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Experimental and numerical evaluation of longitudinally finned latent heat thermal storage systems
Accepted Manuscript Title: Experimental and Numerical Evaluation of Longitudinally Finned Latent Heat Thermal Storage Systems Author: M.J. Hosseini A.A. Ranjbar M. Rahimi R. Bahrampoury PII: DOI: Reference:
S0378-7788(15)00344-8 http://dx.doi.org/doi:10.1016/j.enbuild.2015.04.045 ENB 5837
To appear in:
ENB
Received date: Revised date: Accepted date:
3-2-2015 20-4-2015 22-4-2015
Please cite this article as: M.J. Hosseini, A.A. Ranjbar, M. Rahimi, R. Bahrampoury, Experimental and Numerical Evaluation of Longitudinally Finned Latent Heat Thermal Storage Systems, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.04.045 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights: Experimental and numerical analysis is presented on a PCM storage system. Flow field, melting front and energy absorption capability of the system are studied.
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Stephan number and fin height are studied on longitudinally finned HX.
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Results indicate that fin extension improves thermal conditions of the system.
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Experimental and Numerical Evaluation of Longitudinally Finned Latent Heat Thermal Storage Systems M.J. Hosseini a,*, A.A. Ranjbar b, M. Rahimi a, R. Bahrampoury c
c
School of Mechanical Engineering, Babol University of Technology, POB 484, Babol, Iran
Department of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran
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b
Department of Mechanical Engineering, Golestan University, POB 155, Gorgan, Iran
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a
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Abstract
In this study the effect of longitudinal fins in a double pipe heat exchanger containing PCM is examined during charging process. Therefore 8 rectangular fins are mounted around the HTF (heat
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transfer fluid) carrying tube. Two fins’ heights and three Stefan numbers are chosen in order to examine the effect of these two parameters on thermal performance of the heat exchanger. In order to study the heat exchanger experimentally, 3 sections are chosen and several thermocouples are located
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in the sections. Observing thermal distribution, melting front, temperature and velocity contours and liquid fraction versus time, detailed behavior of melting process is explained. The process of heat
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absorption versus time is also discussed. Results show that fins extension leads to the less melting time and deeper penetration of heat. It is also shown that the process of heat absorption power is a
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function of fins height at initial steps of the charging process.
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Key words: longitudinal fins, double tube heat exchanger, phase change material. Nomenclatures
Specific heat capacity (J/Kg. K) Gravity (m/s2)
Sensible enthalpy (J/kg) Total enthalpy (J)
Thermal conductivity (W/m. K) Latent heat (J/kg) Mass flow rate (kg/s)
*
Corresponding Author: (Seiyed Mohammad Javad Hosseini) Department of Mechanical Engineering, Golestan University, P.O. Box 155, Gorgan, Iran. Tel/Fax: +98 17 32440206, Email: [email protected]
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Pressure (Pa) Thermal instantaneous power (J/s) Cumulative energy (J) r
Radial distances from the center of HTF tube (m)
Ste
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Source term Stefan number
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Temperature (K) Velocity vector (m/s)
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Greek symbols Expansion coefficient (1/K)
λ
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Dynamic viscosity (Pa. s) Liquid fraction Density (kg/m3)
Mushy zone
m
Melting
ref
Reference
H
Hot water
In
Inlet water
Ini Out
d
mush
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Charge
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ch
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Subscripts
PCM
Initial
Outlet water
Phase change material Solid
Liquid
Heat exchanger
1. Introduction The increasing gap between the amounts of energy generation and its consumption has attempted engineers to seek for a solution. Nowadays, regarding lack of available energy and the prediction of this source of energy depletion, and considering inevitable pollution consequences of employing fossil fuel as the only source to supply the world energy requirement, has led to increased significance of proposing renewable energy sources. The cited consequences of employing this source of energy have 3 Page 3 of 31
offered an opportunity for solar energy to compete almost one hundred-year-old fossil fuel, especially in countries where vast amount of solar energy is available. Utilizing this vast renewable energy as new source of energy brings about diverse types of challenges. One of the most challenging subjects in its employment is related to its storage. There are kinds of storage systems that are categorized based on the way heat is stored; sensible,
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latent and thermal–chemical. Among these thermal energy storage methods, latent heat thermal energy storage (LHTES) system in which a phase change material (PCM) is utilized, seems to be the most favorable for its high energy storage density with small temperature variations [1]. Zalba et al.
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[2] performed a detailed review on thermal energy storage which deals with PCM, heat transfer studies and applications. Farid et al. [3] also presented a review on the PCM analysis for different
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applications including hermetic encapsulation.
Several publications deal with numerical study and experimental investigation of geometrically varying PCM storage systems. Some of the cited configurations are sphere [4-7], rectangular [8-12] which comprise more than 70% of the literature [2].
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and shell and tube designs [13-18]. Most of the analyses in this field belong to shell and tube systems
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Jesumathy et al. [17] experimentally studied melting and solidification processes of paraffin wax as PCM in a horizontal double pipe heat exchanger. Their study focuses on investigation of increasing heat transfer fluid (HTF) inlet temperature and its mass flow rate consequences on both charging and
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discharging processes. Their results indicate that melting process is dominated by natural convection in liquid phase due to buoyancy effects while conduction heat transfer mechanism is more effective in
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solidification. Also their results imply that heat transfer coefficient between HTF and PCM is affected by Reynolds number more during melting process than solidification.
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Hosseini et al. [13, 15-16] investigated melting and solidification on a PCM in a shell and tube heat exchanger for various operating conditions. The operating variables are limited to HTF inlet temperature and its flow rate. Results present a quantitative data on variation of melting time versus inlet temperature.
Since PCMs are generally weak thermal conductive materials, different techniques are employed to promote melting process as well as solidification. To overcome this lack of thermophysical property, extended surfaces are frequently proposed in geometrically different configurations in literature. Numerous studies are conducted to investigate consequences of using such extended surfaces in melting and solidification processes in which natural convection is disregarded in PCM melt [19-21]. Ignorance of this heat transfer improving mechanism has aroused the need of experimental simulation. The effect of longitude fins inside a horizontal cylindrical latent heat energy storage system in order for its thermal enhancement has also been examined by Liu et al. [22]. In their study, both straight and angled longitudinal fins are investigated. It was observed that conduction is the dominant heat transfer mechanism during initial stages of charging, and natural convection dominates once enough liquid 4 Page 4 of 31
PCM is present inside the system. On the other hand, conduction dominates during the entire solidification process. Complete melting time is strongly affected by HTF inlet temperature whereas HTF flow rate is much less influential on the melting time. Castell et al. [23] have proved that adding vertical fins to HTF side of the tube also enhances the performance of LHTEs during solidification. They focused on calculation of heat transfer coefficient
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through which it was found that solidification time in the finned system was considerably less, as compared to finless system. Their results show that while fins' height rises, the heat transfer coefficient varies in the studied vertically positioned heat exchanger. So that, the longer fins were
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used, due to dampening effect on natural convection, heat transfer coefficient lowers. Nevertheless, the solidification time remains less because of the increase in heat transfer area.
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Velraj et al. [24] studied the consequences of employing different number of longitudinal fins as well as their height on solidification process in a circular vertical PCM containing shell. Their study has been carried out numerically and experimentally in which RT60 is chosen as the phase change
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material.
Ismail et al. [25] investigated the effect of employing longitudinal fins and influences of varying
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geometrical specification of the fins including number of fins, their height and thickness as well as aspect ratio in a vertical circular cylinder on solidification process. Conduction is the only heat transfer mechanism considered in the study which can be justified only for vertical orientation of the
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shell, therefore a slice restricted to fins has been considered as a symmetrical piece to be numerically analyzed. Considering the above mentioned papers on phase change processes, most of the papers are
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numerical while in this paper both numerical and experimental study is accomplished. The effect of fins' height variation as well as inlet temperature on different decision parameters in such a
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comprehensive extend is among the differences between this paper and similar previous studies. In the present study, melting of a specific PCM is explored in a horizontal longitudinally finned shell and tube heat exchanger in which PCM is located in a circular shell. HTF carrying tube is located centrally with the circular cylindrical shell and provides melting thermal energy. Fins' height and Stephan number are considered as decision variables on the process and the effect of these two (including two fins' height and three Stefan numbers) has been investigated on temperature distribution, melting front, liquid fraction, total melting time and absorbed heat during charging process. The experimental study includes temperature record via 18 thermocouples at different sections of the heat exchanger.
2. Geometric details of the heat exchanger The longitudinally finned heat exchanger which its schematic is shown in Figure 1(a) is investigated for two fins' height. Figure 1 (b) illustrates a 3D exploded section view of the 13 mm-fin heat exchanger for which the longitudinal fins are present on the whole length of the central tube. 5 Page 5 of 31
Figure 2(c) shows the same heat exchanger enhanced with fins of 26 mm height. As can be seen the number of radial fins around the tube is 8 for both heat exchangers which are symmetrically mounted along the tube in a way that 2 fins are horizontal, 2 vertical and the remaining 4 fins are tilted with 45 degree angle over the horizon. It is clear from the colors of the figure that, the central tube and its surrounding radial fins are made of copper while the shell is Ironic. The outer covering is the
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insulation layer made of glass wool with 0.04 W/m K which leads to negligible heat loss of the heat exchanger. Quantitive details of the heat exchanges are given in Table 1. The 3 white sections in the shell are experimental measured sections in which thermocouples are placed in different radial
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distances and varying angular directions. The longitudinal distances of the sections are symmetric therefore the middle section is at 500 mm from both ends and the right section is 200mm away from
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the right cap. The symmetry implies the similar distance has been considered for the left section to the left cap. Exact locations of each thermocouple in their related sections are exhibited in Figure 2. As can be seen in the figure, the numbers of thermocouples in both right and left sections are similar, 6,
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while the number of thermocouple in the middle section is selected to be 4.
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3. Setup and procedure
Figure 3 illustrates a schematic diagram of the experimental apparatus in which loop components as well as measuring instrumentation are presented. As the study includes merely discharging process, a
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loop is designed to provide hot utility for the process in which hot bath joins to produce the required
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heat. As flow rate is an indispensable component of heat transfer rate calculation, a rotameter is applied in the experiment. As observed in Figure 2, three sections are designated for thermal
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measurement. The two end sections include 6 thermocouples while the middle one involves 4. The exact longitudinal distance of the sections shown in figure 1 has been explained through the text whereas angular position and radial distances of every thermocouple is presented in Figure 2. Considering these 16 thermocouples as well as the HTF inlet and outlet thermal measuring thermocouples, 18 thermocouples are incorporated in the experimental setup. Nowadays, various types of PCMs with different melting temperature are available for every application. In this study RT50 (Rubitherm GmbH) for which density and Specific heat capacity are 780 kg/m3 and 2000 J/kg.K respectively, is selected as PCM to be inserted into the shell. The selection of this PCM for which melting temperature is between 45 to 51 ºC refers to its appropriate melting temperature that matches well with low temperature heat sources like solar systems and power plants exhaust. The characteristics of the material including its stability and corrosiveness as well as its Thermophysical properties involving its viscosity, thermal conductivity and latent heat has been explained by Hosseini et. al [15].
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4. Methodology of tests After the heat exchanger is filled up with liquid PCM and no leakage was observed, a few runs are made in order to calibrate the system. Then the charging process starts, while the solid PCM is at thermal equilibrium with the conditioned lab temperature (23–25 ºC). During the charging process,
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inlet HTF temperature, TH, is maintained at a set temperature using a PID controlled hot water bath. Using the apparatus and procedures described above, several experiments have been conducted to study the behavior of the PCM during charging process. As at mid-latitude areas and where direct
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radiation is available, double glazing flat solar collectors are able to provide hot water with more than 70 ºC centigrade degrees [26], and also there should be a reasonable temperature difference between
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hot and cold sources to keep the melting time in an acceptable limit, this range is chosen for the current study. The experiments are performed for different inlet temperatures (70, 75 and 80 ºC) of the HTF and fins' height (13 and 26 mm). Corresponding Stephan number (Ste) (the ratio of sensible heat
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to latent heat) as defined in equation (1) for each of these hot HTFs are calculated in which the only
(1)
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varying parameter is the cited inlet temperature.
Where Cp, L, and Tm are the specific heat, the latent heat and the mean melting temperature of PCM
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((Ts+ Tliq)/2) and TH is the temperature of hot inlet water. In this paper, the Stefan numbers for the
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three inlet HTF temperatures are calculated which are 0.26, 0.32 and 0.38. The volumetric flow rate is 1 L/min which leads to a laminar flow regime. The assumption of laminar flow is a simplifying
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hypothesis which is considered to keep the possibility of intended parameters variation including Stefan number. Indeed, consideration of flow regime may be a bulky discussion for which a separate study is required. It is obvious that, turbulence leads to an increase to convective heat transfer coefficient inside the tube and consequently rate of heat transfer rises. 5. Data reduction
Varying thermal power ( ) and aggregated energy given by water (
) during charging can be
obtained as below:
(2) (3) where
represents the mass flow rate,
signifies the specific heat capacity,
and
are
temperatures at inlet and outlet of heating HTF respectively.
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As the process is transient, the heat emerged from the HTF ( absorbed heat (
) doesn't equal the aggregated PCM
) since a portion of the heat is transferred to the equipment. These parameters
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may be estimated as below:
and
is the mass of sole device,
stands for the specific heat for heat exchanger and
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Where
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(4)
represent the PCM temperatures respectively at the beginning and the end of the process,
Also the aggregated energy charged by the PCM,
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, can be calculated by the following equation: (5)
) during the charging process as largest amount of
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The maximum theoretical energy absorbed ( heat given to the PCM can be evaluated as below:
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is the PCM's mass,
signifies the PCM specific heat,
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Where
of solid and liquid PCM at boundaries of melting process and
and
are temperatures
is the PCM's latent heat of phase
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change.
(6)
6. Numerical models
In order to simulate phase change of melting in a shell and tube heat exchanger, enthalpy-porosity method [27-28] is used. In the present study, both PCM and water flows are considered to be unsteady, laminar, incompressible and three-dimensional. The viscous dissipation term is considered negligible so that the viscous incompressible flow and the temperature distribution in annulus space can be described by the Navier-Stokes and thermal energy equations, respectively. Also dynamic viscosity, considered as a function of temperature, is also used [15]. In addition, the density change within the liquid phase that drives natural convection is only considered in the body force terms (Boussinesq approximation) in which variable density is defined as [29]: (7)
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for 51º C T 100 º C in the liquid state. The initial temperature of the whole system is
.
Also the lateral surface of the outer tube is assumed to be insulated. Consequently, continuity, momentum, and thermal energy equations can be expressed as follows: Continuity:
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(8)
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Momentum:
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Thermal Energy:
(9)
(10)
The enthalpy of the material is computed as the sum of the sensible enthalpy, and the latent heat,
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:
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Where
(11)
(12)
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The latent heat content, , can be written in terms of the latent heat of the material:
where
may vary from zero (solid) to
In Eq. (8),
(13)
(liquid). Therefore, the liquid fraction, , can be defined
(14)
is the Darcy’s law damping terms (as source term) that is added to the momentum
equation due to phase change effects on convective heat transfer which is defined as [30]:
(15)
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The coefficient
is mushy zone factor. This parameter is of a large value, usually between 104
and 107. In the current study
is assumed to be constant and is set to 106 which is validated for
same material and cylinder in [15].
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6.1. Computational methodology The SIMPLE algorithm [31] is utilized to couple pressure–velocity governing differential equations and QUICK differencing scheme is employed for solving momentum and energy ones within a 3D in-
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house developed code [15], whereas the PRESTO scheme is adopted for the pressure correction equation. The under-relaxation coefficient for momentum, pressure, density, melting fraction and
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thermal energy are 0.7, 0.3, 1, 0.9 and 1, respectively. An arrangement of 450,000 nodes which is shown in Figure 4 is found to be sufficient for the present study. The time step in the calculations is as small as 0.05 s and the number of iterations for each time step is 400. The grid size and the time step
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were chosen after careful examination of the independency of the results to these parameters. The convergence is checked at each time step, with the convergence criterion of 10-7 for all variables. As the PCM is same for this study and the one done by Hosseini et al. [15], and the same cylinder is also
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considered, that code is developed for this paper, therefore, the validation also hold for this work. 7. Result and discussion
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In this paper the results of temperature distribution and energy related results are derived from
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experimental runs whereas temperature contours and melting front progression, velocity field and
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liquid fraction variation are related to the computational simulation. 7.1. Thermal response
Figure 5 illustrates temperature distribution at the 3 selected sections, right, middle and left at different radius distances (r=12.5 mm and r=32.5 mm) and angular directions in the 13 mm-fin heat exchanger as well as 26 mm-fin one at Stefan number of 0.26. As is obvious, the nearer position to the central HTF carrying tube is more rapidly affected by the heat. Comparing the temperature values for a specific moment, the temperature of r=12.5 mm is much higher than that of r= 32.5 mm especially at initial stages of the experiment. Considering the figure, it can be seen that for the 3 cited sections
and for both radius distances, regardless of time, the temperature value at 0∘ (above the tube) is higher
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than similar studied points at other angular directions (90∘ and 180∘). Similar but more pronounced
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trend can be reported for 90∘ in comparison with 180∘ (below the tube). Such behavior is due to
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natural convection which is originated from vortices formation and these vortices’ penetration to the
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upper regions. The phenomenon that lateral direction temperature is higher than downward direction
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is due to this penetration development to lateral regions. Temperature reduction between 90∘ and 180∘
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is much more noticeable for 13mm-fin heat exchanger than 26 mm-fin one which may be explained
by velocity field (figure 7). Since 180∘ demonstrates the least value, when the temperature of this
angular direction especially the farther one (r=32.5 mm) leaves the melting zone, it can be concluded that almost all the PCM in the shell has been melted. Therefore, comparing these two heat exchangers,
as the temperature value of the point at 180∘ and radius of 32.5 mm remains in the melting zone even
after 150 minutes for the 13 mm-fin heat exchanger unlike 26 mm-fin heat exchanger, it can be 11 Page 11 of 31
deduced that increasing the extended surfaces at fins’ length direction leads to faster development of melting front. The extent of the effect of applying higher fins can be realized when considering the
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departure of 180∘ and 32.5 mm radius mostly at 60 min for the 3 sections. The fact that the slop of the
lines for the 26mm-fin heat exchanger is less than the same criterion for shorter fin, implies that temperature distribution of higher fin leads to smoother distribution of temperature. Comparing
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temperature distribution for different sections (along the tube), it can be seen that temperatures don't vary significantly longitudinally which is due to heat penetration resulted from high thermal
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conduction of longitudinal copper tubes and fins. Figure 6 exhibits the melting front of the heat exchanger’s mid-section for the 13mm-fin and 26 mm-fin heat exchanger during charging process. Regarding the figure, at early stages of melting front formation, a symmetrical melting front at the
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cited section appears. When the melting process advances, the trend of the symmetry persists until the front boundary covers a farther distance than the fins’ tips’. Afterward as the melting front grows, the symmetry vanishes which is due to the natural convection consequences. Therefore for 13 mm-fin
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heat exchanger, the melting front becomes asymmetric earlier in comparison with the 26 mm-fin one which intensifies as the Stefan number increases. In addition, this figure implies that increasing fins’
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height increases the rate of melting front development which is due to enhanced conduction
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mechanism that improves heat penetration to farther distances of the PCM. The discussion made on
the passing melting zone for 180∘ angle and 32.5 mm radial distance in figure 1 is confirmed by
considering the first row of figure 6 (Ste=0.26) in which the presence of solid PCM in the shell of the 13mm-fin heat exchanger and absence of PCM for the 26 mm-fin heat exchanger after 150 min is evident. In figure 7 temperature and velocity field contours for considered fins’ height and cited Stefan number is presented at every 30 minutes. Considering the figure, as soon as the melting process establishes, vortices are formed in melt region. It can also be recognized that increasing Stefan number for both heat exchangers leads to enlargement of vortices for the both heat exchangers at a specific moment. In addition it is apparent that for the 13 mm-fin heat exchanger soon after small vortices formation at initial stages of melting process, the vortices merge and form larger a vortex. In reverse, for the 26 mm-fin heat exchanger, the extension of the fins blocks the merging process at initial stages which leads to larger local vortices. 12 Page 12 of 31
Considering temperature contours presented in figure 7, it is noticeable that increasing fins’ height leads to a sensible increase in heat flux penetration in PCM. Moreover, it can be seen that employing 26mm-fin leads to total melting time reduction for the 3 Stefan numbers. Therefore after 60 minutes of the experiment initiation a homogeneous temperature distribution appears in the shell section. Figure 8 demonstrates the liquid fraction during melting process. The specified time in the figure is
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related to complete melting after which no solid remaining exists in shell. Regarding the given data on the figure, it can be understood that the trend of total melting time varies for the two heat exchangers; for 13mm-fin heat exchanger, increasing Stefan number from 0.26 to 0.32 and after 0.32 to 0.38,
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melting time reduces 20% and 12.5% respectively. These values for 26 mm- fin heat exchanger are
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13.2% and 15.3%. 7.2. PCM absorbed energy
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Figure 9 shows the variation of stored thermal power versus time during charging process for different Stefan numbers. Considering the figure it can be seen that although varying Stefan number for a specific fins' height doesn’t influence the PCM heat absorption power to a noticeable extent,
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employing 26mm-fin heat exchanger leads to an extra absorption power especially at initial steps of the charging process which is the result of higher level of thermal potential at these portions of time. Subsequently since the thermal potential between these two decreases, a diminishing trend for the heat
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absorption is observed. The figure also states that, regardless of Stefan number, the heat absorption
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for each of the heat exchangers converges to a specific value. Comparing the figures a and b, the heat absorption of the heat exchanger is function of fins' height especially at initiation of the experiment while the time passes, heat absorption power of the heat exchangers approaches to a similar value.
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Tables (2) and (3) illustrate some quantitive results during charging for the heat exchanger for varying Stefan numbers and the two fins’ height. Considering data tabled, increasing Stefan number while fins’ height increases, the PCM average temperature at the end of the process faces a lower rate of increase; so that, increasing Stefan number from 0.26 to 0.38, the rate of final average PCM temperature during the process lowers from 11.1 % to 3.9 %. In simpler words, employing higher fins for larger Stefan numbers avoids intense elevation of temperature. It can be seen in the table that, extending fins' height, for the Stefan number of 0.26, a much greater absorbed heat by the PCM is observed in comparison with the two other Stefan numbers. (27.4% versus 14.9%) Conclusion In this investigation, the effect of utilizing longitudinal fins with two heights for different Stefan numbers in a double tube heat exchanger which contains PCM is investigated. A summary of conclusions is as below: Considering temperature distribution for 13 mm-fin and 26 mm-fin heat exchanger, employing 26 mm fins lead a smoother distribution of temperature in the heat exchanger. Moreover, employing the heat 13 Page 13 of 31
exchanger with 26 mm fins causes the recorded temperature of the lower thermocouple to depart the melting zone sooner. Regarding the melting front, development of the front to the tips of melting region is symmetrical and afterward it becomes asymmetric. Therefore the presence of higher fins leads to extra amount of symmetric melting. Increasing Stefan number results in a raise in the rate of melting front development. Studying the flow field during charging, it is clear that higher fins leads to
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a blockage of vortices merger and therefore large vortices form while for smaller fins, this behavior takes place much more restricted and the vortices are smaller. Increasing Stefan number results in vortices development with a more rapid rate. Comparing the rate of heat absorption versus time, it is
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clear that increasing fins’ height leads to better absorption especially at initial stages. Also results show that, increasing fins’ height is much more effective for lower Stefan number in comparison with
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higher value. Although fins' height improves thermal conditions of the system, increasing this value to a large extend leads to reduction of PCM amount and consequent less capability of the system to absorb energy. Moreover this variation results to heavier and more expensive heat exchanger.
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Therefore there is an optimum value for the height if a more comprehensive study which includes all
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these factors in its objective function is taken into account.
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[10] U. Stritih, An experimental study of enhanced heat transfer in rectangular PCM storage, International Journal of Heat and Mass Transfer 47 (2004) 2841–47. [11] M. Rahimi, A.A. Ranjbar, D.D. Ganji, K. Sedighi, and M.J. Hosseini, Experimental Investigation of Phase Change inside a Finned-Tube Heat Exchanger, Hindawi Publishing Corporation Journal of Engineering Volume 2014, Article ID 641954, 11 pages.
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and tube heat exchanger as a PCM thermal storage system, International Communications in Heat and Mass Transfer 50 (2014) 128–136
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[16] M.J. Hosseini, A.A. Ranjbar, K. Sedighi, M. Rahimi, Melting of Nanoprticle-Enhanced Phase Change Material inside Shell and Tube Heat Exchanger, Hindawi Publishing Corporation Journal of Engineering Volume 2013, Article ID 784681, 8 pages
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[17] S.P. Jesumathy, M. Udayakumar, S. Suresh , S. Jegadheeswaran, An experimental study on heat
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transfer characteristics of paraffin wax in horizontal double pipe heat latent heat storage unit, Journal of the Taiwan Institute of Chemical Engineers 45(4) (2014) 1298–1306
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[18] F. Agyenim, N. Hewitt, The development of a finned phase change material (PCM) storage system to take advantage of off-peak electricity tariff for improvement in cost of heat pump operation, Energy and Buildings 42 (2010) 1552–60. [19] W. Ogoh, D. Groulx, Effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study, International Journal of Heat and Mass Transfer 48 (2012) 1825-35. [20] R.V. Seeniraj, N. L. Narasimhan, Performance enhancement of a solar dynamic LHTS module having both fins and multiple PCMs, Solar Energy 82 (2008) 535-42. [21] V. Shatikian, G. Ziskind, R. Letan, Numerical investigation of a PCM-based heat sink with internal fins, International Journal of Heat and Mass Transfer 48 (2005) 3689-706.
16 Page 16 of 31
[22] C. Liu, D. Groulx, Experimental study of the phase change heat transfer inside a horizontal cylindrical latent heat energy storage system, International Journal of Thermal Sciences 82 (2014) 100-110 [23] A. Castella, C. Soléa, M. Medranoa, J. Rocaa, L.F. Cabezaa, D. García, Natural convection heat
ip t
transfer coefficients in phase change material (PCM) modules with external vertical fins, Applied Thermal Engineering 28 (2008) 1676–1686
[24] R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, K. Scwharzer, Experimental analysis and
cr
numerical modelling of inward solidification on a finned vertical tube for a latent heat storage
us
unit, Solar Energy 60 (5) (1997) 281–290.
[25] 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, Applied Thermal
an
Engineering 21 (2001) 53–77.
[26] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley & Sons, New
M
York, 1980.
[27] A.D. Brent, V.R. Voller, K. J. Reid, Enthalpy-porosity technique for modeling convectionB 13 (1988) 297-318.
d
diffusion phase change: application to the melting of a pure metal, Numerical Heat Transfer Part
te
[28] Z.X. Gong, S. Devahastin, A.S. Mujumdar, Enhanced heat transfer in free convection-dominated melting in a rectangular cavity with an isothermal vertical wall, Applied Thermal Engineering 19
Ac ce p
(1999) 1237-51.
[29] E.A. Spiegel, G. Veronis, On the Boussinesq approximation for a compressible fluid, The Astrophysical Journal 131 (1960) 442-447. [30] H. Darcy, Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856. [31] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.
17 Page 17 of 31
Table Captions: Table 1. Detailed specifications.
Ac ce p
te
d
M
an
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Table 3. Data from charging process for the 26mm-fin heat exchanger.
ip t
Table 2. Data from charging process for the 13mm-fin heat exchanger.
18 Page 18 of 31
Figure Captions: Figure 1. 3D exploded section view of the studied PCM containing heat exchangers (a) schematic of the heat exchanger and its' section view (b) 13mm-fin heat exchanger (c) 26mm-fin heat
ip t
exchanger. Figure 2. Thermocouples radial and angular positions in each of sections.
Figure 3. Schematic of the experimental setup: 1-the longitudinally finned heat exchanger, 2-
cr
thermocouples, 3-rotameter, 4-control valve, 5- water pump, 6-hot tank, 7-electrical heater, Figure 4. Sample of grid arrangements for the simulation.
us
8-data logger and 9-PC.
Figure 5. Temperature distribution of the 3 sections (3 rows, respectively 1st: right section, 2nd: middle
an
and 3rd: left section) at different radial distances and for different fins' height for Ste=0.26. Figure 6. Melting front position during charging process at the middle section of 13mm-fin and 26mm-fin heat exchangers for different Ste numbers.
M
Figure 7. Temperatue distribution and velocity field at middle section of the heat exchangers (13mmfin and 26mm-fin) for analyzed Stefan numbers (0.26, 0.32 and 0.38). Figure 8. Liquid fraction variation versus time at different Stefan numbers (a) 13mm-fin heat
d
exchanger (b) 26mm-fin heat exchanger. Figure 9. Thermal power absorbed by PCM versus time for different Stefan number a) 13mm-fin heat
Ac ce p
te
exchanger b) 26 mm fin heat exchanger.
19 Page 19 of 31
Table 1 Type/ value
Shell’s material
Iron
Shell inner diameter (mm)
85
Shell length (mm)
1000
Shell thickness (mm)
1
tubes' material
Copper 21
0.5
an
tube thickness (mm) Fins’ material
Copper 13&26
M
Fins' height (mm)
Number of fins
cr
us
tube inner diameter (mm)
Fins 'thickness (mm)
ip t
Specification
1 8
Glass wool
Insulation thickness (mm)
60
Ac ce p
te
d
Insulation material
20 Page 20 of 31
Table 2
(°C) 58.9 66.3 71.9
(kJ) 1030.7 1080.3 1128.1
(kJ) 1126.2 1287.1 1397.2
(kJ) 134.2 156.1 177
(kJ) 922 1131 1220.2
Ac ce p
te
d
M
an
us
cr
0.26 0.32 0.38
(°C) 22.8 24.1 24.3
ip t
Ste
21 Page 21 of 31
Table 3
(°C) 65.4 69.9 74.7
(kJ) 1074 1106 1148.1
(kJ) 1353 1491.5 1614.4
(kJ) 175.5 191.1 211.7
(kJ) 1174.5 1300.4 1402.7
Ac ce p
te
d
M
an
us
cr
0.26 0.32 0.38
(°C) 22.7 23.4 23.2
ip t
Ste
22 Page 22 of 31
cr
ip t te
(c)
Figure 1
Ac ce p
(b)
d
M
an
us
(a)
23 Page 23 of 31
ip t Right section
Ac ce p
te
d
M
an
Figure 2
cr
Middle section
us
Left section
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ip t cr us an
Ac ce p
te
d
M
Figure 3
25 Page 25 of 31
ip t Ac ce p
te
d
M
an
Figure 4
cr
(b)
us
(a)
26 Page 26 of 31
30
30
20
20
20
10
10
70 60 50
30
30
20
20
10
10
Melting period
40
Angle
Angle
Melting period
40
Position C
70 60 50
20
20
10
10
Angle
o
10
Position B
70 60 50
20 10
Melting period
40
20
Angle
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position C
80 70 60 50
Melting period
40
90
70 60 50
20
20
Angle
r=12.5 mm
r=32.5 mm
Melting period
40 30
5 min 15 min 90 min 135 min 150 min
Position C 80
30
10
5 min 15 min 90 min 135 min 150 min
80
30
Angle
90
30
Angle
Ac ce p
r=32.5 mm
Melting period
40 30
5 min 15 min 90 min 135 min 150 min
80
30
Melting period
40
90
o
60
50
M
70
90
d
Position C 80
Melting period
40
Angle
te
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Temperature (oC)
90
60
10
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position B 80 70
an
Melting period
40
5 min 15 min 90 min 135 min 150 min
Temperature (oC)
60
o
o
Temperature ( C)
70
50
90
Position B 80
Temperature ( C)
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position B 80
50
Angle
90
50
20
Angle
90
o
60
30
o
Angle
Temperature ( C)
40
30
10
Melting period
50
ip t
40
60
cr
Melting period
70
o
o
50
5 min 15 min 90 min 135 min 150 min
Position A 80
Temperature ( C)
40
60
90
Temperature ( C)
Melting period
us
50
70
Temperature ( C)
o
60
70
80
Temperature ( C)
70
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position A
5 min 15 min 90 min 135 min 150 min
80
o
80
Position A
Temperature ( C)
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position A
Temperature ( C)
Fins' height of 26 mm 90
90
Temperature ( C)
Fins' height of 13 mm 90
10
Angle
r=12.5 mm
Figure 5
27 Page 27 of 31
Fins' height of 13 mm
Fins' height of 26 mm
10 min
10 min
ip t
30 min
Ste=0.26
30 min
cr
60 min
60 min
90 min
us
150 min
90 min
30 min
30 min
10 min
M
Ste=0.32
an
10 min
60 min
te
d
90 min
60 min
30 min
10 min
Ste=0.36
Ac ce p
10 min
60 min
30 min
90 min
60 min
Figure 6
28 Page 28 of 31
ip t cr us an M d te Ac ce p Figure 7
29 Page 29 of 31
1.0
1.0
0.8
0.8
ip t
Liquid fraction
154 min 0.4
0.6 83 min
0.4
176 min
0
50
0.2
100
150
0
200
Time (minutes)
us
0
Ste=0.26 Ste=0.32 Ste=0.38
cr
Ste=0.26 Ste=0.32 Ste=0.38
0.2
20
40
60
80
98 min
100
120
Time (minutes)
(a)
(b)
te
d
M
an
Figure 8
Ac ce p
Liquid fraction
72 min 123 min 0.6
30 Page 30 of 31
700
700
200
ip t
300
400
300
200
cr
Thermal Power (W)
400
500
3000
6000
0
9000
Time (s)
us
100
100
3000
6000
9000
Time (s)
(a)
(b)
te
d
M
an
Figure 9
Ac ce p
Thermal Power (W)
500
0
Ste=0.26 Ste=0.32 Ste=0.38
600
Ste=0.26 Ste=0.32 Ste=0.38
600
31 Page 31 of 31
S0378-7788(15)00344-8 http://dx.doi.org/doi:10.1016/j.enbuild.2015.04.045 ENB 5837
To appear in:
ENB
Received date: Revised date: Accepted date:
3-2-2015 20-4-2015 22-4-2015
Please cite this article as: M.J. Hosseini, A.A. Ranjbar, M. Rahimi, R. Bahrampoury, Experimental and Numerical Evaluation of Longitudinally Finned Latent Heat Thermal Storage Systems, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.04.045 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights: Experimental and numerical analysis is presented on a PCM storage system. Flow field, melting front and energy absorption capability of the system are studied.
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Stephan number and fin height are studied on longitudinally finned HX.
Ac ce p
te
d
M
an
us
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Results indicate that fin extension improves thermal conditions of the system.
1 Page 1 of 31
Experimental and Numerical Evaluation of Longitudinally Finned Latent Heat Thermal Storage Systems M.J. Hosseini a,*, A.A. Ranjbar b, M. Rahimi a, R. Bahrampoury c
c
School of Mechanical Engineering, Babol University of Technology, POB 484, Babol, Iran
Department of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran
cr
b
Department of Mechanical Engineering, Golestan University, POB 155, Gorgan, Iran
ip t
a
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Abstract
In this study the effect of longitudinal fins in a double pipe heat exchanger containing PCM is examined during charging process. Therefore 8 rectangular fins are mounted around the HTF (heat
an
transfer fluid) carrying tube. Two fins’ heights and three Stefan numbers are chosen in order to examine the effect of these two parameters on thermal performance of the heat exchanger. In order to study the heat exchanger experimentally, 3 sections are chosen and several thermocouples are located
M
in the sections. Observing thermal distribution, melting front, temperature and velocity contours and liquid fraction versus time, detailed behavior of melting process is explained. The process of heat
d
absorption versus time is also discussed. Results show that fins extension leads to the less melting time and deeper penetration of heat. It is also shown that the process of heat absorption power is a
te
function of fins height at initial steps of the charging process.
Ac ce p
Key words: longitudinal fins, double tube heat exchanger, phase change material. Nomenclatures
Specific heat capacity (J/Kg. K) Gravity (m/s2)
Sensible enthalpy (J/kg) Total enthalpy (J)
Thermal conductivity (W/m. K) Latent heat (J/kg) Mass flow rate (kg/s)
*
Corresponding Author: (Seiyed Mohammad Javad Hosseini) Department of Mechanical Engineering, Golestan University, P.O. Box 155, Gorgan, Iran. Tel/Fax: +98 17 32440206, Email: [email protected]
2 Page 2 of 31
Pressure (Pa) Thermal instantaneous power (J/s) Cumulative energy (J) r
Radial distances from the center of HTF tube (m)
Ste
ip t
Source term Stefan number
cr
Temperature (K) Velocity vector (m/s)
us
Greek symbols Expansion coefficient (1/K)
λ
an
Dynamic viscosity (Pa. s) Liquid fraction Density (kg/m3)
Mushy zone
m
Melting
ref
Reference
H
Hot water
In
Inlet water
Ini Out
d
mush
te
Charge
Ac ce p
ch
M
Subscripts
PCM
Initial
Outlet water
Phase change material Solid
Liquid
Heat exchanger
1. Introduction The increasing gap between the amounts of energy generation and its consumption has attempted engineers to seek for a solution. Nowadays, regarding lack of available energy and the prediction of this source of energy depletion, and considering inevitable pollution consequences of employing fossil fuel as the only source to supply the world energy requirement, has led to increased significance of proposing renewable energy sources. The cited consequences of employing this source of energy have 3 Page 3 of 31
offered an opportunity for solar energy to compete almost one hundred-year-old fossil fuel, especially in countries where vast amount of solar energy is available. Utilizing this vast renewable energy as new source of energy brings about diverse types of challenges. One of the most challenging subjects in its employment is related to its storage. There are kinds of storage systems that are categorized based on the way heat is stored; sensible,
ip t
latent and thermal–chemical. Among these thermal energy storage methods, latent heat thermal energy storage (LHTES) system in which a phase change material (PCM) is utilized, seems to be the most favorable for its high energy storage density with small temperature variations [1]. Zalba et al.
cr
[2] performed a detailed review on thermal energy storage which deals with PCM, heat transfer studies and applications. Farid et al. [3] also presented a review on the PCM analysis for different
us
applications including hermetic encapsulation.
Several publications deal with numerical study and experimental investigation of geometrically varying PCM storage systems. Some of the cited configurations are sphere [4-7], rectangular [8-12] which comprise more than 70% of the literature [2].
an
and shell and tube designs [13-18]. Most of the analyses in this field belong to shell and tube systems
M
Jesumathy et al. [17] experimentally studied melting and solidification processes of paraffin wax as PCM in a horizontal double pipe heat exchanger. Their study focuses on investigation of increasing heat transfer fluid (HTF) inlet temperature and its mass flow rate consequences on both charging and
d
discharging processes. Their results indicate that melting process is dominated by natural convection in liquid phase due to buoyancy effects while conduction heat transfer mechanism is more effective in
te
solidification. Also their results imply that heat transfer coefficient between HTF and PCM is affected by Reynolds number more during melting process than solidification.
Ac ce p
Hosseini et al. [13, 15-16] investigated melting and solidification on a PCM in a shell and tube heat exchanger for various operating conditions. The operating variables are limited to HTF inlet temperature and its flow rate. Results present a quantitative data on variation of melting time versus inlet temperature.
Since PCMs are generally weak thermal conductive materials, different techniques are employed to promote melting process as well as solidification. To overcome this lack of thermophysical property, extended surfaces are frequently proposed in geometrically different configurations in literature. Numerous studies are conducted to investigate consequences of using such extended surfaces in melting and solidification processes in which natural convection is disregarded in PCM melt [19-21]. Ignorance of this heat transfer improving mechanism has aroused the need of experimental simulation. The effect of longitude fins inside a horizontal cylindrical latent heat energy storage system in order for its thermal enhancement has also been examined by Liu et al. [22]. In their study, both straight and angled longitudinal fins are investigated. It was observed that conduction is the dominant heat transfer mechanism during initial stages of charging, and natural convection dominates once enough liquid 4 Page 4 of 31
PCM is present inside the system. On the other hand, conduction dominates during the entire solidification process. Complete melting time is strongly affected by HTF inlet temperature whereas HTF flow rate is much less influential on the melting time. Castell et al. [23] have proved that adding vertical fins to HTF side of the tube also enhances the performance of LHTEs during solidification. They focused on calculation of heat transfer coefficient
ip t
through which it was found that solidification time in the finned system was considerably less, as compared to finless system. Their results show that while fins' height rises, the heat transfer coefficient varies in the studied vertically positioned heat exchanger. So that, the longer fins were
cr
used, due to dampening effect on natural convection, heat transfer coefficient lowers. Nevertheless, the solidification time remains less because of the increase in heat transfer area.
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Velraj et al. [24] studied the consequences of employing different number of longitudinal fins as well as their height on solidification process in a circular vertical PCM containing shell. Their study has been carried out numerically and experimentally in which RT60 is chosen as the phase change
an
material.
Ismail et al. [25] investigated the effect of employing longitudinal fins and influences of varying
M
geometrical specification of the fins including number of fins, their height and thickness as well as aspect ratio in a vertical circular cylinder on solidification process. Conduction is the only heat transfer mechanism considered in the study which can be justified only for vertical orientation of the
d
shell, therefore a slice restricted to fins has been considered as a symmetrical piece to be numerically analyzed. Considering the above mentioned papers on phase change processes, most of the papers are
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numerical while in this paper both numerical and experimental study is accomplished. The effect of fins' height variation as well as inlet temperature on different decision parameters in such a
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comprehensive extend is among the differences between this paper and similar previous studies. In the present study, melting of a specific PCM is explored in a horizontal longitudinally finned shell and tube heat exchanger in which PCM is located in a circular shell. HTF carrying tube is located centrally with the circular cylindrical shell and provides melting thermal energy. Fins' height and Stephan number are considered as decision variables on the process and the effect of these two (including two fins' height and three Stefan numbers) has been investigated on temperature distribution, melting front, liquid fraction, total melting time and absorbed heat during charging process. The experimental study includes temperature record via 18 thermocouples at different sections of the heat exchanger.
2. Geometric details of the heat exchanger The longitudinally finned heat exchanger which its schematic is shown in Figure 1(a) is investigated for two fins' height. Figure 1 (b) illustrates a 3D exploded section view of the 13 mm-fin heat exchanger for which the longitudinal fins are present on the whole length of the central tube. 5 Page 5 of 31
Figure 2(c) shows the same heat exchanger enhanced with fins of 26 mm height. As can be seen the number of radial fins around the tube is 8 for both heat exchangers which are symmetrically mounted along the tube in a way that 2 fins are horizontal, 2 vertical and the remaining 4 fins are tilted with 45 degree angle over the horizon. It is clear from the colors of the figure that, the central tube and its surrounding radial fins are made of copper while the shell is Ironic. The outer covering is the
ip t
insulation layer made of glass wool with 0.04 W/m K which leads to negligible heat loss of the heat exchanger. Quantitive details of the heat exchanges are given in Table 1. The 3 white sections in the shell are experimental measured sections in which thermocouples are placed in different radial
cr
distances and varying angular directions. The longitudinal distances of the sections are symmetric therefore the middle section is at 500 mm from both ends and the right section is 200mm away from
us
the right cap. The symmetry implies the similar distance has been considered for the left section to the left cap. Exact locations of each thermocouple in their related sections are exhibited in Figure 2. As can be seen in the figure, the numbers of thermocouples in both right and left sections are similar, 6,
an
while the number of thermocouple in the middle section is selected to be 4.
M
3. Setup and procedure
Figure 3 illustrates a schematic diagram of the experimental apparatus in which loop components as well as measuring instrumentation are presented. As the study includes merely discharging process, a
d
loop is designed to provide hot utility for the process in which hot bath joins to produce the required
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heat. As flow rate is an indispensable component of heat transfer rate calculation, a rotameter is applied in the experiment. As observed in Figure 2, three sections are designated for thermal
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measurement. The two end sections include 6 thermocouples while the middle one involves 4. The exact longitudinal distance of the sections shown in figure 1 has been explained through the text whereas angular position and radial distances of every thermocouple is presented in Figure 2. Considering these 16 thermocouples as well as the HTF inlet and outlet thermal measuring thermocouples, 18 thermocouples are incorporated in the experimental setup. Nowadays, various types of PCMs with different melting temperature are available for every application. In this study RT50 (Rubitherm GmbH) for which density and Specific heat capacity are 780 kg/m3 and 2000 J/kg.K respectively, is selected as PCM to be inserted into the shell. The selection of this PCM for which melting temperature is between 45 to 51 ºC refers to its appropriate melting temperature that matches well with low temperature heat sources like solar systems and power plants exhaust. The characteristics of the material including its stability and corrosiveness as well as its Thermophysical properties involving its viscosity, thermal conductivity and latent heat has been explained by Hosseini et. al [15].
6 Page 6 of 31
4. Methodology of tests After the heat exchanger is filled up with liquid PCM and no leakage was observed, a few runs are made in order to calibrate the system. Then the charging process starts, while the solid PCM is at thermal equilibrium with the conditioned lab temperature (23–25 ºC). During the charging process,
ip t
inlet HTF temperature, TH, is maintained at a set temperature using a PID controlled hot water bath. Using the apparatus and procedures described above, several experiments have been conducted to study the behavior of the PCM during charging process. As at mid-latitude areas and where direct
cr
radiation is available, double glazing flat solar collectors are able to provide hot water with more than 70 ºC centigrade degrees [26], and also there should be a reasonable temperature difference between
us
hot and cold sources to keep the melting time in an acceptable limit, this range is chosen for the current study. The experiments are performed for different inlet temperatures (70, 75 and 80 ºC) of the HTF and fins' height (13 and 26 mm). Corresponding Stephan number (Ste) (the ratio of sensible heat
an
to latent heat) as defined in equation (1) for each of these hot HTFs are calculated in which the only
(1)
M
varying parameter is the cited inlet temperature.
Where Cp, L, and Tm are the specific heat, the latent heat and the mean melting temperature of PCM
d
((Ts+ Tliq)/2) and TH is the temperature of hot inlet water. In this paper, the Stefan numbers for the
te
three inlet HTF temperatures are calculated which are 0.26, 0.32 and 0.38. The volumetric flow rate is 1 L/min which leads to a laminar flow regime. The assumption of laminar flow is a simplifying
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hypothesis which is considered to keep the possibility of intended parameters variation including Stefan number. Indeed, consideration of flow regime may be a bulky discussion for which a separate study is required. It is obvious that, turbulence leads to an increase to convective heat transfer coefficient inside the tube and consequently rate of heat transfer rises. 5. Data reduction
Varying thermal power ( ) and aggregated energy given by water (
) during charging can be
obtained as below:
(2) (3) where
represents the mass flow rate,
signifies the specific heat capacity,
and
are
temperatures at inlet and outlet of heating HTF respectively.
7 Page 7 of 31
As the process is transient, the heat emerged from the HTF ( absorbed heat (
) doesn't equal the aggregated PCM
) since a portion of the heat is transferred to the equipment. These parameters
ip t
may be estimated as below:
and
is the mass of sole device,
stands for the specific heat for heat exchanger and
us
Where
cr
(4)
represent the PCM temperatures respectively at the beginning and the end of the process,
Also the aggregated energy charged by the PCM,
an
, can be calculated by the following equation: (5)
) during the charging process as largest amount of
M
The maximum theoretical energy absorbed ( heat given to the PCM can be evaluated as below:
d
is the PCM's mass,
signifies the PCM specific heat,
te
Where
of solid and liquid PCM at boundaries of melting process and
and
are temperatures
is the PCM's latent heat of phase
Ac ce p
change.
(6)
6. Numerical models
In order to simulate phase change of melting in a shell and tube heat exchanger, enthalpy-porosity method [27-28] is used. In the present study, both PCM and water flows are considered to be unsteady, laminar, incompressible and three-dimensional. The viscous dissipation term is considered negligible so that the viscous incompressible flow and the temperature distribution in annulus space can be described by the Navier-Stokes and thermal energy equations, respectively. Also dynamic viscosity, considered as a function of temperature, is also used [15]. In addition, the density change within the liquid phase that drives natural convection is only considered in the body force terms (Boussinesq approximation) in which variable density is defined as [29]: (7)
8 Page 8 of 31
for 51º C T 100 º C in the liquid state. The initial temperature of the whole system is
.
Also the lateral surface of the outer tube is assumed to be insulated. Consequently, continuity, momentum, and thermal energy equations can be expressed as follows: Continuity:
ip t
(8)
cr
Momentum:
an
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Thermal Energy:
(9)
(10)
The enthalpy of the material is computed as the sum of the sensible enthalpy, and the latent heat,
M
:
te
d
Where
(11)
(12)
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The latent heat content, , can be written in terms of the latent heat of the material:
where
may vary from zero (solid) to
In Eq. (8),
(13)
(liquid). Therefore, the liquid fraction, , can be defined
(14)
is the Darcy’s law damping terms (as source term) that is added to the momentum
equation due to phase change effects on convective heat transfer which is defined as [30]:
(15)
9 Page 9 of 31
The coefficient
is mushy zone factor. This parameter is of a large value, usually between 104
and 107. In the current study
is assumed to be constant and is set to 106 which is validated for
same material and cylinder in [15].
ip t
6.1. Computational methodology The SIMPLE algorithm [31] is utilized to couple pressure–velocity governing differential equations and QUICK differencing scheme is employed for solving momentum and energy ones within a 3D in-
cr
house developed code [15], whereas the PRESTO scheme is adopted for the pressure correction equation. The under-relaxation coefficient for momentum, pressure, density, melting fraction and
us
thermal energy are 0.7, 0.3, 1, 0.9 and 1, respectively. An arrangement of 450,000 nodes which is shown in Figure 4 is found to be sufficient for the present study. The time step in the calculations is as small as 0.05 s and the number of iterations for each time step is 400. The grid size and the time step
an
were chosen after careful examination of the independency of the results to these parameters. The convergence is checked at each time step, with the convergence criterion of 10-7 for all variables. As the PCM is same for this study and the one done by Hosseini et al. [15], and the same cylinder is also
M
considered, that code is developed for this paper, therefore, the validation also hold for this work. 7. Result and discussion
d
In this paper the results of temperature distribution and energy related results are derived from
te
experimental runs whereas temperature contours and melting front progression, velocity field and
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liquid fraction variation are related to the computational simulation. 7.1. Thermal response
Figure 5 illustrates temperature distribution at the 3 selected sections, right, middle and left at different radius distances (r=12.5 mm and r=32.5 mm) and angular directions in the 13 mm-fin heat exchanger as well as 26 mm-fin one at Stefan number of 0.26. As is obvious, the nearer position to the central HTF carrying tube is more rapidly affected by the heat. Comparing the temperature values for a specific moment, the temperature of r=12.5 mm is much higher than that of r= 32.5 mm especially at initial stages of the experiment. Considering the figure, it can be seen that for the 3 cited sections
and for both radius distances, regardless of time, the temperature value at 0∘ (above the tube) is higher
10 Page 10 of 31
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than similar studied points at other angular directions (90∘ and 180∘). Similar but more pronounced
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trend can be reported for 90∘ in comparison with 180∘ (below the tube). Such behavior is due to
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natural convection which is originated from vortices formation and these vortices’ penetration to the
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upper regions. The phenomenon that lateral direction temperature is higher than downward direction
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is due to this penetration development to lateral regions. Temperature reduction between 90∘ and 180∘
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is much more noticeable for 13mm-fin heat exchanger than 26 mm-fin one which may be explained
by velocity field (figure 7). Since 180∘ demonstrates the least value, when the temperature of this
angular direction especially the farther one (r=32.5 mm) leaves the melting zone, it can be concluded that almost all the PCM in the shell has been melted. Therefore, comparing these two heat exchangers,
as the temperature value of the point at 180∘ and radius of 32.5 mm remains in the melting zone even
after 150 minutes for the 13 mm-fin heat exchanger unlike 26 mm-fin heat exchanger, it can be 11 Page 11 of 31
deduced that increasing the extended surfaces at fins’ length direction leads to faster development of melting front. The extent of the effect of applying higher fins can be realized when considering the
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departure of 180∘ and 32.5 mm radius mostly at 60 min for the 3 sections. The fact that the slop of the
lines for the 26mm-fin heat exchanger is less than the same criterion for shorter fin, implies that temperature distribution of higher fin leads to smoother distribution of temperature. Comparing
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temperature distribution for different sections (along the tube), it can be seen that temperatures don't vary significantly longitudinally which is due to heat penetration resulted from high thermal
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conduction of longitudinal copper tubes and fins. Figure 6 exhibits the melting front of the heat exchanger’s mid-section for the 13mm-fin and 26 mm-fin heat exchanger during charging process. Regarding the figure, at early stages of melting front formation, a symmetrical melting front at the
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cited section appears. When the melting process advances, the trend of the symmetry persists until the front boundary covers a farther distance than the fins’ tips’. Afterward as the melting front grows, the symmetry vanishes which is due to the natural convection consequences. Therefore for 13 mm-fin
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heat exchanger, the melting front becomes asymmetric earlier in comparison with the 26 mm-fin one which intensifies as the Stefan number increases. In addition, this figure implies that increasing fins’
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height increases the rate of melting front development which is due to enhanced conduction
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mechanism that improves heat penetration to farther distances of the PCM. The discussion made on
the passing melting zone for 180∘ angle and 32.5 mm radial distance in figure 1 is confirmed by
considering the first row of figure 6 (Ste=0.26) in which the presence of solid PCM in the shell of the 13mm-fin heat exchanger and absence of PCM for the 26 mm-fin heat exchanger after 150 min is evident. In figure 7 temperature and velocity field contours for considered fins’ height and cited Stefan number is presented at every 30 minutes. Considering the figure, as soon as the melting process establishes, vortices are formed in melt region. It can also be recognized that increasing Stefan number for both heat exchangers leads to enlargement of vortices for the both heat exchangers at a specific moment. In addition it is apparent that for the 13 mm-fin heat exchanger soon after small vortices formation at initial stages of melting process, the vortices merge and form larger a vortex. In reverse, for the 26 mm-fin heat exchanger, the extension of the fins blocks the merging process at initial stages which leads to larger local vortices. 12 Page 12 of 31
Considering temperature contours presented in figure 7, it is noticeable that increasing fins’ height leads to a sensible increase in heat flux penetration in PCM. Moreover, it can be seen that employing 26mm-fin leads to total melting time reduction for the 3 Stefan numbers. Therefore after 60 minutes of the experiment initiation a homogeneous temperature distribution appears in the shell section. Figure 8 demonstrates the liquid fraction during melting process. The specified time in the figure is
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related to complete melting after which no solid remaining exists in shell. Regarding the given data on the figure, it can be understood that the trend of total melting time varies for the two heat exchangers; for 13mm-fin heat exchanger, increasing Stefan number from 0.26 to 0.32 and after 0.32 to 0.38,
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melting time reduces 20% and 12.5% respectively. These values for 26 mm- fin heat exchanger are
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13.2% and 15.3%. 7.2. PCM absorbed energy
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Figure 9 shows the variation of stored thermal power versus time during charging process for different Stefan numbers. Considering the figure it can be seen that although varying Stefan number for a specific fins' height doesn’t influence the PCM heat absorption power to a noticeable extent,
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employing 26mm-fin heat exchanger leads to an extra absorption power especially at initial steps of the charging process which is the result of higher level of thermal potential at these portions of time. Subsequently since the thermal potential between these two decreases, a diminishing trend for the heat
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absorption is observed. The figure also states that, regardless of Stefan number, the heat absorption
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for each of the heat exchangers converges to a specific value. Comparing the figures a and b, the heat absorption of the heat exchanger is function of fins' height especially at initiation of the experiment while the time passes, heat absorption power of the heat exchangers approaches to a similar value.
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Tables (2) and (3) illustrate some quantitive results during charging for the heat exchanger for varying Stefan numbers and the two fins’ height. Considering data tabled, increasing Stefan number while fins’ height increases, the PCM average temperature at the end of the process faces a lower rate of increase; so that, increasing Stefan number from 0.26 to 0.38, the rate of final average PCM temperature during the process lowers from 11.1 % to 3.9 %. In simpler words, employing higher fins for larger Stefan numbers avoids intense elevation of temperature. It can be seen in the table that, extending fins' height, for the Stefan number of 0.26, a much greater absorbed heat by the PCM is observed in comparison with the two other Stefan numbers. (27.4% versus 14.9%) Conclusion In this investigation, the effect of utilizing longitudinal fins with two heights for different Stefan numbers in a double tube heat exchanger which contains PCM is investigated. A summary of conclusions is as below: Considering temperature distribution for 13 mm-fin and 26 mm-fin heat exchanger, employing 26 mm fins lead a smoother distribution of temperature in the heat exchanger. Moreover, employing the heat 13 Page 13 of 31
exchanger with 26 mm fins causes the recorded temperature of the lower thermocouple to depart the melting zone sooner. Regarding the melting front, development of the front to the tips of melting region is symmetrical and afterward it becomes asymmetric. Therefore the presence of higher fins leads to extra amount of symmetric melting. Increasing Stefan number results in a raise in the rate of melting front development. Studying the flow field during charging, it is clear that higher fins leads to
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a blockage of vortices merger and therefore large vortices form while for smaller fins, this behavior takes place much more restricted and the vortices are smaller. Increasing Stefan number results in vortices development with a more rapid rate. Comparing the rate of heat absorption versus time, it is
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clear that increasing fins’ height leads to better absorption especially at initial stages. Also results show that, increasing fins’ height is much more effective for lower Stefan number in comparison with
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higher value. Although fins' height improves thermal conditions of the system, increasing this value to a large extend leads to reduction of PCM amount and consequent less capability of the system to absorb energy. Moreover this variation results to heavier and more expensive heat exchanger.
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Therefore there is an optimum value for the height if a more comprehensive study which includes all
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these factors in its objective function is taken into account.
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References [1] H. Mehling, L.F Cabeza, Phase change materials and their basic properties, In: Paksoy HO, editor. Thermal Energy Storage for Sustainable Energy Consumption, Springer, Netherlands (2007) 257– 277.
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[2] B. Zalba, J.M. Marin, L.F. Cabeza, H. Mehling, Review on Thermal Energy Storage with Phase Change Materials, Heat Transfer Analysis and Applications, Applied Thermal Engineering 23 (3)
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(2003) 251-83.
[3] M.M. Farid, A.M. Khudhair, S. Al-Hallaj, A Review on Phase Change Energy Storage, Materals
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and Applications, Energy Conversion and Management 45 (9-10) (2004) 1597-1615.
[4] F.L. Tan, Constrained and unconstrained melting inside a sphere. International Communication
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Heat and Mass Transfer 35 (2008) 466–75.
[5] F.L. Tan, S.F. Hosseinizadeh, J.M. Khodadadi, L. Fan, Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule, International
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Journal of Heat and Mass Transfer 52 (2009) 3464–72
[6] E. Assis, L. Katsman, G. Ziskind, , R. Letan, Numerical and experimental study of melting in a
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spherical shell, International Journal of Heat and Mass Transfer 50(9) (2007) 1790-1804.
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[7] J. M. Khodadadi, Y. Zhang, Effects of buoyancy-driven convection on melting within spherical containers, International Journal of Heat and Mass Transfer 44(8) (2001) 1605-1618.
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[8] M. Rahimi, A.A. Ranjbar, D.D. Ganji, K. Sedighi, M.J. Hosseini, R. Bahrampoury, Analysis of geometrical and operational parameters of PCM in a fin and tube heat exchanger, International Communications in Heat and Mass Transfer 53 (2014) 109–115 [9] P. Lamberg, R. Lehtiniemi, A.M. Henell, Numerical and experimental investigation of melting and freezing processes in phase change material storage, International Journal of Thermal Sciences 43 (2004) 277–87.
[10] U. Stritih, An experimental study of enhanced heat transfer in rectangular PCM storage, International Journal of Heat and Mass Transfer 47 (2004) 2841–47. [11] M. Rahimi, A.A. Ranjbar, D.D. Ganji, K. Sedighi, and M.J. Hosseini, Experimental Investigation of Phase Change inside a Finned-Tube Heat Exchanger, Hindawi Publishing Corporation Journal of Engineering Volume 2014, Article ID 641954, 11 pages.
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[12] Y. Jellouli, R. Chouikh, A. Guizani, A. Belghith, Numerical study of the moving boundary problem during melting process in a rectangular cavity heated from below, American Journal of Applied Sciences 4 (2007) 251–56. [13] M.J. Hosseini, A.A. Ranjbar, K. Sedighi, M. Rahimi, A combined experimental and
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computational study on the melting behavior of a medium temperature phase change storage material inside shell and tube heat exchanger, International Communications in Heat and Mass Transfer 9 (39) (2012) 1416–24.
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[14] F. Agyenim, P. Eames, M. Smyth, Heat transfer enhancement in medium temperature thermal energy storage system using a multitube heat transfer array, Renewable Energy 35 (2010) 198–
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207.
[15] M.J. Hosseini , M. Rahimi , R. Bahrampoury, Experimental and computational evolution of a shell
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and tube heat exchanger as a PCM thermal storage system, International Communications in Heat and Mass Transfer 50 (2014) 128–136
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[16] M.J. Hosseini, A.A. Ranjbar, K. Sedighi, M. Rahimi, Melting of Nanoprticle-Enhanced Phase Change Material inside Shell and Tube Heat Exchanger, Hindawi Publishing Corporation Journal of Engineering Volume 2013, Article ID 784681, 8 pages
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[17] S.P. Jesumathy, M. Udayakumar, S. Suresh , S. Jegadheeswaran, An experimental study on heat
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transfer characteristics of paraffin wax in horizontal double pipe heat latent heat storage unit, Journal of the Taiwan Institute of Chemical Engineers 45(4) (2014) 1298–1306
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[18] F. Agyenim, N. Hewitt, The development of a finned phase change material (PCM) storage system to take advantage of off-peak electricity tariff for improvement in cost of heat pump operation, Energy and Buildings 42 (2010) 1552–60. [19] W. Ogoh, D. Groulx, Effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study, International Journal of Heat and Mass Transfer 48 (2012) 1825-35. [20] R.V. Seeniraj, N. L. Narasimhan, Performance enhancement of a solar dynamic LHTS module having both fins and multiple PCMs, Solar Energy 82 (2008) 535-42. [21] V. Shatikian, G. Ziskind, R. Letan, Numerical investigation of a PCM-based heat sink with internal fins, International Journal of Heat and Mass Transfer 48 (2005) 3689-706.
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[22] C. Liu, D. Groulx, Experimental study of the phase change heat transfer inside a horizontal cylindrical latent heat energy storage system, International Journal of Thermal Sciences 82 (2014) 100-110 [23] A. Castella, C. Soléa, M. Medranoa, J. Rocaa, L.F. Cabezaa, D. García, Natural convection heat
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transfer coefficients in phase change material (PCM) modules with external vertical fins, Applied Thermal Engineering 28 (2008) 1676–1686
[24] R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, K. Scwharzer, Experimental analysis and
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numerical modelling of inward solidification on a finned vertical tube for a latent heat storage
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unit, Solar Energy 60 (5) (1997) 281–290.
[25] 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, Applied Thermal
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Engineering 21 (2001) 53–77.
[26] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley & Sons, New
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York, 1980.
[27] A.D. Brent, V.R. Voller, K. J. Reid, Enthalpy-porosity technique for modeling convectionB 13 (1988) 297-318.
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diffusion phase change: application to the melting of a pure metal, Numerical Heat Transfer Part
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[28] Z.X. Gong, S. Devahastin, A.S. Mujumdar, Enhanced heat transfer in free convection-dominated melting in a rectangular cavity with an isothermal vertical wall, Applied Thermal Engineering 19
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(1999) 1237-51.
[29] E.A. Spiegel, G. Veronis, On the Boussinesq approximation for a compressible fluid, The Astrophysical Journal 131 (1960) 442-447. [30] H. Darcy, Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856. [31] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.
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Table Captions: Table 1. Detailed specifications.
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Table 3. Data from charging process for the 26mm-fin heat exchanger.
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Table 2. Data from charging process for the 13mm-fin heat exchanger.
18 Page 18 of 31
Figure Captions: Figure 1. 3D exploded section view of the studied PCM containing heat exchangers (a) schematic of the heat exchanger and its' section view (b) 13mm-fin heat exchanger (c) 26mm-fin heat
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exchanger. Figure 2. Thermocouples radial and angular positions in each of sections.
Figure 3. Schematic of the experimental setup: 1-the longitudinally finned heat exchanger, 2-
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thermocouples, 3-rotameter, 4-control valve, 5- water pump, 6-hot tank, 7-electrical heater, Figure 4. Sample of grid arrangements for the simulation.
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8-data logger and 9-PC.
Figure 5. Temperature distribution of the 3 sections (3 rows, respectively 1st: right section, 2nd: middle
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and 3rd: left section) at different radial distances and for different fins' height for Ste=0.26. Figure 6. Melting front position during charging process at the middle section of 13mm-fin and 26mm-fin heat exchangers for different Ste numbers.
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Figure 7. Temperatue distribution and velocity field at middle section of the heat exchangers (13mmfin and 26mm-fin) for analyzed Stefan numbers (0.26, 0.32 and 0.38). Figure 8. Liquid fraction variation versus time at different Stefan numbers (a) 13mm-fin heat
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exchanger (b) 26mm-fin heat exchanger. Figure 9. Thermal power absorbed by PCM versus time for different Stefan number a) 13mm-fin heat
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exchanger b) 26 mm fin heat exchanger.
19 Page 19 of 31
Table 1 Type/ value
Shell’s material
Iron
Shell inner diameter (mm)
85
Shell length (mm)
1000
Shell thickness (mm)
1
tubes' material
Copper 21
0.5
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tube thickness (mm) Fins’ material
Copper 13&26
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Fins' height (mm)
Number of fins
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tube inner diameter (mm)
Fins 'thickness (mm)
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Specification
1 8
Glass wool
Insulation thickness (mm)
60
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Insulation material
20 Page 20 of 31
Table 2
(°C) 58.9 66.3 71.9
(kJ) 1030.7 1080.3 1128.1
(kJ) 1126.2 1287.1 1397.2
(kJ) 134.2 156.1 177
(kJ) 922 1131 1220.2
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te
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0.26 0.32 0.38
(°C) 22.8 24.1 24.3
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Ste
21 Page 21 of 31
Table 3
(°C) 65.4 69.9 74.7
(kJ) 1074 1106 1148.1
(kJ) 1353 1491.5 1614.4
(kJ) 175.5 191.1 211.7
(kJ) 1174.5 1300.4 1402.7
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te
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0.26 0.32 0.38
(°C) 22.7 23.4 23.2
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Ste
22 Page 22 of 31
cr
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(c)
Figure 1
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(b)
d
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(a)
23 Page 23 of 31
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Figure 2
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Middle section
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Left section
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Figure 3
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Figure 4
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(b)
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(a)
26 Page 26 of 31
30
30
20
20
20
10
10
70 60 50
30
30
20
20
10
10
Melting period
40
Angle
Angle
Melting period
40
Position C
70 60 50
20
20
10
10
Angle
o
10
Position B
70 60 50
20 10
Melting period
40
20
Angle
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position C
80 70 60 50
Melting period
40
90
70 60 50
20
20
Angle
r=12.5 mm
r=32.5 mm
Melting period
40 30
5 min 15 min 90 min 135 min 150 min
Position C 80
30
10
5 min 15 min 90 min 135 min 150 min
80
30
Angle
90
30
Angle
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r=32.5 mm
Melting period
40 30
5 min 15 min 90 min 135 min 150 min
80
30
Melting period
40
90
o
60
50
M
70
90
d
Position C 80
Melting period
40
Angle
te
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Temperature (oC)
90
60
10
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position B 80 70
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Melting period
40
5 min 15 min 90 min 135 min 150 min
Temperature (oC)
60
o
o
Temperature ( C)
70
50
90
Position B 80
Temperature ( C)
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position B 80
50
Angle
90
50
20
Angle
90
o
60
30
o
Angle
Temperature ( C)
40
30
10
Melting period
50
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40
60
cr
Melting period
70
o
o
50
5 min 15 min 90 min 135 min 150 min
Position A 80
Temperature ( C)
40
60
90
Temperature ( C)
Melting period
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50
70
Temperature ( C)
o
60
70
80
Temperature ( C)
70
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position A
5 min 15 min 90 min 135 min 150 min
80
o
80
Position A
Temperature ( C)
15 min 30 min 45 min 60 min 75 min 90 min 105 min 120 min 135 min 150 min
Position A
Temperature ( C)
Fins' height of 26 mm 90
90
Temperature ( C)
Fins' height of 13 mm 90
10
Angle
r=12.5 mm
Figure 5
27 Page 27 of 31
Fins' height of 13 mm
Fins' height of 26 mm
10 min
10 min
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30 min
Ste=0.26
30 min
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60 min
60 min
90 min
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150 min
90 min
30 min
30 min
10 min
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Ste=0.32
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10 min
60 min
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90 min
60 min
30 min
10 min
Ste=0.36
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10 min
60 min
30 min
90 min
60 min
Figure 6
28 Page 28 of 31
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29 Page 29 of 31
1.0
1.0
0.8
0.8
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Liquid fraction
154 min 0.4
0.6 83 min
0.4
176 min
0
50
0.2
100
150
0
200
Time (minutes)
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0
Ste=0.26 Ste=0.32 Ste=0.38
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Ste=0.26 Ste=0.32 Ste=0.38
0.2
20
40
60
80
98 min
100
120
Time (minutes)
(a)
(b)
te
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Figure 8
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Liquid fraction
72 min 123 min 0.6
30 Page 30 of 31
700
700
200
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300
400
300
200
cr
Thermal Power (W)
400
500
3000
6000
0
9000
Time (s)
us
100
100
3000
6000
9000
Time (s)
(a)
(b)
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Figure 9
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Thermal Power (W)
500
0
Ste=0.26 Ste=0.32 Ste=0.38
600
Ste=0.26 Ste=0.32 Ste=0.38
600
31 Page 31 of 31