methods pertaining to the shortcut leakage flow have been investigated experimentally or numerically. Stehlik et al. [5,6] suggested using axial overlap baffles to reduce the helix pitch while keeping greater baffle incline angle. Wang [7] studied flow fields of axial overlap baffled helical heat exchangers with positive assessment. Zhang et al. [8,9] simulated several shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles, and experimentally measured four middle overlapped schemes of helix heat exchangers with different tube lengths and cylinder diameters and found that the optimum scheme was the one with incline angle of 30°. Wang et al. [10] tried to block the triangular notches with plates, but the experimental results indicated that the comprehensive index of heat transfer coefficient per pressure drop was lower than that of the non-block scheme as the pressure drop increased much faster than the shell side heat transfer coefficient did. Dong and Chen [11] numerically simulated the flow and heat transfer performances of four middle-axial-overlap trisection helical baffled heat exchangers of 36° baffle incline angle and with different blockage configurations of the X-type notches at conjunction of adjacent baffles that blocking all triangular notches, only the outer triangular notches, the outermost strip notches and without any blockage. The results showed that the scheme blocked only the outmost strip notches had better comprehensive index of heat transfer coefficient per pressure drop and feasibility in installation. Cao et al. [12] numerically studied the impact of the overlap size on the heat transfer performance at certain helical pitch, and found that both the heat transfer coefficient and pressure drop increased with the increase of overlap size at identical mass flow rate, whereas the heat transfer coefficient decreased at identical pressure drop. It indicates that with identical helical pitch, the greater incline angled middle-overlap baffle scheme is inferior to the smaller incline angled end-to-end (adjacent baffles touching at periphery) baffle scheme in both evaluation indexes of heat transfer coefficient and heat transfer coefficient per pressure drop. Considering most heat exchangers adopt equilateral triangle tube layout, and the quadrant division does not suit the natural intervals of such tube layout, Chen [13] and Chen et al. [14] proposed trisection helical baffled heat exchangers, particularly the circumferential overlap trisection helical baffled shell-and-tube heat exchanger (cothSTHX) scheme, which put the straight edges of sector baffles in the natural intervals between tube rows with at least one row of tubes situated in the circumferential overlapped
Greek symbols b incline angle of helical baffles (°) Dp pressure drop (Pa, kPa) Dtm logarithmic mean temperature difference (K) k thermal conductivity (W m1 K1) l dynamic viscosity (kg m1 s1) q density (kg m3) Subscripts i tube side o shell side w wall h hydraulic seg segmental baffled scheme
area of adjacent baffles to minimize the short-cut leakage loss at triangular conjunction notches and to improve the rigidity of the heat exchanger tube bundle as well. The figures on the meridian, transverse and unfolded concentric hexagonal sections of the pressure or velocity nephograms with superimposed velocity vectors demonstrate clearly the secondary vortex flow and shortcut leakage flow patterns which are the key impact factors for heat transfer enhancement in the cothSTHXs. Chen et al. [15] also experimentally investigated the performances of five cothSTHXs with baffle incline angles from 20° to 32° and a segmental one for comparison. The results showed that the helical baffled scheme with incline angle 20° performed better than other schemes with both indexes of heat transfer coefficient and heat transfer coefficient per pressure drop. Dong et al. [16] numerically investigated four trisection helical baffled heat exchangers with identical helical pitch and tube layout but different baffle shapes or connections including a circumferential overlap (CO) scheme, an end-to-end (EE) scheme, a blocked V-notches (BV) scheme, and a middle axial overlap (MO) scheme. The results show that the CO scheme has the highest shell-side heat transfer coefficient and comprehensive index ho/Dpo; and the average values of comprehensive index ho/Dpo of CO scheme in the calculated range is respectively 16.5%, 27.3% and 13.5% higher than that of the EE, BV and MO schemes. Wen et al. [17] studied a ladder-type fold baffled heat exchangers which adopted two circumferential overlapped baffles in a helical cycle and also takes advantage of blocking part of the triangular leakage zones, and the simulation results showed that the thermal performance factor TEF enhanced by 28.4–30.7%. Wang et al. [18] summarized the recent development in helical baffle heat exchangers, and implied that the helical baffle heat exchangers would be evolved from the ones with discontinue baffles such as quadrant and trisection baffles to the continuous baffled ones with several very complicated structures. Nevertheless, the cost and manufacture feasibility are always the main considerations for real engineering applications, and what will be eventually populated is definitely the simple and concise one, which is the correct development or evolution direction guided by the pioneers Lutcha and Nemcansky [1] with their historical innovation of the quadrant helical baffle heat exchangers. The heat transfer performance prediction is very important for heat exchanger design and a lot of efforts [1–4,7,9,14,15] have been conducted on the performance study of HSTHXs, but very few correlation formulae have been presented. Seyed and Mahdi Saeedan [19] obtained Nusselt number and friction factor in the helical heat exchanger in terms of Reynolds number and volume fraction of Water–Al2O3 nanofluid using neural network, and presented the
462
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
results in figures and tables. Lahiri and Khalfe [20] adopted hybrid differential evolution and ant colony optimization technique for design optimization of shell and tube heat exchangers from economic point of view. Zhang et al. [9] presented experimental results of the shell side heat transfer coefficient of different baffle angled helical heat exchangers and correlated them with different coefficient c1 and exponent m1 in the formula (1).
Nu ¼ c1 Rem1 Pr 1=3
ð1Þ
Zhang LH et al. [21] performed experiment on heat exchangers with shell diameter of 500 mm and tube length of 6 m with helical baffle angles of 7°, 13° and 25° and a segmental one. The results showed that both the shell side heat transfer rate and the shell side pressure drop were at peak when helical angle equals 7°, while the shell side heat transfer rate per unit pressure drop at this angle was at the nadir. The result figures were presented with abscissa of both volume flow rate and Reynolds number of shell side fluid. As the trend lines of experimental performance data with different baffle angles are not continued or coincide in the figures with shell side Reynolds number abscissa, the shell side heat transfer coefficients of different angled helical baffle heat exchangers were correlated in the formula (1) with different coefficient c1 and exponent m1. The friction factors were presented in similar way. The performance formulae for HSTHX design are not easy to construct as there are so many influence factors with diverse configurations of the helical baffle structure and arrangement such as quadrant baffle and trisection one, end-to-end, axial overlap with different overlap size, circumferential overlap, folded baffle, blocked plate for the V-notch in adjacent baffle conjunctions and so on apart from the ordinary parameters of STHXs. For instance, the heat transfer coefficient and pressure drop could be very different with same baffle shape and incline angle but different axial overlap size in a same shell cylinder. Numerical simulation plays a crucial role in explaining how structural factors influence flow and heat transfer of a heat exchanger, and many experts [2,8,11,12,14,16,17,22] adopted 3D CFD methods for numerically simulation of variety helical baffled heat exchangers. However, experimental research is still an indispensable step before a new type of heat exchangers being put into use. The features of low pressure drop and higher heat transfer coefficient per pressure drop of helical baffled heat exchangers have been generally recognized; however, many literatures [3,4,9] showed that the heat transfer coefficients of helical baffled heat exchangers were inferior to that of the conventional segmental baffled heat exchangers at same shell side flow rate and tube layout. It means that the heat transfer capacity might be less than that of the segmental baffled one or more heat transfer areas should be used, thus it may not be accepted by industry users. Efforts must be taken to ensure heat transfer enhanced rather than only the comprehensive index increased in evaluation of any scheme in engineering applications. On this issue, the structure and installation configuration of the helical baffles should be reconsidered. The baffle incline angle needs to be reduced if the volume flow rate of the shell-side fluid is low, so that the fluid velocity can be increased to augment heat transfer coefficient by taking advantage of the low pressure drop feature of HSTHXs.
diagram and the photo of the test rig for heat transfer are shown in Fig. 1(a) and (b) respectively. The test rig includes two separate systems for both oil–water and water–water heat transfer. The tube-side fluid of the testing heat exchanger is municipal water, while the shell side fluid is heat transfer oil or hot water. The heat fluid raises pressure in a pump and is heated in an electric heater before entering the testing heat exchanger. The heating power is adjusted by solid state relay. As shown in the Fig. 1, an upper tank is installed above the circulation loop to provide a positive suction head for pump and also to compensate the volume expansion or contraction due to temperature variation. A bottom tank is set for accumulating the fluid drained from the testing heat exchanger for draining and filling the system before and after changing a tube
upper oil tank compressed air cooling water out
flowmeter
testing heat exchanger sight glass tube
cooling water in
p
elec. heater
bottom oil tank
filter pump
(a) Schematic diagram of test rig (oil-water)
2. Materials and methods 2.1. Performance test rig The experiments were conducted on five cothSTHXs with relatively small baffle incline angles ranging from 12° to 28° and a segmental baffled heat exchanger as a contrast. The schematic
(b) Photo of test rig (oil-water and water-water) Fig. 1. Schematic diagram of heat transfer test rig.
463
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
bundle core. To facilitate draining the fluid from testing heat exchanger, a compressed air line is connected to the system through a valve. A small pump is used to transport fliud from the bottom tank to the upper tank. The cylinder shell of the testing heat exchanger is a common one, while the tube bundle core could be replaced as shown in Fig. 2. Both sides of the heat exchanger are one-way layouts in counter flow directions. The inner diameter of the shell of the heat exchanger is £81 mm, and the diameter of the baffles is £80 mm; the effective geometry (outer diameter thickness length) of the heat transfer tubes is £10 mm 1 mm 832 mm, the number of heat transfer tubes is 16 and the tubes are equilateral triangularly arranged. There are also 3 sets of rods and spanning tubes for fixing the baffles. The other geometric parameters are shown in Table 1. The performance tests of heat transfer were conducted on five cothSTHXs with incline angles of 12°, 16°, 20°, 24° and 28° and a segmental baffled one. Fig. 3 shows the projection view of both
helical and segmental baffle shapes. Each helical baffle is angled to the axis of the heat exchanger and the baffle occupies more than one third cross section of the heat exchanger shell to put the straight edges of the baffles in the natural intervals between tube rows, and with adjacent baffles circumferential overlapped to accommodate a row of tubes for dampening reverse leakage. The adjacent baffles touch at the periphery, and forming a pseudo helix. 2.2. Experiment data process During the oil-to-water performance tests, the heating oil flow rate was adjusted by changing the oil pump motor frequency with an inverter from 25 Hz to 50 Hz with 5 Hz step; and the heating oil inlet temperature kept 60, 70 and 85 (±0.5) °C respectively controlled with a solid state relay to the electric heater. The inlet temperature and the flow rate of cooling water in tube-side were kept 11(±0.4) °C and 0.20 (±2.5%) kg/s respectively (Reynolds number about 2000). During the water-to-water performance tests, the hot water inlet temperature kept 50, 60 and 70 (±0.5) °C respectively, while the inlet temperature and the flow rate of cooling water in tube-side were kept 15.1 (±0.4) °C and 0.22 (±2.5%) kg/s respectively (Reynolds number about 2500). The overall heat transfer coefficient K can be obtained from the measuring data during the experiment of the flow rates, inlet and outlet temperatures of both heating and cooling fluids.
K¼
Qi þ Qo 2ADtm
ð2Þ
where Qi and Qo are the transferring heat at tube-side and shell-side respectively; A is the heat transfer area; Dtm is the logarithmic mean temperature difference. The turbulent flow of tube side heat transfer coefficient hi can be estimated by Gnielinski equation [23]
hi ¼
ki f w ðRei 1000ÞPri di 8
," 1 þ 12:7
# rffiffiffiffiffi f w 2=3 di 1þ Pri 1 2 l
From left to right: 12°, 16°, 20°, 24°, 28° and seg Fig. 2. Photo of tube bundles of testing heat exchangers.
ð3Þ where fw is the tube wall friction factor calculated by:
f w ¼ ð1:82 lg Rei 1:64Þ Table 1 Geometric parameters of testing helical and segmental baffled heat exchangers. Item
cothSTHX
Inclined angle (°) Baffle number Helical pitch (mm)
12 50 47.2
16 38 62.7
Segment STHX 20 30 78.8
24 25 95.8
28 21 113.9
0 10 75.5
2
ð4Þ
The physical properties of water are calculated with polynomial formula using mean temperature of fluids at the inlet and outlet of the heat exchanger as the characteristic variable. Then the heat transfer coefficient ho of shell side can be separated according to Eq. (5). Because the tube bundles of the testing heat exchangers are new, the fouling resistance is not considered.
Fig. 3. Projection view of helical (left) and segmental (right) baffles of testing heat exchangers.
464
1 1 K
do ddi ho i 2k ln
i
ð5Þ
do di
where do and di are the tube outer and inner diameters respectively, k is the thermal conductivity of material of the tubes. 2.3. Uncertainty analyses Both mass flow rate and volume flow rate of heating oil are measured with a MicroMotion F025 mass flow meter (uncertainty Table 2 Uncertainty calculation results.
±0.15%), while the volume flow rate of cooling water is measured with a turbo-flow-meter (uncertainty ±0.5%). The temperature is measured with platinum resistance thermometers (uncertainty ±0.15 °C). And the shell side pressure drop is measured with a Rosemount 3051S differential pressure transmitter (uncertainty ±0.15%). The temperature and pressure measuring points are arranged at the tubular bent conjunctions to the inlets and outlets of the testing heat exchanger. The experimental data were collected and processed through an Agilent 34970A data acquisition instrument to a computer with operation software programmed on the platform of LabView.The uncertainty of overall heat transfer coefficient K is estimated with Eq. (6).
eK ¼
Uncertainty item
Symbol
Unit
Value
Shell side inlet temperature Shell side outlet temperature Shell side mass flow rate Shell side pressure drop Tube side inlet temperature Tube side outlet temperature Tube side mass flow rate Shell side transferring heat Tube side transferring heat Average transferring heat Overall h.t.c.
eTo eTo eGo eDpo eTi eTi eGi eQo eQi eQ eK
% % % % % % % % % % %
±(0.21–0.22) ±(0.24–0.26) ±(0.15) ±(0.15) ±(1.37–1.43) ±(0.69–0.80) ±(0.5) ±(1.39–2.20) ±(1.67–2.19) ±(2.49–2.76) ±(4.60–6.45)
0
00
0
00
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2Q þ e2A þ e2Dtm
eQ ¼
pffiffiffiffiffiffiffiffiffiffiffiffi
eQ j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2Gj þ e2cp;j þ e2Dtj
eQi eQo
700
-1
Overall h.t.c. K /W m K
-2
340
300 280 260 240 220
12°
16°
20°
24°
28°
seg
ð7Þ ð8Þ
j¼i;o
The results of maximum uncertainties of some directly measured parameters and the overall heat transfer coefficient (h.t.c.) K are given in Table 2.
360
320
ð6Þ
The uncertainty of transferring heat Q is estimated with Eqs. (7) and (8).
H.t.c. of shell side h o /W m-2 K-1
ho ¼ h
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
12°
16°
20°
24°
28°
seg
600
500
400
300
200 180
0.2
0.25
0.3
0.35
0.4
0.45
200 0.2
0.5
0.4
0.45
(a) Oil-water
0.5
10000 12°
16°
20°
24°
28°
seg
H.t.c. of shell side h o / W·m-2·K-1
Overall h.t.c. K / W·m-2·K-1
0.35
(a) Oil-water
940
900
860
820 0.22
0.3
Flow rate of shell side G o /kg s-1
-1
980
0.25
Flow rate of shell side Go /kg s
0.26
0.3
0.34
0.38
0.42
0.46
9000
12°
16°
20°
24°
28°
seg
8000 7000 6000 5000 4000 3000 0.22
0.26
0.3
0.34
0.38
0.42
Flow rate of shell side Go / kg· s
Flow rate of shell side Go / kg· s-1
(b) Water-water
(b) Water-water
-1
Fig. 4. Overall heat transfer coefficient versus shell side flow rate.
0.46
Fig. 5. Shell side heat transfer coefficient versus shell side flow rate of six schemes.
465
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
3.1. Performances of heat transfer Taking into account all the experiments were completed within the same shell and both the size and the tube number of the replaceable tube bundles are identical, so the shell side flow rate Go is used reasonably as the independent variable for comparing characteristics of different schemes. The curves of the overall heat transfer coefficient (h.t.c.) K, shell side h.t.c. ho, pressure drop Dpo, the comprehensive index ho/Dpo are suggested to demonstrate the performances of both heat transfer and flow resistance of the different schemes. As there are too many data with all the schemes, for simplicity, only the results under the temperature 60 °C of heating fluid are presented in detail. Figs. 4–7 show the curves of the overall h.t.c. K, the shell side h.t.c. ho, the shell side pressure drop Dpo and the comprehensive index of ho/Dpo vary with the shell side flow rate Go for both oil-to-water (o–w) and water-to-water (w–w) heat transfer respectively. From the figures it could be seen that the overall h.t.c. K and the shell side h.t.c. ho and the shell side pressure
Pressure drop of shell side Δ po /kPa
36 32 28
12°
16°
20°
24°
28°
seg
40 35
12°
16°
20°
24°
28°
seg
30 25 20 15 10 0.2
0.3
0.4
0.5
Flow rate of shell side Go /kg s-1
(a) Oil-water 400
350
12°
16°
20°
24°
28°
seg
300
250
200
150 0.22
24
0.26
0.3
0.34
0.38
0.42
0.46
Flow rate of shell side Go /kg s-1
(b) Water-water
20
Fig. 7. Comprehensive index of ho Dp1 o versus shell side flow rate Go.
16 12 8 0.2
0.3
0.4
0.5
Flow rate of shell side Go /kg s -1
(a) Oil-water 40
Pressure drop of shell side Δp o / kPa
Comprehensive indexho·Δpo-1
3. Experimental results and discussions
45
Comprehensive indexho·Δpo-1
Table 2 shows that the maximum uncertainty of the overall heat transfer coefficient K is ±6.45%, thus the experiment data are effective and reliable.
12°
16°
20°
24°
28°
seg
35
30
25
20
15
10 0.22
0.26
0.3
0.34
0.38
0.42
0.46
Flow rate of shell side G o / kg·s-1
(b) Water-water Fig. 6. Shell side pressure drop versus shell side flow rate of six schemes.
drop Dpo increase with the increase of the shell side flow rate Go for all schemes and they also increase with the decrease of the baffle incline angle at constant flow rate for the helical schemes. The segmental baffled scheme has the lowest in oil–water and second lowest in water–water average values of overall h.t.c. and shell side h.t.c. and the second highest average value of shell side pressure drop. As the flow rate is changed with pump frequency inverter in steps without any other valve control, it can be seen from the Fig. 6 that the flow rate increases but the pressure drop reduces somewhat with the increase of the baffle angle with the same pump frequency. Fig. 7 shows that the curves of the comprehensive index of ho/Dpo of the 12° and 16° helical baffled schemes are tied for first, followed with 20°, 24° and 28° helical baffled schemes sequentially, and with the segmental baffled scheme ranks the last. It shows that the curves of ho/Dpo decrease with the increase of the shell side flow rate for all schemes. The average values of the ratios of overall h.t.c. K, shell side h.t.c. ho, pressure drops Dpo and comprehensive index ho Dp1 o of all the helical baffled schemes over the trend curves of those of the segmental baffled scheme are shown in Table 3. The results indicate that the smaller the baffle incline angle is, the higher the overall h.t.c., shell side h.t.c. and pressure drop of the testing helical baffled schemes are. The shell side h.t.c. ho and comprehensive index ho Dp1 o of the 12° helical scheme are about 50% higher than those of the segmental baffled scheme with approximate pressure drop, which are quite attractive indicating the superior features of the cothSTHXs. The results indicated that it is no need for cothSTHXs
466
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Table 3 Average relative performance values of helical schemes over segmental scheme. Items/scheme
12°
16°
20°
24°
28°
o–w
Overall h.t.c. K Shell side h.t.c. ho Shell side pressure drop Dpo Comprehensive index ho Dp1 o
1.338 1.613 1.035 1.557
1.259 1.448 0.890 1.533
1.188 1.290 0.917 1.404
1.099 1.146 0.873 1.310
1.024 1.030 0.834 1.232
w–w
Overall h.t.c. K Shell side h.t.c. ho Shell side pressure drop Dpo Comprehensive index ho Dp1 o
1.075 1.637 1.098 1.491
1.065 1.432 0.969 1.478
1.034 1.241 0.886 1.399
1.017 1.089 0.818 1.332
0.992 0.968 0.768 1.260
3.2. Correlation of the testing results For correlation the testing results, dimensionless criteria numbers have to be applied. Because the shell-side Reynolds number Reo demonstrates no additional merit but difficult in calculating the cross section of the helical channel, the shell-side axial Reynolds number Rezo defined in Eq. (9) is used reasonably as the independent variable for comparing different schemes, which
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
60 55 50
Nuo
45 40 35 30 25 20 0.5
1
1.5
2
2.5
3
3.5
4
actually corresponds to the flow rate in the shell side. The axial velocity wo for calculation of Rezo is calculated with Eq. (10). The shell-side Nusselt number Nuo and the shell-side hydraulic diameter dho are defined respectively in Eqs. (11) and (12). For the similar reason that the friction factor needs to know the length of the helical channel which is quite difficult to determine with diverse configurations of baffle shapes and conjunctions, the shell-side axial Euler number Euzo is adopted and defined in Eq. (13) which is a dimensionless criterion that reflects the shell side flow friction factor of different baffle schemes based on the Fanning formula. The shell side pressure drop could be determined from the Eq. (13) as long as the shell-side axial Euler number Euzo is obtained from the correlation equation.
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
0.45
0.4
Euzo
to deliberately pursue large baffle incline angle with greater difficulty in manufacturing helical baffles for small volumetric liquid fluids. The lower increment of overall h.t.c. in water–water heat transfer lies in that the control thermal resistance is at tube side.
0.35
0.3
0.25
0.2 0.5
4.5
1
1.5
Rezo
130
Nuo
3.5
4
4.5
110 90
70
5000
0.65
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70
0.6 0.55
Euzo
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70 4000
3
(a) Oil-water
150
3000
2.5
Rezo
(a) Oil-water
50 2000
2
0.5
0.45 0.4 0.35 0.3 2000
3000
4000
Rezo
Rezo
(b) Water-water
(b) Water-water
Fig. 8. Shell side Nusselt numbers versus shell side axial Reynolds number.
5000
Fig. 9. Shell side axial Euler numbers versus shell side axial Reynolds number.
467
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Rezo ¼ wo ¼
ð9Þ
m 4 Go ðD2s
pq
Nuo ¼
dho
wo do
2
ð10Þ
2
Ndo ndr Þ
ho dho ko
ð11Þ
pffiffiffi pffiffiffi 2 3a2 =4 p do =8 2 3a2 ¼4 ¼ do p do =2 p do
Euzo ¼
ð12Þ
2Dpo g qo w2o
ð13Þ
where Go is the mass flow rate of the shell side; Ds, dr and a are the shell inner diameter, the spanning tube diameter and the tube pitch respectively; N and n are the tube number and rod number in the radius of the shell respectively. Figs. 8 and 9 show the shell side Nusselt number Nuo and the shell side axial Euler number Euzo vary with the shell side axial Reynolds number Rezo of three cothSTHXs with baffle angles of 12°, 20° and 28° and a segmental one for both oil-to-water (o–w) and water-to-water (w–w) heat transfer. The inlet temperatures of heating fluids are set 85, 70 and 60 °C for oil-to-water and 70, 60 and 50 °C for water-to-water heat transfer. Unlike the
linear-like increasing curves of Nusselt number, each curve of Euler number has shape decrease gradient at smaller axial Reynolds number and then falls slower with the increase of axial Reynolds number. The Nusselt number Nuo increases somewhat with increased inlet temperature of the heating oil but decreases somewhat with increased inlet temperature of the hot water with the identical pump frequency and same heat exchanger core scheme due to the different dynamic viscosity features of oil and water. Fig. 10 shows the comprehensive index of Nuo Re1 zo varies with the shell side axial Reynolds number Rezo of these schemes. The positive proportional trend of the curves of comprehensive index Nuo Eu1 zo versus Reynolds number is quite different from that of the decreased trend of the comprehensive index ho Dp1 o versus shell side flow rate as shown in Fig. 7. The shell side Nusselt number of cothSTHX for both oil and water are respectively correlated in Eqs. (14) and (15) in consideration of the impact factors of axial Reynolds number, Prandtl number, dynamic viscosity, and incline angle of helical baffles. 1=3 1 Nuo ¼ c1 Rem zo Pr o ðsin bÞ
m2
1=3 1 Nuo ¼ c1 Rem zo Pr o ðsin bÞ
m2
m4 3 Euzo ¼ c2 Rem zo Pr o ðsin bÞ
150 130 110 90 70 50
ð15Þ
m5
ð16Þ
55 50
106% 40
94% 35 30 25 20
1
1.5
2
2.5
3
3.5
4
4.5
20
25
30
35
160
240 200 160 120
5000
Rezo
(b) Water-water Fig. 10. Comprehensive indexes Nuo Eu1 zo versus shell side axial Reynolds number.
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70
140 120
Nuo,exp
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70
280
-1
45
50
55
60
65
(a) Oil-water
320
4000
40
Nuo,cal
(a) Oil-water
3000
12°-85 20°-85 28°-85 12°-70 20°-70 28°-70 12°-60 20°-60 28°-60
45
Rezo
Nu o·Eu zo
ð14Þ
60
Nuo,exp
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
170
80 2000
0:14
65
190
Nu o·Eu zo-1
lo lw
The shell side Euler number of cothSTHX is correlated in Eq. (16).
210
30 0.5
100
110
90%
80 60 40 40
60
80
100
120
140
160
Nuo,cal
(b) Water-water Fig. 11. Comparison of values of shell side Nusselt number Nuo from correlation equations with experimental ones.
468
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Table 4 Correlated coefficients and exponents in the Eqs. (14)–(16).
o–w, Eqs. (14) and (16) w–w, Eqs. (15) and (16)
4. Conclusion
c1
m1
m2
c2
m3
m4
m5
58 0.99
0.5 0.8
0.4 0.6
1.62 13.5
0.5 0.4
0.6 0.5
0.22 0.4
0.45
Euzo,exp
0.4
0.35
106%
0.3
12°-85 20°-85 28°-85 12°-70 20°-70 28°-70 12°-60 20°-60 28°-60
94%
0.25
0.2 0.2
0.25
0.3
0.35
0.4
0.45
Euzo,cal
(1) The heat transfer performances of both heat transfer oil to cooling water and hot water to cooling water with different testing schemes were conducted on a test rig. The testing schemes include five circumferential overlap trisection helical baffle heat exchangers (cothSTHXs) with incline angles of 12°, 16°, 20°, 24°, 28° and a segmental baffled one. (2) The heat transfer performance test results are presented including both overall h.t.c. K and shell side h.t.c. ho, pressure drop Dpo and the comprehensive index ho/Dpo vary with the shell side flow rate. In the testing scope, the small angled helical scheme demonstrates better performance that the shell side heat transfer coefficient ho and comprehensive index ho Dp1 of the 12° helical scheme are about 50% o higher than those of the segmental baffled one with approximate pressure drop in both oil–water and water–water tests, which also verifies the superior heat transfer features of the cothSTHXs. (3) The correlation equations of shell side Nusselt number and shell side axial Euler number are presented with variables of shell side axial Reynolds number, Prandtl number and the incline angle of helical baffles at both turbulent and laminar flow ranges, and the deviations are less than ±5% to ±10%.
(a) Oil-water Acknowledgement
0.65 12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70
0.6
Euzo,exp
0.55 0.5
This work is supported by the National Nature Science Foundation Programs of China (51276035 and 51206022).
105%
References
95%
0.45 0.4 0.35 0.3 0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Euzo,cal
(b) Water-water Fig. 12. Comparison of values of shell side axial Euler number Euzo from correlation equation with experimental ones.
where b is the incline angle of helical baffles; l and Pr are the dynamic viscosity and Prandtl number of fluid; the subscripts o and w refer respectively properties of shell side fluid at the mean temperature and at wall temperature. The Table 4 shows the correlated coefficients and exponents in the Eqs. (14)–(16) from the experimental results of heat transfer with both heating oil to cooling water (o–w) and hot water to cooling water (w–w) in the cothSTHXs. The testing ranges of shell side axial Reynolds numbers of both oil–water and water–water heat transfer are from 0.5 to 4.5 and from 2200 to 5200, indicating at laminar flow and turbulent flow respectively. The Figs. 11 and 12 show the calculation results with correlation Eqs. (14)–(16) compared with the experimental results of the shell side Nusselt number and axial Euler number in both oil–water and water–water heat transfer in the cothSTHXs. The figures show that the deviations are within ±5% to ±10% which verifies that the correlation equation patterns presented in this paper are applicable.
[1] Lutcha J, Nemcansky J. Performance improvement of tubular heat exchangers by helical baffles. Chem Eng Res Des 1990;68(3):263–70. [2] Jafari Nasr MR, Shafeghat A. Fluid flow analysis and extension of rapid design algorithm for helical baffle heat exchangers. Appl Therm Eng 2008;28(11– 12):1324–32. [3] Zhang JF, Guo SL, Li ZZ, Wang JP, He YL, Tao WQ. Experimental performance comparison of shell-and-tube oil coolers with overlapped helical baffles and segmental baffles. Appl Therm Eng 2013;58:336–43. [4] Zeyninejad MS, Nemati TF, Razmi K, Tasouji AR. Tube bundle replacement for segmental and helical shell and tube heat exchangers: Performance comparison and fouling investigation on the shell side. Appl Therm Eng 2013;51:1162–9. [5] Stehlik P, Nemcansky J, Kral D. Comparison of correction factors for shell-andtube heat exchangers with segmental or helical baffles. Heat Transfer Eng 1994;15(1):55–65. [6] Stehlik P, Wadekar V. Different strategies to improve industrial heat exchange. Heat Transfer Eng 2002;23(6):36–48. [7] Wang SL. Hydrodynamic studies on heat exchangers with helical baffles. Heat Transfer Eng 2002;23(3):43–9. [8] Zhang JF, He YL, Tao WQ. 3D numerical simulation on shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles-Part II: Simulation results of periodic model and comparison between continuous and noncontinuous helical baffles. Int J Heat Mass Transfer 2009;52(23– 24):5381–9. [9] Zhang JF, Li B, Huang WJ, Lei YG, He YL, Tao WQ. Experimental performance comparison of shell side heat transfer for shell-and-tube Heat exchangers with middle-overlapped helical baffles and segmental baffles. Chem Eng Sci 2009;64(8):1643–53. [10] Wang L, Luo LQ, Wang QW, Zeng M, Tao WQ. Effect of inserting block plates on pressure drop and heat transfer in shell-and-tube heat exchangers with helical baffles. J Eng Thermophys 2001;22(s):173–6 (in Chinese). [11] Dong C, Chen YP. Impact of block plates on the flow and heat transfer performance of middle-axial-overlap helical baffle heat exchangers. J Mech Eng 2014;50(6):135–40 (in Chinese). [12] Cao X, Du WJ, Ji S. Effects of baffle connection manner on shell side performance of heat exchanger with helical baffles. CIESC J 2011;62(12): 3367–72. [13] Chen YP. A novel helix baffled heat exchanger suitable for tube bundle arrangement with equilateral triangles. Petro-Chem Equip 2008;37(6):1–5 (in Chinese). [14] Chen YP, Sheng YJ, Dong C, Wu JF. Numerical simulation on flow field in circumferential overlap trisection helical baffle heat exchanger. Appl Therm Eng 2013;50:1035–43.
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469 [15] Chen YP, Cao RB, Wu JF, Dong C, Sheng YJ. Experimental study on shell side heat transfer performance of circumferential overlap trisection helical baffle heat exchangers. In: Proceedings of the ASME 2011 international mechanical engineering congress and exposition. IMECE2011-63254, Denver, Colorado, USA; Nov 2011. [16] Dong C, Chen YP, Wu JF. Influence of baffle configurations on flow and heat transfer characteristics of trisection helical baffle heat exchangers. Energy Convers Manage 2014;88:251–8. [17] Wen J, Yang HZ, Wang SM, Xu SF, Xue YL, Tuo HF. Numerical investigation on baffle configuration improvement of the heat exchanger with helical baffles. Energy Convers Manage 2015;89:438–48. [18] Wang QW, Zeng M, Ma T, Du XP, Yang JF. Recent development and application of several high-efficiency surface heat exchangers for energy conversion and utilization. Appl Energy 2014;135:748–77.
469
[19] Seyed MB, Mahdi Saeedan MH. Prediction of Nusselt number and friction factor of water–Al2O3 nanofluid flow in shell-and-tube heat exchanger with helical baffles. Chem Eng Commun 2015;202:260–8. [20] Lahiri SK, Khalfe N. Improve shell and tube heat exchangers design by hybrid differential evolution and ant colony optimization technique. Asia-Pac J Chem Eng 2014;9:431–48. [21] Zhang LH, Xia YM, Jiang B, Xiao XM, Yang XL. Pilot experimental study on shell and tube heat exchangers with small-angles helical baffles. Chem Eng Proc 2013;69:112–8. [22] Andrews MJ, Master BI. Three-dimensional modeling of a helixchanger heat exchanger using CFD. Heat Trans Eng 2005;26(6):22–31. [23] Gnielinski V. New equations for heat mass transfer in turbulent pipe and channel flows. Int Chem Eng 1976;16:359–68.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Experimental investigation on performances of trisection helical baffled heat exchangers for oil–water heat transfer Ya-Ping Chen a,⇑, Wei-han Wang b, Jia-Feng Wu a, Cong Dong c a
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China College of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China c School of Mechanical and Automotive Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, China b
a r t i c l e
i n f o
Article history: Received 25 February 2015 Accepted 16 May 2015
Keywords: Heat transfer enhancement Performance experiments Helical baffled heat exchangers Circumferential overlap of baffles Incline angle of baffle
a b s t r a c t The trisection helical baffled shell-and-tube heat exchangers have structural features of more suitable to the equilateral triangular tube layouts and less baffle parts. In particular the circumferential overlap trisection helical baffled shell-and-tube heat exchangers are of anti-shortcut structure that accommodates one row tubes in each circumferential overlapped zone between adjacent baffles for dampening shortcut leakage. The performance tests were conducted on both oil–water and water–water heat transfer in heat exchangers with equilateral triangle tube layout of 16 tubes including five helical baffle schemes with incline angles of 12°, 16°, 20°, 24°, 28° and a segmental baffled one for comparison. The test results show that both the shell side heat transfer coefficient ho and pressure drop Dpo increase but the comprehensive index ho/Dpo decreases with the increase of the mass flow rate of all schemes; and that the shell side heat transfer coefficient, pressure drop and the comprehensive index ho/Dpo decrease with the increase of the baffle incline angle at certain mass flow rate, except that the curves of comprehensive index ho/Dpo of 12° and 16° helical baffle schemes are almost coincide. The average values of shell side heat transfer coefficient, the comprehensive index ho/Dpo of the 12° helical baffled scheme are about 50% higher than those of the segmental one with almost same pressure drop. The correlation equations for shell side Nusselt number and axial Euler number are presented varying with axial Reynolds number, Prandtl number and helical baffle incline angle. Ó 2015 Published by Elsevier Ltd.
1. Introduction The shell-and-tube heat exchangers (STHXs) are widely used in industries such as petroleum refining, chemical engineering, power plants and food processing, and most of them are segmental baffled type. The segmental baffled heat exchangers are mature in design and manufacture, robust and flexible for almost all heat and mass transfer processes; however, they have some drawbacks including stagnant zones, higher pressure drops, and a propensity to induce vibration and fouling. These problems could be ameliorated by replacing segmental baffles with the helical ones. Since Lutcha and Nemcansky [1] proposed the helical baffled heat exchangers (HSTHX) with quadrant sector baffles, many specialists and researchers studied the novel heat exchangers. The mostly investigated items are the optimum incline angle of the sector baffles and the baffle shapes and connection configurations. It is clear that the smaller the incline angle of the sector baffles are, the higher both the heat transfer coefficient and the pressure drop ⇑ Corresponding author. Tel.: +86 (0)13851729402. E-mail address: [email protected] (Y.-P. Chen). http://dx.doi.org/10.1016/j.enconman.2015.05.042 0196-8904/Ó 2015 Published by Elsevier Ltd.
are with increased velocity. Lutcha and Nemcansky [1] indicated that the optimum incline angle of the sector baffles is 40° in the chart of heat transfer coefficient ho versus pressure drop Dpo. However, Jafari Nasr and Shafeghat [2] obtained a fluctuated curve of heat transfer coefficient versus incline angle. Zhang et al. [3] investigated the performance of oil cooler with helical baffles (OCHB) and compared with that of the segmental one (OCSB) with practical size, and also found that the shell side heat transfer coefficients and the shell-side pressure drop of the OCHB are respectively lower than and far lower than those of the OCSB. Zeyninejad et al. [4] presented a site application result of a mid-overlapped helical baffle heat exchanger with 40° incline angled baffles and compared with a segmental one in a petrochemical plant, and the results indicated that the helical one had better comprehensive performance of the shell side heat transfer coefficient per unit pressure drop but its heat transfer coefficient was 15–57% lower than that of the segmental one at same flow rate. As the heat transfer coefficient is of vital importance to an application in fulfilling a certain task, so called optimum baffle incline angle of 40° as universal truth is questionable.
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
461
Nomenclature A cp d, D Eu G h K l Nu p Pr Q T,t Re
area (m2) specific heat (kJ kg1 K1) diameter (m) Euler number flow rate (kg s1) heat transfer coefficient (W m2 K1) overall heat transfer coefficient (W m2 K1) tube length (m) Nusselt number pressure (Pa) Prandtl number transferring heat (kJ) temperature (K, °C) Reynolds number
As the non-continuous helical baffles exhibit shortcut leakage flows at the conjunction of adjacent baffles, it is generally believed as one of major factors hindering heat transfer performance. Many improved methods pertaining to the shortcut leakage flow have been investigated experimentally or numerically. Stehlik et al. [5,6] suggested using axial overlap baffles to reduce the helix pitch while keeping greater baffle incline angle. Wang [7] studied flow fields of axial overlap baffled helical heat exchangers with positive assessment. Zhang et al. [8,9] simulated several shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles, and experimentally measured four middle overlapped schemes of helix heat exchangers with different tube lengths and cylinder diameters and found that the optimum scheme was the one with incline angle of 30°. Wang et al. [10] tried to block the triangular notches with plates, but the experimental results indicated that the comprehensive index of heat transfer coefficient per pressure drop was lower than that of the non-block scheme as the pressure drop increased much faster than the shell side heat transfer coefficient did. Dong and Chen [11] numerically simulated the flow and heat transfer performances of four middle-axial-overlap trisection helical baffled heat exchangers of 36° baffle incline angle and with different blockage configurations of the X-type notches at conjunction of adjacent baffles that blocking all triangular notches, only the outer triangular notches, the outermost strip notches and without any blockage. The results showed that the scheme blocked only the outmost strip notches had better comprehensive index of heat transfer coefficient per pressure drop and feasibility in installation. Cao et al. [12] numerically studied the impact of the overlap size on the heat transfer performance at certain helical pitch, and found that both the heat transfer coefficient and pressure drop increased with the increase of overlap size at identical mass flow rate, whereas the heat transfer coefficient decreased at identical pressure drop. It indicates that with identical helical pitch, the greater incline angled middle-overlap baffle scheme is inferior to the smaller incline angled end-to-end (adjacent baffles touching at periphery) baffle scheme in both evaluation indexes of heat transfer coefficient and heat transfer coefficient per pressure drop. Considering most heat exchangers adopt equilateral triangle tube layout, and the quadrant division does not suit the natural intervals of such tube layout, Chen [13] and Chen et al. [14] proposed trisection helical baffled heat exchangers, particularly the circumferential overlap trisection helical baffled shell-and-tube heat exchanger (cothSTHX) scheme, which put the straight edges of sector baffles in the natural intervals between tube rows with at least one row of tubes situated in the circumferential overlapped
Greek symbols b incline angle of helical baffles (°) Dp pressure drop (Pa, kPa) Dtm logarithmic mean temperature difference (K) k thermal conductivity (W m1 K1) l dynamic viscosity (kg m1 s1) q density (kg m3) Subscripts i tube side o shell side w wall h hydraulic seg segmental baffled scheme
area of adjacent baffles to minimize the short-cut leakage loss at triangular conjunction notches and to improve the rigidity of the heat exchanger tube bundle as well. The figures on the meridian, transverse and unfolded concentric hexagonal sections of the pressure or velocity nephograms with superimposed velocity vectors demonstrate clearly the secondary vortex flow and shortcut leakage flow patterns which are the key impact factors for heat transfer enhancement in the cothSTHXs. Chen et al. [15] also experimentally investigated the performances of five cothSTHXs with baffle incline angles from 20° to 32° and a segmental one for comparison. The results showed that the helical baffled scheme with incline angle 20° performed better than other schemes with both indexes of heat transfer coefficient and heat transfer coefficient per pressure drop. Dong et al. [16] numerically investigated four trisection helical baffled heat exchangers with identical helical pitch and tube layout but different baffle shapes or connections including a circumferential overlap (CO) scheme, an end-to-end (EE) scheme, a blocked V-notches (BV) scheme, and a middle axial overlap (MO) scheme. The results show that the CO scheme has the highest shell-side heat transfer coefficient and comprehensive index ho/Dpo; and the average values of comprehensive index ho/Dpo of CO scheme in the calculated range is respectively 16.5%, 27.3% and 13.5% higher than that of the EE, BV and MO schemes. Wen et al. [17] studied a ladder-type fold baffled heat exchangers which adopted two circumferential overlapped baffles in a helical cycle and also takes advantage of blocking part of the triangular leakage zones, and the simulation results showed that the thermal performance factor TEF enhanced by 28.4–30.7%. Wang et al. [18] summarized the recent development in helical baffle heat exchangers, and implied that the helical baffle heat exchangers would be evolved from the ones with discontinue baffles such as quadrant and trisection baffles to the continuous baffled ones with several very complicated structures. Nevertheless, the cost and manufacture feasibility are always the main considerations for real engineering applications, and what will be eventually populated is definitely the simple and concise one, which is the correct development or evolution direction guided by the pioneers Lutcha and Nemcansky [1] with their historical innovation of the quadrant helical baffle heat exchangers. The heat transfer performance prediction is very important for heat exchanger design and a lot of efforts [1–4,7,9,14,15] have been conducted on the performance study of HSTHXs, but very few correlation formulae have been presented. Seyed and Mahdi Saeedan [19] obtained Nusselt number and friction factor in the helical heat exchanger in terms of Reynolds number and volume fraction of Water–Al2O3 nanofluid using neural network, and presented the
462
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
results in figures and tables. Lahiri and Khalfe [20] adopted hybrid differential evolution and ant colony optimization technique for design optimization of shell and tube heat exchangers from economic point of view. Zhang et al. [9] presented experimental results of the shell side heat transfer coefficient of different baffle angled helical heat exchangers and correlated them with different coefficient c1 and exponent m1 in the formula (1).
Nu ¼ c1 Rem1 Pr 1=3
ð1Þ
Zhang LH et al. [21] performed experiment on heat exchangers with shell diameter of 500 mm and tube length of 6 m with helical baffle angles of 7°, 13° and 25° and a segmental one. The results showed that both the shell side heat transfer rate and the shell side pressure drop were at peak when helical angle equals 7°, while the shell side heat transfer rate per unit pressure drop at this angle was at the nadir. The result figures were presented with abscissa of both volume flow rate and Reynolds number of shell side fluid. As the trend lines of experimental performance data with different baffle angles are not continued or coincide in the figures with shell side Reynolds number abscissa, the shell side heat transfer coefficients of different angled helical baffle heat exchangers were correlated in the formula (1) with different coefficient c1 and exponent m1. The friction factors were presented in similar way. The performance formulae for HSTHX design are not easy to construct as there are so many influence factors with diverse configurations of the helical baffle structure and arrangement such as quadrant baffle and trisection one, end-to-end, axial overlap with different overlap size, circumferential overlap, folded baffle, blocked plate for the V-notch in adjacent baffle conjunctions and so on apart from the ordinary parameters of STHXs. For instance, the heat transfer coefficient and pressure drop could be very different with same baffle shape and incline angle but different axial overlap size in a same shell cylinder. Numerical simulation plays a crucial role in explaining how structural factors influence flow and heat transfer of a heat exchanger, and many experts [2,8,11,12,14,16,17,22] adopted 3D CFD methods for numerically simulation of variety helical baffled heat exchangers. However, experimental research is still an indispensable step before a new type of heat exchangers being put into use. The features of low pressure drop and higher heat transfer coefficient per pressure drop of helical baffled heat exchangers have been generally recognized; however, many literatures [3,4,9] showed that the heat transfer coefficients of helical baffled heat exchangers were inferior to that of the conventional segmental baffled heat exchangers at same shell side flow rate and tube layout. It means that the heat transfer capacity might be less than that of the segmental baffled one or more heat transfer areas should be used, thus it may not be accepted by industry users. Efforts must be taken to ensure heat transfer enhanced rather than only the comprehensive index increased in evaluation of any scheme in engineering applications. On this issue, the structure and installation configuration of the helical baffles should be reconsidered. The baffle incline angle needs to be reduced if the volume flow rate of the shell-side fluid is low, so that the fluid velocity can be increased to augment heat transfer coefficient by taking advantage of the low pressure drop feature of HSTHXs.
diagram and the photo of the test rig for heat transfer are shown in Fig. 1(a) and (b) respectively. The test rig includes two separate systems for both oil–water and water–water heat transfer. The tube-side fluid of the testing heat exchanger is municipal water, while the shell side fluid is heat transfer oil or hot water. The heat fluid raises pressure in a pump and is heated in an electric heater before entering the testing heat exchanger. The heating power is adjusted by solid state relay. As shown in the Fig. 1, an upper tank is installed above the circulation loop to provide a positive suction head for pump and also to compensate the volume expansion or contraction due to temperature variation. A bottom tank is set for accumulating the fluid drained from the testing heat exchanger for draining and filling the system before and after changing a tube
upper oil tank compressed air cooling water out
flowmeter
testing heat exchanger sight glass tube
cooling water in
p
elec. heater
bottom oil tank
filter pump
(a) Schematic diagram of test rig (oil-water)
2. Materials and methods 2.1. Performance test rig The experiments were conducted on five cothSTHXs with relatively small baffle incline angles ranging from 12° to 28° and a segmental baffled heat exchanger as a contrast. The schematic
(b) Photo of test rig (oil-water and water-water) Fig. 1. Schematic diagram of heat transfer test rig.
463
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
bundle core. To facilitate draining the fluid from testing heat exchanger, a compressed air line is connected to the system through a valve. A small pump is used to transport fliud from the bottom tank to the upper tank. The cylinder shell of the testing heat exchanger is a common one, while the tube bundle core could be replaced as shown in Fig. 2. Both sides of the heat exchanger are one-way layouts in counter flow directions. The inner diameter of the shell of the heat exchanger is £81 mm, and the diameter of the baffles is £80 mm; the effective geometry (outer diameter thickness length) of the heat transfer tubes is £10 mm 1 mm 832 mm, the number of heat transfer tubes is 16 and the tubes are equilateral triangularly arranged. There are also 3 sets of rods and spanning tubes for fixing the baffles. The other geometric parameters are shown in Table 1. The performance tests of heat transfer were conducted on five cothSTHXs with incline angles of 12°, 16°, 20°, 24° and 28° and a segmental baffled one. Fig. 3 shows the projection view of both
helical and segmental baffle shapes. Each helical baffle is angled to the axis of the heat exchanger and the baffle occupies more than one third cross section of the heat exchanger shell to put the straight edges of the baffles in the natural intervals between tube rows, and with adjacent baffles circumferential overlapped to accommodate a row of tubes for dampening reverse leakage. The adjacent baffles touch at the periphery, and forming a pseudo helix. 2.2. Experiment data process During the oil-to-water performance tests, the heating oil flow rate was adjusted by changing the oil pump motor frequency with an inverter from 25 Hz to 50 Hz with 5 Hz step; and the heating oil inlet temperature kept 60, 70 and 85 (±0.5) °C respectively controlled with a solid state relay to the electric heater. The inlet temperature and the flow rate of cooling water in tube-side were kept 11(±0.4) °C and 0.20 (±2.5%) kg/s respectively (Reynolds number about 2000). During the water-to-water performance tests, the hot water inlet temperature kept 50, 60 and 70 (±0.5) °C respectively, while the inlet temperature and the flow rate of cooling water in tube-side were kept 15.1 (±0.4) °C and 0.22 (±2.5%) kg/s respectively (Reynolds number about 2500). The overall heat transfer coefficient K can be obtained from the measuring data during the experiment of the flow rates, inlet and outlet temperatures of both heating and cooling fluids.
K¼
Qi þ Qo 2ADtm
ð2Þ
where Qi and Qo are the transferring heat at tube-side and shell-side respectively; A is the heat transfer area; Dtm is the logarithmic mean temperature difference. The turbulent flow of tube side heat transfer coefficient hi can be estimated by Gnielinski equation [23]
hi ¼
ki f w ðRei 1000ÞPri di 8
," 1 þ 12:7
# rffiffiffiffiffi f w 2=3 di 1þ Pri 1 2 l
From left to right: 12°, 16°, 20°, 24°, 28° and seg Fig. 2. Photo of tube bundles of testing heat exchangers.
ð3Þ where fw is the tube wall friction factor calculated by:
f w ¼ ð1:82 lg Rei 1:64Þ Table 1 Geometric parameters of testing helical and segmental baffled heat exchangers. Item
cothSTHX
Inclined angle (°) Baffle number Helical pitch (mm)
12 50 47.2
16 38 62.7
Segment STHX 20 30 78.8
24 25 95.8
28 21 113.9
0 10 75.5
2
ð4Þ
The physical properties of water are calculated with polynomial formula using mean temperature of fluids at the inlet and outlet of the heat exchanger as the characteristic variable. Then the heat transfer coefficient ho of shell side can be separated according to Eq. (5). Because the tube bundles of the testing heat exchangers are new, the fouling resistance is not considered.
Fig. 3. Projection view of helical (left) and segmental (right) baffles of testing heat exchangers.
464
1 1 K
do ddi ho i 2k ln
i
ð5Þ
do di
where do and di are the tube outer and inner diameters respectively, k is the thermal conductivity of material of the tubes. 2.3. Uncertainty analyses Both mass flow rate and volume flow rate of heating oil are measured with a MicroMotion F025 mass flow meter (uncertainty Table 2 Uncertainty calculation results.
±0.15%), while the volume flow rate of cooling water is measured with a turbo-flow-meter (uncertainty ±0.5%). The temperature is measured with platinum resistance thermometers (uncertainty ±0.15 °C). And the shell side pressure drop is measured with a Rosemount 3051S differential pressure transmitter (uncertainty ±0.15%). The temperature and pressure measuring points are arranged at the tubular bent conjunctions to the inlets and outlets of the testing heat exchanger. The experimental data were collected and processed through an Agilent 34970A data acquisition instrument to a computer with operation software programmed on the platform of LabView.The uncertainty of overall heat transfer coefficient K is estimated with Eq. (6).
eK ¼
Uncertainty item
Symbol
Unit
Value
Shell side inlet temperature Shell side outlet temperature Shell side mass flow rate Shell side pressure drop Tube side inlet temperature Tube side outlet temperature Tube side mass flow rate Shell side transferring heat Tube side transferring heat Average transferring heat Overall h.t.c.
eTo eTo eGo eDpo eTi eTi eGi eQo eQi eQ eK
% % % % % % % % % % %
±(0.21–0.22) ±(0.24–0.26) ±(0.15) ±(0.15) ±(1.37–1.43) ±(0.69–0.80) ±(0.5) ±(1.39–2.20) ±(1.67–2.19) ±(2.49–2.76) ±(4.60–6.45)
0
00
0
00
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2Q þ e2A þ e2Dtm
eQ ¼
pffiffiffiffiffiffiffiffiffiffiffiffi
eQ j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2Gj þ e2cp;j þ e2Dtj
eQi eQo
700
-1
Overall h.t.c. K /W m K
-2
340
300 280 260 240 220
12°
16°
20°
24°
28°
seg
ð7Þ ð8Þ
j¼i;o
The results of maximum uncertainties of some directly measured parameters and the overall heat transfer coefficient (h.t.c.) K are given in Table 2.
360
320
ð6Þ
The uncertainty of transferring heat Q is estimated with Eqs. (7) and (8).
H.t.c. of shell side h o /W m-2 K-1
ho ¼ h
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
12°
16°
20°
24°
28°
seg
600
500
400
300
200 180
0.2
0.25
0.3
0.35
0.4
0.45
200 0.2
0.5
0.4
0.45
(a) Oil-water
0.5
10000 12°
16°
20°
24°
28°
seg
H.t.c. of shell side h o / W·m-2·K-1
Overall h.t.c. K / W·m-2·K-1
0.35
(a) Oil-water
940
900
860
820 0.22
0.3
Flow rate of shell side G o /kg s-1
-1
980
0.25
Flow rate of shell side Go /kg s
0.26
0.3
0.34
0.38
0.42
0.46
9000
12°
16°
20°
24°
28°
seg
8000 7000 6000 5000 4000 3000 0.22
0.26
0.3
0.34
0.38
0.42
Flow rate of shell side Go / kg· s
Flow rate of shell side Go / kg· s-1
(b) Water-water
(b) Water-water
-1
Fig. 4. Overall heat transfer coefficient versus shell side flow rate.
0.46
Fig. 5. Shell side heat transfer coefficient versus shell side flow rate of six schemes.
465
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
3.1. Performances of heat transfer Taking into account all the experiments were completed within the same shell and both the size and the tube number of the replaceable tube bundles are identical, so the shell side flow rate Go is used reasonably as the independent variable for comparing characteristics of different schemes. The curves of the overall heat transfer coefficient (h.t.c.) K, shell side h.t.c. ho, pressure drop Dpo, the comprehensive index ho/Dpo are suggested to demonstrate the performances of both heat transfer and flow resistance of the different schemes. As there are too many data with all the schemes, for simplicity, only the results under the temperature 60 °C of heating fluid are presented in detail. Figs. 4–7 show the curves of the overall h.t.c. K, the shell side h.t.c. ho, the shell side pressure drop Dpo and the comprehensive index of ho/Dpo vary with the shell side flow rate Go for both oil-to-water (o–w) and water-to-water (w–w) heat transfer respectively. From the figures it could be seen that the overall h.t.c. K and the shell side h.t.c. ho and the shell side pressure
Pressure drop of shell side Δ po /kPa
36 32 28
12°
16°
20°
24°
28°
seg
40 35
12°
16°
20°
24°
28°
seg
30 25 20 15 10 0.2
0.3
0.4
0.5
Flow rate of shell side Go /kg s-1
(a) Oil-water 400
350
12°
16°
20°
24°
28°
seg
300
250
200
150 0.22
24
0.26
0.3
0.34
0.38
0.42
0.46
Flow rate of shell side Go /kg s-1
(b) Water-water
20
Fig. 7. Comprehensive index of ho Dp1 o versus shell side flow rate Go.
16 12 8 0.2
0.3
0.4
0.5
Flow rate of shell side Go /kg s -1
(a) Oil-water 40
Pressure drop of shell side Δp o / kPa
Comprehensive indexho·Δpo-1
3. Experimental results and discussions
45
Comprehensive indexho·Δpo-1
Table 2 shows that the maximum uncertainty of the overall heat transfer coefficient K is ±6.45%, thus the experiment data are effective and reliable.
12°
16°
20°
24°
28°
seg
35
30
25
20
15
10 0.22
0.26
0.3
0.34
0.38
0.42
0.46
Flow rate of shell side G o / kg·s-1
(b) Water-water Fig. 6. Shell side pressure drop versus shell side flow rate of six schemes.
drop Dpo increase with the increase of the shell side flow rate Go for all schemes and they also increase with the decrease of the baffle incline angle at constant flow rate for the helical schemes. The segmental baffled scheme has the lowest in oil–water and second lowest in water–water average values of overall h.t.c. and shell side h.t.c. and the second highest average value of shell side pressure drop. As the flow rate is changed with pump frequency inverter in steps without any other valve control, it can be seen from the Fig. 6 that the flow rate increases but the pressure drop reduces somewhat with the increase of the baffle angle with the same pump frequency. Fig. 7 shows that the curves of the comprehensive index of ho/Dpo of the 12° and 16° helical baffled schemes are tied for first, followed with 20°, 24° and 28° helical baffled schemes sequentially, and with the segmental baffled scheme ranks the last. It shows that the curves of ho/Dpo decrease with the increase of the shell side flow rate for all schemes. The average values of the ratios of overall h.t.c. K, shell side h.t.c. ho, pressure drops Dpo and comprehensive index ho Dp1 o of all the helical baffled schemes over the trend curves of those of the segmental baffled scheme are shown in Table 3. The results indicate that the smaller the baffle incline angle is, the higher the overall h.t.c., shell side h.t.c. and pressure drop of the testing helical baffled schemes are. The shell side h.t.c. ho and comprehensive index ho Dp1 o of the 12° helical scheme are about 50% higher than those of the segmental baffled scheme with approximate pressure drop, which are quite attractive indicating the superior features of the cothSTHXs. The results indicated that it is no need for cothSTHXs
466
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Table 3 Average relative performance values of helical schemes over segmental scheme. Items/scheme
12°
16°
20°
24°
28°
o–w
Overall h.t.c. K Shell side h.t.c. ho Shell side pressure drop Dpo Comprehensive index ho Dp1 o
1.338 1.613 1.035 1.557
1.259 1.448 0.890 1.533
1.188 1.290 0.917 1.404
1.099 1.146 0.873 1.310
1.024 1.030 0.834 1.232
w–w
Overall h.t.c. K Shell side h.t.c. ho Shell side pressure drop Dpo Comprehensive index ho Dp1 o
1.075 1.637 1.098 1.491
1.065 1.432 0.969 1.478
1.034 1.241 0.886 1.399
1.017 1.089 0.818 1.332
0.992 0.968 0.768 1.260
3.2. Correlation of the testing results For correlation the testing results, dimensionless criteria numbers have to be applied. Because the shell-side Reynolds number Reo demonstrates no additional merit but difficult in calculating the cross section of the helical channel, the shell-side axial Reynolds number Rezo defined in Eq. (9) is used reasonably as the independent variable for comparing different schemes, which
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
60 55 50
Nuo
45 40 35 30 25 20 0.5
1
1.5
2
2.5
3
3.5
4
actually corresponds to the flow rate in the shell side. The axial velocity wo for calculation of Rezo is calculated with Eq. (10). The shell-side Nusselt number Nuo and the shell-side hydraulic diameter dho are defined respectively in Eqs. (11) and (12). For the similar reason that the friction factor needs to know the length of the helical channel which is quite difficult to determine with diverse configurations of baffle shapes and conjunctions, the shell-side axial Euler number Euzo is adopted and defined in Eq. (13) which is a dimensionless criterion that reflects the shell side flow friction factor of different baffle schemes based on the Fanning formula. The shell side pressure drop could be determined from the Eq. (13) as long as the shell-side axial Euler number Euzo is obtained from the correlation equation.
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
0.45
0.4
Euzo
to deliberately pursue large baffle incline angle with greater difficulty in manufacturing helical baffles for small volumetric liquid fluids. The lower increment of overall h.t.c. in water–water heat transfer lies in that the control thermal resistance is at tube side.
0.35
0.3
0.25
0.2 0.5
4.5
1
1.5
Rezo
130
Nuo
3.5
4
4.5
110 90
70
5000
0.65
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70
0.6 0.55
Euzo
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70 4000
3
(a) Oil-water
150
3000
2.5
Rezo
(a) Oil-water
50 2000
2
0.5
0.45 0.4 0.35 0.3 2000
3000
4000
Rezo
Rezo
(b) Water-water
(b) Water-water
Fig. 8. Shell side Nusselt numbers versus shell side axial Reynolds number.
5000
Fig. 9. Shell side axial Euler numbers versus shell side axial Reynolds number.
467
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Rezo ¼ wo ¼
ð9Þ
m 4 Go ðD2s
pq
Nuo ¼
dho
wo do
2
ð10Þ
2
Ndo ndr Þ
ho dho ko
ð11Þ
pffiffiffi pffiffiffi 2 3a2 =4 p do =8 2 3a2 ¼4 ¼ do p do =2 p do
Euzo ¼
ð12Þ
2Dpo g qo w2o
ð13Þ
where Go is the mass flow rate of the shell side; Ds, dr and a are the shell inner diameter, the spanning tube diameter and the tube pitch respectively; N and n are the tube number and rod number in the radius of the shell respectively. Figs. 8 and 9 show the shell side Nusselt number Nuo and the shell side axial Euler number Euzo vary with the shell side axial Reynolds number Rezo of three cothSTHXs with baffle angles of 12°, 20° and 28° and a segmental one for both oil-to-water (o–w) and water-to-water (w–w) heat transfer. The inlet temperatures of heating fluids are set 85, 70 and 60 °C for oil-to-water and 70, 60 and 50 °C for water-to-water heat transfer. Unlike the
linear-like increasing curves of Nusselt number, each curve of Euler number has shape decrease gradient at smaller axial Reynolds number and then falls slower with the increase of axial Reynolds number. The Nusselt number Nuo increases somewhat with increased inlet temperature of the heating oil but decreases somewhat with increased inlet temperature of the hot water with the identical pump frequency and same heat exchanger core scheme due to the different dynamic viscosity features of oil and water. Fig. 10 shows the comprehensive index of Nuo Re1 zo varies with the shell side axial Reynolds number Rezo of these schemes. The positive proportional trend of the curves of comprehensive index Nuo Eu1 zo versus Reynolds number is quite different from that of the decreased trend of the comprehensive index ho Dp1 o versus shell side flow rate as shown in Fig. 7. The shell side Nusselt number of cothSTHX for both oil and water are respectively correlated in Eqs. (14) and (15) in consideration of the impact factors of axial Reynolds number, Prandtl number, dynamic viscosity, and incline angle of helical baffles. 1=3 1 Nuo ¼ c1 Rem zo Pr o ðsin bÞ
m2
1=3 1 Nuo ¼ c1 Rem zo Pr o ðsin bÞ
m2
m4 3 Euzo ¼ c2 Rem zo Pr o ðsin bÞ
150 130 110 90 70 50
ð15Þ
m5
ð16Þ
55 50
106% 40
94% 35 30 25 20
1
1.5
2
2.5
3
3.5
4
4.5
20
25
30
35
160
240 200 160 120
5000
Rezo
(b) Water-water Fig. 10. Comprehensive indexes Nuo Eu1 zo versus shell side axial Reynolds number.
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70
140 120
Nuo,exp
12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70 seg-50 seg-60 seg-70
280
-1
45
50
55
60
65
(a) Oil-water
320
4000
40
Nuo,cal
(a) Oil-water
3000
12°-85 20°-85 28°-85 12°-70 20°-70 28°-70 12°-60 20°-60 28°-60
45
Rezo
Nu o·Eu zo
ð14Þ
60
Nuo,exp
12°-85 20°-85 28°-85 seg-85 12°-70 20°-70 28°-70 seg-70 12°-60 20°-60 28°-60 seg-60
170
80 2000
0:14
65
190
Nu o·Eu zo-1
lo lw
The shell side Euler number of cothSTHX is correlated in Eq. (16).
210
30 0.5
100
110
90%
80 60 40 40
60
80
100
120
140
160
Nuo,cal
(b) Water-water Fig. 11. Comparison of values of shell side Nusselt number Nuo from correlation equations with experimental ones.
468
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469
Table 4 Correlated coefficients and exponents in the Eqs. (14)–(16).
o–w, Eqs. (14) and (16) w–w, Eqs. (15) and (16)
4. Conclusion
c1
m1
m2
c2
m3
m4
m5
58 0.99
0.5 0.8
0.4 0.6
1.62 13.5
0.5 0.4
0.6 0.5
0.22 0.4
0.45
Euzo,exp
0.4
0.35
106%
0.3
12°-85 20°-85 28°-85 12°-70 20°-70 28°-70 12°-60 20°-60 28°-60
94%
0.25
0.2 0.2
0.25
0.3
0.35
0.4
0.45
Euzo,cal
(1) The heat transfer performances of both heat transfer oil to cooling water and hot water to cooling water with different testing schemes were conducted on a test rig. The testing schemes include five circumferential overlap trisection helical baffle heat exchangers (cothSTHXs) with incline angles of 12°, 16°, 20°, 24°, 28° and a segmental baffled one. (2) The heat transfer performance test results are presented including both overall h.t.c. K and shell side h.t.c. ho, pressure drop Dpo and the comprehensive index ho/Dpo vary with the shell side flow rate. In the testing scope, the small angled helical scheme demonstrates better performance that the shell side heat transfer coefficient ho and comprehensive index ho Dp1 of the 12° helical scheme are about 50% o higher than those of the segmental baffled one with approximate pressure drop in both oil–water and water–water tests, which also verifies the superior heat transfer features of the cothSTHXs. (3) The correlation equations of shell side Nusselt number and shell side axial Euler number are presented with variables of shell side axial Reynolds number, Prandtl number and the incline angle of helical baffles at both turbulent and laminar flow ranges, and the deviations are less than ±5% to ±10%.
(a) Oil-water Acknowledgement
0.65 12°-50 20°-50 28°-50 12°-60 20°-60 28°-60 12°-70 20°-70 28°-70
0.6
Euzo,exp
0.55 0.5
This work is supported by the National Nature Science Foundation Programs of China (51276035 and 51206022).
105%
References
95%
0.45 0.4 0.35 0.3 0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Euzo,cal
(b) Water-water Fig. 12. Comparison of values of shell side axial Euler number Euzo from correlation equation with experimental ones.
where b is the incline angle of helical baffles; l and Pr are the dynamic viscosity and Prandtl number of fluid; the subscripts o and w refer respectively properties of shell side fluid at the mean temperature and at wall temperature. The Table 4 shows the correlated coefficients and exponents in the Eqs. (14)–(16) from the experimental results of heat transfer with both heating oil to cooling water (o–w) and hot water to cooling water (w–w) in the cothSTHXs. The testing ranges of shell side axial Reynolds numbers of both oil–water and water–water heat transfer are from 0.5 to 4.5 and from 2200 to 5200, indicating at laminar flow and turbulent flow respectively. The Figs. 11 and 12 show the calculation results with correlation Eqs. (14)–(16) compared with the experimental results of the shell side Nusselt number and axial Euler number in both oil–water and water–water heat transfer in the cothSTHXs. The figures show that the deviations are within ±5% to ±10% which verifies that the correlation equation patterns presented in this paper are applicable.
[1] Lutcha J, Nemcansky J. Performance improvement of tubular heat exchangers by helical baffles. Chem Eng Res Des 1990;68(3):263–70. [2] Jafari Nasr MR, Shafeghat A. Fluid flow analysis and extension of rapid design algorithm for helical baffle heat exchangers. Appl Therm Eng 2008;28(11– 12):1324–32. [3] Zhang JF, Guo SL, Li ZZ, Wang JP, He YL, Tao WQ. Experimental performance comparison of shell-and-tube oil coolers with overlapped helical baffles and segmental baffles. Appl Therm Eng 2013;58:336–43. [4] Zeyninejad MS, Nemati TF, Razmi K, Tasouji AR. Tube bundle replacement for segmental and helical shell and tube heat exchangers: Performance comparison and fouling investigation on the shell side. Appl Therm Eng 2013;51:1162–9. [5] Stehlik P, Nemcansky J, Kral D. Comparison of correction factors for shell-andtube heat exchangers with segmental or helical baffles. Heat Transfer Eng 1994;15(1):55–65. [6] Stehlik P, Wadekar V. Different strategies to improve industrial heat exchange. Heat Transfer Eng 2002;23(6):36–48. [7] Wang SL. Hydrodynamic studies on heat exchangers with helical baffles. Heat Transfer Eng 2002;23(3):43–9. [8] Zhang JF, He YL, Tao WQ. 3D numerical simulation on shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles-Part II: Simulation results of periodic model and comparison between continuous and noncontinuous helical baffles. Int J Heat Mass Transfer 2009;52(23– 24):5381–9. [9] Zhang JF, Li B, Huang WJ, Lei YG, He YL, Tao WQ. Experimental performance comparison of shell side heat transfer for shell-and-tube Heat exchangers with middle-overlapped helical baffles and segmental baffles. Chem Eng Sci 2009;64(8):1643–53. [10] Wang L, Luo LQ, Wang QW, Zeng M, Tao WQ. Effect of inserting block plates on pressure drop and heat transfer in shell-and-tube heat exchangers with helical baffles. J Eng Thermophys 2001;22(s):173–6 (in Chinese). [11] Dong C, Chen YP. Impact of block plates on the flow and heat transfer performance of middle-axial-overlap helical baffle heat exchangers. J Mech Eng 2014;50(6):135–40 (in Chinese). [12] Cao X, Du WJ, Ji S. Effects of baffle connection manner on shell side performance of heat exchanger with helical baffles. CIESC J 2011;62(12): 3367–72. [13] Chen YP. A novel helix baffled heat exchanger suitable for tube bundle arrangement with equilateral triangles. Petro-Chem Equip 2008;37(6):1–5 (in Chinese). [14] Chen YP, Sheng YJ, Dong C, Wu JF. Numerical simulation on flow field in circumferential overlap trisection helical baffle heat exchanger. Appl Therm Eng 2013;50:1035–43.
Y.-P. Chen et al. / Energy Conversion and Management 101 (2015) 460–469 [15] Chen YP, Cao RB, Wu JF, Dong C, Sheng YJ. Experimental study on shell side heat transfer performance of circumferential overlap trisection helical baffle heat exchangers. In: Proceedings of the ASME 2011 international mechanical engineering congress and exposition. IMECE2011-63254, Denver, Colorado, USA; Nov 2011. [16] Dong C, Chen YP, Wu JF. Influence of baffle configurations on flow and heat transfer characteristics of trisection helical baffle heat exchangers. Energy Convers Manage 2014;88:251–8. [17] Wen J, Yang HZ, Wang SM, Xu SF, Xue YL, Tuo HF. Numerical investigation on baffle configuration improvement of the heat exchanger with helical baffles. Energy Convers Manage 2015;89:438–48. [18] Wang QW, Zeng M, Ma T, Du XP, Yang JF. Recent development and application of several high-efficiency surface heat exchangers for energy conversion and utilization. Appl Energy 2014;135:748–77.
469
[19] Seyed MB, Mahdi Saeedan MH. Prediction of Nusselt number and friction factor of water–Al2O3 nanofluid flow in shell-and-tube heat exchanger with helical baffles. Chem Eng Commun 2015;202:260–8. [20] Lahiri SK, Khalfe N. Improve shell and tube heat exchangers design by hybrid differential evolution and ant colony optimization technique. Asia-Pac J Chem Eng 2014;9:431–48. [21] Zhang LH, Xia YM, Jiang B, Xiao XM, Yang XL. Pilot experimental study on shell and tube heat exchangers with small-angles helical baffles. Chem Eng Proc 2013;69:112–8. [22] Andrews MJ, Master BI. Three-dimensional modeling of a helixchanger heat exchanger using CFD. Heat Trans Eng 2005;26(6):22–31. [23] Gnielinski V. New equations for heat mass transfer in turbulent pipe and channel flows. Int Chem Eng 1976;16:359–68.