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Experimental study of mixed convection heat transfer in vertical helically coiled tube heat exchangers
Experimental Thermal and Fluid Science 34 (2010) 900–905
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of mixed convection heat transfer in vertical helically coiled tube heat exchangers N. Ghorbani a, H. Taherian b, M. Gorji c, H. Mirgolbabaei d,* a
School of Mechanical Engineering, University of Leeds, Leeds, England, UK Department of Engineering Technology and Industrial Distribution, Texas A&M University, College Station, TX, USA c Department of Mechanical Engineering, Babol Noushirvani University of Technology, Babol, Iran d Department of Mechanical Engineering, Islamic Azad University, Jouybar branch, Jouybar, Iran b
a r t i c l e
i n f o
Article history: Received 26 October 2009 Received in revised form 25 December 2009 Accepted 15 February 2010
Keywords: Experimental study Shell-and-coil heat exchanger Heat transfer Mixed convection
a b s t r a c t In this study the mixed convection heat transfer in a coil-in-shell heat exchanger for various Reynolds numbers, various tube-to-coil diameter ratios and different dimensionless coil pitch was experimentally investigated. The experiments were conducted for both laminar and turbulent flow inside coil. Effects of coil pitch and tube diameters on shell-side heat transfer coefficient of the heat exchanger were studied. Different characteristic lengths were used in various Nusselt number calculations to determine which length best fits the data and several equations were proposed. The particular difference in this study in comparison with the other similar studies was the boundary conditions for the helical coils. The results indicate that the equivalent diameter of shell is the best characteristic length. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Heat transfer in curved and helical circular tubes has been the subject of several studies and it has been widely reported in literature that heat transfer rates in helical coils are higher as compared to a straight tube. They are widely used in industrial applications such as power generation, nuclear industry, process plants, heat recovery systems, refrigeration, food industry, etc. The main application of coil-in-shell heat exchanger is in solar domestic hot water (SDHW) systems. However, their use in heat recovery systems for space heating also has been reported [1]. The compactness and the high heat transfer performance are the main characteristics of coiled pipes. In spite of numerical and experimental studies that have been done in relation to tube-side heat transfer coefficient, there are not many investigations on shell-side mixed convection heat transfer coefficient of shell-andcoil heat exchangers. The main characteristics of coiled pipes are the compactness and the high heat transfer performance. Srinivasan et al. [1] experimented on various coils to determine friction factors. The helical coils were made of 12.5 mm ID tube having various coil diameters in the range of 92–1282 mm. Four different coil pitches of 2.5, 3.3, 6.6 and 13.2 tube diameters were tested and graphs of friction factors with respect to the Dean number were produced. All the graphs showed breakpoints which were
* Corresponding author.Tel.: +98 9111139195. E-mail address: [email protected] (H. Mirgolbabaei). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.02.004
interpreted as the critical Reynolds number value so that equation was found to describe this critical value for different tube diameter to shell diameter ratio. Rogrers and Mayhew [2] concentrated their attention on heat transfer and pressure loss in helically coiled tubes with turbulent flow. Three different coils having mean diameters of 10.2, 12.5 and 190 mm, made of 9.45 mm ID copper tubes were heated by steam at slightly above atmospheric pressure. The heat transfer data resulted in the empirical equation for the Reynolds number of 104–105 through which the flow was assumed turbulent. Manlapaz and Churchill [3] studied the laminar convection heat transfer in helical coils and proposed correlations of friction factor and Nusselt number for the case of coils with constant wall heat flux and constant wall temperature. Taherian and Allen [4] considered the natural convection heat transfer on shell-and-coil heat exchanger. The effects of tube diameter, coil diameter, coil surface and shell diameter on the shell-side heat transfer coefficient of shell-and-coil natural convection heat exchanger were studied. The Nusselt number was correlated with the Rayleigh number based on the hydraulic diameter of the heat exchanger. A correlation for the Nusselt number values versus the heat flux Rayleigh number based on Dhx. Their correlation is suggested for range 6 104 < Raq,Dhx < 2 1010. A numerical investigation of the forced convection heat transfer from vertical helically coiled tubes at various Reynolds and Rayleigh numbers, various coil-to-tube diameter ratios and nondimensional coil pitches was studied by Mirgolbabaei et al.
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
901
Nomenclature A Ac,f D, d Deq Dhx He Nu Pr Ra Re De T UA Ap H L LMTD N Q
total coil surface (m2) flow cross-section area (m2) diameter (m) 4V equivalent diameter of shell, pDtfL (m) 4A H heat exchanger hydraulic diameter, Ac;fp (m) 2 1=2 helical coil number, De 1 þ ppDc
V P Cp g h k _ m
Nusellt number, hD k Prandtl number, am 3 Rayleigh number, gbDaTD m Reynolds number, VD t ffiffiffiffiffiffiffiffiffiffi r Dt Dean number, Re Dc temperature (K) overall conductance of heat exchanger (W/K) wetted surface area on the shell side (m2) heat exchanger height (m) total length of coils (m) logarithmic mean temperature difference number of coils heat transfer rate (W)
Greek symbols a thermal diffusivity (m/s2)
[5]. They found that with increasing dimensionless coil pitch in medium range, the heat transfer coefficient decreases while with increasing the pitch to 2 tube diameter, heat transfer coefficient is increased. Also it was concluded that heat transfer coefficient decreases by increasing the tube diameter for the same dimensionless coil pitch. They used different characteristic lengths in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell-side of the heat exchanger reasonably demonstrates the desired location. Moawed [6] reported an experimental investigation of steady state natural convection heat transfer from uniformly heated helicoidal pipes oriented vertically and horizontally. He did the experiment to four helicoidal pipes having different ratios of coil diameter to pipe diameter (D/do), pitch to pipe diameter (p/do) and length to pipe diameter (L/do) with a range of Rayleigh numbers from 1.5 103 to 1.1 105. The results showed that the overall Nusselt number increases with the increase of (D/do), (p/do) and (L/do) for the vertical helicoidal pipes. For the horizontal helicoidal pipes, the overall Nusselt number increases with the increase of (p/ do) and (L/do), but it decreases with the increase of (D/do). Two different equations used to correlate the Nusselt number for horizontal and vertical helicoidal pipes were presented. Ali [7] studied natural convection heat transfer from helical coils immersed in a large water tank. Two different tube diameters, 8 mm and 12 mm OD, with five coil diameters and up to five different pitches of 1.5–4 with 5 or 10 turns were tested. Finally two correlations were presented for the Nusselt number data based on the coil length, for 12 and 8 mm OD tubes respectively. Their correlations show that the heat transfer coefficient for the 12 mm OD tube decreases with increased length, while for the 8 mm OD tube, an increase in length of the coil will increase the heat transfer coefficient considerably. No explanations were provided for this unexpected behavior. Prabhanjan et al. [8] performed an experimental investigation of natural convection heat transfer from helical coiled tubes in water. They correlated outside Nusselt number to the Rayleigh number using different characteristic lengths and finally considered the coil height as the best representation for a
q b
q
velocity (m/s) coil pitch (m) specific heat (J/kg K) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) mass flow rate (kg/s)
mass density (kg/m3) coefficient of volumetric thermal expansion (1/K) kinematic viscosity (m2/s)
Subscripts c coil h hot water i inner, tube side S shell t tube o outer, shell side
vertical coil. Their prediction procedure shows a promise as a method of predicting the outlet temperature from a coil given the inlet temperature, both temperature and coil dimensions. Xin and Ebadian [9] studied shell-and-coil natural convection heat exchangers experimentally. They proposed several correlations for Nusselt numbers versus Rayleigh numbers based on different characteristic length. Ajele [10] proposed a correlation for natural convection heat transfer in shell and coil heat exchanger, using experimental work. Conte et al. [11] performed numerical investigations to understand forced laminar fluid flow over coiled pipes with circular cross-section. They focused on exploring the convective heat transfer from conical and helical coils with comparative studies. The same numerical investigation method was applied to the two differentially coiled pipes (helical and conical) and for different Reynolds numbers corresponding to five cases of exterior flow arrangement. The results show better heat transfer performance for cases of conical coils where much flow turbulence was observed due to an effective flow arrangement. Although there are many works in coil side of shell-and-coil heat exchanger correlated to heat transfer coefficient and natural convection on shell-side, but there are not many investigations on shell side and forced and mixed convection. In the present study the mixed convection heat transfer in a coil-in-shell heat exchanger for various Reynolds numbers, various tube-to-coil diameter ratios and different dimensionless coil pitch was experimentally investigated. The experiments were conducted for both laminar and turbulent flow inside coil. 2. Experimental apparatus and test section Fig. 1 shows the apparatus arranged for heat exchanger experiments. Water was used as the hot and cold fluid whereas hot water was pumped to the tank and coil, passing through six electric heaters. A valve is installed at the inlet of the heat exchanger to control the flow rate and cold water taken from urban water in the shell side. The flow rate was measured by using a calibrated measuring cylinder and a stopwatch positioned at the outlet of heat exchanger. The temperature of the inlet water of coiled tube
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N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
3. Heat transfer For determining the heat flux rate, we assumed that the thermal resistance of the copper tube wall was negligible. A temperature of coil surfaces was taken as equal to the water temperature inside the coil at the same location in order to calculate local heat flux. According to the research of Srinivasan [1], the critical Reynolds number for the helical pipe flow, which determines the flow is laminar or turbulent, is related to the curvature ratio as follows:
h i Recrit: ¼ 2100 1 þ 12ðd=DÞ0:5
ð1Þ
The values of heat transfer rate and ho are calculated using Eqs. (2)–(5). All these properties were averaged over inlet and outlet of the fluid flow in each side. The values of Reynolds, Rayleigh and Nusselt numbers will be obtained from Eqs. (6)–(8) respectively.
_ c cpc ðT h;i T h;o Þ Qh ¼ m LMTD ¼
ð2Þ
ðT h;i T c;o Þ ðT h;o T c;i Þ T T ln T h;i Tc;oc;i
ð3Þ
h;o
UA ¼
_ c cpc ðT h;i T h;o Þ m LMTD
ð4Þ
1 1 1 ¼ ho U hi Res ¼ Fig. 1. (a) Apparatus for heat exchanger experiments, and (b) schematic diagram of a shell-and-coil mixed convection heat exchanger.
to the heat exchanger was controlled by thermostat. Four constant temperatures (50, 60, 70 and 80 °C) were considered for inlet mass flow rate of coil and the temperature of shell side inlet was also temperature of the tap water. These temperatures are in accordance with the outlet temperature of a flat plate solar collector. The mass flow rates for both shell- and coil-side were 0.03, 0.05, 0.09, and 0.113 kg/s, as well. The specification of heat exchanger is shown in Table 1. The coil was formed carefully by using 9.52 and 12.5 mm OD straight copper tube. Care was taken to locate the coil into the middle of the circular space between inner and outer shells of heat exchanger. Temperatures were measured using four K-type thermocouples placed at equally distanced locations in order to measure the coil surface and the fluid temperature. Four other thermocouples were located at inlets and outlets of heat exchanger to measure the temperatures of the hot and cold fluids. A data acquisition device made by Advantech model USB 4718 having a capacity of eight analog input channels in connection with a PC was used to record all temperature measurements. All tests were performed under steady state conditions. A Visual Basic code was written to retrieve and store temperature data and to perform calculations. The data acquisition system stored data every 5 s. The measured values were averaged over a period of 4 min.
Ras ¼
Nu ¼
ð5Þ
V sL
ð6Þ
m gbDTL3
ð7Þ
am ho d k
ð8Þ
4. Experimental uncertainty analysis As with report of every experimental research, the analysis of the experimental uncertainties in calculating the results must be given proper attention. The method proposed by Kline and McClintock [14] seems to be widely accepted among the authors of technical papers. The uncertainty in calculating the major heat transfer and hydraulic parameters were evaluated based on the mentioned method. The results are reported in Table 2. Table 2 Experimental uncertainties of important parameters. Parameter
Uncertainty (%)
Parameter
Uncertainty (%)
LMTD U Nui NuDeq St NTU
5.8 9.5 1 6.6 7.1 11.97 1
_c m _s m ReDeq Q hi ho
1 1.6 1.74 2.47 1.14 6.43 1
e0
e
Table 1 Geometrical characteristics of the heat exchanger. No.
Dt,o (mm)
Dt,i (mm)
Dc (mm)
Ds,i (mm)
Ds,o (mm)
H (mm)
p (mm)
N
1 2 3
9.47 12.59 12.59
7.77 10.82 10.82
125.71 128.31 128.31
88.9 88.9 88.9
157 157 157
383 383 383
16.47 16.47 23.57
23.25 23.25 16.25
903
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
Fig. 2. Shell-side heat transfer coefficient versus heat transfer rate for various tube diameter.
5. Results The effects of tube diameter, coil surface area and dimensionless pitch are reported in this study. In turbulent flow over a single circular cylinder, the effect of the cylinder diameter is known to be insignificant [12]. Since the flow regime is believed to be turbulent in the current experiment, it is expected that, there will be negligible influence of the tube diameter on ho. Fig. 2 indicates that tube diameter does not influence the heat transfer coefficient for the same dimensionless pitch noticeably. As a result, the Nusselt number could not be correlated satisfactorily with the Reynolds num-
ber based on the tube diameter. The insignificant effect of the tube diameter on ho was also reported by Taherian and Allen [4]. The coil surface area was the most influential geometrical parameter on the heat transfer coefficient. Fig. 3 is the plot of the heat transfer coefficient as a function of coil surface area at the fixed heat transfer rate. It could be deduced from Fig. 3 that the heat transfer coefficient decreases rapidly as the coil surface area increases. This indicates that increasing the coil surface area in order to increase the UA product of the heat exchanger can not be done without paying 1600
1100
1400
ho(W/m2.K)
ho(W/m2.K)
1000 900 800
1200 1000 800
700 600
600
400 2000
500 400 0.2
0.25
0.3
0.35
A(m2) Fig. 3. Shell-side heat transfer coefficient versus coil surface area.
0.4
12000
22000
32000
42000
q(W/m2) Coil #2
Coil #3
Fig. 4. ho versus heat flux for various coil pitch.
52000
904
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905 500
35
450
30
400
25
300
NuDt
UA(W/ºC)
350
250
20 15
200 150
10
100 50
5 0.00E+00
0 0
1000
2000
3000
4000
5000
5.00E+05
1.00E+06
QA(W.m2)
1.50E+06
2.00E+06
2.50E+06
RaDt
6000
Fig. 7. The Nusselt number versus the Rayleigh number based on tube diameter.
Fig. 5. Variation of the overall heat transfer coefficient versus the heat rate.
the price of reduced U. Taherian and Allen [4] in their study of natural convection shell-and-coil heat exchanger also found that the heat transfer coefficient decreased as the surface area increased. This was also observed by Keyhani and Dalton [15] in their study of natural convection heat transfer in horizontal rod-bundle enclosure, which has some similarities to the case of shell-and-coil heat exchanger. They also found that the heat transfer coefficient decreased as the surface area increased. The shell-side heat transfer coefficient data was plotted versus heat flux for different coil pitch in Fig. 4. As the figure shows, the heat transfer coefficient enhances with increasing the dimensionless coil pitch. This is the same results in comparison with the results of Ref. [13]. The UA product, called overall heat transfer coefficient, of the heat exchanger indicates the ability of the exchanger to transfer heat between the hot and cold streams at a certain mean temperature difference. The overall heat transfer coefficient of the heat exchanger increases with increasing the rate of heat transfer, because the both shell-side and tube-side heat transfer coefficient increase as a result of heat transfer rate increase. This is evident from Fig. 5 which includes the data from all tests. The UA product is plotted against the heat transfer rate multiplied by surface area to isolate the effect of the surface area on the UA product.
show Nusselt number versus Reynolds and Rayleigh numbers based on tube diameter. Better correlations, can be achieved between the data by introducing the heat exchanger hydraulic diameter as the characteristic length. Fig. 8 shows the Nusselt number data based on Dhx versus Rayleigh, Reynolds and Prandtl numbers. Eq. (9) is the result of the curve fitting for the range of 2.5 107 < RaDhx < 3.5 108, 150 < ReDhx < 1200. 0:2 0:3 NuDhx ¼ 0:0013Ra0:5128 Dhx ReDhx Prs
ð9Þ
Fig. 9 plots the Nusselt number data based on Dhx against the modified Rayleigh and Reynolds numbers which are based on the heat exchanger hydraulic diameter as well. The correlation of the current data obtained from the curve fitness in Fig. 9, for the range of 5 105 < RaDhx < 2 107 is as follow:
6. Nusselt number correlation Although, for a shell-and-coil heat exchanger the tube diameter is clearly not a good choice to be considered as characteristic length, the Nusselt number based on the tube diameter can be used to compare the current results with those by Ref. [4]. Figs. 6 and 7
Fig. 8.
NuDhx Re0:2 Pr0:3 Dhx s
versus RaDhx.
1000
35 30
NuDhx
100
NuDt
25 20
10
15 10
1 1.E+03
5 0
50
100
150
200
250
ReDt Fig. 6. The Nusselt number versus the Reynolds number based on tube diameter.
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
Ra*Dhx Taherian and Allen [4]
Current study
Fig. 9. NuDhx versus RaDhx in comparison with the results of Taherian and Allen [4].
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
transfer coefficient reduction. On the other hand, the convection heat transfer coefficient of shell-side increases when the coil pitch increases. The overall heat transfer coefficient of heat exchanger increases as the heat transfer rate increases. Different features of the heat exchanger have been studied to find the most suitable characteristic length upon which the correlation between the Nusselt number and the Rayleigh and Reynolds numbers could be obtained and finally it has been shown that, the equivalent diameter of the shell-side of the heat exchanger reasonably demonstrates the desired relation.
100
NuDeq/(ReDeq0.2Prs0.3)
905
10
References
1 1.00E+07
1.00E+08
1.00E+09
RaDeq Fig. 10.
NuDeq 0:2 ReDeq Pr0:3 s
NuDhx ¼ 0:1314Ra0:4278 Dhx
versus RaDeq.
ð10Þ
The agreement between Eq. (10) and Taherian and Allen’s correlations is satisfactory. As shown in Fig. 9 the results of the current study is a little more than ones of Ref. [4]. This is because of the impact of Reynolds number in mixed convection. Another characteristic length that could be better in correlation of Nusselt number is equivalent diameter of shell. Fig. 10 plots the Nusselt number data based on equivalent diameter of shell against the Rayleigh and Reynolds numbers. The correlation of the data for the range 120 < ReDeq < 1200 and 1.2 107 < RaDeq < 3.2 108 is presented in Eq. (11) with a coefficient of determination of r2 = 0.9. 0:2 0:3 NuDeq ¼ 0:0041Ra04533 Deq ReDeq Prs
ð11Þ
The Eq. (11) indicates a good correlation of Nusselt number based on equivalent diameter of shell. It could be suggested as the most suitable characteristic length to correlate the Nusselt number versus the Rayleigh and Reynolds numbers. 7. Conclusions In this study the mixed convection heat transfer in helical coiled tube heat exchanger was investigated experimentally. The tube diameter was found to have negligible influence on the shell-side heat transfer coefficient. The coil surface area showed a negative effect on ho so that increasing the coil surface resulted in heat
[1] P.S. Srinivasan, S.S. Nandapurkar, F.A. Holand, Friction factors for coils, Institution of Chemical Engineering Transaction 48 (1970) T156–T161. [2] G.F.C. Rogrers, Y.R. Mayhew, Heat transfer and pressure loss in helically coiled tubes with turbulent flow, International Journal of Heat and Mass Transfer 7 (1964) 1207–1216. [3] R.L. Manlapaz, S.W. Churchill, Fully developed laminar convection from a helically coil, Chemical Engineering Communication 9 (1981) 185–200. [4] H. Taherian, Peter L. Allen, Experimental study of natural convection shell-andcoil heat exchanger, the american society of mechanical engineers, in: ASME Proceeding of the 7th AIAA/ASME, HTD-vol. 357-2, 1998. [5] H. Mirgolbabaei, H. Taherian, G. Domairry, N. Ghorbani, Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers, International Journal for Numerical Methods in Fluids, in press. doi:10.1002/fld.2284. [6] M. Moawed, Experimental investigation of natural convection from vertical and horizontal helicoidal pipes in HVAC applications, Energy Conservation and Management 46 (2005) 2996–3013. [7] M.E. Ali, Experimental investigations of natural convection from vertical helical coiled tubes, International Journal of Heat and Mass Transfer 37 (1994) 665–671. [8] D.G. Prabhanjan, T.J. Rennie, G.S.V. Raghavan, Natural convection heat transfer from helical coiled tubes, International Journal of Thermal Sciences 43 (2004) 359–365. [9] R.C. Xin, M.A. Ebadian, Natural convection heat transfer from helicoidal pipes, Journal of Thermophysics and Heat Transfer 10 (2) (1996) 297–302. [10] Ajele, Natural Convection Heat Transfer from Enclosed Helical Coils, PhD Thesis, Technical University of Nova Scotia, 1995. [11] I. Conté, X.F. Peng, B.X. Wang, Numerical investigation of forced fluid flow and heat transfer from conically coiled pipes, Numerical Heat Transfer Part A: Applications 53 (9) (2008) 945–965. [12] W.H. McAdams, Heat Transmission, third ed., McGraw-Hill, New York, NY, 1954. [13] H. Taherian, Natural Convection Heat Transfer in Heat Exchanger with Vertical Coils, PhD Thesis, Dalhouise University, Daltech, Halifax, Nova Scotia, Canada, 1998. [14] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiments, Mechanical Engineering 75 (1953) 3–9. [15] M. Keyhani, T. Dalton, Natural convection heat transfer in horizontal rodbundle enclosure, Journal of Heat Transfer 118 (1996) 598–605.
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of mixed convection heat transfer in vertical helically coiled tube heat exchangers N. Ghorbani a, H. Taherian b, M. Gorji c, H. Mirgolbabaei d,* a
School of Mechanical Engineering, University of Leeds, Leeds, England, UK Department of Engineering Technology and Industrial Distribution, Texas A&M University, College Station, TX, USA c Department of Mechanical Engineering, Babol Noushirvani University of Technology, Babol, Iran d Department of Mechanical Engineering, Islamic Azad University, Jouybar branch, Jouybar, Iran b
a r t i c l e
i n f o
Article history: Received 26 October 2009 Received in revised form 25 December 2009 Accepted 15 February 2010
Keywords: Experimental study Shell-and-coil heat exchanger Heat transfer Mixed convection
a b s t r a c t In this study the mixed convection heat transfer in a coil-in-shell heat exchanger for various Reynolds numbers, various tube-to-coil diameter ratios and different dimensionless coil pitch was experimentally investigated. The experiments were conducted for both laminar and turbulent flow inside coil. Effects of coil pitch and tube diameters on shell-side heat transfer coefficient of the heat exchanger were studied. Different characteristic lengths were used in various Nusselt number calculations to determine which length best fits the data and several equations were proposed. The particular difference in this study in comparison with the other similar studies was the boundary conditions for the helical coils. The results indicate that the equivalent diameter of shell is the best characteristic length. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Heat transfer in curved and helical circular tubes has been the subject of several studies and it has been widely reported in literature that heat transfer rates in helical coils are higher as compared to a straight tube. They are widely used in industrial applications such as power generation, nuclear industry, process plants, heat recovery systems, refrigeration, food industry, etc. The main application of coil-in-shell heat exchanger is in solar domestic hot water (SDHW) systems. However, their use in heat recovery systems for space heating also has been reported [1]. The compactness and the high heat transfer performance are the main characteristics of coiled pipes. In spite of numerical and experimental studies that have been done in relation to tube-side heat transfer coefficient, there are not many investigations on shell-side mixed convection heat transfer coefficient of shell-andcoil heat exchangers. The main characteristics of coiled pipes are the compactness and the high heat transfer performance. Srinivasan et al. [1] experimented on various coils to determine friction factors. The helical coils were made of 12.5 mm ID tube having various coil diameters in the range of 92–1282 mm. Four different coil pitches of 2.5, 3.3, 6.6 and 13.2 tube diameters were tested and graphs of friction factors with respect to the Dean number were produced. All the graphs showed breakpoints which were
* Corresponding author.Tel.: +98 9111139195. E-mail address: [email protected] (H. Mirgolbabaei). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.02.004
interpreted as the critical Reynolds number value so that equation was found to describe this critical value for different tube diameter to shell diameter ratio. Rogrers and Mayhew [2] concentrated their attention on heat transfer and pressure loss in helically coiled tubes with turbulent flow. Three different coils having mean diameters of 10.2, 12.5 and 190 mm, made of 9.45 mm ID copper tubes were heated by steam at slightly above atmospheric pressure. The heat transfer data resulted in the empirical equation for the Reynolds number of 104–105 through which the flow was assumed turbulent. Manlapaz and Churchill [3] studied the laminar convection heat transfer in helical coils and proposed correlations of friction factor and Nusselt number for the case of coils with constant wall heat flux and constant wall temperature. Taherian and Allen [4] considered the natural convection heat transfer on shell-and-coil heat exchanger. The effects of tube diameter, coil diameter, coil surface and shell diameter on the shell-side heat transfer coefficient of shell-and-coil natural convection heat exchanger were studied. The Nusselt number was correlated with the Rayleigh number based on the hydraulic diameter of the heat exchanger. A correlation for the Nusselt number values versus the heat flux Rayleigh number based on Dhx. Their correlation is suggested for range 6 104 < Raq,Dhx < 2 1010. A numerical investigation of the forced convection heat transfer from vertical helically coiled tubes at various Reynolds and Rayleigh numbers, various coil-to-tube diameter ratios and nondimensional coil pitches was studied by Mirgolbabaei et al.
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
901
Nomenclature A Ac,f D, d Deq Dhx He Nu Pr Ra Re De T UA Ap H L LMTD N Q
total coil surface (m2) flow cross-section area (m2) diameter (m) 4V equivalent diameter of shell, pDtfL (m) 4A H heat exchanger hydraulic diameter, Ac;fp (m) 2 1=2 helical coil number, De 1 þ ppDc
V P Cp g h k _ m
Nusellt number, hD k Prandtl number, am 3 Rayleigh number, gbDaTD m Reynolds number, VD t ffiffiffiffiffiffiffiffiffiffi r Dt Dean number, Re Dc temperature (K) overall conductance of heat exchanger (W/K) wetted surface area on the shell side (m2) heat exchanger height (m) total length of coils (m) logarithmic mean temperature difference number of coils heat transfer rate (W)
Greek symbols a thermal diffusivity (m/s2)
[5]. They found that with increasing dimensionless coil pitch in medium range, the heat transfer coefficient decreases while with increasing the pitch to 2 tube diameter, heat transfer coefficient is increased. Also it was concluded that heat transfer coefficient decreases by increasing the tube diameter for the same dimensionless coil pitch. They used different characteristic lengths in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell-side of the heat exchanger reasonably demonstrates the desired location. Moawed [6] reported an experimental investigation of steady state natural convection heat transfer from uniformly heated helicoidal pipes oriented vertically and horizontally. He did the experiment to four helicoidal pipes having different ratios of coil diameter to pipe diameter (D/do), pitch to pipe diameter (p/do) and length to pipe diameter (L/do) with a range of Rayleigh numbers from 1.5 103 to 1.1 105. The results showed that the overall Nusselt number increases with the increase of (D/do), (p/do) and (L/do) for the vertical helicoidal pipes. For the horizontal helicoidal pipes, the overall Nusselt number increases with the increase of (p/ do) and (L/do), but it decreases with the increase of (D/do). Two different equations used to correlate the Nusselt number for horizontal and vertical helicoidal pipes were presented. Ali [7] studied natural convection heat transfer from helical coils immersed in a large water tank. Two different tube diameters, 8 mm and 12 mm OD, with five coil diameters and up to five different pitches of 1.5–4 with 5 or 10 turns were tested. Finally two correlations were presented for the Nusselt number data based on the coil length, for 12 and 8 mm OD tubes respectively. Their correlations show that the heat transfer coefficient for the 12 mm OD tube decreases with increased length, while for the 8 mm OD tube, an increase in length of the coil will increase the heat transfer coefficient considerably. No explanations were provided for this unexpected behavior. Prabhanjan et al. [8] performed an experimental investigation of natural convection heat transfer from helical coiled tubes in water. They correlated outside Nusselt number to the Rayleigh number using different characteristic lengths and finally considered the coil height as the best representation for a
q b
q
velocity (m/s) coil pitch (m) specific heat (J/kg K) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) mass flow rate (kg/s)
mass density (kg/m3) coefficient of volumetric thermal expansion (1/K) kinematic viscosity (m2/s)
Subscripts c coil h hot water i inner, tube side S shell t tube o outer, shell side
vertical coil. Their prediction procedure shows a promise as a method of predicting the outlet temperature from a coil given the inlet temperature, both temperature and coil dimensions. Xin and Ebadian [9] studied shell-and-coil natural convection heat exchangers experimentally. They proposed several correlations for Nusselt numbers versus Rayleigh numbers based on different characteristic length. Ajele [10] proposed a correlation for natural convection heat transfer in shell and coil heat exchanger, using experimental work. Conte et al. [11] performed numerical investigations to understand forced laminar fluid flow over coiled pipes with circular cross-section. They focused on exploring the convective heat transfer from conical and helical coils with comparative studies. The same numerical investigation method was applied to the two differentially coiled pipes (helical and conical) and for different Reynolds numbers corresponding to five cases of exterior flow arrangement. The results show better heat transfer performance for cases of conical coils where much flow turbulence was observed due to an effective flow arrangement. Although there are many works in coil side of shell-and-coil heat exchanger correlated to heat transfer coefficient and natural convection on shell-side, but there are not many investigations on shell side and forced and mixed convection. In the present study the mixed convection heat transfer in a coil-in-shell heat exchanger for various Reynolds numbers, various tube-to-coil diameter ratios and different dimensionless coil pitch was experimentally investigated. The experiments were conducted for both laminar and turbulent flow inside coil. 2. Experimental apparatus and test section Fig. 1 shows the apparatus arranged for heat exchanger experiments. Water was used as the hot and cold fluid whereas hot water was pumped to the tank and coil, passing through six electric heaters. A valve is installed at the inlet of the heat exchanger to control the flow rate and cold water taken from urban water in the shell side. The flow rate was measured by using a calibrated measuring cylinder and a stopwatch positioned at the outlet of heat exchanger. The temperature of the inlet water of coiled tube
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3. Heat transfer For determining the heat flux rate, we assumed that the thermal resistance of the copper tube wall was negligible. A temperature of coil surfaces was taken as equal to the water temperature inside the coil at the same location in order to calculate local heat flux. According to the research of Srinivasan [1], the critical Reynolds number for the helical pipe flow, which determines the flow is laminar or turbulent, is related to the curvature ratio as follows:
h i Recrit: ¼ 2100 1 þ 12ðd=DÞ0:5
ð1Þ
The values of heat transfer rate and ho are calculated using Eqs. (2)–(5). All these properties were averaged over inlet and outlet of the fluid flow in each side. The values of Reynolds, Rayleigh and Nusselt numbers will be obtained from Eqs. (6)–(8) respectively.
_ c cpc ðT h;i T h;o Þ Qh ¼ m LMTD ¼
ð2Þ
ðT h;i T c;o Þ ðT h;o T c;i Þ T T ln T h;i Tc;oc;i
ð3Þ
h;o
UA ¼
_ c cpc ðT h;i T h;o Þ m LMTD
ð4Þ
1 1 1 ¼ ho U hi Res ¼ Fig. 1. (a) Apparatus for heat exchanger experiments, and (b) schematic diagram of a shell-and-coil mixed convection heat exchanger.
to the heat exchanger was controlled by thermostat. Four constant temperatures (50, 60, 70 and 80 °C) were considered for inlet mass flow rate of coil and the temperature of shell side inlet was also temperature of the tap water. These temperatures are in accordance with the outlet temperature of a flat plate solar collector. The mass flow rates for both shell- and coil-side were 0.03, 0.05, 0.09, and 0.113 kg/s, as well. The specification of heat exchanger is shown in Table 1. The coil was formed carefully by using 9.52 and 12.5 mm OD straight copper tube. Care was taken to locate the coil into the middle of the circular space between inner and outer shells of heat exchanger. Temperatures were measured using four K-type thermocouples placed at equally distanced locations in order to measure the coil surface and the fluid temperature. Four other thermocouples were located at inlets and outlets of heat exchanger to measure the temperatures of the hot and cold fluids. A data acquisition device made by Advantech model USB 4718 having a capacity of eight analog input channels in connection with a PC was used to record all temperature measurements. All tests were performed under steady state conditions. A Visual Basic code was written to retrieve and store temperature data and to perform calculations. The data acquisition system stored data every 5 s. The measured values were averaged over a period of 4 min.
Ras ¼
Nu ¼
ð5Þ
V sL
ð6Þ
m gbDTL3
ð7Þ
am ho d k
ð8Þ
4. Experimental uncertainty analysis As with report of every experimental research, the analysis of the experimental uncertainties in calculating the results must be given proper attention. The method proposed by Kline and McClintock [14] seems to be widely accepted among the authors of technical papers. The uncertainty in calculating the major heat transfer and hydraulic parameters were evaluated based on the mentioned method. The results are reported in Table 2. Table 2 Experimental uncertainties of important parameters. Parameter
Uncertainty (%)
Parameter
Uncertainty (%)
LMTD U Nui NuDeq St NTU
5.8 9.5 1 6.6 7.1 11.97 1
_c m _s m ReDeq Q hi ho
1 1.6 1.74 2.47 1.14 6.43 1
e0
e
Table 1 Geometrical characteristics of the heat exchanger. No.
Dt,o (mm)
Dt,i (mm)
Dc (mm)
Ds,i (mm)
Ds,o (mm)
H (mm)
p (mm)
N
1 2 3
9.47 12.59 12.59
7.77 10.82 10.82
125.71 128.31 128.31
88.9 88.9 88.9
157 157 157
383 383 383
16.47 16.47 23.57
23.25 23.25 16.25
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Fig. 2. Shell-side heat transfer coefficient versus heat transfer rate for various tube diameter.
5. Results The effects of tube diameter, coil surface area and dimensionless pitch are reported in this study. In turbulent flow over a single circular cylinder, the effect of the cylinder diameter is known to be insignificant [12]. Since the flow regime is believed to be turbulent in the current experiment, it is expected that, there will be negligible influence of the tube diameter on ho. Fig. 2 indicates that tube diameter does not influence the heat transfer coefficient for the same dimensionless pitch noticeably. As a result, the Nusselt number could not be correlated satisfactorily with the Reynolds num-
ber based on the tube diameter. The insignificant effect of the tube diameter on ho was also reported by Taherian and Allen [4]. The coil surface area was the most influential geometrical parameter on the heat transfer coefficient. Fig. 3 is the plot of the heat transfer coefficient as a function of coil surface area at the fixed heat transfer rate. It could be deduced from Fig. 3 that the heat transfer coefficient decreases rapidly as the coil surface area increases. This indicates that increasing the coil surface area in order to increase the UA product of the heat exchanger can not be done without paying 1600
1100
1400
ho(W/m2.K)
ho(W/m2.K)
1000 900 800
1200 1000 800
700 600
600
400 2000
500 400 0.2
0.25
0.3
0.35
A(m2) Fig. 3. Shell-side heat transfer coefficient versus coil surface area.
0.4
12000
22000
32000
42000
q(W/m2) Coil #2
Coil #3
Fig. 4. ho versus heat flux for various coil pitch.
52000
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N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905 500
35
450
30
400
25
300
NuDt
UA(W/ºC)
350
250
20 15
200 150
10
100 50
5 0.00E+00
0 0
1000
2000
3000
4000
5000
5.00E+05
1.00E+06
QA(W.m2)
1.50E+06
2.00E+06
2.50E+06
RaDt
6000
Fig. 7. The Nusselt number versus the Rayleigh number based on tube diameter.
Fig. 5. Variation of the overall heat transfer coefficient versus the heat rate.
the price of reduced U. Taherian and Allen [4] in their study of natural convection shell-and-coil heat exchanger also found that the heat transfer coefficient decreased as the surface area increased. This was also observed by Keyhani and Dalton [15] in their study of natural convection heat transfer in horizontal rod-bundle enclosure, which has some similarities to the case of shell-and-coil heat exchanger. They also found that the heat transfer coefficient decreased as the surface area increased. The shell-side heat transfer coefficient data was plotted versus heat flux for different coil pitch in Fig. 4. As the figure shows, the heat transfer coefficient enhances with increasing the dimensionless coil pitch. This is the same results in comparison with the results of Ref. [13]. The UA product, called overall heat transfer coefficient, of the heat exchanger indicates the ability of the exchanger to transfer heat between the hot and cold streams at a certain mean temperature difference. The overall heat transfer coefficient of the heat exchanger increases with increasing the rate of heat transfer, because the both shell-side and tube-side heat transfer coefficient increase as a result of heat transfer rate increase. This is evident from Fig. 5 which includes the data from all tests. The UA product is plotted against the heat transfer rate multiplied by surface area to isolate the effect of the surface area on the UA product.
show Nusselt number versus Reynolds and Rayleigh numbers based on tube diameter. Better correlations, can be achieved between the data by introducing the heat exchanger hydraulic diameter as the characteristic length. Fig. 8 shows the Nusselt number data based on Dhx versus Rayleigh, Reynolds and Prandtl numbers. Eq. (9) is the result of the curve fitting for the range of 2.5 107 < RaDhx < 3.5 108, 150 < ReDhx < 1200. 0:2 0:3 NuDhx ¼ 0:0013Ra0:5128 Dhx ReDhx Prs
ð9Þ
Fig. 9 plots the Nusselt number data based on Dhx against the modified Rayleigh and Reynolds numbers which are based on the heat exchanger hydraulic diameter as well. The correlation of the current data obtained from the curve fitness in Fig. 9, for the range of 5 105 < RaDhx < 2 107 is as follow:
6. Nusselt number correlation Although, for a shell-and-coil heat exchanger the tube diameter is clearly not a good choice to be considered as characteristic length, the Nusselt number based on the tube diameter can be used to compare the current results with those by Ref. [4]. Figs. 6 and 7
Fig. 8.
NuDhx Re0:2 Pr0:3 Dhx s
versus RaDhx.
1000
35 30
NuDhx
100
NuDt
25 20
10
15 10
1 1.E+03
5 0
50
100
150
200
250
ReDt Fig. 6. The Nusselt number versus the Reynolds number based on tube diameter.
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
Ra*Dhx Taherian and Allen [4]
Current study
Fig. 9. NuDhx versus RaDhx in comparison with the results of Taherian and Allen [4].
N. Ghorbani et al. / Experimental Thermal and Fluid Science 34 (2010) 900–905
transfer coefficient reduction. On the other hand, the convection heat transfer coefficient of shell-side increases when the coil pitch increases. The overall heat transfer coefficient of heat exchanger increases as the heat transfer rate increases. Different features of the heat exchanger have been studied to find the most suitable characteristic length upon which the correlation between the Nusselt number and the Rayleigh and Reynolds numbers could be obtained and finally it has been shown that, the equivalent diameter of the shell-side of the heat exchanger reasonably demonstrates the desired relation.
100
NuDeq/(ReDeq0.2Prs0.3)
905
10
References
1 1.00E+07
1.00E+08
1.00E+09
RaDeq Fig. 10.
NuDeq 0:2 ReDeq Pr0:3 s
NuDhx ¼ 0:1314Ra0:4278 Dhx
versus RaDeq.
ð10Þ
The agreement between Eq. (10) and Taherian and Allen’s correlations is satisfactory. As shown in Fig. 9 the results of the current study is a little more than ones of Ref. [4]. This is because of the impact of Reynolds number in mixed convection. Another characteristic length that could be better in correlation of Nusselt number is equivalent diameter of shell. Fig. 10 plots the Nusselt number data based on equivalent diameter of shell against the Rayleigh and Reynolds numbers. The correlation of the data for the range 120 < ReDeq < 1200 and 1.2 107 < RaDeq < 3.2 108 is presented in Eq. (11) with a coefficient of determination of r2 = 0.9. 0:2 0:3 NuDeq ¼ 0:0041Ra04533 Deq ReDeq Prs
ð11Þ
The Eq. (11) indicates a good correlation of Nusselt number based on equivalent diameter of shell. It could be suggested as the most suitable characteristic length to correlate the Nusselt number versus the Rayleigh and Reynolds numbers. 7. Conclusions In this study the mixed convection heat transfer in helical coiled tube heat exchanger was investigated experimentally. The tube diameter was found to have negligible influence on the shell-side heat transfer coefficient. The coil surface area showed a negative effect on ho so that increasing the coil surface resulted in heat
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