An experimental study of thermal performance of shell-and ... - UGent

International Communications in Heat and Mass Transfer 37 (2010) 775–781

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International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t

An experimental study of thermal performance of shell-and-coil heat exchangers☆ Nasser Ghorbani a, Hessam Taherian b, Mofid Gorji b, Hessam Mirgolbabaei c,⁎ a b c

School of Mechanical Engineering, University of Leeds, Leeds, England Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol 47144, Iran Department of Mechanical Engineering, Islamic Azad University, Jouybar branch, Jouybar, Iran

a r t i c l e

i n f o

Available online 19 March 2010 Keywords: Heat exchanger Helical coil Forced convection Heat transfer

a b s t r a c t In the present study an experimental investigation of the mixed convection heat transfer in a coil-in-shell heat exchanger is reported for various Reynolds and Rayleigh numbers, various tube-to-coil diameter ratios and dimensionless coil pitch. The purpose of this article is to assess the influence of the tube diameter, coil pitch, shell-side and tube-side mass flow rate over the performance coefficient and modified effectiveness of vertical helical coiled tube heat exchangers. The calculations have been performed for the steady-state and the experiments were conducted for both laminar and turbulent flow inside coil. It was found that the mass flow rate of tube-side to shell-side ratio was effective on the axial temperature profiles of heat exchanger. The results also indicate that the ɛ − NTU relation of the mixed convection heat exchangers was the same as that of a pure counter-flow heat exchanger. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Reports on extensive numerical and experimental investigations are available to be used for both laminar and turbulent flow in straight tubes. However, flow through or over coiled pipes with curvature and torsion is still under exploration. Heat exchangers are vastly used in many industrial processes. Use of helical coils adds efficiency to the heat exchanger performance. Shell-and-coil heat exchangers have been used mainly in solar domestic hot water (SDHW) systems because of their high heat transfer and smaller space requirement, their use in heat recovery systems for space heating also has been reported [1]. Therefore, it is worthy to study heat transfer, pressure drop and thermal performance of the shell side of helical or spiral coil used in heat exchangers. In spite of numerical and experimental studies which have been carried out in relation to tube-side heat transfer coefficient, there are not many investigations on the shell-side mixed convection heat transfer coefficient of shell-and-coil heat exchangers. The heat transfer and performance of a spirally coiled, finned-tube, in a steel shell heat exchanger was investigated by Wongwises et al. [2]. The spiral coil consists of a tube with 9.6 mm in diameter, having four turns and six layers. Air and water were used for shell side and tube side, respectively. They have illustrated that with increasing mass flow rate in tube side the effectiveness of the heat exchanger decreased and had a slight increase with increasing water mass flow rate.

☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (H. Mirgolbabaei). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.02.001

Thermal performance and pressure drop of the helical coil with and without fins of heat exchanger were investigated by Naphon [3]. Two different coil diameters with 9.5 mm diameter copper tube having thirteen turns were used. Hot and cold water were used as working fluid in the range between 0.10 and 0.22 kg/s and between 0.02 and 0.12 kg/s, respectively. They have shown that with increasing hot water mass flow rate friction factor decreased. An extra parameter has been introduced by Kharat et al. [4] to cover coil gap in multi helical coils in heat exchangers. A wide range of Reynolds numbers from 20,000 to 150,000 has been analyzed. They have also used Fluent 6.3.26 to compare data. Various helical coils made of 12.5 mm ID tube with various coil diameters ranging from 92 to 1282 mm to determine friction factors have been investigated by Srinivasan et al. [1]. 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 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. Tube in tube helical coil heat exchanger has been investigated to study fluid flow and heat transfer under turbulent condition by Mandal and Nigam [5]. Hot air and cold water were used in inner tube and outer tube as working fluid. Moreover, the Reynolds number in inner tube for air was ranged from 14,000 to 86,000. A CFD work investigation has been done to cover the experimental data. Rogres and Mayhew [6] concentrated their attention on heat transfer and pressure loss in helically coiled tubes with turbulent flow having mean diameters of 10.2, 12.5 and 190 mm, made of 9.45 mm ID copper tubes heated by steam at slightly above atmospheric pressure. The heat transfer data resulted in the empirical equation for the Reynolds

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Nomenclature Ac,f Ap C Cr D, d De Dhx g h H He k L LMTD ṁ N NTU Nu P Pr Q Ra Re Rm T UA V

Flow cross-section area, (m2) Wetted surface area on the shell side, (m2) Specific heat, (J/kg·K) Heat capacity ratio of the two fluids (Cmin/Cmax) Diameter, (m) sffiffiffiffiffiffiffiffiffiffiffiffiffi Dt Dean number, Re Dc 4Ac;f H Heat exchanger hydraulic diameter, , (m) Ap 2 Gravitational acceleration, (m/s ) Heat transfer coefficient, (W/m2·K) Heat exchanger height, (m) " #−1 = 2 p 2 Helical coil number, De 1 + πDc Thermal conductivity, (W/m·K) Total length of coils, (m) Logarithmic mean temperature difference Mass flow rate, (kg/s) Number of coils turns Number of (heat) transfer units hD Nusselt number, k Coil pitch, (m) ν Prandtl number, α Heat transfer rate, (W) gβΔTD3 Rayleigh number, αν VD Reynolds number, υ Tube-side to shell-side mass flow rate ratio (mc/ms, mg/ms) Temperature, (K) Overall conductance of heat exchanger (W/K) Velocity, (m/s)

Greek symbols α Thermal diffusivity, (m2/s) β Coefficient of volumetric thermal expansion, (1/K) ε Heat exchanger effectiveness ε′ Modified effectiveness ν Kinematic viscosity, (m2/s) ρ Mass density, (kg/m3)

Subscripts C Coil c Cold water h Hot water i Inner, tube side s Shell t tube

number of104to 105 through which the flow was assumed turbulent. Manlapaz and Churchill [7] have also worked on fully developed laminar convection in helical coils. Reviewing and employing previously published work of other authors, new correlations of friction factor and Nusselt number in helical coiled tubes with constant wall heat flux and constant wall temperature has been developed by Manlapaz and Churchill [7]. Natural convection heat transfer in shellin-coil heat exchangers has been studied by Taherian and Allen [8], [9]. An aqueous solution of propylene glycol was pumped from a tank into

the coils through an electric heater and a distributor manifold and recirculated after passing through rotameters. The effects of tube diameter, coil diameter, coil surface and shell diameter on the shellside heat transfer coefficient of a shell-and-coil natural convection heat exchanger which is commonly used in solar domestic hot water (SDHW) systems, were studied. They found that the modified effectiveness decreased with increasing mass flow rate ratio and developed a correlation between these two factors and the shell-andcoil heat exchanger compactness ratio, for 0:3bRm ðH =LÞ0:3 and 1:85 × 10−3 ≤ m˙ g ≤34:3 × 10−3 kg =s . The ɛ – NTU relation of the natural convection heat exchangers was similar to those of a pure counter-flow heat exchanger. The logarithmic mean temperature difference was found to decrease with increasing the mass flow rate ratio. They found that the ratio of the glycol to water mass flow rate (Rm) was influential on the axial temperature profiles of heat exchanger. For Rm greater than unity, the temperature profiles were of quadratic form from bottom to top of the heat exchanger. The profiles were linear for Rm close to unity and when the mass flow rate ratio was considerably less than unity, the temperature profiles were of the logarithmic form. The effect of increasing the heat transfer rate was to increase the slope of axial temperature profiles. Fraser et al. [10] assumed that the curves of the modified effectiveness versus the water mass flow rate are universal when the shell-side mass flow rate is fixed. They made use of the assumption of universality in order to develop an empirical model for natural convection heat exchangers in SDHW systems. Mixed convection heat transfer from the vertical helical coils was investigated numerically by Mirgolbabaei et al. [11]. It was concluded that coil pitch has significant effect on shell-side heat transfer coefficient. With increasing dimensionless coil pitch in medium range, the heat transfer coefficient decreases while with increasing pitch to 2 tube diameter, heat transfer coefficient is increased. Also it was found that heat transfer coefficient decreases as the tube diameter increases, for the same dimensionless coil pitch. Finally they provided a correlation for Nusselt number on the shell-side. Moawed [12] reported an experimental investigation of steady-state natural convection heat transfer from uniformly heated helicoidal pipes oriented vertically and horizontally. His experimental investigation was conducted on four helicoidal pipes having different ratios of coil diameter to pipe diameter, pitch to pipe diameter and length to pipe diameter with the range of Rayleigh number1.5 × 103b Ra b 1.1 × 105. His results showed that the overall Nusselt number increases with the increase of coil to tube diameter ratio, dimensional pitch and length of coil to tube diameter for the vertical helicoidal pipes. For the horizontal helicoidal pipes, the overall Nusselt number increased with the increase of dimensional pitch and length of coil to tube diameter, but it decreased with the increase of coil to tube diameter ratio. He presented two different equations to correlate the Nusselt number for horizontal and vertical helicoidal pipes. Different characteristic lengths to correlate the outside Reynolds number with the Rayleigh number are investigated in natural convection heat transfer from helical coil by Prabhanjan et al. [13]. It was finally found that the coil height has best fit results for vertical coil. In addition, they have developed a method of predicting the outlet temperature from a coil, using the inlet temperature, bath temperature and coil dimensions. Xin and Ebadian [14] have experimentally studied shell-in-coil natural convection heat exchangers. Several correlations for Nusselt number versus Rayleigh number based on different characteristic lengths have been proposed. Ajele [15] studied shell-and-coil natural convection heat exchangers experimentally. Combinations of up to four coils, as well as single coil were tested in a 100 mm inner diameter shell. He proposed a correlation for multiple coi1 tests of shell-and-coil natural convection heat exchangers. Hollands and Brunger [16] pointed to the existence of an optimum value for tube mass flow rate. Numerical investigations were conducted to understand forced laminar fluid flow over coiled pipes


777

Fig. 1. a) Apparatus for heat exchanger experiments, b) Schematic diagram of a shell-and-coil mixed convection heat exchanger.

with circular cross-section by Conte et al. [17]. The focus of their study was concentrated on exploring the convective heat transfer from conical and helical coils with comparative studies. The same numerical investigation method was applied to two differentially coiled pipes (helical and conical) and for different Reynolds numbers corresponding to five cases of exterior flow arrangement. The results showed better heat transfer performance for cases of conical coils whereas much flow turbulence was observed due to an effective flow arrangement. Although there are many works done in tube-side of helical coiled tube heat exchangers also on the natural convection on shell-side, there are not many investigations on forced and mixed convection considering the both side of the heat exchanger. The present study covers both laminar and turbulent flow regimes inside the coiled tube depending on different mass flow rates.

2. Experimental apparatus and test section Fig. 1 is a picture of the apparatus arranged for heat exchanger experiments. The experimental procedure is the same as Ghorbani et al [18]. Hot water was pumped to the tank, passing through six electric

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

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

9.47 12.59 12.59

778


Table 2 Experimental uncertainties of important parameters. Parameter

Uncertainty

Parameter

Uncertainty

LMTD NTU ɛ′ ṁc

5.8% 11.97% 1% 1%

ṁs ɛ Q

1.6% 1% 2.47%

heaters and a valve that was installed at the inlet of the heat exchanger to control the flow rate. Cold water in the shell side was taken from urban water supply. The temperature of the inlet water of coiled tube to the heat exchanger was controlled by a thermostat. Four different constant temperatures of 50, 60, 70, and 80 °C were considered for inlet mass flow rate of coil. These temperatures are in accord with the outlet temperature of a flat plate solar collector. The temperature of shell-side inlet was equal to the temperature of tap water. The flow rate was measured using a calibrated measuring cylinder and a stopwatch positioned at the outlet of heat exchanger. The mean mass flow rates of shell-side and coil-side are 0.024, 0.05, 0.09 and 0.113 kg/s respectively. These mass flow rates are selected according to the outlet mass flow rate of a solar collector working in SDHW system [7]. The coil was formed carefully by using 9.52 and 12.5 mm OD straight copper tubing. Care was taken to locate the coil into the middle of the circular space between inner and outer shells of heat exchanger. The specification of heat exchanger is shown in Table 1. Temperatures were measured by 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 8 analog input channels was used to record all temperature measurements. All tests were performed under steadystate conditions. A Visual Basic code was written to retrieve and store

Fig. 2. Temperature distribution for coil #1.


Fig. 4. Temperature distribution for coil # 4.

temperature data and to perform calculations. The data acquisition system scanned and stored data every 5 s and the measured values were averaged over a period of 4 min. 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 [19] 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. 3. Results and discussion Figs. 2–4 show typical temperature distributions inside the heat exchanger for fixed inlet conditions(Rm ≅ 1 and Th,i = 80 °C). In all graphs of the axial temperature profile, the zero value on the abscissa corresponds to the bottom of the exchanger whereas the value of one indicates the top. The axial temperature profile is very close to linear (R2 = 0.97) for all graphs. Figs. 5–7 show typical temperature distributions inside the heat exchanger for fixed inlet conditions(Rm ≅ 0.21 and Th,i = 80°C). The





axial temperature profile of the coil surface is far from being linear for those figures. This deviation from a linear profile is influenced by the mass flow rate ratio. The nonlinearity is such that the profiles tend to be concave up, which means that the coil surface temperature is higher than usual at the top and then it drops faster than usual while moving towards the bottom of the heat exchanger. The value of Rm ≅ 1 seems to be the critical point. For Rm significantly less than unity the curves deviate greatly from being linear whereas the curves are close to a straight line for Rm ≈ 1. The linear temperature profile means that the shell-side heat transfer coefficient is constant along the axis of the heat exchanger. There is a notable drop in coil surface temperature. The curves suggest that the shell-side heat transfer coefficient is no longer constant. Since it is reasonable to assume that the heat flux is uniform, the product (hoΔT) is constant along the coil surface. Therefore a smaller temperature difference means a higher ho value. The magnitude of ho starts from a low value at the top and gradually increases to its highest value at the bottom of the heat exchanger. Obviously this situation is not desirable since the hot stream forfeits its heat very quickly and therefore the heat exchanger does not operate at its full


capacity. It can be concluded that for such a low shell-side mass flow rate, the heat exchanger is oversized in terms of the surface area. Figs. 8–10 show typical temperature distributions inside the heat exchanger for fixed inlet conditions(Rm ≅ 4.7 and Th,i = 80 °C). The axial temperature profile of the shell-side water is far from being linear for those figures. In these cases, the profiles tend to be concave down as opposed to the trend in Figs. 5–7. It can be seen that as the mass flow rate ratio changes, the temperature profile changes from an initially concave-up profile to concave-down one. In other words the coil surface is colder than usual at the top part and its temperature gradually decreases until it reaches its lowest value at the bottom of heat exchanger. The logarithmic mean temperature difference (LMTD) decreases as the mass flow rate ratio increases for each heat flux. This is evident from Fig. 11 which is typical of the behavior of LMTD. Also it is seen that for a fixed value of Rm, the effect of increased heat rate is to increase the value of LMTD. Also each individual curve experiences a flattening effect as the mass flow rate ratio increases, especially for

Fig. 11. LMTD versus Rm for different heat transfer rates. Fig. 8. Temperature distribution for coil #1.


779

Fig. 12. Modified effectiveness for all test configurations.

780


lower rates of heat transfer. In other words, further increment of the tube-side mass flow rate, when the heat rate is relatively low, will not decrease the value of LMTD further. This implies that the combination of low heat rate and high tube-side mass flow rate will not result in an increase of overall conductance of heat exchanger (UA) value. Therefore the extra electrical power utilized by the tube-side loop pump has not brought any extra performance to the heat transfer process. This once again points to the existence of an optimum value for shell-side mass flow rate as stated by Hollands and Brunger [16]. In Fig. 12 the modified effectiveness as defined by Eq. (1) is plotted as a function of the mass flow rate ratio. ε′ =

Th;i −Tc;o Th;i −Tc;i

ð1Þ

As can be seen in Fig. 12, the slope of the curve falls rapidly as the value of the corrected mass flow rate increases. For all mass flow rate ratios less than unity, a slight decrease will result in a considerable improvement of heat exchanger effectiveness, while for values larger than 2 the modified effectiveness remains nearly unchanged. This means that for a certain heat exchanger, increment of tube-side mass flow rate will always downgrade the effectiveness. The data can be correlated by a simple power equation. Eq. (2) is recommended for predicting the effectiveness of heat exchanger in the range of Rm from 0.33 to 5. ε′ = 0:4744

m˙ s m˙ c

0:4627 ð2Þ

The tube diameter has little effect on the modified effectiveness since it does not appear in Eq. (2). This equation indicates that ɛ′ is a strong function of the mass flow rate ratios. The shell-side water mass flow rate has a favorable effect and tube-side mass flow rate has an adverse effect on the modified effectiveness of the heat exchanger. Physically, more shell-side water flow means more heat extracted from the hot stream and therefore a greater temperature fall in that stream which translates into better effectiveness. On the contrary, more tube-side mass flow rate leads to less temperature fall in the hot stream and consequently worsens the effectiveness of the heat exchanger. The two mass flow rates, therefore act against each other with the same strength. Using the definition of the modified effectiveness and Eq. (2), one can easily derive equations for predicting the tube-side and shell-side outlet temperature. Th;o = Th;i −0:4744

m˙ s m˙ c

Tc;o = Tc;i + 0:4744

cp;c cp;s

0:4627

m˙ c m˙ s

Th;i −Tc;i

0:5373 Th;i −Tc;i

Fig. 13. Comparison of effectiveness data with standard heat exchanger configurations.

0:8 h i D Dt 0:8 0:4 Nui = 1 + 3:6 1− t 0:0023Rei Pri Dc Dc

ð7Þ

In order to establish the effectiveness–NTU relations for the shelland-coil heat exchangers, the data was plotted together with the plots for some standard configurations in Fig. 13. As it could be observed in Fig. 13, the ɛ – NTU relationship for parallel and counter-flow concentric tube heat exchangers, cross flow with both fluids unmixed and cross flow with the Cmin fluid mixed are plotted for the case Cr = 0.5 as an average value. In addition, for the sake of comparison the general ɛ – NTU for all heat exchangers with Cr = 0 has also been presented in the same figure. From Fig. 13 the effectiveness of the parallel-flow concentric tube heat exchanger is the lowest of all and is far below the values observed in current experiments. The case of Cr = 0 would over predict the effectiveness if used for the current case. This case can be attributed to the situation where the flow rate of one of the fluids is so small that it can be considered stagnant. If the relationship of the cross-flow type heat exchanger with one of the fluids mixed is used for current situation, the data would be under predicted and therefore the relationship is not suitable. Two cases that can closely predict the data are the cross flow with both fluids unmixed and the counter-flow concentric tube heat exchangers. Among them, the counter-flow configuration is closest in reality and also on the graph. In order to double check this observation, Fig. 14 must be considered.

ð3Þ

ð4Þ

In general, the inlet temperatures are known, thus making the prediction of the outlet temperatures possible by using Eqs. (3) and (4). According to the research by Srinivasan et al. [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 d 0:5 Recrit: = 2100 1 + 12 =D Þ

ð5Þ

To calculate the Nusselt number for the laminar and turbulent regimes, Eqs. (6) and (7) are used respectively [3,4]: 20 !3 !3 = 31 = 3 2 51 = 48 He 11 5 + Nu = 4@ + 1:816 1342 1:15 11 1 + PrHe2 1 + Pr

ð6Þ

Fig. 14. The effectiveness–NTU data compared with the counter-flow concentric tube heat exchanger for different values of Cr.


In Fig. 14, the results of the current experiment are compared with the standard counter-flow relations for different Cr values of 0.2, 0.5 and 0.8. It can be resulted that the current data are reasonably correlated by counter-flow relations. In conclusion, it is suggested to use the ɛ − NTU relations of counter-flow heat exchanger to predict the effectiveness of the mixed convection shell-and-coil heat exchangers and also for design purposes. The standard counter-flow relation, taken from Kays and London [20] is reproduced here as Eq. (8): ε=

1− exp½−NTU ð1−Cr Þ : 1−Cr exp½−NTU ð1−Cr Þ

ð8Þ

4. Conclusions In the present study, an experimental investigation of the mixed convection heat transfer in helically coiled tube heat exchanger, as one of the most applicable compact heat exchangers is reported. The mass flow rate of tube-side to shell-side ratio (Rm) was found to be effective on the axial temperature profiles of heat exchanger. The results indicate that for Rm greater than unity, the temperature profiles were of quadratic form from bottom to top of the heat exchanger. The profiles were linear for Rm close to unity and when the mass flow rate ratio was considerably less than unity, the temperature profiles were of the logarithmic form. With increasing mass flow rate ratio the logarithmic mean temperature difference was decreased. The modified effectiveness decreased with increasing mass flow rate ratio. An equation was found to correlate the modified effectiveness data to the mass flow rate ratio for 0.15 b Rm b 5. The ɛ − NTU relation of the mixed convection heat exchangers was same to those of a pure counter-flow heat exchanger. References [1] P.S. Srinivasan, S.S. Nandapurkar, F.A. Holland, Friction factors for coils, Institution of Chemical Engineering Transactions 48 (1970) T156–T161. [2] S. Wongwises, P. Naphon, Heat Transfer Characteristics of a Spirally Coiled, Finned-Tube Heat Exchanger under Dry-Surface Conditions, Heat Transfer Engineering 27 (1) (2006) 25–34.

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