- Email: [email protected]
Correlations for predicting the performance of axial finned tubes submersed in PCM
Journal of Energy Storage 26 (2019) 100973
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Correlations for predicting the performance of axial finned tubes submersed in PCM
T
⁎
Cláudia R.E.S. Nóbrega, Kamal A.R. Ismail , Fátima A.M. Lino State University of Campinas, Faculty of Mechanical Engineering, Energy Department, Mendeleiev street, 200, Cidade Universitária “Zeferino Vaz”, Barão Geraldo, Campinas 13083-860, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Fins Solidification PCM Correlations Interface velocity Time for complete phase change
Experimental correlations for phase change around finned tubes submersed in PCM are scarce in the literature. These correlations are useful for validation of numerical models and simulations as well as for predicting the performance of storage systems. The objective of this study is to develop correlations for axially finned tubes to predict the effects of the number of fins, fins width, mass flow rate of the heat transfer fluid and its temperature. Solidification experiments were done on tubes with fin width varying from 30 mm to 110 mm, number of fins varying from 3 to 6, wall temperatures in the range-5 to −20 °C and mass flow rates of the heat transfer fluid in the range from 0.068 to 0.141 kg/s. The same tests were conducted on a finless tube to serve as reference for comparisons. The correlations were developed and validated against other experimental and numerical results showing good agreement. The correlation for the interface position showed a deviation varying from 2 to 13% when compared with experimental measurements. The interface velocity showed a deviation of about 12%. The solidified mass and the total time for complete phase change showed deviations of 16% and 3 to 8%, respectively.
1. Introduction Latent heat storage systems are widely accepted as superior in performance in comparison with sensible heat storage units due to their smaller size and nearly isothermal charge and discharge thermal characteristics [1,2]. Their main drawbacks include low thermal conductivity and possible super cooling; both affect the thermal performance of the storage unit and can cause significant increase in the charge and discharge periods. Many research efforts and experimental and numerical studies were dedicated to improve the heat transfer process during phase change [3].One of the most popular methods is incorporating fins to the tubes to increase the heat transfer area, consequently enhance the heat transfer process and shortens the time for complete phase change. Fins of different geometries and configurations were numerically simulated and experimentally tested for both cooling and heating applications. Some phase change parameters such as interface velocity, solidified mass and the time for complete phase change are important not only for validation of simulation processes and comparisons but also for predicting the performance of new and real operating systems. Numerical and experimental studies on finned tubes for use in energy storage systems included assessing the effects of number of fins, fin ⁎
thickness and fin length to determine their effects on the solidified mass, total stored energy and the time for complete solidification. The results confirmed the influence of the fins on delaying natural convection effects during the solidification process [4]. In another study, Bilir and Ilken [5] investigated numerically the problem of solidification of PCM (Phase Change Material) inside cylindrical and spherical geometries. They determined the time for complete phase change and developed correlations in terms of Stefan and Biot numbers and the degree of superheat. Agarwal and Sarviya [6] presented a review on the results of many studies devoted to increase the thermal conductivity of PCM and improve the heat transfer rates within annular space arrangement. The geometry of the latent heat storage system plays crucial role in determining its thermal performance. Al-Abidi et al. [7] investigated experimentally a heat exchanger with internal and external fins and evaluated the effects of the inlet temperature and mass flow rate. The results indicated that the variation of the inlet temperature produces more significant effects than the variation of the mass flow rate. Experimental studies [8,9] were conducted to investigate the melting and solidification processes of PCM. The results showed that natural convection is dominant during melting while conduction is dominant during solidification. It is also found that both the mass flow rate and
Corresponding author. E-mail address: [email protected] (K.A.R. Ismail).
https://doi.org/10.1016/j.est.2019.100973 Received 3 July 2019; Received in revised form 26 August 2019; Accepted 18 September 2019 Available online 26 September 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
parameters such as fin width, number of fins were investigated to assess their effects on the interface position, interface velocity, solidified mass, stored energy and on the time for complete phase change. Based on these experimental data correlations were developed and validated against experimental results. The main contribution of the present study is the development and validation of experimentally based correlations for the phase change parameters such as the interface velocity, solidified mass, stored energy and the time for complete phase change. These correlations are important not only for validation and simulation processes but also for quick estimates in latent heat storage operation and design.
inlet temperature affect the phase change process but temperature effects were more significant. Yang et al. [10] conducted a numerical investigation on melting in a shell-and-tube latent heat storage to investigate the effects of fin number, height and thickness on the phase change process. Results demonstrated that the full melting time is reduced by 65% by inserting annular fins. Later, Yang et al. [11] investigated the effect porous metal foam on the heat transfer rate in a tube and the comparison of their numerical results with experiments showed good agreement. In another work, Yang et al. [12] investigated annular space filled with metallic foam and found a reduction of 64% in the melting time. In a related study Yang et al. [13] investigated the effect of inclination on the thermal performance of pure PCM and in composite form and demonstrated that the inclination angle affects the formation of natural convection during melting. In the case of open-cell metal foam the inclination angle has little effect. Yazici et al. [14] investigated the effect of eccentricity of a horizontal tube-in-shell storage unit on solidification of a PCM and found that increasing the eccentricity increases the total solidification time. Latent heat storage with finned tubes received a lot of attention from specialists due to its simplicity and effectiveness. Different fins were investigated including internal and external fins, radial and axial fins, spiral fins and many other geometries. Axial and radial fins are more popular than other configurations due to their simple geometry.Rathod and Banerjee [15] investigated the augmentation in the heat transfer rate of PCMs by installation of longitudinal fins. Experimental results showed that the heat transfer rate augmentation is more sensitive to increase in HTF (Heat Transfer Fluid) inlet temperature as compared to increase in mass flow rate of HTF. Solidification time was reduced by about 43.6% by installation of three fins. Numerical and experimental investigations on fins included the effects of fins height, Stefan number, melting and solidification times, liquid mass fraction, melting and solidification fronts on the thermal performance of latent heat storage tanks. Results showed that fins extension leads to the less melting time and deeper penetration of heat. It is also shown that heat absorption is function of fins height at the initial stages of the charging process [16,17]. Literature reviews highlighted many studies dedicated to investigate the different techniques adopted for energy and exergy performance enhancements. Various factors were investigated including the heat transfer fluid mass flow rate, inlet temperature, PCM, melting temperature, additives for PCM, storage unit geometry and surface enhancement [18–23]. Other aspects including operating conditions and design parameters were presented in-depth with more attention focused on the heattransfer enhancement techniques. The best enhancement was achieved by using longitudinal finned configuration and was dependent on increasing the number and dimensions of the fins [24–28]. Table 1 presents a summary of the cited literature and the associated covered topics. From the literature review one can observe the relatively small number of experimental data in comparison with numerical results especially in connection with phase change parameters such as interface velocity, solidified mass, time for complete phase change. The present work is intended to produce results and experimental data to allow developing correlations to cover this gap. Working parameters such as temperature of the working fluid, its flow rate, geometrical
2. Experimental rig and procedure In order to obtain the necessary data for the elaboration of the experimental correlations an existing experimental rig shown in Fig. 1a is used. The experimental rig is composed of a conventional refrigeration circuit to produce low temperature primary refrigerant, which is used in a secondary circuit to cool the heat transfer fluid, ethanol. The temperature of the secondary fluid is controlled by a calibrated thermostatic sensor while the mass flow rate is measured by a calibrated orifice plate and adjusted manually by using a sensitive regulating valve. The test section is in the form of a transparent quartz cylinder of 300 mm diameter, 300 mm height and 15 mm in thickness with the top and bottom endplates made of acrylic sheet of 15 mm thickness. The endplates are designed to allow changing the test tube easily as can be seen in Fig. 1b. The test tube is made of copper and the fins are fixed to the tube of 27 mm at equal angles and passes along the centerline of the quartz cylinder where it is connected at the two extremities to the feeding and discharge tubes of the secondary fluid circuit. To fix the fin to the tube a shallow long groove is made parallel to the tube axis with width equal to the fin thickness, that is 1 mm. The groove and the fin are thoroughly cleaned and a thermal contact paste of thermal conductivity of 1.5 W/mK is placed in the groove. The fin is then forced into the groove and a fine trace of thermal glue is applied along the external contact line. The thermal contact resistance between the tube and fin is estimated as in [28]
R c, past =
L 1.10−3m = = 6.66 × 10−4m2 . K / W k 1.5W / mK
A photographic camera is focused on the top section of the finned tube where a precision scale is fixed beside the finned tube to serve as a physical dimensional reference. Calibrated thermocouples are installed as follows: six thermocouples are fixed along one fin to measure the temperature distribution along the fin width, three thermocouples at fixed at three points in the test section to ensure that the temperature of the liquid PCM is uniform, two thermocouples are fixed at entry and exit of the test section and three thermocouples are placed in the secondary fluid cooling tank to ensure uniform temperature within the tank. In order to collect the necessary experimental data, experiments were conducted for both the development and validation of the proposed correlations. Tubes of diameter of 27 mm having 3, 4, 5 and 6 fins were used in the tests beside the finless tube used as a reference. The fins were made of copper of 1 mm thickness and 300 mm length along
Table 1 Summary of the references used in this work. Study
References
Numerical and experimental studies of the phase change parameters and their effects on the process. Literature reviews of studies on the thermal conductivity of PCM. Experimental studies on latent heat storage tanks with internally and externally finned tubes. Experimental studies on the phase change processes in PCM. Studies on finned tubes to enhance the thermal performance of PCM storage systems.
[4,5,14,16,17,18,19,20,21,22,23] [6,15] [7] [1,2,3,8,9,10,11,12,13] [24,25,26,27,28]
2
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 1. Experimental rig: (a) scheme; (b) finned tube. Table 2 Summary of experimental tests. Nominal temperature (°C)
Number of fins
Fins of the width (mm)
Mass flow (kg/s)
−20, −15, −10 and −5 −20, −15, −10 and - 5 −20 and −10
3, 4, 5, 6 and bare tube Bare tube, 4 and 6 3 and 4
50 50 30, 50, 70, 90 and 110 and bare tube
0.100 and 0.068 0.141 0.100 and 0.068
the tube. Fins of width of 30, 50, 70 and 110 mm were tried. The test temperature was varied from −5 °C to −20 °C. Table 2 presents a summary of the experimental tests.
thermocouples connected to the data acquisition system. The quartz cylinder is then filled with cold water (approximately 0 °C). The temperature of the working fluid is chosen and fixed on the control panel of the Ethanol cooling system. With all components of the two circuits connected and adjusted, the circuit of the primary refrigerant is switched on to cool down the Ethanol to the required temperature, part of the cold Ethanol is circulated to keep the tube temperature at zero °C.
2.1. Experimental procedure Initially the test tube is installed in the test section with all 3
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 2. Tracker software used for treating the digitalized photographs.
3. Experimental assessment of the parameters
When all the Ethanol reaches the pre-established working temperature, the cooling circuit is opened so that the Ethanol can flow with the preestablished mass flow rate in the finned tube. All temperatures are registered each five minutes and with the camera positioned in place photographs are taken of the finned tube, the layer of formed ice around the finned tube and the reference scale fixed to the side of the tube as can be seen in Fig. 2. The Photographs are analyzed by the software Tracker and the real dimensions of the interface are determined. From the measured interface positions and the corresponding time intervals one can also calculate the interface velocity and the solidified mass. The measurements were conducted such that the test tube is photographed from the top in intervals of 5 min during the first two hours and then at intervals of 30 min for five hours from the start of the test. After this period the photographs were taken at intervals of 50 min until the experiment is finished. The adopted criterion for ending the experiment is that there is no more increase of the interface position during three successive measurements. Achieving this condition the whole system is switched off to prepare for the subsequent experiment. The solidification process is a dynamic thermal process and the development of the solidified layer is of extreme importance especially around finned tubes. Images in Fig. 3 are for the case of three fins at six different time intervals. These images show clearly the progress of the solidification around the tube and the attached fins. Images in Figs. 4–6 are for the cases of four, five and six fins, respectively.
3.1. Effect of the number of fins Fig. 7 shows the variation of the interface position with time for four finned tubes, mass flow rate of 0.1 kg/s and temperature of −10.3 °C. As can be seen, the increase of the number of fins increases the interface position. One can also observe that the rate of increase of the interface position with the increase of the number fins shows a decreasing tendency as can be verified from the curves for 3–6 fins. 3.2. Effect of the fin width Fig. 8a,b shows the variation of the interface position with the fin width. As can be seen the increase of the fin width more than a value of about 50 mm reduces gradually the interface position and consequently the solidified mass around the finned tube. Also, the increase of the mass flow rate from 0.068 kg/s to 0.100 kg/s increases the interface position from 72.16 mm to 72.94 mm for the case of fin width of 50 mm. This shows that the increase of the mass flow rate increases slightly the interface position. Fig. 9 shows the variation of the terminal solidified mass with the fin width for a working temperature of Tw = −20.1 °C and two mass flow rates of the secondary fluid of 0.100 kg / s and 0.068 kg/ s. As can be seen the maximum value of the terminal solidified mass increased with the increase of the mass flow rate to 6.30 kg and 6.59 kg, respectively. This is due to the increase of Reynolds number which increases the Nusselt number and consequently the heat transfer coefficient between the tube surface temperature and the PCM. The terminal solidified mass is found to increase with the increase of the fin width up to about 50 mm after which more increase in the fin width seems to reduce slightly the terminal solidified mass. This effect was further verified and confirmed by measuring the temperature distribution along the fin width. It is found that the temperature ditribution shows a continuous temperature decrease along the fin width causing a decrease of the terminal solidified mass.
2.2. Error analysis Calibrated thermocouples of type T of precision ± 0.5 °C were used in the experimental rig. The images of the interface positions were converted to physical dimensions with precision of ± 0.5 mm, while the mass flow rate of the secondary fluid was measured within ± 10−4 kg/ s. The uncertainty of the interface velocity varied in the range ± 5.25 × 10−7 and ± 7.73 × 10−6 mm/min, while the uncertainty in the solidified mass is within ± 4.25 × 10−3and ± 5.52 × 10−2 kg. 4
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 3. Solidified mass around the tube with 3 fins of 50 mm width and tube surface temperature of −20 °C.
the solidified mass of the PCM. This effect is due to the increase of the heat transfer area between the cold tube surface and the surrounding PCM. Also one can observe that the decrease of the tube wall temperature enhances the solidified mass due to the increase of the temperature gradient between the tube surface and the PCM. Fig. 12 shows the effects of varying the tube wall temperature and number of fins on the time for complete solidification. It is found that the decrease of the wall temperature increases the temperature gradient between the wall surface and the PCM which enhances the solidification process and shortens the time for complete solidification. Considering the effects due to variation of wall temperature from −5.2 °C to −20.1 °C, the reduction of complete solidification time is found to be 40%, 38% and 39% for the cases of 6, 4 and no fins, respectively. Also,
3.3. Effect of wall temperature Fig. 10 shows the variation of the interface position with the tube wall temperature for finned and finless tubes. As can be seen the decrease of the wall temperature increases the temperature gradient between the tube wall and the surrounding PCM and this increases the interface position. Also, it is found that the increase of the number of fins increases the interface position in comparison with the finless case, but this effect is attenuated with further increase of the number of fins as can be verified from Fig. 10. Fig. 11 shows the variation of the terminal solidified mass in terms of the tube wall temperature for finned tubes in comparison with the bare tube. As can be seen the increase of the number of fins increases
Fig. 4. Solidified mass around the tube with 4 fins of 50 mm width and tube surface temperature of −20 °C. 5
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 5. Solidified mass around the tube with 5 fins of 50 mm width and tube surface temperature of −20 °C.
for complete solidification (τ). For developing the correlation we assume a general relation of the
comparing the three graphs one can observe the attenuation of the effect of fins with the increase of their numbers.
Φ = AN bW c T d t e
4. Development and validation of the correlations
(1)
where Φ is an arbitrary function which can represent the dependent parameters such as the interface position (I), the interface velocity (V) and the PCM solidified mass (M), while (t)is any time instant but not the time for complete solidification. The constants A, b, c, d, e are obtained by forming five independent equations using a set of experimental data and the resulting five equations are solved to determine the corresponding constants. This procedure is repeated for each of the dependent variables (I), (V) and (M). In the case of the correlation for the time for complete solidification, Φ = τ and the proposed correlation can be written as:
4.1. Development of the correlations This section is devoted to the development of correlations for the important parameters of the phase change around axially finned tubes which strongly affect their thermal performance. The considered parameters include the tube wall temperature, mass flow rate of the heat transfer fluid, number of fins (N) and width of fin (W). The dependent parameters which are to be correlated include the interface position (I), the interface velocity (V), solidified mass (M) and the time
Fig. 6. Solidified mass around the tube with 6 fins of 50 mm width and tube surface temperature of −20 °C. 6
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 7. Variation of the interface position with time for tubes with multi fins.
Fig. 9. Variation of the terminal solidified mass with fin width: (a) 0.100 kg/s; (b) 0.068 kg/s.
Fig. 8. Variation of the terminal interface position with fin width: (a) 0.100 kg/ s; (b) 0.068 kg/s.
Φ = τ = AN bW c T d
Fig. 10. Variation of the terminal interface position with tube wall temperature for mass flow rate of 0.068 kg/s.
(2)
Again to determine the constants in Eq. (2), a set of experimental data is used to form four equations for the unknown constants. The equations are solved and the constants are determined. The correlations obtained following the above procedures are presented below,
Eqs. (3)–(6).
I = 3.91. 10−2N 0.1681W 0.035 T 0.489 t 0.537 7
(3)
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Table 3 Values of Pearson’s coefficient r and the corresponding comparative figures. Pearson’s coefficient (r)
0.97
0.99
0.95
0.95
0.99
0.99
0.99
0.96
0.95
0.96
Figure
13
14
15
16
17
18
19
20
21
22
Fig. 11. Variation of the terminal solidified mass with tube wall temperature.
Fig. 13. Comparison of the effect of the number of fins on the predicted and experimental interface positions.
4.2.1. Effect of the number of fins As was shown the number of fins plays an important role in the process of heat transfer with phase change. The predicted interface position from the correlation is compared with the measured interface position as shown in Fig. 13. It is found that the agreement is good showing a deviation of about 8% and having Pearson’s correlation coefficient r = 0.97. The deviations between the experiments and the correlations prediction can be attributed to the temperature variations in the laboratory since it is not air conditioned and most of the experiments lasted at least 800 min. In some experiments, the transparent top of the test section was slightly foggy, even though it is usually wiped off before photographing, this might cause some blurring provoking error in determining the interface position. The variation of the solidified mass with the number of fins is an important parameter in the design of a latent heat storage system. The solidified mass predicted from the correlation is compared with the solidified mass experimentally determined under the same conditions as in Fig. 14. As can be seen the agreement is good showing a deviation of 7%, and having Pearson’s correlation coefficient r = 0.99. The effect of the number of fins on the interface velocity is presented in Fig. 15 where the predicted interface velocity from the correlation is compared with experimental measurements. As can be observed the agreement is good showing a deviation of about 10%, and having Pearson’s correlation coefficient r = 0.95. The predicted results from the correlation for predicting the time for complete solidification is compared with the experimental results as shown in Fig. 16. One can observe that the increase of the number of fins reduces the time for complete solidification. The results indicate an agreement between the predictions from the correlation and the experimental results within a deviation of about 8%, and having Pearson’s correlation coefficient r = 0.95.
Fig. 12. Variation of the time for complete solidification with the tube wall temperature.
M = 2.72. 10−4N 0.197W 0.116 T 0.737 t 0.671
(4)
V = 7.734N 0.339W −0.225 T 0.326 t −0.532
(5)
τ = 6, 982N−0.3235W −0.1683 T −0.3725
(6)
4.2. Validation of the correlations To validate the correlations different experimental sets were used for this purpose. The same experimental parameters were used in the correlations and the predicted results are then compared. Pearson correlation coefficient with limits of 95% confidence interval was used as indicator of the precision of the correlations. This coefficient given by [29] is
r=
∑ (x i − x¯)(yi − y¯) ∑ (x i − x¯)2 ∑ (yi − y¯)2
(7)
where r is Pearson’s coefficient, xi corresponds to the experimental measurements, x¯ is the mean of the experimental measurements, yi corresponds to the values from the correlation, and y¯ is the mean of the values from the correlation. Table 3 shows the values of Pearson’s coefficient r for the corresponding curves.
4.2.2. Effect of wall temperature Tube wall temperature is one of the most important driving forces for the phase change process. The predicted interface position from the correlation is compared with experimental measurements as presented 8
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 14. Comparison of the effect of the number of fins on the predicted and experimental solidified mass.
Fig. 16. Comparison of the effect of the number of fins on the predicted and experimental complete solidification time.
Fig. 17. Comparison of the effect of the tube wall temperature on the predicted and experimental interface position.
Fig. 15. Comparison of the effect of the number of fins on the predicted and experimental interface velocity.
in Fig. 17 showing agreement within margin of deviation of about 13%, and having Pearson’s correlation coefficient r = 0.99. The tube wall temperature has a strong effect on the solidified mass. The solidified mass is an important parameter in latent heat storage systems. The predicted solidified mass from the correlation is compared with the experimentally measured solidified mass as presented in Fig. 18. As can be seen the agreement is reasonably good with maximum deviation of about 16%, and having Pearson’s correlation coefficient r = 0.99. The tube wall temperature has a direct impact on the time for complete phase change since the tube wall temperature is one of the main driving forces of the phase change process. Comparison of the predicted solidification time with the experimental measurements is shown in Fig. 19. As can be seen the predicted time seems to agree well with the experiments with maximum deviation of 3% at temperatures of −10.0, −15.0 and −20.0 °C, while for the temperature of −5 °C the deviation is 1%, and having Pearson’s correlation coefficient r = 0.99. Fig. 18. Comparison of the effect of the tube wall temperature on the predicted and experimental solidified mass.
4.2.3. Effect of the width of the fin Phase change materials have poor thermal conductivity which 9
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 19. Comparison of the effect of the tube wall temperature on the predicted and experimental time for complete solidification.
Fig. 21. Comparison of the effect of the fin width on the predicted and experimental interface positions.
Fig. 20. Comparison of the effect of the fin width on the predicted and experimental complete solidification time.
Fig. 22. Comparison of the effect of the fin width on the predicted and experimental interface velocity.
impacts negatively their thermal performance. The increase of the heat transfer area is a mechanism which can improve the latent heat storage systems. The increase of the heat transfer area can be done by increasing the number of fins and/or their width. The effect of the fin width on the predicted time for complete solidification calculated from the correlation and the results obtained experimentally are presented in Fig. 20. The analysis shows good agreement with maximum deviation of about 4% for the case of fin width of 30 mm, and having Pearson’s correlation coefficient r = 0.96. The effect of the fin width on the predicted interface position is presented in Fig. 21 together with measured results for two wall temperatures. As can be seen the general trends are similar showing an increase of the interface position with the increase of the fin width. The results agree well within a deviation of 2 to 3%, and having Pearson’s correlation coefficient r = 0.95. Fig. 22 shows the effect of the fin width on the predicted and measured interface velocity. As can be seen the predicted results agree with the experimental measurements with maximum deviation of about 12%, and having Pearson’s correlation coefficient r = 0.96.
a tube with four fins working at −33 °C and for fin width of 16, 12 and 8 mm. For the same conditions the predicted results from the correlation are plotted together with the results from [28] as shown in Fig. 23. As can be seen the agreement is good with R2 of 0.96, 0.95 and 0.93, respectively. It is important to inform that the use of the above correlations is subject to the following conditions: 1. 2. 3. 4.
Same material for the tube and fin, Initial PCM temperature is close to zero, Strictly for solidification of PCM, Correlations are only for finned tubes.
Some parameters which could be investigated to widen the scope of application of these correlations include: a) Develop correlations for long finned tubes. We already have some results for long bare tubes but need to be completed for finned tubes, b) Develop correlations for melting of PCM around finned and bare tubes.
4.2.4. Comparison with other available numerical results The present numerical predictions are compared with the results from Sheikholeslami et al. [28]. The numerical results from [28] are for 10
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 23. Comparison of the effect of the predictions from the correlations with the numerical results of Sheikholeslami et al. [30].
5. Conclusion
Acknowledgments
The experimental results show that the increase of the number of fins increases the interface position and interface velocity and reduces the time for complete phase change. The width of the fin enhances the heat transfer rate and increases the solidified mass. Reducing the wall temperature enhances the heat transfer rate and produces more solidified mass, increases both the interface position and interface velocity and reduces the time for complete solidification. The correlation to predict the effects of the number of fins is found to agree well with experimental results with a deviation of about 7% for the solidified mass, 8% for the interface position and 10% for interface velocity. The correlation for predicting the effects of the fin width shows a deviation in comparison with the experimental measurements of 3% for the interface position and 4% for the time for complete phase change. The correlation for predicting the effects tube wall surface temperature shows a reasonable agreement in comparison with the experimental measurements with a deviation of 16% for the solidified mass, 8% for the interface position and 3%.for the time for complete solidification.
The first author wishes to acknowledge the support given by Fapema in the form of a doctorate scholarship and the second author wishes to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the PQ Research Grant 304372/2016-1. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.est.2019.100973. References [1] A. Abhat, Low temperature latent heat thermal energy storage: heat storage materials, Solar Energy 30 (10) (1983) 313–332. [2] A. Al Robaidi, Development of novel polymer phase change material for heat storage application, Int. J. Mater. Sci. Appl. 2 (2013) 168, https://doi.org/10.11648/j. ijmsa.20130206.11. [3] A. Agarwal, R.M. Sarviya, An experimental investigation of shell and tube latent heat storage for solar dryer using paraffin wax as heat storage material, Eng. Sci. Technol. Int. J. 19 (2016) 619–631, https://doi.org/10.1016/j.jestch.2015.09.014. [4] K.A.R. Ismail, C.L.F. Alves, M.S. Modesto, Numerical and experimental study on the solidification of PCM around a vertical axially finned isothermal cylinder, Appl. Therm. Eng. 21 (2001) 53–77, https://doi.org/10.1016/S1359-4311(00)00002-8. [5] L. Bilir, Z. Ilken, Total solidification time of a liquid phase change material enclosed in cylindrical/spherical containers, Appl. Therm. Eng. 25 (2005) 1488–1502, https://doi.org/10.1016/j.applthermaleng.2004.10.005. [6] A. Agarwal, R.M. Sarviya, Thermal conductivity enhancement of PCMs in annular tube heat storage : a review, Int. J. Res. Appl. Sci. Eng. Technol. 2 (2014) 69–73. [7] A.A. Al-Abidi, S. Mat, K. Sopian, M.Y. Sulaiman, A.T. Mohammad, Experimental
Declaration of Competing Interest None.
11
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
https://doi.org/10.1016/j.applthermaleng.2015.12.080. [20] Y. Wang, L. Wang, N. Xie, X. Lin, H. Chen, Experimental study on the melting and solidification behavior of erythritol in a vertical shell-and-tube latent heat thermal storage unit, Int. J. Heat Mass Transfer (2016), https://doi.org/10.1016/j. ijheatmasstransfer.2016.03.125. [21] Z. Khan, Z. Khan, K. Tabeshf, Parametric investigations to enhance thermal performance of paraffin through a novel geometrical configuration of shell and tube latent thermal storage system, Energy Convers. Manage. 127 (2016) 355–365, https://doi.org/10.1016/j.enconman.2016.09.030. [22] M. Mastani, F. Haghighat, S. Seddegh, A.A. Al-abidi, Heat transfer enhancement of phase change materials by fi ns under simultaneous charging and discharging, Energy Convers. Manage. 152 (2017) 136–156, https://doi.org/10.1016/j. enconman.2017.09.018. [23] R. Kothari, S.K. Sahu, S.I. Kundalwal, Comprehensive analysis of melting and solidification of a phase change material in an annulus, Heat Mass Transfer 55 (2019) 769–790. [24] A. Sciacovelli, E. Guelpa, V. Verda, Second law optimization of a PCM based latent heat thermal energy storage system with tree shaped fins, 17 (2014) 127–136. doi:10.5541/ijot.549. [25] S. Lohrasbi, M.G. Bandpy, D.D. Ganji, Response surface method optimization of Vshaped fin assisted latent heat thermal energy storage system during discharging process, Alexandria Eng. J. 55 (2016) 2065–2076, https://doi.org/10.1016/j.aej. 2016.07.004. [26] A.M. Abdulateef, S. Mat, J. Abdulateef, K. Sopian, A.A. Al-Abidi, Geometric and design parameters of fins employed for enhancing thermal energy storage systems: a review, Renew. Sustain. Energy Rev. 82 (2018) 1620–1635, https://doi.org/10. 1016/j.rser.2017.07.009. [27] L. Kalapala, J.K. Devanuri, Influence of operational and design parameters on the performance of a pcm based heat exchanger for thermal energy storage – A review, J. Energy Storage 20 (2018) 497–519, https://doi.org/10.1016/j.est.2018.10.024. [28] Y.A. Çengel, A.J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, 4th, Boston, 1998. [29] R.J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley & Sons, Inc., New York, 1980, https://doi.org/10.1002/9780470316481. [30] M. Sheikholeslami, R. Haq, A. Shafee, Z. Li, Heat transfer behavior of nanoparticle enhanced PCM solidification through an enclosure with V shaped fins, Int. J. Heat Mass Transfer 130 (2019) 1322–1342, https://doi.org/10.1016/j. ijheatmasstransfer.2018.11.020.
study of melting and solidification of PCM in a triplex tube heat exchanger with fins, Energy Build 68 (2014) 33–41, https://doi.org/10.1016/j.enbuild.2013.09. 007. S.P. Jesumathy, M. Udayakumar, S. Suresh, S. Jegadheeswaran, An experimental study on heat transfer characteristics of paraffin wax in horizontal double pipe heat latent heat storage unit, J. Taiwan Inst. Chem. Eng. 45 (2014) 1298–1306, https:// doi.org/10.1016/j.jtice.2014.03.007. J. Yang, L. Yang, C. Xu, X. Du, Experimental study on enhancement of thermal energy storage with phase-change material, Appl. Energy 169 (2016) 164–176, https://doi.org/10.1016/j.apenergy.2016.02.028. X. Yang, Z. Lu, Q. Bai, Q. Zhang, L. Jin, J. Yan, Thermal performance of a shell-andtube latent heat thermal energy storage unit: role of annular fins, Appl. Energy 202 (2017) 558–570, https://doi.org/10.1016/j.apenergy.2017.05.007. X. Yang, J. Yu, Z. Guo, L. Jin, Y.L. He, Role of porous metal foam on the heat transfer enhancement for a thermal energy storage tube, Appl. Energy 239 (2019) 142–156, https://doi.org/10.1016/j.apenergy.2019.01.075. X. Yang, P. Wei, X. Cui, L. Jin, Y.L. He, Thermal response of annuli filled with metal foam for thermal energy storage: an experimental study, Appl. Energy 250 (2019) 1457–1467, https://doi.org/10.1016/j.apenergy.2019.05.096. X. Yang, Z. Guo, Y. Liu, L. Jin, Y.L. He, Effect of inclination on the thermal response of composite phase change materials for thermal energy storage, Appl. Energy 238 (2019) 22–33, https://doi.org/10.1016/j.apenergy.2019.01.074. M.Y. Yazici, M. Avci, O. Aydin, M. Akgun, On the effect of eccentricity of a horizontal tube-in-shell storage unit on solidification of a PCM, Appl. Therm. Eng. 64 (2014) 1–9, https://doi.org/10.1016/j.applthermaleng.2013.12.005. M.K. Rathod, J. Banerjee, Thermal performance enhancement of shell and tube latent heat storage unit using longitudinal fins, Appl. Therm. Eng. 75 (2015) 1084–1092, https://doi.org/10.1016/j.applthermaleng.2014.10.074. M.J. Hosseini, M. Rahimi, R. Bahrampoury, Thermal analysis of PCM containing heat exchanger enhanced with normal annular fines, Int. J. Mech. Sci. 6 (2015) 221–234, https://doi.org/10.5194/ms-6-221-2015. M.J. Hosseini, A.A. Ranjbar, M. Rahimi, R. Bahrampoury, Experimental and numerical evaluation of longitudinally finned latent heat thermal storage systems, Energy Build. 99 (2015) 263–272, https://doi.org/10.1016/j.enbuild.2015.04.045. G. Li, Energy and exergy performance assessments for latent heat thermal energy storage systems, Renew. Sustain. Energy Rev 51 (2015) 926–954, https://doi.org/ 10.1016/j.rser.2015.06.052. M. Kabbara, D. Groulx, A. Joseph, Experimental investigations of a latent heat energy storage unit using finned tubes, Appl. Therm. Eng. 101 (2016) 601–611,
12
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Correlations for predicting the performance of axial finned tubes submersed in PCM
T
⁎
Cláudia R.E.S. Nóbrega, Kamal A.R. Ismail , Fátima A.M. Lino State University of Campinas, Faculty of Mechanical Engineering, Energy Department, Mendeleiev street, 200, Cidade Universitária “Zeferino Vaz”, Barão Geraldo, Campinas 13083-860, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Fins Solidification PCM Correlations Interface velocity Time for complete phase change
Experimental correlations for phase change around finned tubes submersed in PCM are scarce in the literature. These correlations are useful for validation of numerical models and simulations as well as for predicting the performance of storage systems. The objective of this study is to develop correlations for axially finned tubes to predict the effects of the number of fins, fins width, mass flow rate of the heat transfer fluid and its temperature. Solidification experiments were done on tubes with fin width varying from 30 mm to 110 mm, number of fins varying from 3 to 6, wall temperatures in the range-5 to −20 °C and mass flow rates of the heat transfer fluid in the range from 0.068 to 0.141 kg/s. The same tests were conducted on a finless tube to serve as reference for comparisons. The correlations were developed and validated against other experimental and numerical results showing good agreement. The correlation for the interface position showed a deviation varying from 2 to 13% when compared with experimental measurements. The interface velocity showed a deviation of about 12%. The solidified mass and the total time for complete phase change showed deviations of 16% and 3 to 8%, respectively.
1. Introduction Latent heat storage systems are widely accepted as superior in performance in comparison with sensible heat storage units due to their smaller size and nearly isothermal charge and discharge thermal characteristics [1,2]. Their main drawbacks include low thermal conductivity and possible super cooling; both affect the thermal performance of the storage unit and can cause significant increase in the charge and discharge periods. Many research efforts and experimental and numerical studies were dedicated to improve the heat transfer process during phase change [3].One of the most popular methods is incorporating fins to the tubes to increase the heat transfer area, consequently enhance the heat transfer process and shortens the time for complete phase change. Fins of different geometries and configurations were numerically simulated and experimentally tested for both cooling and heating applications. Some phase change parameters such as interface velocity, solidified mass and the time for complete phase change are important not only for validation of simulation processes and comparisons but also for predicting the performance of new and real operating systems. Numerical and experimental studies on finned tubes for use in energy storage systems included assessing the effects of number of fins, fin ⁎
thickness and fin length to determine their effects on the solidified mass, total stored energy and the time for complete solidification. The results confirmed the influence of the fins on delaying natural convection effects during the solidification process [4]. In another study, Bilir and Ilken [5] investigated numerically the problem of solidification of PCM (Phase Change Material) inside cylindrical and spherical geometries. They determined the time for complete phase change and developed correlations in terms of Stefan and Biot numbers and the degree of superheat. Agarwal and Sarviya [6] presented a review on the results of many studies devoted to increase the thermal conductivity of PCM and improve the heat transfer rates within annular space arrangement. The geometry of the latent heat storage system plays crucial role in determining its thermal performance. Al-Abidi et al. [7] investigated experimentally a heat exchanger with internal and external fins and evaluated the effects of the inlet temperature and mass flow rate. The results indicated that the variation of the inlet temperature produces more significant effects than the variation of the mass flow rate. Experimental studies [8,9] were conducted to investigate the melting and solidification processes of PCM. The results showed that natural convection is dominant during melting while conduction is dominant during solidification. It is also found that both the mass flow rate and
Corresponding author. E-mail address: [email protected] (K.A.R. Ismail).
https://doi.org/10.1016/j.est.2019.100973 Received 3 July 2019; Received in revised form 26 August 2019; Accepted 18 September 2019 Available online 26 September 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
parameters such as fin width, number of fins were investigated to assess their effects on the interface position, interface velocity, solidified mass, stored energy and on the time for complete phase change. Based on these experimental data correlations were developed and validated against experimental results. The main contribution of the present study is the development and validation of experimentally based correlations for the phase change parameters such as the interface velocity, solidified mass, stored energy and the time for complete phase change. These correlations are important not only for validation and simulation processes but also for quick estimates in latent heat storage operation and design.
inlet temperature affect the phase change process but temperature effects were more significant. Yang et al. [10] conducted a numerical investigation on melting in a shell-and-tube latent heat storage to investigate the effects of fin number, height and thickness on the phase change process. Results demonstrated that the full melting time is reduced by 65% by inserting annular fins. Later, Yang et al. [11] investigated the effect porous metal foam on the heat transfer rate in a tube and the comparison of their numerical results with experiments showed good agreement. In another work, Yang et al. [12] investigated annular space filled with metallic foam and found a reduction of 64% in the melting time. In a related study Yang et al. [13] investigated the effect of inclination on the thermal performance of pure PCM and in composite form and demonstrated that the inclination angle affects the formation of natural convection during melting. In the case of open-cell metal foam the inclination angle has little effect. Yazici et al. [14] investigated the effect of eccentricity of a horizontal tube-in-shell storage unit on solidification of a PCM and found that increasing the eccentricity increases the total solidification time. Latent heat storage with finned tubes received a lot of attention from specialists due to its simplicity and effectiveness. Different fins were investigated including internal and external fins, radial and axial fins, spiral fins and many other geometries. Axial and radial fins are more popular than other configurations due to their simple geometry.Rathod and Banerjee [15] investigated the augmentation in the heat transfer rate of PCMs by installation of longitudinal fins. Experimental results showed that the heat transfer rate augmentation is more sensitive to increase in HTF (Heat Transfer Fluid) inlet temperature as compared to increase in mass flow rate of HTF. Solidification time was reduced by about 43.6% by installation of three fins. Numerical and experimental investigations on fins included the effects of fins height, Stefan number, melting and solidification times, liquid mass fraction, melting and solidification fronts on the thermal performance of latent heat storage tanks. Results showed that fins extension leads to the less melting time and deeper penetration of heat. It is also shown that heat absorption is function of fins height at the initial stages of the charging process [16,17]. Literature reviews highlighted many studies dedicated to investigate the different techniques adopted for energy and exergy performance enhancements. Various factors were investigated including the heat transfer fluid mass flow rate, inlet temperature, PCM, melting temperature, additives for PCM, storage unit geometry and surface enhancement [18–23]. Other aspects including operating conditions and design parameters were presented in-depth with more attention focused on the heattransfer enhancement techniques. The best enhancement was achieved by using longitudinal finned configuration and was dependent on increasing the number and dimensions of the fins [24–28]. Table 1 presents a summary of the cited literature and the associated covered topics. From the literature review one can observe the relatively small number of experimental data in comparison with numerical results especially in connection with phase change parameters such as interface velocity, solidified mass, time for complete phase change. The present work is intended to produce results and experimental data to allow developing correlations to cover this gap. Working parameters such as temperature of the working fluid, its flow rate, geometrical
2. Experimental rig and procedure In order to obtain the necessary data for the elaboration of the experimental correlations an existing experimental rig shown in Fig. 1a is used. The experimental rig is composed of a conventional refrigeration circuit to produce low temperature primary refrigerant, which is used in a secondary circuit to cool the heat transfer fluid, ethanol. The temperature of the secondary fluid is controlled by a calibrated thermostatic sensor while the mass flow rate is measured by a calibrated orifice plate and adjusted manually by using a sensitive regulating valve. The test section is in the form of a transparent quartz cylinder of 300 mm diameter, 300 mm height and 15 mm in thickness with the top and bottom endplates made of acrylic sheet of 15 mm thickness. The endplates are designed to allow changing the test tube easily as can be seen in Fig. 1b. The test tube is made of copper and the fins are fixed to the tube of 27 mm at equal angles and passes along the centerline of the quartz cylinder where it is connected at the two extremities to the feeding and discharge tubes of the secondary fluid circuit. To fix the fin to the tube a shallow long groove is made parallel to the tube axis with width equal to the fin thickness, that is 1 mm. The groove and the fin are thoroughly cleaned and a thermal contact paste of thermal conductivity of 1.5 W/mK is placed in the groove. The fin is then forced into the groove and a fine trace of thermal glue is applied along the external contact line. The thermal contact resistance between the tube and fin is estimated as in [28]
R c, past =
L 1.10−3m = = 6.66 × 10−4m2 . K / W k 1.5W / mK
A photographic camera is focused on the top section of the finned tube where a precision scale is fixed beside the finned tube to serve as a physical dimensional reference. Calibrated thermocouples are installed as follows: six thermocouples are fixed along one fin to measure the temperature distribution along the fin width, three thermocouples at fixed at three points in the test section to ensure that the temperature of the liquid PCM is uniform, two thermocouples are fixed at entry and exit of the test section and three thermocouples are placed in the secondary fluid cooling tank to ensure uniform temperature within the tank. In order to collect the necessary experimental data, experiments were conducted for both the development and validation of the proposed correlations. Tubes of diameter of 27 mm having 3, 4, 5 and 6 fins were used in the tests beside the finless tube used as a reference. The fins were made of copper of 1 mm thickness and 300 mm length along
Table 1 Summary of the references used in this work. Study
References
Numerical and experimental studies of the phase change parameters and their effects on the process. Literature reviews of studies on the thermal conductivity of PCM. Experimental studies on latent heat storage tanks with internally and externally finned tubes. Experimental studies on the phase change processes in PCM. Studies on finned tubes to enhance the thermal performance of PCM storage systems.
[4,5,14,16,17,18,19,20,21,22,23] [6,15] [7] [1,2,3,8,9,10,11,12,13] [24,25,26,27,28]
2
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 1. Experimental rig: (a) scheme; (b) finned tube. Table 2 Summary of experimental tests. Nominal temperature (°C)
Number of fins
Fins of the width (mm)
Mass flow (kg/s)
−20, −15, −10 and −5 −20, −15, −10 and - 5 −20 and −10
3, 4, 5, 6 and bare tube Bare tube, 4 and 6 3 and 4
50 50 30, 50, 70, 90 and 110 and bare tube
0.100 and 0.068 0.141 0.100 and 0.068
the tube. Fins of width of 30, 50, 70 and 110 mm were tried. The test temperature was varied from −5 °C to −20 °C. Table 2 presents a summary of the experimental tests.
thermocouples connected to the data acquisition system. The quartz cylinder is then filled with cold water (approximately 0 °C). The temperature of the working fluid is chosen and fixed on the control panel of the Ethanol cooling system. With all components of the two circuits connected and adjusted, the circuit of the primary refrigerant is switched on to cool down the Ethanol to the required temperature, part of the cold Ethanol is circulated to keep the tube temperature at zero °C.
2.1. Experimental procedure Initially the test tube is installed in the test section with all 3
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 2. Tracker software used for treating the digitalized photographs.
3. Experimental assessment of the parameters
When all the Ethanol reaches the pre-established working temperature, the cooling circuit is opened so that the Ethanol can flow with the preestablished mass flow rate in the finned tube. All temperatures are registered each five minutes and with the camera positioned in place photographs are taken of the finned tube, the layer of formed ice around the finned tube and the reference scale fixed to the side of the tube as can be seen in Fig. 2. The Photographs are analyzed by the software Tracker and the real dimensions of the interface are determined. From the measured interface positions and the corresponding time intervals one can also calculate the interface velocity and the solidified mass. The measurements were conducted such that the test tube is photographed from the top in intervals of 5 min during the first two hours and then at intervals of 30 min for five hours from the start of the test. After this period the photographs were taken at intervals of 50 min until the experiment is finished. The adopted criterion for ending the experiment is that there is no more increase of the interface position during three successive measurements. Achieving this condition the whole system is switched off to prepare for the subsequent experiment. The solidification process is a dynamic thermal process and the development of the solidified layer is of extreme importance especially around finned tubes. Images in Fig. 3 are for the case of three fins at six different time intervals. These images show clearly the progress of the solidification around the tube and the attached fins. Images in Figs. 4–6 are for the cases of four, five and six fins, respectively.
3.1. Effect of the number of fins Fig. 7 shows the variation of the interface position with time for four finned tubes, mass flow rate of 0.1 kg/s and temperature of −10.3 °C. As can be seen, the increase of the number of fins increases the interface position. One can also observe that the rate of increase of the interface position with the increase of the number fins shows a decreasing tendency as can be verified from the curves for 3–6 fins. 3.2. Effect of the fin width Fig. 8a,b shows the variation of the interface position with the fin width. As can be seen the increase of the fin width more than a value of about 50 mm reduces gradually the interface position and consequently the solidified mass around the finned tube. Also, the increase of the mass flow rate from 0.068 kg/s to 0.100 kg/s increases the interface position from 72.16 mm to 72.94 mm for the case of fin width of 50 mm. This shows that the increase of the mass flow rate increases slightly the interface position. Fig. 9 shows the variation of the terminal solidified mass with the fin width for a working temperature of Tw = −20.1 °C and two mass flow rates of the secondary fluid of 0.100 kg / s and 0.068 kg/ s. As can be seen the maximum value of the terminal solidified mass increased with the increase of the mass flow rate to 6.30 kg and 6.59 kg, respectively. This is due to the increase of Reynolds number which increases the Nusselt number and consequently the heat transfer coefficient between the tube surface temperature and the PCM. The terminal solidified mass is found to increase with the increase of the fin width up to about 50 mm after which more increase in the fin width seems to reduce slightly the terminal solidified mass. This effect was further verified and confirmed by measuring the temperature distribution along the fin width. It is found that the temperature ditribution shows a continuous temperature decrease along the fin width causing a decrease of the terminal solidified mass.
2.2. Error analysis Calibrated thermocouples of type T of precision ± 0.5 °C were used in the experimental rig. The images of the interface positions were converted to physical dimensions with precision of ± 0.5 mm, while the mass flow rate of the secondary fluid was measured within ± 10−4 kg/ s. The uncertainty of the interface velocity varied in the range ± 5.25 × 10−7 and ± 7.73 × 10−6 mm/min, while the uncertainty in the solidified mass is within ± 4.25 × 10−3and ± 5.52 × 10−2 kg. 4
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 3. Solidified mass around the tube with 3 fins of 50 mm width and tube surface temperature of −20 °C.
the solidified mass of the PCM. This effect is due to the increase of the heat transfer area between the cold tube surface and the surrounding PCM. Also one can observe that the decrease of the tube wall temperature enhances the solidified mass due to the increase of the temperature gradient between the tube surface and the PCM. Fig. 12 shows the effects of varying the tube wall temperature and number of fins on the time for complete solidification. It is found that the decrease of the wall temperature increases the temperature gradient between the wall surface and the PCM which enhances the solidification process and shortens the time for complete solidification. Considering the effects due to variation of wall temperature from −5.2 °C to −20.1 °C, the reduction of complete solidification time is found to be 40%, 38% and 39% for the cases of 6, 4 and no fins, respectively. Also,
3.3. Effect of wall temperature Fig. 10 shows the variation of the interface position with the tube wall temperature for finned and finless tubes. As can be seen the decrease of the wall temperature increases the temperature gradient between the tube wall and the surrounding PCM and this increases the interface position. Also, it is found that the increase of the number of fins increases the interface position in comparison with the finless case, but this effect is attenuated with further increase of the number of fins as can be verified from Fig. 10. Fig. 11 shows the variation of the terminal solidified mass in terms of the tube wall temperature for finned tubes in comparison with the bare tube. As can be seen the increase of the number of fins increases
Fig. 4. Solidified mass around the tube with 4 fins of 50 mm width and tube surface temperature of −20 °C. 5
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 5. Solidified mass around the tube with 5 fins of 50 mm width and tube surface temperature of −20 °C.
for complete solidification (τ). For developing the correlation we assume a general relation of the
comparing the three graphs one can observe the attenuation of the effect of fins with the increase of their numbers.
Φ = AN bW c T d t e
4. Development and validation of the correlations
(1)
where Φ is an arbitrary function which can represent the dependent parameters such as the interface position (I), the interface velocity (V) and the PCM solidified mass (M), while (t)is any time instant but not the time for complete solidification. The constants A, b, c, d, e are obtained by forming five independent equations using a set of experimental data and the resulting five equations are solved to determine the corresponding constants. This procedure is repeated for each of the dependent variables (I), (V) and (M). In the case of the correlation for the time for complete solidification, Φ = τ and the proposed correlation can be written as:
4.1. Development of the correlations This section is devoted to the development of correlations for the important parameters of the phase change around axially finned tubes which strongly affect their thermal performance. The considered parameters include the tube wall temperature, mass flow rate of the heat transfer fluid, number of fins (N) and width of fin (W). The dependent parameters which are to be correlated include the interface position (I), the interface velocity (V), solidified mass (M) and the time
Fig. 6. Solidified mass around the tube with 6 fins of 50 mm width and tube surface temperature of −20 °C. 6
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 7. Variation of the interface position with time for tubes with multi fins.
Fig. 9. Variation of the terminal solidified mass with fin width: (a) 0.100 kg/s; (b) 0.068 kg/s.
Fig. 8. Variation of the terminal interface position with fin width: (a) 0.100 kg/ s; (b) 0.068 kg/s.
Φ = τ = AN bW c T d
Fig. 10. Variation of the terminal interface position with tube wall temperature for mass flow rate of 0.068 kg/s.
(2)
Again to determine the constants in Eq. (2), a set of experimental data is used to form four equations for the unknown constants. The equations are solved and the constants are determined. The correlations obtained following the above procedures are presented below,
Eqs. (3)–(6).
I = 3.91. 10−2N 0.1681W 0.035 T 0.489 t 0.537 7
(3)
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Table 3 Values of Pearson’s coefficient r and the corresponding comparative figures. Pearson’s coefficient (r)
0.97
0.99
0.95
0.95
0.99
0.99
0.99
0.96
0.95
0.96
Figure
13
14
15
16
17
18
19
20
21
22
Fig. 11. Variation of the terminal solidified mass with tube wall temperature.
Fig. 13. Comparison of the effect of the number of fins on the predicted and experimental interface positions.
4.2.1. Effect of the number of fins As was shown the number of fins plays an important role in the process of heat transfer with phase change. The predicted interface position from the correlation is compared with the measured interface position as shown in Fig. 13. It is found that the agreement is good showing a deviation of about 8% and having Pearson’s correlation coefficient r = 0.97. The deviations between the experiments and the correlations prediction can be attributed to the temperature variations in the laboratory since it is not air conditioned and most of the experiments lasted at least 800 min. In some experiments, the transparent top of the test section was slightly foggy, even though it is usually wiped off before photographing, this might cause some blurring provoking error in determining the interface position. The variation of the solidified mass with the number of fins is an important parameter in the design of a latent heat storage system. The solidified mass predicted from the correlation is compared with the solidified mass experimentally determined under the same conditions as in Fig. 14. As can be seen the agreement is good showing a deviation of 7%, and having Pearson’s correlation coefficient r = 0.99. The effect of the number of fins on the interface velocity is presented in Fig. 15 where the predicted interface velocity from the correlation is compared with experimental measurements. As can be observed the agreement is good showing a deviation of about 10%, and having Pearson’s correlation coefficient r = 0.95. The predicted results from the correlation for predicting the time for complete solidification is compared with the experimental results as shown in Fig. 16. One can observe that the increase of the number of fins reduces the time for complete solidification. The results indicate an agreement between the predictions from the correlation and the experimental results within a deviation of about 8%, and having Pearson’s correlation coefficient r = 0.95.
Fig. 12. Variation of the time for complete solidification with the tube wall temperature.
M = 2.72. 10−4N 0.197W 0.116 T 0.737 t 0.671
(4)
V = 7.734N 0.339W −0.225 T 0.326 t −0.532
(5)
τ = 6, 982N−0.3235W −0.1683 T −0.3725
(6)
4.2. Validation of the correlations To validate the correlations different experimental sets were used for this purpose. The same experimental parameters were used in the correlations and the predicted results are then compared. Pearson correlation coefficient with limits of 95% confidence interval was used as indicator of the precision of the correlations. This coefficient given by [29] is
r=
∑ (x i − x¯)(yi − y¯) ∑ (x i − x¯)2 ∑ (yi − y¯)2
(7)
where r is Pearson’s coefficient, xi corresponds to the experimental measurements, x¯ is the mean of the experimental measurements, yi corresponds to the values from the correlation, and y¯ is the mean of the values from the correlation. Table 3 shows the values of Pearson’s coefficient r for the corresponding curves.
4.2.2. Effect of wall temperature Tube wall temperature is one of the most important driving forces for the phase change process. The predicted interface position from the correlation is compared with experimental measurements as presented 8
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 14. Comparison of the effect of the number of fins on the predicted and experimental solidified mass.
Fig. 16. Comparison of the effect of the number of fins on the predicted and experimental complete solidification time.
Fig. 17. Comparison of the effect of the tube wall temperature on the predicted and experimental interface position.
Fig. 15. Comparison of the effect of the number of fins on the predicted and experimental interface velocity.
in Fig. 17 showing agreement within margin of deviation of about 13%, and having Pearson’s correlation coefficient r = 0.99. The tube wall temperature has a strong effect on the solidified mass. The solidified mass is an important parameter in latent heat storage systems. The predicted solidified mass from the correlation is compared with the experimentally measured solidified mass as presented in Fig. 18. As can be seen the agreement is reasonably good with maximum deviation of about 16%, and having Pearson’s correlation coefficient r = 0.99. The tube wall temperature has a direct impact on the time for complete phase change since the tube wall temperature is one of the main driving forces of the phase change process. Comparison of the predicted solidification time with the experimental measurements is shown in Fig. 19. As can be seen the predicted time seems to agree well with the experiments with maximum deviation of 3% at temperatures of −10.0, −15.0 and −20.0 °C, while for the temperature of −5 °C the deviation is 1%, and having Pearson’s correlation coefficient r = 0.99. Fig. 18. Comparison of the effect of the tube wall temperature on the predicted and experimental solidified mass.
4.2.3. Effect of the width of the fin Phase change materials have poor thermal conductivity which 9
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 19. Comparison of the effect of the tube wall temperature on the predicted and experimental time for complete solidification.
Fig. 21. Comparison of the effect of the fin width on the predicted and experimental interface positions.
Fig. 20. Comparison of the effect of the fin width on the predicted and experimental complete solidification time.
Fig. 22. Comparison of the effect of the fin width on the predicted and experimental interface velocity.
impacts negatively their thermal performance. The increase of the heat transfer area is a mechanism which can improve the latent heat storage systems. The increase of the heat transfer area can be done by increasing the number of fins and/or their width. The effect of the fin width on the predicted time for complete solidification calculated from the correlation and the results obtained experimentally are presented in Fig. 20. The analysis shows good agreement with maximum deviation of about 4% for the case of fin width of 30 mm, and having Pearson’s correlation coefficient r = 0.96. The effect of the fin width on the predicted interface position is presented in Fig. 21 together with measured results for two wall temperatures. As can be seen the general trends are similar showing an increase of the interface position with the increase of the fin width. The results agree well within a deviation of 2 to 3%, and having Pearson’s correlation coefficient r = 0.95. Fig. 22 shows the effect of the fin width on the predicted and measured interface velocity. As can be seen the predicted results agree with the experimental measurements with maximum deviation of about 12%, and having Pearson’s correlation coefficient r = 0.96.
a tube with four fins working at −33 °C and for fin width of 16, 12 and 8 mm. For the same conditions the predicted results from the correlation are plotted together with the results from [28] as shown in Fig. 23. As can be seen the agreement is good with R2 of 0.96, 0.95 and 0.93, respectively. It is important to inform that the use of the above correlations is subject to the following conditions: 1. 2. 3. 4.
Same material for the tube and fin, Initial PCM temperature is close to zero, Strictly for solidification of PCM, Correlations are only for finned tubes.
Some parameters which could be investigated to widen the scope of application of these correlations include: a) Develop correlations for long finned tubes. We already have some results for long bare tubes but need to be completed for finned tubes, b) Develop correlations for melting of PCM around finned and bare tubes.
4.2.4. Comparison with other available numerical results The present numerical predictions are compared with the results from Sheikholeslami et al. [28]. The numerical results from [28] are for 10
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
Fig. 23. Comparison of the effect of the predictions from the correlations with the numerical results of Sheikholeslami et al. [30].
5. Conclusion
Acknowledgments
The experimental results show that the increase of the number of fins increases the interface position and interface velocity and reduces the time for complete phase change. The width of the fin enhances the heat transfer rate and increases the solidified mass. Reducing the wall temperature enhances the heat transfer rate and produces more solidified mass, increases both the interface position and interface velocity and reduces the time for complete solidification. The correlation to predict the effects of the number of fins is found to agree well with experimental results with a deviation of about 7% for the solidified mass, 8% for the interface position and 10% for interface velocity. The correlation for predicting the effects of the fin width shows a deviation in comparison with the experimental measurements of 3% for the interface position and 4% for the time for complete phase change. The correlation for predicting the effects tube wall surface temperature shows a reasonable agreement in comparison with the experimental measurements with a deviation of 16% for the solidified mass, 8% for the interface position and 3%.for the time for complete solidification.
The first author wishes to acknowledge the support given by Fapema in the form of a doctorate scholarship and the second author wishes to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the PQ Research Grant 304372/2016-1. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.est.2019.100973. References [1] A. Abhat, Low temperature latent heat thermal energy storage: heat storage materials, Solar Energy 30 (10) (1983) 313–332. [2] A. Al Robaidi, Development of novel polymer phase change material for heat storage application, Int. J. Mater. Sci. Appl. 2 (2013) 168, https://doi.org/10.11648/j. ijmsa.20130206.11. [3] A. Agarwal, R.M. Sarviya, An experimental investigation of shell and tube latent heat storage for solar dryer using paraffin wax as heat storage material, Eng. Sci. Technol. Int. J. 19 (2016) 619–631, https://doi.org/10.1016/j.jestch.2015.09.014. [4] K.A.R. Ismail, C.L.F. Alves, M.S. Modesto, Numerical and experimental study on the solidification of PCM around a vertical axially finned isothermal cylinder, Appl. Therm. Eng. 21 (2001) 53–77, https://doi.org/10.1016/S1359-4311(00)00002-8. [5] L. Bilir, Z. Ilken, Total solidification time of a liquid phase change material enclosed in cylindrical/spherical containers, Appl. Therm. Eng. 25 (2005) 1488–1502, https://doi.org/10.1016/j.applthermaleng.2004.10.005. [6] A. Agarwal, R.M. Sarviya, Thermal conductivity enhancement of PCMs in annular tube heat storage : a review, Int. J. Res. Appl. Sci. Eng. Technol. 2 (2014) 69–73. [7] A.A. Al-Abidi, S. Mat, K. Sopian, M.Y. Sulaiman, A.T. Mohammad, Experimental
Declaration of Competing Interest None.
11
Journal of Energy Storage 26 (2019) 100973
C.R.E.S. Nóbrega, et al.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
https://doi.org/10.1016/j.applthermaleng.2015.12.080. [20] Y. Wang, L. Wang, N. Xie, X. Lin, H. Chen, Experimental study on the melting and solidification behavior of erythritol in a vertical shell-and-tube latent heat thermal storage unit, Int. J. Heat Mass Transfer (2016), https://doi.org/10.1016/j. ijheatmasstransfer.2016.03.125. [21] Z. Khan, Z. Khan, K. Tabeshf, Parametric investigations to enhance thermal performance of paraffin through a novel geometrical configuration of shell and tube latent thermal storage system, Energy Convers. Manage. 127 (2016) 355–365, https://doi.org/10.1016/j.enconman.2016.09.030. [22] M. Mastani, F. Haghighat, S. Seddegh, A.A. Al-abidi, Heat transfer enhancement of phase change materials by fi ns under simultaneous charging and discharging, Energy Convers. Manage. 152 (2017) 136–156, https://doi.org/10.1016/j. enconman.2017.09.018. [23] R. Kothari, S.K. Sahu, S.I. Kundalwal, Comprehensive analysis of melting and solidification of a phase change material in an annulus, Heat Mass Transfer 55 (2019) 769–790. [24] A. Sciacovelli, E. Guelpa, V. Verda, Second law optimization of a PCM based latent heat thermal energy storage system with tree shaped fins, 17 (2014) 127–136. doi:10.5541/ijot.549. [25] S. Lohrasbi, M.G. Bandpy, D.D. Ganji, Response surface method optimization of Vshaped fin assisted latent heat thermal energy storage system during discharging process, Alexandria Eng. J. 55 (2016) 2065–2076, https://doi.org/10.1016/j.aej. 2016.07.004. [26] A.M. Abdulateef, S. Mat, J. Abdulateef, K. Sopian, A.A. Al-Abidi, Geometric and design parameters of fins employed for enhancing thermal energy storage systems: a review, Renew. Sustain. Energy Rev. 82 (2018) 1620–1635, https://doi.org/10. 1016/j.rser.2017.07.009. [27] L. Kalapala, J.K. Devanuri, Influence of operational and design parameters on the performance of a pcm based heat exchanger for thermal energy storage – A review, J. Energy Storage 20 (2018) 497–519, https://doi.org/10.1016/j.est.2018.10.024. [28] Y.A. Çengel, A.J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, 4th, Boston, 1998. [29] R.J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley & Sons, Inc., New York, 1980, https://doi.org/10.1002/9780470316481. [30] M. Sheikholeslami, R. Haq, A. Shafee, Z. Li, Heat transfer behavior of nanoparticle enhanced PCM solidification through an enclosure with V shaped fins, Int. J. Heat Mass Transfer 130 (2019) 1322–1342, https://doi.org/10.1016/j. ijheatmasstransfer.2018.11.020.
study of melting and solidification of PCM in a triplex tube heat exchanger with fins, Energy Build 68 (2014) 33–41, https://doi.org/10.1016/j.enbuild.2013.09. 007. S.P. Jesumathy, M. Udayakumar, S. Suresh, S. Jegadheeswaran, An experimental study on heat transfer characteristics of paraffin wax in horizontal double pipe heat latent heat storage unit, J. Taiwan Inst. Chem. Eng. 45 (2014) 1298–1306, https:// doi.org/10.1016/j.jtice.2014.03.007. J. Yang, L. Yang, C. Xu, X. Du, Experimental study on enhancement of thermal energy storage with phase-change material, Appl. Energy 169 (2016) 164–176, https://doi.org/10.1016/j.apenergy.2016.02.028. X. Yang, Z. Lu, Q. Bai, Q. Zhang, L. Jin, J. Yan, Thermal performance of a shell-andtube latent heat thermal energy storage unit: role of annular fins, Appl. Energy 202 (2017) 558–570, https://doi.org/10.1016/j.apenergy.2017.05.007. X. Yang, J. Yu, Z. Guo, L. Jin, Y.L. He, Role of porous metal foam on the heat transfer enhancement for a thermal energy storage tube, Appl. Energy 239 (2019) 142–156, https://doi.org/10.1016/j.apenergy.2019.01.075. X. Yang, P. Wei, X. Cui, L. Jin, Y.L. He, Thermal response of annuli filled with metal foam for thermal energy storage: an experimental study, Appl. Energy 250 (2019) 1457–1467, https://doi.org/10.1016/j.apenergy.2019.05.096. X. Yang, Z. Guo, Y. Liu, L. Jin, Y.L. He, Effect of inclination on the thermal response of composite phase change materials for thermal energy storage, Appl. Energy 238 (2019) 22–33, https://doi.org/10.1016/j.apenergy.2019.01.074. M.Y. Yazici, M. Avci, O. Aydin, M. Akgun, On the effect of eccentricity of a horizontal tube-in-shell storage unit on solidification of a PCM, Appl. Therm. Eng. 64 (2014) 1–9, https://doi.org/10.1016/j.applthermaleng.2013.12.005. M.K. Rathod, J. Banerjee, Thermal performance enhancement of shell and tube latent heat storage unit using longitudinal fins, Appl. Therm. Eng. 75 (2015) 1084–1092, https://doi.org/10.1016/j.applthermaleng.2014.10.074. M.J. Hosseini, M. Rahimi, R. Bahrampoury, Thermal analysis of PCM containing heat exchanger enhanced with normal annular fines, Int. J. Mech. Sci. 6 (2015) 221–234, https://doi.org/10.5194/ms-6-221-2015. M.J. Hosseini, A.A. Ranjbar, M. Rahimi, R. Bahrampoury, Experimental and numerical evaluation of longitudinally finned latent heat thermal storage systems, Energy Build. 99 (2015) 263–272, https://doi.org/10.1016/j.enbuild.2015.04.045. G. Li, Energy and exergy performance assessments for latent heat thermal energy storage systems, Renew. Sustain. Energy Rev 51 (2015) 926–954, https://doi.org/ 10.1016/j.rser.2015.06.052. M. Kabbara, D. Groulx, A. Joseph, Experimental investigations of a latent heat energy storage unit using finned tubes, Appl. Therm. Eng. 101 (2016) 601–611,
12