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Heat transfer and pressure drop performance of twisted oval tube heat exchanger
Applied Thermal Engineering 50 (2013) 374e383
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Heat transfer and pressure drop performance of twisted oval tube heat exchanger Xiang-hui Tan, Dong-sheng Zhu*, Guo-yan Zhou*, Li-ding Zeng Key Laboratory of Pressure Systems and Safety of Ministry of Education, School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, PR China
h i g h l i g h t s < Experimental study of the tube side heat transfer and pressure drop performance of a twisted oval tube heat exchanger. < Experimental study of the shell side heat transfer and pressure drop performance of a twisted oval tube heat exchanger. < Comparatively study of the shell side performance of a twisted oval tube heat exchanger with a rod baffle heat exchanger. < Analyzing of the overall performance of the twisted oval tube heat exchanger.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 January 2012 Accepted 21 June 2012 Available online 29 June 2012
Twisted oval tube heat exchanger is a type of heat exchanger that aims at improving the heat transfer coefficient of the tube side and also decreasing the pressure drop of the shell side. In the present work, tube side and shell side heat transfer and pressure drop performances of a twisted oval tube heat exchanger has been experimentally studied. The tube side study shows that the tube side heat transfer coefficient and pressure drop in a twisted oval tube are both higher than in a smooth round tube. The shell side study shows that the lower the modified Froude number FrM, the higher the shell side heat transfer coefficient and pressure drop. In order to comparatively analyze its shell side performance of the heat exchanger, a rod baffle heat exchanger with similar size of the twisted oval tube heat exchanger is designed and its performance is calculated with Gentry’s method. The comparative study shows that the heat transfer coefficient of the twisted oval tube heat exchanger is higher and the pressure drop is lower than the rod baffle heat exchanger. In order to evaluate the overall performance of the twisted oval tube heat exchanger, a performance evaluation criterion considering both the tube side and shell side performance of a heat exchanger is proposed and applied. The analyze of the overall performance of the twisted oval tube shows that the twisted oval tube heat exchangers works more effective at low tube side flow rate and high shell side flow rate. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Twisted oval tube heat exchanger Heat transfer performance Pressure drop performance Overall performance
1. Introduction Heat transfer enhancement technique is a very important technique to improve the efficiency of heat exchangers. From the point of energy saving, improving the efficiency of heat exchangers can be realized in two ways: promoting the heat transfer coefficient to decrease the heat transfer area, decreasing the pressure drop to save the cost of pump. Both active and passive techniques were used to increase the heat transfer coefficient of a heat exchanger over a century ago [1,2]. Twisted oval tube heat exchanger is a type of
* Corresponding authors. Tel./fax: þ86 21 64253708. E-mail addresses: [email protected] (D.-s. Zhu), [email protected] (G.-y. Zhou). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.037
heat exchanger that aims at promoting the heat transfer coefficient of the tube side and also decreasing the pressure drop of the shell side. Applications of the twisted oval tube in chemical field can also be found in [3]. Nowadays, more and more attention are paid on the performance of the twisted oval tube heat exchanger [4,5]. Tubes that play an important role in this heat transfer enhancement technique are made from normal round tubes. They are formed into an oval section with a superimposed twist by some special techniques. Two ends of the tubes remain round on the consideration of assembling them with the tube sheet. Sketch of this tube can be found in Fig. 1a. Geometrical parameters of the twisted oval tube are 360 twist pitch(S), major axis (A) of the oval section and minor axis (B) of the oval section. As has been shown in Fig. 1b, when the tubes are arrayed in a same direction, they can be supported by the tubes themselves but not baffles or rods that
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Nomenclature A Ac As At B Cp d de dh dm f F FrM gM G h j jl jt K Kb L m n Nr Nu Pr Q T Re
major axis of the twisted oval tube, m sectional area, m2 shell side flow area, m2 tube side flow area, m2 minor axis of the twisted oval tube, m specific heat, J/(kg$K) smooth round tube diameter, m equivalent diameter, m hydraulic diameter, m logarithmic mean diameter, m friction factor heat transfer area, m2 modified Froude number maximum centrifugal acceleration, m/s2 mass flow rate, kg/s heat transfer coefficient, W/(m2$K) heat transfer factor j factor- laminar flow j factor- turbulent flow overall heat transfer coefficient,W/(m2$K) pressure drop coefficient length of tube, m constants for fitting correlations constants for fitting correlations rod baffle number Nusselt number Prandtl number heat duty, W temperature, K Reynolds number
a normal shell tube heat exchanger needs. This special geometrical characteristic can form a longitude flow channel which will considerably reduce the pressure drop of the heat exchanger. From the point of analyzing the heat transfer and pressure drop performance of the tube side of a twisted oval tube heat exchanger, Asmantas et al. [6] tested the performance of twisted oval tube to
Fig. 1. Sketch of twisted oval tube and self supported twisted oval tubes a. Sketch of twisted oval tube. b. Sketch of self supported oval tubes.
S Tf Tw u uq,max V
375
360 twist pitch, m fluid temperature, K wall temperature, K velocity, m/s maximum tangential velocity, m/s volume flow rate, m3/s
Greek symbols DP total pressure drop, Pa DPb baffle flow pressure drop, Pa DPl longitude flow pressure drop, Pa DTm Logarithmic mean temperature difference, K h overall performance hM modified overall performance l thermal conductivity, W/(m$K) m dynamic viscosity, Pa s r density, kg/m3 4 viscosity correction factor Subscripts b baffle flow l longitude flow t tube side s shell side M modified h hydraulic j heat transfer factor f friction factor o outlet/outer side i inlet/inner side w wall
get the heat transfer and pressure drop correlations in the early stage. Considering the effect of Pr and geometrical parameters on the performance of the twisted oval tube, Si et al. and Gao et al. [7,8] tested the performance of twisted oval tubes with different A, B and S in turbulent state. In their experiments, diesel oil, water and air are all chosen as the flowing media. Their result shows that the twisted oval tube will perform better at low Re and high viscosity. Bishara et al. [9] simulated the laminar flow in a twisted oval tube at Re < 1200. They found that it is the secondary flow that caused by the torsion of the tubes that resulted in the heat transfer enhancement and pressure drop increment. Gao et al. [10] also studied the phenomenon of boiling when the twisted oval tube technique is combined with porous media technique. On the purpose of obtaining the heat transfer and pressure drop correlations, Meng et al. [11] also studied the flow in a twisted oval tube numerically at Re ¼ 500e1500. Yang et al. [12] studied the performance of the twisted oval tube from laminar state to turbulent state. Performances of the twisted oval tube were also compared with normal round tube in their study. Results show that the heat transfer coefficient and pressure drop of a twisted oval tube are both higher than a smooth round tube. Correlations that reflect the heat transfer and pressure drop performance of twisted oval tube heat exchanger have also been reviewed by Yang et al. [12]. On the aspect of the shell side, many researches focused on the research of turbulent intensity [13], boundary layer depth [14] and heat diffusion coefficient [15]. Numerical models for predicting the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger has also been published in the past few decades [16]. Based on the shell side heat and fluid flow
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characteristics of the twisted oval tube heat exchanger [17], optimization methods for the twisted oval tube heat exchanger have also been proposed [18]. Influenced by the centrifugal force field, criterions that characterize the twisting of the flow in the twisted oval tube bundle are Reynolds number Re and Froude number Fr. Fr can be calculated asFr ¼ u2s =ðdh;t;o gM Þ.WheregM ¼ 2u2q;max =A. Considering the time cost when the fluid flow past a helical pitch with uq,max is the same with the time cost when the fluid flow past axial length S with us. So uq,max can be calculated as: uq;max ¼ pAus =S.Then Fr can be expressed asFr ¼ S2 =ð2p2 Adh;t;o Þ. Omitting the constant 2p2, the modified Froude number FrM can be defined asFrM ¼ S2 =ðAdh;t;o Þ. Based on this, experimental and numerical studies have also been applied on the purpose of obtaining the shell side heat transfer and pressure drop correlations of the twisted oval tube heat exchanger [7,19e21]. Correlations of the shell side heat transfer factor and friction factor can be found in Si et al.’s [7] and Dzyubenko et al.’s [19e21] research in Table 1. Among these three sets of correlations, two sets of Dzyubenko et al.’s correlations are derived based on a heat exchanger with a hexagonal shell. It is also the same with the present study. Their correlations are fitted in the range of FrM ¼ 64,231 < FrM < 392 and 232 < FrM<2440 as described in Table 1. From all of the above we can find that most of the researches focused on the heat transfer and pressure drop of just one side of the twisted oval tube heat exchanger. Only the tube side performance of the twisted oval tube heat exchanger has been compared with traditional shell-tube heat exchangers. Nevertheless, when twisted oval tube technique is used as a heat transfer enhancement technique, two sides of the heat transfer and pressure drop performances will both be different from traditional heat exchangers. So the evaluation of the twisted oval tube heat exchanger should be carried out based on the performance of the two sides of the heat exchanger. Aiming at obtaining the overall performance of the twisted oval tube heat exchanger, the heat transfer and pressure drop performance of the two sides of the twisted oval tube heat exchanger will be experimentally studied in the present work. A rod baffle heat exchanger will be designed and compared to analyze the overall performance of the tested twisted oval tube heat exchanger. Also a new criterion for evaluating the overall performance of heat exchangers will be established and used to evaluate the performance of twisted oval tube heat exchanger.
2. Experimental study of tube side heat transfer and pressure drop performance 2.1. Tube side experimental apparatus and data reduction 2.1.1. Experimental apparatus An experimental system for testing the heat transfer coefficient and pressure drop performance of a twisted oval tube is illustrated in Fig. 2. A double-pipe heat exchanger with hot water flowing in the shell side and cold water flowing in the tube side is applied. The outer tube of the heat exchanger is a round tube with inner diameter equals 40 mm and wall thickness equals 2.5 mm. The inner tube is twisted oval tube. Detailed sectional parameters of the double tube heat exchanger can be found in Fig. 3 Units in Fig. 3 are mm. Before the tests start, water in hot water tank would be heated by the steam which flows in the coiled pipes, and also it will be self circulated by a centrifugal pump to ensure the homogeneity of temperature. Both the cold water tank and hot water tank are equipped to 30 m3 to fulfill the demand of water during the tests. Length of the tested section is 3 m. The upstream tube section of the tested tube is made long and straight in order to ensure a fully developed flow. Shut-off valves are installed to regulate the velocity of the hot water and cold water. The whole system including the two tanks, the test section and the pipes that connect all of them are wrapped with glass fiber to insulate them from the surroundings. Parameters that measured are shell/tube side volume flow rate, shell/tube side inlet/outlet bulk temperature and tube side pressure drop. All of the temperatures are measured with T-type thermocouples which are calibrated in a same temperature with an accuracy of 0.25%. Two electromagnetic flow meters with an uncertainty of 0.5% are equipped to measure the shell/tube side flow rate. Pressure drop of the tested twisted oval tube is measured using the differential pressure transmitter with an accuracy of 0.075%. In addition, the measurement uncertainties of tube diameter and tube length are about 0.5% and 0.04%, respectively. The relative accuracy of each physical parameter is about 0.5%. During the tests, cold water in the tube side is pumped from the cold water tank, and it is heated in the double-pipe heat exchanger by the hot water which flows in the shell side. The shell side flow rate is fixed at its maximum value and tube side flow rate is regulated to ensure that the temperature of the shell side water changes little. It means that the shell side Re and Pr can be assumed as constants. For each test run with a constant shell and tube side flow rate, the system is assumed to be in a steady state on the
Table 1 Shell side heat transfer and pressure drop correlations of twisted oval tube heat exchangers. Researchers
Range and parameters
Si Qin et al. [6]
7 tubes Shell diameter 0.08 m S/de ¼ 6.86e11.9 FrM ¼ 231e392 2000 < Re<104 Fluid: Water and oil 37 tubes FrM ¼ 232e2440 Hexagonal shell Fluid: air 2000 < Re<5 104 37 tubes FrM ¼ 64 Hexagonal shell Fluid: air 2000 < Re<5 104
Dzyubenko et al. [18,19]
Dzyubenkoet al. [20]
Correlations 0:4347 ð1 þ 3:6Fr 0:357 ÞPr0:33 Nu ¼ 0:2379Re0:7602 FrM M 0:078 ð1 þ 3:6Fr 0:357 Þ f ¼ 9:461Re0:4928 FrM M
0:357 Þ Nu ¼ 0:023Re0:8 ð1 þ 3:6FrM 0:357 Þ f ¼ 0:3164Re0:25 ð1 þ 3:6FrM
Nu ¼ 0:0521Re0:8 Pr0:4 f ¼ 1.095Re0.25
Tw Tf
!0:55
Tw Tf
!0:55 Pr0:4
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1.Tube side flow meter 3.Cold water pump
2.Tube side valve 4.Cold water tank
5. Differential pressure transmitter
6.Hot water tank
7.Coiled pipe 8.Hot water pump 9. Shell side valve
10. Shell side flow meter
11. Data Acquisition System 12. Twisted oval tube 13. Twisted oval tube heat exchanger Tube side fluid Shell side fluid Measurement *
Testing point of temperature ×
Testing point of pressure
Fig. 2. Testing system of the tube side heat transfer and pressure drop performance.
condition that all temperature fluctuations of not exceed 0.2 C, and the fluctuation of the pressure difference is less than 1%. A smooth round tube and a twisted oval tube made from the former one are tested with the testing system introduced above. All of the tubes are made of stainless steel with a length of 3 m. Inner and outer diameter of the round tube is 25 mm and 20 mm respectively. The twisted oval tube which is made from the smooth round tube has an oval section. As shown in Fig. 1a, major axis A and minor axis B of the twisted oval tube is 29 mm and 19.5 mm, respectively. The wall thickness is 2.5 mm. The 360 twist pitch is 230 mm. 2.1.2. Data reduction method The fouling resistance of the double-tube heat exchanger is assumed to be zero. From Fourier Law and basic equations of heat transfer process, heat transfer coefficient of the double tube heat exchanger K can be derived as follow:
Qt ¼ Gt Cp;t Tc;o Tc;i
(3b)
Considering the hot fluid flows in the shell side, and there may still exists little heat elimination, Q is assumed to be equal withQt. Because that the twisted oval tube is made from a smooth round tube, the heat transfer area of the tested heat exchanger is calculated as:
F ¼ pdr;o Lt
(4)
Logarithmic mean temperature difference DTm and logarithmic mean diameter dm are calculated as:
DTm ¼
Ts;o Tt;i Ts;i Tt;o ln Ts;o Tt;i Ts;i Tt;o
dh;t;o dh;t;i ln dh;t;o =dh;t;i
(5)
K ¼ Q =ðF DTm Þ
(1)
dm ¼
dr;i ddm 1 1 ¼ þ þ K ht dr;o lw dr;o hs
(2)
Heat transfer performance of fluid flowing in the tube/shell side of the above heat exchanger can be calculated as:
Where ht and hs are the tube side and shell side heat transfer coefficient, respectively. Q is the heat duty. Shell side and tube side heat duty, Qs and Qt can be calculated as:
ht ¼
Qs ¼ Gs Cp;s Th;i Th;o
hs ¼
(3a)
lt dh;t;i
ls dh;s
jt Pr0:4 ¼ t
js Pr0:3 ¼ s
(6)
lt
n
dh;t;i
ls dh;s
mt;j Ret t:j Pr0:4 t
n ;j
ms;j Res s Pr0:3 s
(7)
(8)
Where ht and hs are the Nusselt number of tube side and shell side, respectively. jt and js are tube side and shell side heat transfer factors, respectively. Exponent of Pr are set as 0.4 and 0.3 for fluid that to be heated and cooled, respectively. From Eq. (8) and considering that the shell side Re and Pr is assumed as constants, the heat transfer coefficient of the shell side can be assumed to be a constant. By definingC ¼ 1/ho þ (ddm)/(ldt,o), Eq. (2) can be derived as:
lt 1 n ¼ m Re t;j Pr0:4 t þC K dt;o t;j t Fig. 3. Sketch of shell side cross section of the double tube heat exchanger.
Pressure drop DPt of the tested tubes can be expressed as:
(9)
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DPt ¼ ft
Lt rt u2t dt;i 2
(10)
a
Where ft is the friction factor of the tested tube, ft, ut and Ret can be expressed as:
Vt At
Ret ¼
rt ut dh;t ; mt
(11)
Hydraulic diameters that mentioned above are all calculated with the following method:
dh ¼
4 Ac C
Nusselt number Nu
ut ¼
200
100
(12) 30
So sets of (Ret,K) and (Ret,ft) can be obtained after the experimental tests. With the help of least square method, mt,h, nt,h, C, mt,f, nt,f can be fitted. And the heat transfer coefficient and pressure drop correlations of the tested tubes can be directly derived. Similar testing method and data reduction method can also be found [12]. The uncertainty is estimated with the method suggested by Moffat [22] and Kline [23]. According to the accuracy of the testing apparatuses and the data reduction method the uncertainty of overall heat transfer coefficient and pressure drop are 7.5% and 4.8%, respectively. This degree of accuracy can be accepted by the industry. 2.2. Results and discussions of the tube side heat transfer and pressure drop performance 2.2.1. Verification of the testing system Heat transfer factor and friction factor correlations (shown in Eq. (13a) and Eq. (13b)) of the smooth round tube in a turbulent state are fitted in order to confirm the reliability of the testing system. The Correlations are compared with the predictions of DittuseBoelter correlation (Eq. (14a)) and Blasius correlation (Eq. (14b)) in Fig. 4a and b
j ¼ 0:0420Re0:74
(13a)
f ¼ 0:3474Re0:26
(13b)
j ¼ 0:023Re0:80
(14a)
f ¼ 0:3164Re0:25
(14b)
The heat transfer factor correlation fitted from the experimental data for turbulent flow agrees well with the DittuseBoelter correlation with a deviation between 5.63% and 11%, and the average absolute deviation is 3.58%. The friction factor correlation fitted from the experimental data for turbulent flow agrees well with the Blasius correlation with a deviation between 1.75% and 0.94%, and the absolute deviation is 1.05%. From the comparison, it can be proved that the experimental system and data reduction method for obtaining the heat transfer factor and friction factor correlations of the tested tube are effective. 2.2.2. Heat transfer and pressure drop performance of twisted oval tube With the method mentioned above, heat transfer factor and friction factor of the tested twisted oval tube with S ¼ 230 mm can be fitted as:
j ¼ 0:2363Re0:5728
(15a)
f ¼ 0:1430Re0:1690
(15b)
4000
30000 10000 Reynolds number Re
b 0.04
friction factor f
n
ft ¼ mt;f Ret t;f
Equation (13a) Dittus-Bolter equation (equation (14a))
Equation (13b) Blasius equation (equation (14b))
0.032
0.024
3000
10000 Reynolds number Re
30000
Fig. 4. Verification of the tube side performances of the testing system. a. Verification of the tube side heat transfer performance of the testing system. b. Verification of the tube side pressure drop performance of the testing system.
The distribution of Nu and f with Re are shown in Fig. 5a and b, respectively. In these two figures, heat transfer and pressure drop correlations which are derived from Gao et al. [8] and Yang et al. [12] are also presented. From Fig. 5a, it can be found that Nusselt number correlation fitted from the experimental data agrees well with Yang et al. and Gao et al.’s results. Average difference between Eq. (15a) and Gao et al.’s result is 14.09% and it is 5.19% between Eq. (15a) and Yang et al.’s result. Nevertheless, differences of pressure drop between them are significant. Though the twisted oval tube which is made from the round tube, But it has a different hydraulic diameter with the later one. It means that same Nusselt number and friction factor will result in different h andDP. So analyzing its heat transfer enhancement by comparing Nu and f is not reasonable. So heat transfer and pressure drop performance of the twisted oval tube and smooth round tube is presented in the form of heat transfer coefficient h and pressure dropDP in the present study. They are calculated from, Eq. (7), Eq. (10) and Eq. (15a) and (15b). Fig. 6 gives the distribution of heat transfer coefficient and pressure drop with Re for the tested tubes in the range of 4000 < Re<6 104, Referring to Fig. 6a, it can be observed that the heat transfer performance of the twisted oval tube is higher than the smooth round tube. The improvement ranges from 21% to 31% and it is 24.05% in average. Referring to Fig. 6b, it can be observed that the pressure drop of the twisted oval tube is also higher than the smooth round tube. Bishara et al.’s [9] numerical result shows that there exists intensive secondary flow in the twisted oval tube when
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
a
379
a 9000
[8]
Nusselt number Nu
2
200
heat transfer coefficient h(W/(m ·K))
Gao et al. [12] Yang et al. Derived from equation (15a)
100
30
4000
6000
3000
10000 30000 Reynolds number Re
4000
b 0.08
[8]
b
pressure drop ΔP(Pa)
Gao et al. [12] Yang et al. Equation (15b) fricion factor f
0.04
4000
10000
h derived from equation(13a) for smooth round tube h derived from equation(15a) for twisted oval tube
30000
Reynolds number Re Fig. 5. Fitting curve of tube side heat transfer and pressure drop correlations of the twisted oval tube with S ¼ 230 mm a. Fitting curve of tube side heat transfer correlation. b. Fitting curve of tube side pressure drop correlation.
Re is low. This also may be the mechanism of heat transfer enhancement and pressure drop increment of the twisted oval tube when the fluid is in turbulent state. 3. Experimental study of shell side heat transfer and pressure drop performance 3.1. Shell side experimental apparatus and data reduction 3.1.1. Experimental apparatus A testing system for testing the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger is shown in Fig. 7. Length of the tested shell side is 2.5 m. Tubes with the same size of twisted oval tube that has been tested mentioned above are applied in the twisted oval tube heat exchanger. Sectional parameters of the shell side can be found in Fig. 8. Units in Fig. 8 are mm. The circulating system is almost the same with Fig. 1 but changes the double-pipe heat exchanger to a twisted oval tube heat exchanger. Hot water which has been heated by the coiled pipe in the hot water tank flows in the shell side. And it will be cooled by the cold water which flows in the tube side. All of the fluids in the system are circulated by centrifugal pumps. Pipes that connecting all of the components are zinc planted to avoid corrosion. The whole system including the water tank, the test unit and the pipes are wrapped with glass fiber to insulate them from surroundings.
10000 Reynolds number Re
30000
ΔP derived from equation (13b) for smooth round tube ΔP derived from equation (13b) for twisted oval tube
1000
100
4000
10000 Reynolds number Re
30000
Fig. 6. Heat transfer and pressure drop performances of smooth round tube and twisted oval tube. a. Heat transfer performances of smooth round tube and twisted oval tube. b. Pressure drop performances of smooth round tube and twisted oval tube.
The volume flow rate of the water are measured with a electromagnetic flow meters with an accuracy of 0.5%. Inlet/outlet temperatures of the shell/tube fluids are measured with T-type thermocouples with an accuracy of 0.25%. Pressure drop of the shell side fluid is measured with a differential pressure transmitter with an accuracy of 0.075%. The testing points of the shell side pressure drop are set to exclude the pressure drop of the inlet/ outlet nozzles and the pressure drop between the nozzles and the shell. In addition, the measurement uncertainties of tube diameter and tube length are about 0.5% and 0.04%, respectively. The relative accuracy of each physical parameter is about 0.5%. During the test, the volume flow rate of the tube side fluid is assigned to be a constant, and the volume rate of the shell side fluid ranges from 8 to 120 m3/h. And it is adjusted by a butterfly valve. Fluid is assumed to be in a steady state on the condition that the fluctuations of all temperatures not exceed 0.2 C, and the fluctuation of the pressure difference was less than 1%. Five minutes later after the fluid is in a steady state, all the temperature, pressure difference and flow rate will be saved by an Agilent 34970A automatically every 5 s. 3.1.2. Data reduction During the data reduction, all fouling thermal resistances are set as zero. Considering that the twisted oval tubes are all formed from a round tube, the heat transfer area of the heat exchanger can be calculated asF ¼ 37pdt,oLt.
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1.Tube side flow meter 3.Cold water pump
2.Tube side valve 4.Cold water tank
5. Differential pressure transmitter
6.Hot water tank
7.Coiled pipe 8.Hot water pump 9. Shell side valve
10. Shell side flow meter
11. Data Acquisition System 12. Twisted oval tube 13. Twisted oval tube heat exchanger Tube side fluid Shell side fluid Measurement *
Testing point of temperature ×
Testing point of pressure
Fig. 7. Testing system of shell side heat transfer and pressure drop performance.
Heat transfer coefficient of the tube side can be calculated from Eq. (15a). Then from Eq. (8) and Eq. (15a), the shell side heat transfer coefficient can be derived:
hs ¼
1 dr;i ddm 1 þ 0:4 l K 0:2363Re0:5728 w dr;o Pr d r;o t t
(16)
The heat transfer coefficient of the shell side can also be expressed as:
hs ¼
ls dh;s
js Pr0:3 ¼ s
ls dh;s
n
ms;h Res s;h Pr0:3 s
(17)
The pressure drop of the shell side can be expressed as follow:
DPs ¼ fs
Ls rs u2s dh;s 2
(18)
Where the pressure drop DPs can be measured by the differential pressure transmitter, fs, us and Res can be expressed as follow: n
fs ¼ ms;f Res s;f ;
us ¼
Vs As
rs us dh;s Res ¼ ms
(19)
The equations for calculating heat transfer coefficient K, logarithmic mean temperatureDTm, logarithmic mean diameter dm, and hydraulic diameters mentioned above are the same with Eqs. (1) and (2), Eqs. (5) and (6) and Eq. (12). So sets of(Res,hs) and(Res,fs) can be obtained after the experimental tests. With the help of least square method, ms,h, ns,h, ms,f, ns,f can be fitted. And the heat transfer coefficient and pressure drop correlations of the testes tubes can be directly fitted.
1.inner side of the hexagon shell 2.outer side of the twisted elliptical tube
Fig. 8. Sketch of shell side cross section of the twisted oval tube heat exchanger.
The uncertainty is estimated with the method suggested by Moffat [22] and Kline [23]. According to the accuracy of the testing apparatuses and the data reduction method the uncertainty of shell side heat transfer coefficient and pressure drop are 8.9% and 4.8%, respectively. This degree of accuracy can be accepted by the industry. 3.2. Results and discussions of the shell side heat transfer and pressure drop performance 3.2.1. Shell side heat transfer and pressure drop performance of twisted oval tube heat exchanger Referring to the method that has been used by Dzyubenko [19e21] in analyzing the heat transfer coefficient and pressure drop of a twisted oval tube heat exchanger, The modified Froude number FrM ¼ S2/dh,t,oA is defined and used in the present study. It is 79 for the present heat exchanger. Heat transfer factor j and friction factor f can be correlated as:
j ¼ 0:1255Re0:67
(20a)
When 4000 < Re<85,000,FrM ¼ 79
f ¼ 42:1244Re0:6576
(20b)
When 1000 < Re<8000,FrM ¼ 79
f ¼ 0:6664Re0:1956
(20c)
When 8000 Re<40,000,FrM ¼ 79 The correlations of heat transfer factor and friction factor are also shown in Fig. 9a and b, respectively. From the figures it can be found that the heat transfer factor grows with the Re and the friction factor decrease with the Re. It also can be found that the slope of the friction factor correlation exists a change in Fig. 9b at Re ¼ 8000. It may be caused by the change of the fluid state. Comparisons of heat transfer factor and friction factor of heat exchanger with FrM ¼ 79 and heat exchanger with FrM ¼ 64 can be found in Fig. 9, From Fig. 9 it is clear that the heat transfer performance of heat exchanger with FrM ¼ 64 is better than the heat exchanger with FrM ¼ 79. But in Fig. 9b, it can be found that, their friction factors are almost the same. It denotes that the shell side heat transfer coefficient of the twisted oval tube heat exchanger can
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
heat transfer factor j
a
381
Table 2 Parameters of rod baffle heat exchanger.
Current Data Point Equation (20a) [19] Dzyubenko [20-21] Dzyubenko [7] Si Qin
100
Parameters Items
Shell diameter, mm Baffle ring spacing, mm Tube pitch, mm Baffle ring inner diameter, mm Baffle ring outer diameter, mm
224 230 30 216 220
Parameters
Rod diameter, mm 5 Baffle Number 9 Tube length, mm 2500 Tube Number 37 90 Tube layout angel,
30
also been accepted by the commercial heat exchanger design software HTRI (Heat Transfer Research Inc.). Basic approach of this method is expressed as follow: Calculating of heat transfer performance
10 1000
10000 Reynolds number Re
100000
b Current Data Point Equation (20b) and (20c) [19] B.V. Dzyubenko [20-21] B.V. Dzyubenko [7] Si Qin
0.3 friction factor f
Items
0.1
0.04 1000
10000
100000
Reynolds number Re Fig. 9. Correlations of shell side heat transfer and pressure drop performance. a. Correlation of shell side heat transfer factor j. b. Correlation of shell side friction factor f.
be improved by increasing FrM but will result in little increase of pressure drop. In order to analyze the applicability of these correlations in Table 1 whenFrM ¼ 79, FrM ¼ 79 is substituted into the equations in Table 1 and compared with Eq. (20a),(20b) and (20c) in Fig. 9, Heat transfer and pressure drop correlations of the twisted oval tube heat exchanger with FrM ¼ 64 is also presented from the point of comparative analysis. From Fig. 9a, it can be found that both Dzyubenko and Si’s heat transfer factor correlation consists well with the present data in the range of 4000 < Re < 10,000, But their difference is notable when Re 10,000. From Fig. 9b, it also can be found that Si’s friction factor correlation agrees well with the present data in the range of Re > 8000. 3.2.2. Heat transfer and pressure drop performance compared with rod baffle heat exchanger In order to comparatively analyzing the heat transfer and pressure drop performance of the tested heat exchanger, a rod baffle heat exchanger with similar geometric parameters with the tested twisted oval tube heat exchanger is designed. Commons of the two heat exchangers are that the fluid in the shell side flows both longitudinally and the shell side hydraulic diameters of the two heat exchangers are equal. Details of the rod baffle heat exchanger can be found in Table 2. The tube layout angel is set as 90 according to TEMA. The heat transfer and pressure drop performances of the rod baffle heat exchanger are calculated with Gentry’s [24] method. This method is proposed based on mass of experiments and has
h ¼ 4jPr0:3 l=de
(21)
for laminar flow: j ¼ jl ¼ Cl Re0:6 for turbulent flow: j ¼ jt ¼ Ct Re0:8 WhereCl,Ct are parameters related to the geometric parameters of the rod baffle heat exchanger. Calculating of pressure drop performance:
DPl ¼ 24rfLu2l =dh
(22)
DP b ¼ 0:5Nr Kb ru2b
(23)
DP ¼ DPl þ DPb
(24)
Comparison of the performances of rod baffle heat exchanger and twisted oval tube heat exchanger is presented in Fig. 10. The comparison is carried out in the valuable range of Eq. (20a),(20b) and (20c). From Fig. 10a it can be found that the heat transfer coefficient of the twisted oval tube heat exchanger is 1.7 times of the rod baffle heat exchanger in average. And the pressure drop is 0.27 times of the rod baffle heat exchanger in average. Also it can be found that with the increasing of mass flow rate, the heat transfer coefficient of the twisted oval tube heat exchanger increases significantly but with little increase of the pressure drop. From the calculating result of rod baffle heat exchanger, it can also be found that majority pressure drop of the rod baffle heat exchanger is formed from the rod baffles and it occupies 90.5% in average in the range of 2 kg/sGs 16 kg/s in this case. That’s because when the fluid flowing through the rod baffle, there exists a sudden change of the flow area. It is this change that increases the pressure drop significantly but with little increase of the heat transfer coefficient. But this does not happen in a twisted oval tube heat exchanger. 3.2.3. Overall performance of twisted oval tube heat exchanger On the basis of ration of heat transfer coefficient at the same pressure drop of two heat exchangers, performance evaluation criterion h defined as h ¼ (Nu/Nu0)/(f/f0)1/3 has been proposed by Webb [25]. Parameters with subscript “0” denote that these parameters are from the heat exchanger which is the object to be compared. This performance evaluation criterion has been widely used in evaluating the overall performance of enhanced heat transfer tubes. It is obvious that only one side of the heat exchanger (shell side or tube side) is included in this criterion. But for a twisted oval tube heat exchanger, both the tube side and shell side geometric parameters differs from rod baffle heat exchanger or any other shell-tube type heat exchangers. So both the tube side and the shell side performance should be included in the analysis of its overall performance.
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a Rod baffle heat exchanger Twisted oval tube heat exchanger
2
heat transfer coefficient h (W/m ·K)
10000
8000
6000
4000
2000
0 0
5
10
15 20 25 mass flow rate Gs(kg/s)
30
35
b 10000
pressure drop ΔP (Pa)
8000
Rod baffle heat exchanger Twisted oval tube heat exchanger
6000
4000
2000
0 0
5 10 mass flow rate Gs(kg/s)
15
Fig. 10. Comparison of shell side performances of rod baffle heat exchanger and twisted oval tube heat exchanger. a. Comparison of shell side heat transfer coefficient. b. Comparison shell side pressure drop.
Referring to the performance evaluation criterion proposed by Webb [25], cost of the pump is extended including the pressure drop of both the tube side and the shell side in the present work. And a modified evaluation criterion hM ¼ (K/K0)/((DPtVt þ DPsVs)/ (DPt0Vt0 þ DPs0Vs0)) is defined. By setting rod baffle heat exchangers as the object that to be compared, the distribution of overall performance versus tube/shell side mass flow rate is shown in Fig. 11. Details of the distribution can also be found in Fig. 12.
Fig. 12. Comparison of shell side performances of rod baffle heat exchanger and twisted oval tube heat exchanger. a. Comparison of shell side heat transfer coefficient. b. Comparison shell side pressure drop.
These two figures denote that the twisted oval tube heat exchanger behaves better than the rod baffle heat exchanger and it is 2.75 in average. The overall performance of the twisted oval tube heat exchanger in Fig. 12a can be found increases with the shell side flow rate which varies from 2.23 to 4.4 when the tube side flow rate is 3 kg/s and varies from 1.33 to 2.8 when the tube side flow rate is 12 kg/s. In Fig. 11b, the overall performance factor decreases with the tube side flow rate which varies from 4.38 to 1.26 when the shell side flow rate is 4 kg/s and varies from 4.78 to 2.11 when the shell side flow rate is 13 kg/s. So it can be concluded that the twisted oval tube heat exchangers is preferred to work at low tube side flow rate and high shell side flow rate. 4. Conclusions
Fig. 11. Overall performance of the twisted oval tube heat exchanger.
In the present work, an experimental study of heat transfer and pressure drop performance of twisted oval tube heat exchanger has been carried out. The tube side performance has been compared with smooth round tube and the shell side performance has been compared with rod baffle heat exchanger whose shell side fluid flows also longitudinally. In order to analyze the overall performance of the twisted oval tube heat exchanger, a new performance evaluation criterion of heat exchanger has been established. It has been used to evaluate the overall performance of the twisted oval tube heat exchanger by setting the rod baffle heat exchanger as the object to be compared. Major findings are as follow:
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
(1) An experimental system for testing the heat transfer and pressure drop performance of twisted oval tube is established and verified. Bases on this, a smooth round tube with d ¼ 25 mm and a twisted oval tube with A ¼ 29 mm, B ¼ 19.5 mm and S ¼ 230 mm has been experimentally studied. Heat transfer and pressure drop correlations of the tested tube has also been fitted and compared with the round tube. The result shows that the heat transfer coefficient of the twisted is higher than the smooth round tube at the cost of some increment of pressure drop. (2) An experimental system for testing the shell side heat transfer and pressure drop performance of a twisted oval tube heat exchanger has been established. A twisted oval tube heat exchanger has been assembled. Its shell side heat transfer and pressure drop performance have been studied experimentally. Correlations for calculating its performance are derived out and compared with former studies. The result shows that with the increasing of FrM, the shell side heat transfer coefficient and pressure drop of the twisted oval tube heat exchanger will both be promoted. (3) On the purpose of comparing the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger with other shell tube type heat exchangers, a rod baffle heat exchanger is designed and its heat transfer and pressure drop performance have been calculated with the correlation from Gentry. The comparison result show that the rod baffle heat exchanger works with a higher shell side heat transfer coefficient and lower shell side pressure drop than the rod baffle heat exchanger. (4) Considering that when the twisted oval tube technique is been used as a heat transfer enhancement technique, both the tube side and shell side are different from traditional heat exchangers. So when analyzing the overall performance of the heat exchanger, both the shell side and tube side performance should be included in the overall performance factor. From this point of view, a modified performance criterion evaluation hM is defined and utilized in the analyzing of the overall performance of the twisted oval tube heat exchanger. The analyzing result shows that the twisted oval tube heat exchangers is preferred to work at low tube side flow rate and high shell side flow rate. References [1] A. Bejan, A.D. Kraus, Heat Transfer Handbook, Wiley, New Jersey, 2003, 1029e1130pp. [2] R.L. Webb, Principles of Enhanced Heat Transfer, John Wiley and Sons, Inc., New York, 1994. [3] C.L. Li, Design and application of the new type high-efficient screw oblate tube heat exchangers, Chemical Engineering & Machinery 32 (3) (2005) 162e165 (in Chinese).
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[4] B. Ljubicic, Testing of Twisted Tube Exchangers in Transition Flow Regime, Compact Heat Exchangers and Enhancement Technology for the Process Industries (1999). 135e139. [5] A. Mushabbab, Design and Operate a Fouling Monitoring Device to Study Fouling at Twisted Tube, King Fahd University of Petroleum & Minerals, Dhahran, 2007, 96e135. [6] L.A. Asmantas, M.A. Nemira, V.V. Trilikauskas, Coefficients of heat transfer and hydraulic drag of a twisted oval tube, Heat Transfer-Soviet Research 17 (4) (1985) 103e109. [7] Q. Si, Q. Xia, L.H. Liang, D.X. Li, Investigation of heat transfer and flow resistance on twisted tube heat exchanger, Journal of Chemical Industry and Engineering (China) 46 (5) (1995) 601e608 (in Chinese). [8] X.N. Gao, H.C. Zou, D.Y. Wang, Y.S. Lu, Heat transfer and flow resistance properties in twisted oblate tube with large twist ratio, Journal of South China University of Technology (Natural Science) 36 (11) (2008) 17e21 (in Chinese). [9] F. Bishara, M.A. Jog, R.M. Manglik, Computational simulation of swirl enhanced flow and heat transfer in a twisted oval tube, Journal of Heat Transfer 131 (8) (2009) 080902. [10] X.N. Gao, H.B. Yin, Y.Y. Huang, Y.T. Fang, Z.G. Zhang, Nucleate pool-boiling enhancement outside a horizontal bank of twisted tubes with machined porous surface, Applied Thermal Engineering 29 (2009) 3212e3217. [11] J.A. Meng, Z.X. Li, Z.Y. Guo, S. Wei, Simulation and analysis on laminar flow and heat transfer in twisted ellipse-tube, Journal of Engineering Thermophysics 23 (2002) 117e120 (in Chinese). [12] S. Yang, L. Zhang, H. Xu, Experimental study on convective heat transfer and flow resistance characteristics of water flow in twisted elliptical tubes, Applied Thermal Engineering 31 (2011) 2981e2991. [13] B.V. Dzyubenko, Investigation of the transfer properties of a stream in a heat exchanger with spiral tubes, Journal of Engineering Physics and Thermophysics 38 (6) (1981) 589e593. [14] B.V. Dzyubenko, P.A. Urbonas, L.A. Ashmantas, Inter channel mixing of heat carriers in a bundle of spiral tubes, Journal of Engineering Physics and Thermophysics 45 (1) (1984) 729e733. [15] B.V. Dzyubenko, V.N. Stetsyuk, Effect of flow-twisting intensity on the mixing of a heat-transfer agent in bundles of twisted tubes, Journal of Engineering Physics and Thermophysics 55 (5) (1989) 1195e1200. [16] B.V. Dzyubenko, L.V. Ashamantas, M.D. Segal, Modeling and Design of Twisted Tube Heat Exchanger, Begell House Inc., New York, 2000, 70e83pp. [17] B.V. Dzyubenko, Heat exchanger along the initial segment in a heat exchanger with a helical flow, Journal of Engineering Physics and Thermophysics 42 (2) (1982) 153e157. [18] B.V. Dzyubenko, Estimation of the thermo hydraulic efficiency of heat exchanging apparatuses with twisted tubes, Heat Transfer Research 37 (4) (2006) 349e363. [19] V.M. Levlev, E.K. Kalinin, I.I. Danilov, B.V. Dzyubenko, G.A. Dreitser, Heat transfer in the turbulent swirling flow in a channel of complex shape, in: Heat transfer 1982: Proceedings of the Seventh International Conference, vol. 3, Hemisphere Publishing Corporation, Washington D. C., 1982, pp. 171e176. [20] B.V. Dzyubenko, Drag in heat exchanger with a twisted flow, Journal of Engineering Physics and Thermophysics 44 (3) (1983) 237e241. [21] B.V. Dzyubenko, G.A. Dreitser, Heat transfer and fluid friction in bundles of twisted tubes, Journal of Engineering Physics and Thermophysics 50 (6) (1986) 611e618. [22] R.J. Moffat, Using uncertainty analysis in the planning of an experiment, Journal of Fluids Engineering 107 (2) (1985) 173e178. [23] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiment, ASME Mechanical Engineering 75 (1953) 3e8. [24] C.C. Gentry, Baffle heat transfer technology, Chemical Engineering 86 (7) (1990) 48e57. [25] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surface in heat exchanger design, International Journal of Heat and Mass Transfer 24 (4) (1981) 715e726.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Heat transfer and pressure drop performance of twisted oval tube heat exchanger Xiang-hui Tan, Dong-sheng Zhu*, Guo-yan Zhou*, Li-ding Zeng Key Laboratory of Pressure Systems and Safety of Ministry of Education, School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, PR China
h i g h l i g h t s < Experimental study of the tube side heat transfer and pressure drop performance of a twisted oval tube heat exchanger. < Experimental study of the shell side heat transfer and pressure drop performance of a twisted oval tube heat exchanger. < Comparatively study of the shell side performance of a twisted oval tube heat exchanger with a rod baffle heat exchanger. < Analyzing of the overall performance of the twisted oval tube heat exchanger.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 January 2012 Accepted 21 June 2012 Available online 29 June 2012
Twisted oval tube heat exchanger is a type of heat exchanger that aims at improving the heat transfer coefficient of the tube side and also decreasing the pressure drop of the shell side. In the present work, tube side and shell side heat transfer and pressure drop performances of a twisted oval tube heat exchanger has been experimentally studied. The tube side study shows that the tube side heat transfer coefficient and pressure drop in a twisted oval tube are both higher than in a smooth round tube. The shell side study shows that the lower the modified Froude number FrM, the higher the shell side heat transfer coefficient and pressure drop. In order to comparatively analyze its shell side performance of the heat exchanger, a rod baffle heat exchanger with similar size of the twisted oval tube heat exchanger is designed and its performance is calculated with Gentry’s method. The comparative study shows that the heat transfer coefficient of the twisted oval tube heat exchanger is higher and the pressure drop is lower than the rod baffle heat exchanger. In order to evaluate the overall performance of the twisted oval tube heat exchanger, a performance evaluation criterion considering both the tube side and shell side performance of a heat exchanger is proposed and applied. The analyze of the overall performance of the twisted oval tube shows that the twisted oval tube heat exchangers works more effective at low tube side flow rate and high shell side flow rate. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Twisted oval tube heat exchanger Heat transfer performance Pressure drop performance Overall performance
1. Introduction Heat transfer enhancement technique is a very important technique to improve the efficiency of heat exchangers. From the point of energy saving, improving the efficiency of heat exchangers can be realized in two ways: promoting the heat transfer coefficient to decrease the heat transfer area, decreasing the pressure drop to save the cost of pump. Both active and passive techniques were used to increase the heat transfer coefficient of a heat exchanger over a century ago [1,2]. Twisted oval tube heat exchanger is a type of
* Corresponding authors. Tel./fax: þ86 21 64253708. E-mail addresses: [email protected] (D.-s. Zhu), [email protected] (G.-y. Zhou). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.037
heat exchanger that aims at promoting the heat transfer coefficient of the tube side and also decreasing the pressure drop of the shell side. Applications of the twisted oval tube in chemical field can also be found in [3]. Nowadays, more and more attention are paid on the performance of the twisted oval tube heat exchanger [4,5]. Tubes that play an important role in this heat transfer enhancement technique are made from normal round tubes. They are formed into an oval section with a superimposed twist by some special techniques. Two ends of the tubes remain round on the consideration of assembling them with the tube sheet. Sketch of this tube can be found in Fig. 1a. Geometrical parameters of the twisted oval tube are 360 twist pitch(S), major axis (A) of the oval section and minor axis (B) of the oval section. As has been shown in Fig. 1b, when the tubes are arrayed in a same direction, they can be supported by the tubes themselves but not baffles or rods that
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
Nomenclature A Ac As At B Cp d de dh dm f F FrM gM G h j jl jt K Kb L m n Nr Nu Pr Q T Re
major axis of the twisted oval tube, m sectional area, m2 shell side flow area, m2 tube side flow area, m2 minor axis of the twisted oval tube, m specific heat, J/(kg$K) smooth round tube diameter, m equivalent diameter, m hydraulic diameter, m logarithmic mean diameter, m friction factor heat transfer area, m2 modified Froude number maximum centrifugal acceleration, m/s2 mass flow rate, kg/s heat transfer coefficient, W/(m2$K) heat transfer factor j factor- laminar flow j factor- turbulent flow overall heat transfer coefficient,W/(m2$K) pressure drop coefficient length of tube, m constants for fitting correlations constants for fitting correlations rod baffle number Nusselt number Prandtl number heat duty, W temperature, K Reynolds number
a normal shell tube heat exchanger needs. This special geometrical characteristic can form a longitude flow channel which will considerably reduce the pressure drop of the heat exchanger. From the point of analyzing the heat transfer and pressure drop performance of the tube side of a twisted oval tube heat exchanger, Asmantas et al. [6] tested the performance of twisted oval tube to
Fig. 1. Sketch of twisted oval tube and self supported twisted oval tubes a. Sketch of twisted oval tube. b. Sketch of self supported oval tubes.
S Tf Tw u uq,max V
375
360 twist pitch, m fluid temperature, K wall temperature, K velocity, m/s maximum tangential velocity, m/s volume flow rate, m3/s
Greek symbols DP total pressure drop, Pa DPb baffle flow pressure drop, Pa DPl longitude flow pressure drop, Pa DTm Logarithmic mean temperature difference, K h overall performance hM modified overall performance l thermal conductivity, W/(m$K) m dynamic viscosity, Pa s r density, kg/m3 4 viscosity correction factor Subscripts b baffle flow l longitude flow t tube side s shell side M modified h hydraulic j heat transfer factor f friction factor o outlet/outer side i inlet/inner side w wall
get the heat transfer and pressure drop correlations in the early stage. Considering the effect of Pr and geometrical parameters on the performance of the twisted oval tube, Si et al. and Gao et al. [7,8] tested the performance of twisted oval tubes with different A, B and S in turbulent state. In their experiments, diesel oil, water and air are all chosen as the flowing media. Their result shows that the twisted oval tube will perform better at low Re and high viscosity. Bishara et al. [9] simulated the laminar flow in a twisted oval tube at Re < 1200. They found that it is the secondary flow that caused by the torsion of the tubes that resulted in the heat transfer enhancement and pressure drop increment. Gao et al. [10] also studied the phenomenon of boiling when the twisted oval tube technique is combined with porous media technique. On the purpose of obtaining the heat transfer and pressure drop correlations, Meng et al. [11] also studied the flow in a twisted oval tube numerically at Re ¼ 500e1500. Yang et al. [12] studied the performance of the twisted oval tube from laminar state to turbulent state. Performances of the twisted oval tube were also compared with normal round tube in their study. Results show that the heat transfer coefficient and pressure drop of a twisted oval tube are both higher than a smooth round tube. Correlations that reflect the heat transfer and pressure drop performance of twisted oval tube heat exchanger have also been reviewed by Yang et al. [12]. On the aspect of the shell side, many researches focused on the research of turbulent intensity [13], boundary layer depth [14] and heat diffusion coefficient [15]. Numerical models for predicting the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger has also been published in the past few decades [16]. Based on the shell side heat and fluid flow
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characteristics of the twisted oval tube heat exchanger [17], optimization methods for the twisted oval tube heat exchanger have also been proposed [18]. Influenced by the centrifugal force field, criterions that characterize the twisting of the flow in the twisted oval tube bundle are Reynolds number Re and Froude number Fr. Fr can be calculated asFr ¼ u2s =ðdh;t;o gM Þ.WheregM ¼ 2u2q;max =A. Considering the time cost when the fluid flow past a helical pitch with uq,max is the same with the time cost when the fluid flow past axial length S with us. So uq,max can be calculated as: uq;max ¼ pAus =S.Then Fr can be expressed asFr ¼ S2 =ð2p2 Adh;t;o Þ. Omitting the constant 2p2, the modified Froude number FrM can be defined asFrM ¼ S2 =ðAdh;t;o Þ. Based on this, experimental and numerical studies have also been applied on the purpose of obtaining the shell side heat transfer and pressure drop correlations of the twisted oval tube heat exchanger [7,19e21]. Correlations of the shell side heat transfer factor and friction factor can be found in Si et al.’s [7] and Dzyubenko et al.’s [19e21] research in Table 1. Among these three sets of correlations, two sets of Dzyubenko et al.’s correlations are derived based on a heat exchanger with a hexagonal shell. It is also the same with the present study. Their correlations are fitted in the range of FrM ¼ 64,231 < FrM < 392 and 232 < FrM<2440 as described in Table 1. From all of the above we can find that most of the researches focused on the heat transfer and pressure drop of just one side of the twisted oval tube heat exchanger. Only the tube side performance of the twisted oval tube heat exchanger has been compared with traditional shell-tube heat exchangers. Nevertheless, when twisted oval tube technique is used as a heat transfer enhancement technique, two sides of the heat transfer and pressure drop performances will both be different from traditional heat exchangers. So the evaluation of the twisted oval tube heat exchanger should be carried out based on the performance of the two sides of the heat exchanger. Aiming at obtaining the overall performance of the twisted oval tube heat exchanger, the heat transfer and pressure drop performance of the two sides of the twisted oval tube heat exchanger will be experimentally studied in the present work. A rod baffle heat exchanger will be designed and compared to analyze the overall performance of the tested twisted oval tube heat exchanger. Also a new criterion for evaluating the overall performance of heat exchangers will be established and used to evaluate the performance of twisted oval tube heat exchanger.
2. Experimental study of tube side heat transfer and pressure drop performance 2.1. Tube side experimental apparatus and data reduction 2.1.1. Experimental apparatus An experimental system for testing the heat transfer coefficient and pressure drop performance of a twisted oval tube is illustrated in Fig. 2. A double-pipe heat exchanger with hot water flowing in the shell side and cold water flowing in the tube side is applied. The outer tube of the heat exchanger is a round tube with inner diameter equals 40 mm and wall thickness equals 2.5 mm. The inner tube is twisted oval tube. Detailed sectional parameters of the double tube heat exchanger can be found in Fig. 3 Units in Fig. 3 are mm. Before the tests start, water in hot water tank would be heated by the steam which flows in the coiled pipes, and also it will be self circulated by a centrifugal pump to ensure the homogeneity of temperature. Both the cold water tank and hot water tank are equipped to 30 m3 to fulfill the demand of water during the tests. Length of the tested section is 3 m. The upstream tube section of the tested tube is made long and straight in order to ensure a fully developed flow. Shut-off valves are installed to regulate the velocity of the hot water and cold water. The whole system including the two tanks, the test section and the pipes that connect all of them are wrapped with glass fiber to insulate them from the surroundings. Parameters that measured are shell/tube side volume flow rate, shell/tube side inlet/outlet bulk temperature and tube side pressure drop. All of the temperatures are measured with T-type thermocouples which are calibrated in a same temperature with an accuracy of 0.25%. Two electromagnetic flow meters with an uncertainty of 0.5% are equipped to measure the shell/tube side flow rate. Pressure drop of the tested twisted oval tube is measured using the differential pressure transmitter with an accuracy of 0.075%. In addition, the measurement uncertainties of tube diameter and tube length are about 0.5% and 0.04%, respectively. The relative accuracy of each physical parameter is about 0.5%. During the tests, cold water in the tube side is pumped from the cold water tank, and it is heated in the double-pipe heat exchanger by the hot water which flows in the shell side. The shell side flow rate is fixed at its maximum value and tube side flow rate is regulated to ensure that the temperature of the shell side water changes little. It means that the shell side Re and Pr can be assumed as constants. For each test run with a constant shell and tube side flow rate, the system is assumed to be in a steady state on the
Table 1 Shell side heat transfer and pressure drop correlations of twisted oval tube heat exchangers. Researchers
Range and parameters
Si Qin et al. [6]
7 tubes Shell diameter 0.08 m S/de ¼ 6.86e11.9 FrM ¼ 231e392 2000 < Re<104 Fluid: Water and oil 37 tubes FrM ¼ 232e2440 Hexagonal shell Fluid: air 2000 < Re<5 104 37 tubes FrM ¼ 64 Hexagonal shell Fluid: air 2000 < Re<5 104
Dzyubenko et al. [18,19]
Dzyubenkoet al. [20]
Correlations 0:4347 ð1 þ 3:6Fr 0:357 ÞPr0:33 Nu ¼ 0:2379Re0:7602 FrM M 0:078 ð1 þ 3:6Fr 0:357 Þ f ¼ 9:461Re0:4928 FrM M
0:357 Þ Nu ¼ 0:023Re0:8 ð1 þ 3:6FrM 0:357 Þ f ¼ 0:3164Re0:25 ð1 þ 3:6FrM
Nu ¼ 0:0521Re0:8 Pr0:4 f ¼ 1.095Re0.25
Tw Tf
!0:55
Tw Tf
!0:55 Pr0:4
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
377
1.Tube side flow meter 3.Cold water pump
2.Tube side valve 4.Cold water tank
5. Differential pressure transmitter
6.Hot water tank
7.Coiled pipe 8.Hot water pump 9. Shell side valve
10. Shell side flow meter
11. Data Acquisition System 12. Twisted oval tube 13. Twisted oval tube heat exchanger Tube side fluid Shell side fluid Measurement *
Testing point of temperature ×
Testing point of pressure
Fig. 2. Testing system of the tube side heat transfer and pressure drop performance.
condition that all temperature fluctuations of not exceed 0.2 C, and the fluctuation of the pressure difference is less than 1%. A smooth round tube and a twisted oval tube made from the former one are tested with the testing system introduced above. All of the tubes are made of stainless steel with a length of 3 m. Inner and outer diameter of the round tube is 25 mm and 20 mm respectively. The twisted oval tube which is made from the smooth round tube has an oval section. As shown in Fig. 1a, major axis A and minor axis B of the twisted oval tube is 29 mm and 19.5 mm, respectively. The wall thickness is 2.5 mm. The 360 twist pitch is 230 mm. 2.1.2. Data reduction method The fouling resistance of the double-tube heat exchanger is assumed to be zero. From Fourier Law and basic equations of heat transfer process, heat transfer coefficient of the double tube heat exchanger K can be derived as follow:
Qt ¼ Gt Cp;t Tc;o Tc;i
(3b)
Considering the hot fluid flows in the shell side, and there may still exists little heat elimination, Q is assumed to be equal withQt. Because that the twisted oval tube is made from a smooth round tube, the heat transfer area of the tested heat exchanger is calculated as:
F ¼ pdr;o Lt
(4)
Logarithmic mean temperature difference DTm and logarithmic mean diameter dm are calculated as:
DTm ¼
Ts;o Tt;i Ts;i Tt;o ln Ts;o Tt;i Ts;i Tt;o
dh;t;o dh;t;i ln dh;t;o =dh;t;i
(5)
K ¼ Q =ðF DTm Þ
(1)
dm ¼
dr;i ddm 1 1 ¼ þ þ K ht dr;o lw dr;o hs
(2)
Heat transfer performance of fluid flowing in the tube/shell side of the above heat exchanger can be calculated as:
Where ht and hs are the tube side and shell side heat transfer coefficient, respectively. Q is the heat duty. Shell side and tube side heat duty, Qs and Qt can be calculated as:
ht ¼
Qs ¼ Gs Cp;s Th;i Th;o
hs ¼
(3a)
lt dh;t;i
ls dh;s
jt Pr0:4 ¼ t
js Pr0:3 ¼ s
(6)
lt
n
dh;t;i
ls dh;s
mt;j Ret t:j Pr0:4 t
n ;j
ms;j Res s Pr0:3 s
(7)
(8)
Where ht and hs are the Nusselt number of tube side and shell side, respectively. jt and js are tube side and shell side heat transfer factors, respectively. Exponent of Pr are set as 0.4 and 0.3 for fluid that to be heated and cooled, respectively. From Eq. (8) and considering that the shell side Re and Pr is assumed as constants, the heat transfer coefficient of the shell side can be assumed to be a constant. By definingC ¼ 1/ho þ (ddm)/(ldt,o), Eq. (2) can be derived as:
lt 1 n ¼ m Re t;j Pr0:4 t þC K dt;o t;j t Fig. 3. Sketch of shell side cross section of the double tube heat exchanger.
Pressure drop DPt of the tested tubes can be expressed as:
(9)
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DPt ¼ ft
Lt rt u2t dt;i 2
(10)
a
Where ft is the friction factor of the tested tube, ft, ut and Ret can be expressed as:
Vt At
Ret ¼
rt ut dh;t ; mt
(11)
Hydraulic diameters that mentioned above are all calculated with the following method:
dh ¼
4 Ac C
Nusselt number Nu
ut ¼
200
100
(12) 30
So sets of (Ret,K) and (Ret,ft) can be obtained after the experimental tests. With the help of least square method, mt,h, nt,h, C, mt,f, nt,f can be fitted. And the heat transfer coefficient and pressure drop correlations of the tested tubes can be directly derived. Similar testing method and data reduction method can also be found [12]. The uncertainty is estimated with the method suggested by Moffat [22] and Kline [23]. According to the accuracy of the testing apparatuses and the data reduction method the uncertainty of overall heat transfer coefficient and pressure drop are 7.5% and 4.8%, respectively. This degree of accuracy can be accepted by the industry. 2.2. Results and discussions of the tube side heat transfer and pressure drop performance 2.2.1. Verification of the testing system Heat transfer factor and friction factor correlations (shown in Eq. (13a) and Eq. (13b)) of the smooth round tube in a turbulent state are fitted in order to confirm the reliability of the testing system. The Correlations are compared with the predictions of DittuseBoelter correlation (Eq. (14a)) and Blasius correlation (Eq. (14b)) in Fig. 4a and b
j ¼ 0:0420Re0:74
(13a)
f ¼ 0:3474Re0:26
(13b)
j ¼ 0:023Re0:80
(14a)
f ¼ 0:3164Re0:25
(14b)
The heat transfer factor correlation fitted from the experimental data for turbulent flow agrees well with the DittuseBoelter correlation with a deviation between 5.63% and 11%, and the average absolute deviation is 3.58%. The friction factor correlation fitted from the experimental data for turbulent flow agrees well with the Blasius correlation with a deviation between 1.75% and 0.94%, and the absolute deviation is 1.05%. From the comparison, it can be proved that the experimental system and data reduction method for obtaining the heat transfer factor and friction factor correlations of the tested tube are effective. 2.2.2. Heat transfer and pressure drop performance of twisted oval tube With the method mentioned above, heat transfer factor and friction factor of the tested twisted oval tube with S ¼ 230 mm can be fitted as:
j ¼ 0:2363Re0:5728
(15a)
f ¼ 0:1430Re0:1690
(15b)
4000
30000 10000 Reynolds number Re
b 0.04
friction factor f
n
ft ¼ mt;f Ret t;f
Equation (13a) Dittus-Bolter equation (equation (14a))
Equation (13b) Blasius equation (equation (14b))
0.032
0.024
3000
10000 Reynolds number Re
30000
Fig. 4. Verification of the tube side performances of the testing system. a. Verification of the tube side heat transfer performance of the testing system. b. Verification of the tube side pressure drop performance of the testing system.
The distribution of Nu and f with Re are shown in Fig. 5a and b, respectively. In these two figures, heat transfer and pressure drop correlations which are derived from Gao et al. [8] and Yang et al. [12] are also presented. From Fig. 5a, it can be found that Nusselt number correlation fitted from the experimental data agrees well with Yang et al. and Gao et al.’s results. Average difference between Eq. (15a) and Gao et al.’s result is 14.09% and it is 5.19% between Eq. (15a) and Yang et al.’s result. Nevertheless, differences of pressure drop between them are significant. Though the twisted oval tube which is made from the round tube, But it has a different hydraulic diameter with the later one. It means that same Nusselt number and friction factor will result in different h andDP. So analyzing its heat transfer enhancement by comparing Nu and f is not reasonable. So heat transfer and pressure drop performance of the twisted oval tube and smooth round tube is presented in the form of heat transfer coefficient h and pressure dropDP in the present study. They are calculated from, Eq. (7), Eq. (10) and Eq. (15a) and (15b). Fig. 6 gives the distribution of heat transfer coefficient and pressure drop with Re for the tested tubes in the range of 4000 < Re<6 104, Referring to Fig. 6a, it can be observed that the heat transfer performance of the twisted oval tube is higher than the smooth round tube. The improvement ranges from 21% to 31% and it is 24.05% in average. Referring to Fig. 6b, it can be observed that the pressure drop of the twisted oval tube is also higher than the smooth round tube. Bishara et al.’s [9] numerical result shows that there exists intensive secondary flow in the twisted oval tube when
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
a
379
a 9000
[8]
Nusselt number Nu
2
200
heat transfer coefficient h(W/(m ·K))
Gao et al. [12] Yang et al. Derived from equation (15a)
100
30
4000
6000
3000
10000 30000 Reynolds number Re
4000
b 0.08
[8]
b
pressure drop ΔP(Pa)
Gao et al. [12] Yang et al. Equation (15b) fricion factor f
0.04
4000
10000
h derived from equation(13a) for smooth round tube h derived from equation(15a) for twisted oval tube
30000
Reynolds number Re Fig. 5. Fitting curve of tube side heat transfer and pressure drop correlations of the twisted oval tube with S ¼ 230 mm a. Fitting curve of tube side heat transfer correlation. b. Fitting curve of tube side pressure drop correlation.
Re is low. This also may be the mechanism of heat transfer enhancement and pressure drop increment of the twisted oval tube when the fluid is in turbulent state. 3. Experimental study of shell side heat transfer and pressure drop performance 3.1. Shell side experimental apparatus and data reduction 3.1.1. Experimental apparatus A testing system for testing the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger is shown in Fig. 7. Length of the tested shell side is 2.5 m. Tubes with the same size of twisted oval tube that has been tested mentioned above are applied in the twisted oval tube heat exchanger. Sectional parameters of the shell side can be found in Fig. 8. Units in Fig. 8 are mm. The circulating system is almost the same with Fig. 1 but changes the double-pipe heat exchanger to a twisted oval tube heat exchanger. Hot water which has been heated by the coiled pipe in the hot water tank flows in the shell side. And it will be cooled by the cold water which flows in the tube side. All of the fluids in the system are circulated by centrifugal pumps. Pipes that connecting all of the components are zinc planted to avoid corrosion. The whole system including the water tank, the test unit and the pipes are wrapped with glass fiber to insulate them from surroundings.
10000 Reynolds number Re
30000
ΔP derived from equation (13b) for smooth round tube ΔP derived from equation (13b) for twisted oval tube
1000
100
4000
10000 Reynolds number Re
30000
Fig. 6. Heat transfer and pressure drop performances of smooth round tube and twisted oval tube. a. Heat transfer performances of smooth round tube and twisted oval tube. b. Pressure drop performances of smooth round tube and twisted oval tube.
The volume flow rate of the water are measured with a electromagnetic flow meters with an accuracy of 0.5%. Inlet/outlet temperatures of the shell/tube fluids are measured with T-type thermocouples with an accuracy of 0.25%. Pressure drop of the shell side fluid is measured with a differential pressure transmitter with an accuracy of 0.075%. The testing points of the shell side pressure drop are set to exclude the pressure drop of the inlet/ outlet nozzles and the pressure drop between the nozzles and the shell. In addition, the measurement uncertainties of tube diameter and tube length are about 0.5% and 0.04%, respectively. The relative accuracy of each physical parameter is about 0.5%. During the test, the volume flow rate of the tube side fluid is assigned to be a constant, and the volume rate of the shell side fluid ranges from 8 to 120 m3/h. And it is adjusted by a butterfly valve. Fluid is assumed to be in a steady state on the condition that the fluctuations of all temperatures not exceed 0.2 C, and the fluctuation of the pressure difference was less than 1%. Five minutes later after the fluid is in a steady state, all the temperature, pressure difference and flow rate will be saved by an Agilent 34970A automatically every 5 s. 3.1.2. Data reduction During the data reduction, all fouling thermal resistances are set as zero. Considering that the twisted oval tubes are all formed from a round tube, the heat transfer area of the heat exchanger can be calculated asF ¼ 37pdt,oLt.
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1.Tube side flow meter 3.Cold water pump
2.Tube side valve 4.Cold water tank
5. Differential pressure transmitter
6.Hot water tank
7.Coiled pipe 8.Hot water pump 9. Shell side valve
10. Shell side flow meter
11. Data Acquisition System 12. Twisted oval tube 13. Twisted oval tube heat exchanger Tube side fluid Shell side fluid Measurement *
Testing point of temperature ×
Testing point of pressure
Fig. 7. Testing system of shell side heat transfer and pressure drop performance.
Heat transfer coefficient of the tube side can be calculated from Eq. (15a). Then from Eq. (8) and Eq. (15a), the shell side heat transfer coefficient can be derived:
hs ¼
1 dr;i ddm 1 þ 0:4 l K 0:2363Re0:5728 w dr;o Pr d r;o t t
(16)
The heat transfer coefficient of the shell side can also be expressed as:
hs ¼
ls dh;s
js Pr0:3 ¼ s
ls dh;s
n
ms;h Res s;h Pr0:3 s
(17)
The pressure drop of the shell side can be expressed as follow:
DPs ¼ fs
Ls rs u2s dh;s 2
(18)
Where the pressure drop DPs can be measured by the differential pressure transmitter, fs, us and Res can be expressed as follow: n
fs ¼ ms;f Res s;f ;
us ¼
Vs As
rs us dh;s Res ¼ ms
(19)
The equations for calculating heat transfer coefficient K, logarithmic mean temperatureDTm, logarithmic mean diameter dm, and hydraulic diameters mentioned above are the same with Eqs. (1) and (2), Eqs. (5) and (6) and Eq. (12). So sets of(Res,hs) and(Res,fs) can be obtained after the experimental tests. With the help of least square method, ms,h, ns,h, ms,f, ns,f can be fitted. And the heat transfer coefficient and pressure drop correlations of the testes tubes can be directly fitted.
1.inner side of the hexagon shell 2.outer side of the twisted elliptical tube
Fig. 8. Sketch of shell side cross section of the twisted oval tube heat exchanger.
The uncertainty is estimated with the method suggested by Moffat [22] and Kline [23]. According to the accuracy of the testing apparatuses and the data reduction method the uncertainty of shell side heat transfer coefficient and pressure drop are 8.9% and 4.8%, respectively. This degree of accuracy can be accepted by the industry. 3.2. Results and discussions of the shell side heat transfer and pressure drop performance 3.2.1. Shell side heat transfer and pressure drop performance of twisted oval tube heat exchanger Referring to the method that has been used by Dzyubenko [19e21] in analyzing the heat transfer coefficient and pressure drop of a twisted oval tube heat exchanger, The modified Froude number FrM ¼ S2/dh,t,oA is defined and used in the present study. It is 79 for the present heat exchanger. Heat transfer factor j and friction factor f can be correlated as:
j ¼ 0:1255Re0:67
(20a)
When 4000 < Re<85,000,FrM ¼ 79
f ¼ 42:1244Re0:6576
(20b)
When 1000 < Re<8000,FrM ¼ 79
f ¼ 0:6664Re0:1956
(20c)
When 8000 Re<40,000,FrM ¼ 79 The correlations of heat transfer factor and friction factor are also shown in Fig. 9a and b, respectively. From the figures it can be found that the heat transfer factor grows with the Re and the friction factor decrease with the Re. It also can be found that the slope of the friction factor correlation exists a change in Fig. 9b at Re ¼ 8000. It may be caused by the change of the fluid state. Comparisons of heat transfer factor and friction factor of heat exchanger with FrM ¼ 79 and heat exchanger with FrM ¼ 64 can be found in Fig. 9, From Fig. 9 it is clear that the heat transfer performance of heat exchanger with FrM ¼ 64 is better than the heat exchanger with FrM ¼ 79. But in Fig. 9b, it can be found that, their friction factors are almost the same. It denotes that the shell side heat transfer coefficient of the twisted oval tube heat exchanger can
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
heat transfer factor j
a
381
Table 2 Parameters of rod baffle heat exchanger.
Current Data Point Equation (20a) [19] Dzyubenko [20-21] Dzyubenko [7] Si Qin
100
Parameters Items
Shell diameter, mm Baffle ring spacing, mm Tube pitch, mm Baffle ring inner diameter, mm Baffle ring outer diameter, mm
224 230 30 216 220
Parameters
Rod diameter, mm 5 Baffle Number 9 Tube length, mm 2500 Tube Number 37 90 Tube layout angel,
30
also been accepted by the commercial heat exchanger design software HTRI (Heat Transfer Research Inc.). Basic approach of this method is expressed as follow: Calculating of heat transfer performance
10 1000
10000 Reynolds number Re
100000
b Current Data Point Equation (20b) and (20c) [19] B.V. Dzyubenko [20-21] B.V. Dzyubenko [7] Si Qin
0.3 friction factor f
Items
0.1
0.04 1000
10000
100000
Reynolds number Re Fig. 9. Correlations of shell side heat transfer and pressure drop performance. a. Correlation of shell side heat transfer factor j. b. Correlation of shell side friction factor f.
be improved by increasing FrM but will result in little increase of pressure drop. In order to analyze the applicability of these correlations in Table 1 whenFrM ¼ 79, FrM ¼ 79 is substituted into the equations in Table 1 and compared with Eq. (20a),(20b) and (20c) in Fig. 9, Heat transfer and pressure drop correlations of the twisted oval tube heat exchanger with FrM ¼ 64 is also presented from the point of comparative analysis. From Fig. 9a, it can be found that both Dzyubenko and Si’s heat transfer factor correlation consists well with the present data in the range of 4000 < Re < 10,000, But their difference is notable when Re 10,000. From Fig. 9b, it also can be found that Si’s friction factor correlation agrees well with the present data in the range of Re > 8000. 3.2.2. Heat transfer and pressure drop performance compared with rod baffle heat exchanger In order to comparatively analyzing the heat transfer and pressure drop performance of the tested heat exchanger, a rod baffle heat exchanger with similar geometric parameters with the tested twisted oval tube heat exchanger is designed. Commons of the two heat exchangers are that the fluid in the shell side flows both longitudinally and the shell side hydraulic diameters of the two heat exchangers are equal. Details of the rod baffle heat exchanger can be found in Table 2. The tube layout angel is set as 90 according to TEMA. The heat transfer and pressure drop performances of the rod baffle heat exchanger are calculated with Gentry’s [24] method. This method is proposed based on mass of experiments and has
h ¼ 4jPr0:3 l=de
(21)
for laminar flow: j ¼ jl ¼ Cl Re0:6 for turbulent flow: j ¼ jt ¼ Ct Re0:8 WhereCl,Ct are parameters related to the geometric parameters of the rod baffle heat exchanger. Calculating of pressure drop performance:
DPl ¼ 24rfLu2l =dh
(22)
DP b ¼ 0:5Nr Kb ru2b
(23)
DP ¼ DPl þ DPb
(24)
Comparison of the performances of rod baffle heat exchanger and twisted oval tube heat exchanger is presented in Fig. 10. The comparison is carried out in the valuable range of Eq. (20a),(20b) and (20c). From Fig. 10a it can be found that the heat transfer coefficient of the twisted oval tube heat exchanger is 1.7 times of the rod baffle heat exchanger in average. And the pressure drop is 0.27 times of the rod baffle heat exchanger in average. Also it can be found that with the increasing of mass flow rate, the heat transfer coefficient of the twisted oval tube heat exchanger increases significantly but with little increase of the pressure drop. From the calculating result of rod baffle heat exchanger, it can also be found that majority pressure drop of the rod baffle heat exchanger is formed from the rod baffles and it occupies 90.5% in average in the range of 2 kg/sGs 16 kg/s in this case. That’s because when the fluid flowing through the rod baffle, there exists a sudden change of the flow area. It is this change that increases the pressure drop significantly but with little increase of the heat transfer coefficient. But this does not happen in a twisted oval tube heat exchanger. 3.2.3. Overall performance of twisted oval tube heat exchanger On the basis of ration of heat transfer coefficient at the same pressure drop of two heat exchangers, performance evaluation criterion h defined as h ¼ (Nu/Nu0)/(f/f0)1/3 has been proposed by Webb [25]. Parameters with subscript “0” denote that these parameters are from the heat exchanger which is the object to be compared. This performance evaluation criterion has been widely used in evaluating the overall performance of enhanced heat transfer tubes. It is obvious that only one side of the heat exchanger (shell side or tube side) is included in this criterion. But for a twisted oval tube heat exchanger, both the tube side and shell side geometric parameters differs from rod baffle heat exchanger or any other shell-tube type heat exchangers. So both the tube side and the shell side performance should be included in the analysis of its overall performance.
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a Rod baffle heat exchanger Twisted oval tube heat exchanger
2
heat transfer coefficient h (W/m ·K)
10000
8000
6000
4000
2000
0 0
5
10
15 20 25 mass flow rate Gs(kg/s)
30
35
b 10000
pressure drop ΔP (Pa)
8000
Rod baffle heat exchanger Twisted oval tube heat exchanger
6000
4000
2000
0 0
5 10 mass flow rate Gs(kg/s)
15
Fig. 10. Comparison of shell side performances of rod baffle heat exchanger and twisted oval tube heat exchanger. a. Comparison of shell side heat transfer coefficient. b. Comparison shell side pressure drop.
Referring to the performance evaluation criterion proposed by Webb [25], cost of the pump is extended including the pressure drop of both the tube side and the shell side in the present work. And a modified evaluation criterion hM ¼ (K/K0)/((DPtVt þ DPsVs)/ (DPt0Vt0 þ DPs0Vs0)) is defined. By setting rod baffle heat exchangers as the object that to be compared, the distribution of overall performance versus tube/shell side mass flow rate is shown in Fig. 11. Details of the distribution can also be found in Fig. 12.
Fig. 12. Comparison of shell side performances of rod baffle heat exchanger and twisted oval tube heat exchanger. a. Comparison of shell side heat transfer coefficient. b. Comparison shell side pressure drop.
These two figures denote that the twisted oval tube heat exchanger behaves better than the rod baffle heat exchanger and it is 2.75 in average. The overall performance of the twisted oval tube heat exchanger in Fig. 12a can be found increases with the shell side flow rate which varies from 2.23 to 4.4 when the tube side flow rate is 3 kg/s and varies from 1.33 to 2.8 when the tube side flow rate is 12 kg/s. In Fig. 11b, the overall performance factor decreases with the tube side flow rate which varies from 4.38 to 1.26 when the shell side flow rate is 4 kg/s and varies from 4.78 to 2.11 when the shell side flow rate is 13 kg/s. So it can be concluded that the twisted oval tube heat exchangers is preferred to work at low tube side flow rate and high shell side flow rate. 4. Conclusions
Fig. 11. Overall performance of the twisted oval tube heat exchanger.
In the present work, an experimental study of heat transfer and pressure drop performance of twisted oval tube heat exchanger has been carried out. The tube side performance has been compared with smooth round tube and the shell side performance has been compared with rod baffle heat exchanger whose shell side fluid flows also longitudinally. In order to analyze the overall performance of the twisted oval tube heat exchanger, a new performance evaluation criterion of heat exchanger has been established. It has been used to evaluate the overall performance of the twisted oval tube heat exchanger by setting the rod baffle heat exchanger as the object to be compared. Major findings are as follow:
X.-h. Tan et al. / Applied Thermal Engineering 50 (2013) 374e383
(1) An experimental system for testing the heat transfer and pressure drop performance of twisted oval tube is established and verified. Bases on this, a smooth round tube with d ¼ 25 mm and a twisted oval tube with A ¼ 29 mm, B ¼ 19.5 mm and S ¼ 230 mm has been experimentally studied. Heat transfer and pressure drop correlations of the tested tube has also been fitted and compared with the round tube. The result shows that the heat transfer coefficient of the twisted is higher than the smooth round tube at the cost of some increment of pressure drop. (2) An experimental system for testing the shell side heat transfer and pressure drop performance of a twisted oval tube heat exchanger has been established. A twisted oval tube heat exchanger has been assembled. Its shell side heat transfer and pressure drop performance have been studied experimentally. Correlations for calculating its performance are derived out and compared with former studies. The result shows that with the increasing of FrM, the shell side heat transfer coefficient and pressure drop of the twisted oval tube heat exchanger will both be promoted. (3) On the purpose of comparing the shell side heat transfer and pressure drop performance of the twisted oval tube heat exchanger with other shell tube type heat exchangers, a rod baffle heat exchanger is designed and its heat transfer and pressure drop performance have been calculated with the correlation from Gentry. The comparison result show that the rod baffle heat exchanger works with a higher shell side heat transfer coefficient and lower shell side pressure drop than the rod baffle heat exchanger. (4) Considering that when the twisted oval tube technique is been used as a heat transfer enhancement technique, both the tube side and shell side are different from traditional heat exchangers. So when analyzing the overall performance of the heat exchanger, both the shell side and tube side performance should be included in the overall performance factor. From this point of view, a modified performance criterion evaluation hM is defined and utilized in the analyzing of the overall performance of the twisted oval tube heat exchanger. The analyzing result shows that the twisted oval tube heat exchangers is preferred to work at low tube side flow rate and high shell side flow rate. References [1] A. Bejan, A.D. Kraus, Heat Transfer Handbook, Wiley, New Jersey, 2003, 1029e1130pp. [2] R.L. Webb, Principles of Enhanced Heat Transfer, John Wiley and Sons, Inc., New York, 1994. [3] C.L. Li, Design and application of the new type high-efficient screw oblate tube heat exchangers, Chemical Engineering & Machinery 32 (3) (2005) 162e165 (in Chinese).
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[4] B. Ljubicic, Testing of Twisted Tube Exchangers in Transition Flow Regime, Compact Heat Exchangers and Enhancement Technology for the Process Industries (1999). 135e139. [5] A. Mushabbab, Design and Operate a Fouling Monitoring Device to Study Fouling at Twisted Tube, King Fahd University of Petroleum & Minerals, Dhahran, 2007, 96e135. [6] L.A. Asmantas, M.A. Nemira, V.V. Trilikauskas, Coefficients of heat transfer and hydraulic drag of a twisted oval tube, Heat Transfer-Soviet Research 17 (4) (1985) 103e109. [7] Q. Si, Q. Xia, L.H. Liang, D.X. Li, Investigation of heat transfer and flow resistance on twisted tube heat exchanger, Journal of Chemical Industry and Engineering (China) 46 (5) (1995) 601e608 (in Chinese). [8] X.N. Gao, H.C. Zou, D.Y. Wang, Y.S. Lu, Heat transfer and flow resistance properties in twisted oblate tube with large twist ratio, Journal of South China University of Technology (Natural Science) 36 (11) (2008) 17e21 (in Chinese). [9] F. Bishara, M.A. Jog, R.M. Manglik, Computational simulation of swirl enhanced flow and heat transfer in a twisted oval tube, Journal of Heat Transfer 131 (8) (2009) 080902. [10] X.N. Gao, H.B. Yin, Y.Y. Huang, Y.T. Fang, Z.G. Zhang, Nucleate pool-boiling enhancement outside a horizontal bank of twisted tubes with machined porous surface, Applied Thermal Engineering 29 (2009) 3212e3217. [11] J.A. Meng, Z.X. Li, Z.Y. Guo, S. Wei, Simulation and analysis on laminar flow and heat transfer in twisted ellipse-tube, Journal of Engineering Thermophysics 23 (2002) 117e120 (in Chinese). [12] S. Yang, L. Zhang, H. Xu, Experimental study on convective heat transfer and flow resistance characteristics of water flow in twisted elliptical tubes, Applied Thermal Engineering 31 (2011) 2981e2991. [13] B.V. Dzyubenko, Investigation of the transfer properties of a stream in a heat exchanger with spiral tubes, Journal of Engineering Physics and Thermophysics 38 (6) (1981) 589e593. [14] B.V. Dzyubenko, P.A. Urbonas, L.A. Ashmantas, Inter channel mixing of heat carriers in a bundle of spiral tubes, Journal of Engineering Physics and Thermophysics 45 (1) (1984) 729e733. [15] B.V. Dzyubenko, V.N. Stetsyuk, Effect of flow-twisting intensity on the mixing of a heat-transfer agent in bundles of twisted tubes, Journal of Engineering Physics and Thermophysics 55 (5) (1989) 1195e1200. [16] B.V. Dzyubenko, L.V. Ashamantas, M.D. Segal, Modeling and Design of Twisted Tube Heat Exchanger, Begell House Inc., New York, 2000, 70e83pp. [17] B.V. Dzyubenko, Heat exchanger along the initial segment in a heat exchanger with a helical flow, Journal of Engineering Physics and Thermophysics 42 (2) (1982) 153e157. [18] B.V. Dzyubenko, Estimation of the thermo hydraulic efficiency of heat exchanging apparatuses with twisted tubes, Heat Transfer Research 37 (4) (2006) 349e363. [19] V.M. Levlev, E.K. Kalinin, I.I. Danilov, B.V. Dzyubenko, G.A. Dreitser, Heat transfer in the turbulent swirling flow in a channel of complex shape, in: Heat transfer 1982: Proceedings of the Seventh International Conference, vol. 3, Hemisphere Publishing Corporation, Washington D. C., 1982, pp. 171e176. [20] B.V. Dzyubenko, Drag in heat exchanger with a twisted flow, Journal of Engineering Physics and Thermophysics 44 (3) (1983) 237e241. [21] B.V. Dzyubenko, G.A. Dreitser, Heat transfer and fluid friction in bundles of twisted tubes, Journal of Engineering Physics and Thermophysics 50 (6) (1986) 611e618. [22] R.J. Moffat, Using uncertainty analysis in the planning of an experiment, Journal of Fluids Engineering 107 (2) (1985) 173e178. [23] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiment, ASME Mechanical Engineering 75 (1953) 3e8. [24] C.C. Gentry, Baffle heat transfer technology, Chemical Engineering 86 (7) (1990) 48e57. [25] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surface in heat exchanger design, International Journal of Heat and Mass Transfer 24 (4) (1981) 715e726.