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Improvement of longitudinal fins configuration in latent heat storage systems
Accepted Manuscript Improvement of Longitudinal Fins Configuration in Latent Heat Storage Systems
M. Kazemi, M.J. Hosseini, A.A. Ranjbar, R. Bahrampoury PII:
S0960-1481(17)30967-9
DOI:
10.1016/j.renene.2017.10.006
Reference:
RENE 9294
To appear in:
Renewable Energy
Received Date:
24 April 2017
Revised Date:
21 September 2017
Accepted Date:
02 October 2017
Please cite this article as: M. Kazemi, M.J. Hosseini, A.A. Ranjbar, R. Bahrampoury, Improvement of Longitudinal Fins Configuration in Latent Heat Storage Systems, Renewable Energy (2017), doi: 10.1016/j.renene.2017.10.006
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ACCEPTED MANUSCRIPT Highlights: The angle of longitudinal fins of a shell and tube heat exchanger is studied. Triple-fin and double-fin cases are simulated and compared for different angles. The upper fin of triple-fin cases doesn’t affect the total melting time considerably. An optimum angle for the double-fin case is found which minimizes total melting time.
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Improvement of Longitudinal Fins Configuration in Latent Heat Storage Systems
3
M. Kazemi a, M. J. Hosseinib,*, A. A. Ranjbarc, R. Bahrampouryd
1
4 5 6 7 8 9
a School
of Mechanical Engineering, Mazandaran University of Science and Technology, Babol, Iran of Mechanical Engineering, Golestan University, POB 155, Gorgan, Iran c School of Mechanical Engineering, Babol University of Technology, POB 484, Babol, Iran d Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran b Department
Abstract
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In this study, the consequences of variation of the longitudinal fins angle on the heat transfer
11
improvement during phase change are investigated. Therefore, the melting process of RT 35 as a phase
12
change material is studied for triple-fin and double-fin cases for different angles and the results are
13
compared with of bare tube case. Results indicated that due to the natural convection domination, the
14
upper fin does not leave a great effect on the total melting time. Considering the triple-fin heat
15
exchangers, as the fins angle increases from 60° to 120°, the total melting time reduces. However, when
16
double-fin cases are under consideration, reducing the angle from 150° to 45° results in melting time
17
reduction. More reduction in the angle increases the total melting time. Results also showed that the best
18
cases among triple-fin cases and among the double-fin cases result in 22.5 and 62 percent reduction in
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melting time with respect to the simple heat exchanger.
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Keywords: Phase change material, Melting, Fins angle, Triple-fin heat exchanger
21 22
1. Introduction
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During recent few decades, daily increase in global energy consumption and the fact that fossil fuels are
24
not only pollutant but also are limited in amount have encouraged researchers to find an approach for
25
effective utilization of renewable energy. One of the challenges that industries face when employing
26
renewable energy sources is their unavailability during some intervals during the day. The best method
27
for eliminating this variation in availability is to store energy. Latent heat storage systems have attracted
28
the scientist attentions due to their high energy density, approximately constant operating temperature and
29
small vapor pressure. These heat storage systems absorb thermal energy from a heat source and the
30
included phase change material (PCM) melts which is called charge process. The melt can release its
31
energy and solidifies when the heat source is not available. These days, these PCMs are applied in *
Corresponding Author: (M.J. Hosseini) Department of Mechanical Engineering, Golestan University, P.O. Box 155, Gorgan, Iran, Email: [email protected]
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different fields of industry including refrigeration [1,2], solar energy [3,4], electrical devices [5,6] and
33
heating, ventilation and air conditioning [7,8].
34
Different shell geometries including spherical [9] and rectangular [10] have been considered. However
35
cylindrical shell and tube arrangements constitute the majority of researches in this field, around 70
36
percent. Hosseini et al. [11] studied melting process of RT50 as a PCM in a shell and tube heat exchanger.
37
They reported that the rate of phase change is directly proportional with HTF inlet temperature.
38
In order to develop latent heat storage systems, the best approach is to dilute the consequences of low
39
thermal conductivity of the phase change materials which brings about a practical proposal of these
40
storage systems to the industrial world. Among the techniques, distribution of nanoparticles in PCMs
41
[12], utilization of heat pipes [13] and employment of extended surfaces are some of the popular
42
approaches.
43
Among extended surface enhancement methods, adding fins [14,15] and multi-tube [16] can be
44
mentioned.
45
The research conducted by Agyenim et al. [17] on heat transfer improvement, using multi-tube, circular
46
fins and longitudinal fins, indicated that the system enhanced by longitudinal fins performs better both
47
during charge and discharge processes than the two other methods.
48
Betzel and Beer studied melting process of a heat storage system for a system enhanced with axial fins
49
and also without the fins [18]. Their results revealed that approximately isothermal copper fins and
50
adiabatic PVC fins behave differently regarding the heat transfer characteristics. Moreover, the melting
51
front shape and the rate of heat transfer are dependent to the fins arrangement.
52
Sciacovelli et al. [19] studied phase change process in a double pipe heat exchanger enhanced by single
53
bifurcation and double bifurcation Y-shaped fins. Results indicated that the double bifurcation fins
54
noticeably improve the heat transfer performance of the heat exchanger, 24% promotion in solidification
55
efficiency.
56
Mat et al. [20] numerically studied melting process of a kind of paraffin, RT 82, as a phase change
57
material in a triple tube heat exchanger. They considered different arrangements of fins, internal, external
58
and internal-external for a heat storage system to improve the melting process. They concluded that, the
59
fins presence, regardless of the implemented arrangement, leads to about 34.3% reduction in total melting
60
time in comparison with a finless arrangement. Hosseini et al. [21] examined the consequences of fins
61
height variation for longitudinally arranged fins. They found that increasing the height brings about a
62
more uniform temperature distribution and decreases the melting time. Their results indicated that taller
63
fins improve the melting process especially at the beginning stages which is due to the melting zone
64
penetration to the solid PCM.
2
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Rabienataj Darzi et al. [22] simulated and analyzed two dimensional phase change (solidification and
66
melting) in a double pipe heat exchanger for varying tube geometry, nano-particles distribution and
67
number of fins. They concluded that the rate of melting process is higher in the upper half than the lower
68
one due to the consequences of natural convection. The also reported that although the variation of the
69
shape of the central tube from circular to vertical elliptical does not affect the solidification process,
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installation of extra fins improves the solidification process more in comparison with melting which is
71
due to the obstacles fins leave on the path of the naturally driven streams in the melting process.
72
Yuan et al. studied melting process of a phase change material for in a heat storage system enhanced with
73
two longitudinal fins for different angles and compared the results with bare tube case [23]. Results
74
showed that although the fins reduce the convective heat transfer, they lead to higher rate of heat transfer
75
and less melting time.
76
In order to improve the rate of heat transfer in a latent heat storage system, Liu and Groulx considered
77
two longitudinal straight fins as well as angled fins mounted on the central copper inner tube [24].
78
Comparing the two cases, for the inlet temperature of 50℃, the total melting time of the angled fin case is
79
slightly less than the straight fin case while no significant difference in the melting times is observed for
80
higher inlet temperature (60℃). They also noticed that there is no sensible difference between the two
81
cases when solidification is under consideration.
82
Agyenim et al. [25] experimentally studied phase change of Erythritol as the PCM in a unit enhanced by
83
longitudinal fins. Their experiments demonstrated that the optimum mass flow and HTF inlet temperature
84
which improve the heat absorption characteristics of the system are 30 kg/min and 140℃. Their
85
experimental investigation demonstrated that longitudinally arranged finned system provides charge and
86
discharge thermal potential of a PCM that meets heating requirements of a solar absorption cooling
87
system in wich LiBr/H2O is the HTF.
88
Rathod and Banerjee [26] experimentally studied melting and solidification processes of a shell and tube
89
heat exchanger enhanced with three longitudinal fins. Comparing the considered arrangement with that of
90
finless, illustrated that the rate of heat transfer improves as the fins are employed. The results indicated
91
that the presence of fins reduces the total solidification time up to 43.6% while this reduction for melting
92
process is 12.5% and 24.52% when 80°C and 85°C HTF inlet temperatures are considered, respectively.
93
It is also stated that the inlet mass flow rate affects the rate of heat transfer negligibly. Rosenfeld et al.
94
investigated melting process in a double pipe heat storage that is enhanced with three longitudinal fins
95
[27]. Their research clarified that close-contact melting improves the rate of heat transfer significantly.
96
In this study, continuing the literature, in order to reduce the unfavorable disadvantages of the low
97
conductivity of the phase change material, adding longitudinal fins are considered. Therefore the
98
arrangement of three longitudinal fins, with varying angular arrangements, is considered for the triple-fin 3
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heat exchanger. Afterward the most effective fins arrangement is found through a comparison among the
100
proposed cases. Results indicated that the presence of the upper fin does not have a significant effect on
101
the melting process, therefore its length is distributed on the two lower fins and the consequences of the
102
angle between the fins are studied.
103
2. Numerical approach
104
2.1. Physical model and boundary conditions
105
The studied shell and tube heat exchanger is shown in Fig. 1 in which two concentric pipes of 14 and 60
106
mm diameter are included. The length of the heat exchanger is 500 mm in which there is a 1-mm-thich
107
copper tube. Water as the HTF flows inside the inner tube and the space between the pipes is filled with
108
RT 35 as the PCM the properties of which is shown in Table 1. The proposed geometrical arrangements
109
of the three fins are shown in Fig.2. The fins length and thickness are 10 mm and 1.2 mm for all the cases.
110
The initial temperature of the setup is 25 °C which is less than the phase change temperature. The
111
insulation condition has been considered for the outer surface of the shell as the boundary condition and
112
the inlet temperature and mass flow rate are assumed to be 60 °C and 0.01 kg/s respectively, for all the
113
cases.
Fig. 1. Configuration of physical model.
114
θ=60°
θ=90° Fig. 2. Fins arrangements of the triple-fins heat exchangers 4
θ=120°
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Table 1. Thermophysical properties of RT35 and HTF PCM
Melting temperature range [℃]
𝝆 [kg/m3]
𝑪𝒑 [J/kg.K]
K [W/m.K]
µ [kg/m.s]
L [J/kg]
𝜷 [1/K]
RT35
29-36
815
2000
0.2
0.023
170000
0.6e-3
HTF
Inlet Temperature [ ℃]
𝝆 [kg/m3]
𝑪𝒑 [J/kg.K]
K [W/m.K]
µ [kg/m.s]
Water
60
983.3
4185
0.654
0.467e-3
116
2.2. Assumptions
117
In order to derive the governing physical and mathematical equations the following assumptions are
118
considered:
119
Flow is assumed to be laminar, transient, incompressible and three-dimensional.
120
Viscous dissipation is assumed to be negligible.
121
The thermophysical properties of the materials are assumed to be constant as the temperature varies.
122
Heat is transferred due to conduction and convection mechanisms.
123
2.3. Numerical model
124
In order to simulated the melting process in the latent heat storage system, the enthalpy-porosity method
125
[28,29] is implemented for a three dimensional model. Considering the assumptions made in section 2.2,
126
the continuity, momentum and energy equations can be presented as below:
127
For the HTF:
128
Continuity: (1)
∇.𝑉𝑓 = 0 129
Momentum: ∂𝑉𝑓 ∂𝑡
130
+ 𝑉𝑓 (∇.𝑉𝑓) =
1 ( ‒ ∇𝑃𝑓 + 𝜇𝑓∇2𝑉𝑓 + 𝜌𝑓𝑔) 𝜌𝑓
(2)
Energy: ∂𝐻𝑓 ∂𝑡
(
+ ∇ ∙ (𝑉𝐻𝑓) = ∇
𝑘𝑓
)
∇ℎ 𝜌𝑓𝐶𝑝,𝑓 𝑓
(3)
131 132 133
For the PCM: 5
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134
Continuity: ∇.𝑉𝑝𝑐𝑚 = 0
(4)
Momentum: ∂𝑉𝑝𝑐𝑚 ∂𝑡 135
+ 𝑉𝑝𝑐𝑚 (∇.𝑉𝑝𝑐𝑚) =
1
( ‒ ∇𝑃𝑝𝑐𝑚 + 𝜇𝑝𝑐𝑚∇2𝑉𝑝𝑐𝑚 + 𝜌𝑝𝑐𝑚𝑔𝛽(𝑇 ‒ 𝑇𝑟𝑒𝑓)) + 𝑆
𝜌𝑝𝑐𝑚
(5)
Energy: ∂𝐻𝑝𝑐𝑚 ∂𝑡
(
+ ∇ ∙ (𝑉𝐻𝑝𝑐𝑚) = ∇
𝑘𝑝𝑐𝑚 𝜌𝑝𝑐𝑚𝐶𝑝,𝑝𝑐𝑚
)
∇ℎ𝑝𝑐𝑚
(6)
136
The PCM’s enthalpy can be represented as a summation of sensible enthalpy, ℎ𝑝𝑐𝑚, and latent enthalpy,
137
𝛥𝐻. 𝐻𝑝𝑐𝑚 = ℎ𝑝𝑐𝑚 + 𝛥𝐻
138
(7)
where 𝑇
ℎ𝑝𝑐𝑚 = ℎ𝑟𝑒𝑓 +
∫𝑇
𝐶𝑝,𝑝𝑐𝑚 𝑑𝑇
(8)
𝑟𝑒𝑓
139
in which thermal capacity, 𝐶𝑝,𝑝𝑐𝑚, is a constant factor that can be drawn outside the integral. The value of
140
the latent heat can be calculated using the PCM’s latent heat, 𝐿. (9)
𝛥𝐻 = 𝜆𝐿 141
where liquid fraction 𝜆 varies in the range of zero (solid) to one (liquid) and is defined as below [30].
{
𝛥𝐻 =0 𝐿 𝛥𝐻 =1 𝜆= 𝐿 𝑇 ‒ 𝑇𝑠 𝛥𝐻 = 𝐿 𝑇𝑙𝑖𝑞 ‒ 𝑇𝑠
𝑖𝑓 𝑇 < 𝑇𝑠 𝑖𝑓 𝑇 > 𝑇𝑙𝑖𝑞
(10)
𝑖𝑓 𝑇𝑠 < 𝑇 < 𝑇𝑙𝑖𝑞
142
where 𝑇𝑙𝑖𝑞 and 𝑇𝑠 are the two ends of the melting range of the PCM. Considering equation 2, 𝑆 is the
143
Darcy’s law damping term which is added to the momentum equation to include convection heat transfer
144
in this equation. (1 ‒ 𝜆)2 𝑆= ‒ 3 𝐴𝑚𝑢𝑠ℎ𝑉 𝜆 +𝜀
(11)
145
𝐴𝑚𝑢𝑠ℎ is the mushy zone constant which is conventionally a large number in the range of 104 to 107. A
146
comparatively larger value of the constant is equivalent to higher rate of velocity damping. As this value
147
becomes excessively large, the solution will fluctuate. In the current paper, Amush constant is set on 106
148
and 𝜀 is a very small value parameter which is designated to prevent division to zero. 6
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The effect of mushy zone variation on the melting time of the triple-fin arranged in 120 degree angle is
150
shown in Fig. 3.
151
Fig. 3- Liquid fraction versus time for different mushy zone constant. 152 153
2.4. Numerical schemes and verification
154
The system’s governing equations have been solved employing SIMPLE algorithm via a 3D in-house
155
developed code [31]. In order to discretize the energy and momentum equations the QUICK
156
differentiating scheme is implemented. The pressure equation has been corrected using the PRESTO
157
scheme. In order to achieve a stable solution, under relaxation factors are considered which are 0.3, 0.6, 1
158
and 0.9 respectively for pressure, velocity, energy and volumetric liquid fraction. The convergence
159
tolerances for the continuity equation, momentum equation and energy equation are 10-5, 10-5 and 10-6.
160
In order to study the independency of the numerical solution to the mash grids and the time step, the
161
liquid fraction is studied for varying number of cells and different values of time step. The result of which
162
is summarized in tables 2 and 3. The selected values of the two parameters are highlighted for all the
163
cases. The process of the grid size and time step selection of one of the cases (case of 90°) can be
164
observed in Fig. 4 and the numerical mesh grid is shown in Fig. 5 for this case.
165
The results of the current CFD model has been compared with the experimental analysis on a simple
166
double pipe heat exchanger of Hosseini et al. [31] to validate the employed model. An acceptable match 7
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167
is observed between the two studied from which the average temperature versus time is chosen to be
168
presented in Fig. 6. Moreover a number of validations is also presented for specific points by which the
169
temperatures resulted from the current simulation are compared with the experimental data presented by
170
Jesumathy et al. [32]. As can be seen in Fig. 7, a fine match between the simulation results and the
171
experiment outputs of Jesumathy et al.’s.
172 173
Table 2. Selected cell numbers for different cases. Case
Cell Numbers
Without fin 60°-3 fins 90°-3 fins 120°-3 fins
51400 45190 36080 38000
72000 85100 54400 55130
94620 105000 98960 102200
110190 131078 121840 138200
174 175
Table 3. Selected time steps for different cases. Case
Time steps
Without fin 60°-3 fins 90°-3 fins 120°-3 fins
0.05 0.05 0.05 0.01
0.1 0.1 0.1 0.05
0.5 0.5 0.5 0.1
176 177
(a)
(b)
Fig. 4. Numerical independence (a) grid size (b) time step for the case of 90°. 178
8
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179
180
Fig. 5. Numerical mesh grid for the case of 90°.
Fig. 6. Comparison of average temperature profile between the present work and Hosseini et al. [31].
181 182 183 9
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Fig. 7. The comparison of temperature profiles at different locations between this study and Jesumathy et al.’s [32]. 184 185
3. Results and discussion
186
3.1. Melting process in a triple-fin heat exchanger
187
Melting process of the simple and triple-fin heat exchangers in midway along the length of cylindrical
188
shell are shown in Fig.8 for different fins angles, considering the bare tube heat exchanger, at the
189
beginning of the melting process, a small amount of the PCM has been melted just around the central
190
tube. During this stage, the dominated mechanism of heat transfer is conduction. As time passes, the
191
volumetric fraction of the melt increases which strengthens the buoyancy effect in the melt. The effect
192
pushes the hot liquid upwardly which brings about the superiority of the convection mechanism.
193
However, due to the existence of fins in finned cases, conduction plays a more important role in the
194
melting process. The presence of the fins is so effective that after 30 minutes of the process initiation,
195
upper half of the shell is completely melted in the enhanced cases. It can be seen in the figure that among
196
the finned cases, the one whose fins penetrate to the lower half of the shell (120°) performs more
197
acceptably in melting the PCM. This observation is due to the intrinsic behavior of the buoyancy effect
198
which pushes the hot liquid upwardly. Therefore the presence of fins in the lower half of the heat storage
199
system exposes a larger part of the shell to the buoyancy forces. 10
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200
θ =60°
θ =90°
θ =120°
130 min
80 min
30 min
20 min
10 min
5 min
Without fins
Fig. 8. Liquid fraction contours in midway along the length of the triple-fin cases and the bare tube. case.
11
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201
The variation of liquid fraction versus time for the triple-fin cases and the bare tube one is shown in Fig.9.
202
As the angles 60°, 90° and 120° is used, 6, 10 and 22.5 percent reduction in melting time is observed with
203
respect to the base case. As can be seen until 25 minutes, the rate of heat transfer in the case of 60° is
204
slightly more than others which can be explained via the small space between the three fins. In fact, the
205
limited amount of PCM between the fins melts in this portion and the presence of two hot surfaces next to
206
each other leads to an improved fluid movement and faster melting process. However as the process
207
continues, due to the largest distance between the fins and the lower half of the shell, this case becomes
208
the least capable to melt the remaining solid PCM at the bottom of the shell.
Fig.9. Liquid fraction versus time for the triple-fin cases and the base case. 209
Fig. 10 shows the amount of heat gain in term of time for all the finned tubes. At the initial stages of the
210
melting process, the heat absorption potential is maximum which results in the largest heat storage rate.
211
As the process continues, the PCM temperature rises and the temperature difference between the heat
212
transfer fluid and the PCM diminishes which results in a decrease in heat exchanger’s heat absorption
213
potential. During the above mentioned intervals the absorbed heat is mainly via sensible form. However
214
as the temperature approaches melting temperature, the mechanism of heat absorption changes from
215
sensible to latent and a slight increment in the heat absorption potential is observed (5 to 15 minutes).
216
Afterward, as the melt occupies the upper half of the shell, the mechanism of heat absorption becomes
217
sensible. Therefore the PCM temperature ascends that reduces the thermal potential between the two
218
media. As the thermal potential reduces the rate of heat absorption decreases. The figure also shows that
12
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219
after 25 minutes, the case 120° is able to absorb higher rate of energy due to the existence of two fins in
220
the lower half of the shell in this case.
Fig. 10. Rate of heat storage in the triple-fin heat storage systems. 221
Fig. 11 shows the temperature contours and streamlines for the triple-fin cases in which the angles
222
between the fins vary. As can be seen at the initial minutes of the process, small vortices form just next to
223
the fins surfaces and around the HTF carrying tube. As time passes, due to the buoyancy effect the
224
vortices move upwards. Considering the case 120°, the form of the two lower fins leads to vortices formed
225
between the two to be trapped. As 30 minutes passes, the trapped vortices can join other vortices due to
226
the expansion of the liquid zone which results in larger and stronger vortices with respect to the two other
227
cases. Considering the temperature contours shown on the left half of the figures, after a short time of
228
conduction domination period, the convection mechanism holds the superiority which results in upper
229
half higher temperature with respect to the lower one. In fact the temperature difference between these
230
upper parts plays an important role on creation of the vortices. Considering the temperature contours, it
231
can also be stated that the lower half average temperature of the case 120° , regardless of the moment
232
taken into account exceeds the average temperature of the two other cases due to the presence of
233
extended surface exclusively in the lower half of the shell.
234 235
13
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θ =90°
θ =120°
130 min
80 min
30 min
20 min
10 min
5 min
θ =60°
Fig. 11. temperature contours and streamlines at the midsection of the triplefin heat exchangers. 14
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236
Due to the reduction of the heat transfer fluid temperature as it flows along the heat exchanger, the
237
temperature difference between the two media reduces. This reduction in the thermal potential results in
238
lower values of melt fraction near the HTF outlet. Therefore in order to study the variations along the heat
239
exchanger a horizontal section at the height of y=28mm has been considered and the solid and liquid
240
fronts at the section are demonstrated at 15 minutes after the experiment initiation (Fig. 12). It is
241
noteworthy that the red and blue colors are utilized to show molten and solid PCM. Moreover, the melt
242
penetration length and its rate of increase are shown in Table 4. Results indicate that the increase in the
243
fins’ angle results in longer length of penetration. In other words, when the fins’ angle changes from 60°
244
to 90° and afterward to 120°, the melt penetration increases from 49.6% to 199.2%.
245
15
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Fig. 12. Solid and melt fronts at the height of y=28mm and at 15 minutes after the initiation. 246
16
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247
Table 4: Comparison of penetration length at certain time with changing angle. θ
Δx (mm)
ηΔx= (( Δxθ= 90° & 120°– Δx60°) / Δx60°) ×100
60°
133
_
90°
199
49.6%
120°
398
199.2%
248
The obtained results show that the fins presence in the lower half of the shell influences the complete
249
melting time noticeably while the upper one, although changes the process at the initiation, does not affect
250
the total rate of heat transfer . Therefore, according to Fig. 13, the upper fin in the case 120° has been
251
removed and its length has been added to the two lower fins. Afterward the effect of the angle is studied
252
for the double fin heat exchanger.
Fig. 13. Improvement of triple-fin heat exchanger to double-fin heat exchanger. 253
3.2. melting process in a double-fin heat exchanger
254
The total melting time of the double-fin heat exchanger for different angles is shown in Fig. 14. It is clear
255
that there is an optimum value. In other words as the angle between the two fins diminishes from 150 to
256
45, a decreasing trend is observed which results in 53.5% reduction tin total melting time. However extra
257
reduction in the fins angle leads to longer melting time. It is interesting that at the best case, 45°, 62%
258
total melting time reduction is observed with respect to bare tube heat exchanger.
17
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Fig. 14. total melting time of double-fin cases as the angle changes 259
The melt fraction contours and streamlines of the double-fin heat exchanger for 15, 45, 75 and 120 degree
260
angle are shown in Fig. 15. As can be seen, after 5 minutes a thin layer melt covers the internal tube
261
surface the fins which is due to the conduction mechanism. As the angle between the fins increases, a
262
larger space trapped between the fins prevents the melt from moving to the upper parts of the shell which
263
in turn reduces the natural convection consequences. At 45°, a balance is achieved between both the heat
264
penetration of fins to the lowest parts of the shell and the natural convection. So, in this case, the solid
265
PCM easily melts in the region between than can freely move upwards. Considering the streamlines
266
presented in the figure, at the initial stages of the melting process, small vortices forms at all over the
267
inner tube and the fins. An exception for the space between the fins of the case 15° is due to the small
268
space provided. After some time, except the trapped vortices between the fins that cannot penetrate to the
269
upper half solid front, these vortices merge together because of the buoyancy effect. Moreover, it can be
270
concluded that as the angle reduces to 45°, the melting zone in which the vortices are formed expands
271
which results in accelerated melting process.
272
Results reported in Fig. 16 indicates that for the case of 45°, the 76 percent of the PCM melts in the first
273
30 minutes while the remaining 24 percent requires 35 minutes to melt. Considering the case in which the
274
angle is 120°, the same amount of PCM melts in the first 30 minutes, however in this case in order to melt
275
the remaining 24% percent, double time is essential.
276 277 18
ACCEPTED MANUSCRIPT
θ =45°
θ =75°
θ =120°
65 min
45 min
30 min
15 min
10 min
5 min
θ =15°
Fig. 15. liquid fraction contours and streamlines of double-fin heat exchangers. 19
ACCEPTED MANUSCRIPT
278
Fig. 16. liquid fraction versus time for two cases of double-fin heat exchangers. 279
Conclusion
280
In this paper, the melting process of a PCM in a thermally enhanced heat exchanger is studied. Thus, the
281
effects of variation of longitudinal fins angles is studied on the melting front boundaries, total melting
282
time, rate of melting and the temperature distribution. The obtained results are summarized as below:
283
Considering the triple-fin cases, at initial steps, the highest rate of melting process is related to the
284
case in which the fins' angle is 60 degree. As the process progresses, larger angles improve the
285
melting process and decrease the total melting time.
286
In all the triple-fin cases, the upper half temperature is larger than the lower one. By increasing
287
the fins angle from 60° to 120°, the formation of melting front in lower half of the heat exchanger
288
accelerates and the temperature of this half is the highest when 120° case is considered.
289
Since the natural convection improves the melting process of the upper half of the heat exchanger
290
more than the lower part. Presence of fins in the lower part is more effective on lowering the total
291
melting time.
292 293
Among the double-fin cases, the optimum orientation of fins is related to the case of 45°. Increasing the angle results in blockage of the natural convection streams. While reduction of the
20
ACCEPTED MANUSCRIPT
294
angle to less than 45°prevents the vortices formation between the two fins and increases the total
295
melting time.
296
Nomenclatures
297
𝑐𝑝
Specific heat capacity (J/kg. K)
298
𝑔
Gravity (m/s2)
299
ℎ
Enthalpy (J/kg)
300
𝐻
Total enthalpy (J)
301
𝑘
Thermal conductivity (W/m. K)
302
𝐿
Latent heat (J/kg)
303
𝑃
Pressure (Pa)
304
𝑆
Source term
305
𝑇
Temperature (K)
306
𝑉
Velocity vector (m/s)
307
𝐴
Mushy zone constant (kg/m3. s)
308
Greek symbols
309
𝛽
Expansion coefficient (1/K)
310
𝜆
Liquid fraction
311
𝜇
Dynamic viscosity (Pa. s)
312
𝜌
Density (kg/m3)
313
θ
Fins angle
314
𝜀
Numerical constant
315
η
Efficiency
316
Δx
Penetration length (m)
317
Subscripts
318
lat
Latent
319
ref
Reference
320
s
Solid
321
𝑙𝑖𝑞
Liquid
322
𝑚𝑢𝑠ℎ Mushy zone
323
𝑓
Fluid
324
𝑝𝑐𝑚
Phase change material
325
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24
M. Kazemi, M.J. Hosseini, A.A. Ranjbar, R. Bahrampoury PII:
S0960-1481(17)30967-9
DOI:
10.1016/j.renene.2017.10.006
Reference:
RENE 9294
To appear in:
Renewable Energy
Received Date:
24 April 2017
Revised Date:
21 September 2017
Accepted Date:
02 October 2017
Please cite this article as: M. Kazemi, M.J. Hosseini, A.A. Ranjbar, R. Bahrampoury, Improvement of Longitudinal Fins Configuration in Latent Heat Storage Systems, Renewable Energy (2017), doi: 10.1016/j.renene.2017.10.006
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ACCEPTED MANUSCRIPT Highlights: The angle of longitudinal fins of a shell and tube heat exchanger is studied. Triple-fin and double-fin cases are simulated and compared for different angles. The upper fin of triple-fin cases doesn’t affect the total melting time considerably. An optimum angle for the double-fin case is found which minimizes total melting time.
ACCEPTED MANUSCRIPT
2
Improvement of Longitudinal Fins Configuration in Latent Heat Storage Systems
3
M. Kazemi a, M. J. Hosseinib,*, A. A. Ranjbarc, R. Bahrampouryd
1
4 5 6 7 8 9
a School
of Mechanical Engineering, Mazandaran University of Science and Technology, Babol, Iran of Mechanical Engineering, Golestan University, POB 155, Gorgan, Iran c School of Mechanical Engineering, Babol University of Technology, POB 484, Babol, Iran d Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran b Department
Abstract
10
In this study, the consequences of variation of the longitudinal fins angle on the heat transfer
11
improvement during phase change are investigated. Therefore, the melting process of RT 35 as a phase
12
change material is studied for triple-fin and double-fin cases for different angles and the results are
13
compared with of bare tube case. Results indicated that due to the natural convection domination, the
14
upper fin does not leave a great effect on the total melting time. Considering the triple-fin heat
15
exchangers, as the fins angle increases from 60° to 120°, the total melting time reduces. However, when
16
double-fin cases are under consideration, reducing the angle from 150° to 45° results in melting time
17
reduction. More reduction in the angle increases the total melting time. Results also showed that the best
18
cases among triple-fin cases and among the double-fin cases result in 22.5 and 62 percent reduction in
19
melting time with respect to the simple heat exchanger.
20
Keywords: Phase change material, Melting, Fins angle, Triple-fin heat exchanger
21 22
1. Introduction
23
During recent few decades, daily increase in global energy consumption and the fact that fossil fuels are
24
not only pollutant but also are limited in amount have encouraged researchers to find an approach for
25
effective utilization of renewable energy. One of the challenges that industries face when employing
26
renewable energy sources is their unavailability during some intervals during the day. The best method
27
for eliminating this variation in availability is to store energy. Latent heat storage systems have attracted
28
the scientist attentions due to their high energy density, approximately constant operating temperature and
29
small vapor pressure. These heat storage systems absorb thermal energy from a heat source and the
30
included phase change material (PCM) melts which is called charge process. The melt can release its
31
energy and solidifies when the heat source is not available. These days, these PCMs are applied in *
Corresponding Author: (M.J. Hosseini) Department of Mechanical Engineering, Golestan University, P.O. Box 155, Gorgan, Iran, Email: [email protected]
1
ACCEPTED MANUSCRIPT
32
different fields of industry including refrigeration [1,2], solar energy [3,4], electrical devices [5,6] and
33
heating, ventilation and air conditioning [7,8].
34
Different shell geometries including spherical [9] and rectangular [10] have been considered. However
35
cylindrical shell and tube arrangements constitute the majority of researches in this field, around 70
36
percent. Hosseini et al. [11] studied melting process of RT50 as a PCM in a shell and tube heat exchanger.
37
They reported that the rate of phase change is directly proportional with HTF inlet temperature.
38
In order to develop latent heat storage systems, the best approach is to dilute the consequences of low
39
thermal conductivity of the phase change materials which brings about a practical proposal of these
40
storage systems to the industrial world. Among the techniques, distribution of nanoparticles in PCMs
41
[12], utilization of heat pipes [13] and employment of extended surfaces are some of the popular
42
approaches.
43
Among extended surface enhancement methods, adding fins [14,15] and multi-tube [16] can be
44
mentioned.
45
The research conducted by Agyenim et al. [17] on heat transfer improvement, using multi-tube, circular
46
fins and longitudinal fins, indicated that the system enhanced by longitudinal fins performs better both
47
during charge and discharge processes than the two other methods.
48
Betzel and Beer studied melting process of a heat storage system for a system enhanced with axial fins
49
and also without the fins [18]. Their results revealed that approximately isothermal copper fins and
50
adiabatic PVC fins behave differently regarding the heat transfer characteristics. Moreover, the melting
51
front shape and the rate of heat transfer are dependent to the fins arrangement.
52
Sciacovelli et al. [19] studied phase change process in a double pipe heat exchanger enhanced by single
53
bifurcation and double bifurcation Y-shaped fins. Results indicated that the double bifurcation fins
54
noticeably improve the heat transfer performance of the heat exchanger, 24% promotion in solidification
55
efficiency.
56
Mat et al. [20] numerically studied melting process of a kind of paraffin, RT 82, as a phase change
57
material in a triple tube heat exchanger. They considered different arrangements of fins, internal, external
58
and internal-external for a heat storage system to improve the melting process. They concluded that, the
59
fins presence, regardless of the implemented arrangement, leads to about 34.3% reduction in total melting
60
time in comparison with a finless arrangement. Hosseini et al. [21] examined the consequences of fins
61
height variation for longitudinally arranged fins. They found that increasing the height brings about a
62
more uniform temperature distribution and decreases the melting time. Their results indicated that taller
63
fins improve the melting process especially at the beginning stages which is due to the melting zone
64
penetration to the solid PCM.
2
ACCEPTED MANUSCRIPT
65
Rabienataj Darzi et al. [22] simulated and analyzed two dimensional phase change (solidification and
66
melting) in a double pipe heat exchanger for varying tube geometry, nano-particles distribution and
67
number of fins. They concluded that the rate of melting process is higher in the upper half than the lower
68
one due to the consequences of natural convection. The also reported that although the variation of the
69
shape of the central tube from circular to vertical elliptical does not affect the solidification process,
70
installation of extra fins improves the solidification process more in comparison with melting which is
71
due to the obstacles fins leave on the path of the naturally driven streams in the melting process.
72
Yuan et al. studied melting process of a phase change material for in a heat storage system enhanced with
73
two longitudinal fins for different angles and compared the results with bare tube case [23]. Results
74
showed that although the fins reduce the convective heat transfer, they lead to higher rate of heat transfer
75
and less melting time.
76
In order to improve the rate of heat transfer in a latent heat storage system, Liu and Groulx considered
77
two longitudinal straight fins as well as angled fins mounted on the central copper inner tube [24].
78
Comparing the two cases, for the inlet temperature of 50℃, the total melting time of the angled fin case is
79
slightly less than the straight fin case while no significant difference in the melting times is observed for
80
higher inlet temperature (60℃). They also noticed that there is no sensible difference between the two
81
cases when solidification is under consideration.
82
Agyenim et al. [25] experimentally studied phase change of Erythritol as the PCM in a unit enhanced by
83
longitudinal fins. Their experiments demonstrated that the optimum mass flow and HTF inlet temperature
84
which improve the heat absorption characteristics of the system are 30 kg/min and 140℃. Their
85
experimental investigation demonstrated that longitudinally arranged finned system provides charge and
86
discharge thermal potential of a PCM that meets heating requirements of a solar absorption cooling
87
system in wich LiBr/H2O is the HTF.
88
Rathod and Banerjee [26] experimentally studied melting and solidification processes of a shell and tube
89
heat exchanger enhanced with three longitudinal fins. Comparing the considered arrangement with that of
90
finless, illustrated that the rate of heat transfer improves as the fins are employed. The results indicated
91
that the presence of fins reduces the total solidification time up to 43.6% while this reduction for melting
92
process is 12.5% and 24.52% when 80°C and 85°C HTF inlet temperatures are considered, respectively.
93
It is also stated that the inlet mass flow rate affects the rate of heat transfer negligibly. Rosenfeld et al.
94
investigated melting process in a double pipe heat storage that is enhanced with three longitudinal fins
95
[27]. Their research clarified that close-contact melting improves the rate of heat transfer significantly.
96
In this study, continuing the literature, in order to reduce the unfavorable disadvantages of the low
97
conductivity of the phase change material, adding longitudinal fins are considered. Therefore the
98
arrangement of three longitudinal fins, with varying angular arrangements, is considered for the triple-fin 3
ACCEPTED MANUSCRIPT
99
heat exchanger. Afterward the most effective fins arrangement is found through a comparison among the
100
proposed cases. Results indicated that the presence of the upper fin does not have a significant effect on
101
the melting process, therefore its length is distributed on the two lower fins and the consequences of the
102
angle between the fins are studied.
103
2. Numerical approach
104
2.1. Physical model and boundary conditions
105
The studied shell and tube heat exchanger is shown in Fig. 1 in which two concentric pipes of 14 and 60
106
mm diameter are included. The length of the heat exchanger is 500 mm in which there is a 1-mm-thich
107
copper tube. Water as the HTF flows inside the inner tube and the space between the pipes is filled with
108
RT 35 as the PCM the properties of which is shown in Table 1. The proposed geometrical arrangements
109
of the three fins are shown in Fig.2. The fins length and thickness are 10 mm and 1.2 mm for all the cases.
110
The initial temperature of the setup is 25 °C which is less than the phase change temperature. The
111
insulation condition has been considered for the outer surface of the shell as the boundary condition and
112
the inlet temperature and mass flow rate are assumed to be 60 °C and 0.01 kg/s respectively, for all the
113
cases.
Fig. 1. Configuration of physical model.
114
θ=60°
θ=90° Fig. 2. Fins arrangements of the triple-fins heat exchangers 4
θ=120°
ACCEPTED MANUSCRIPT
115
Table 1. Thermophysical properties of RT35 and HTF PCM
Melting temperature range [℃]
𝝆 [kg/m3]
𝑪𝒑 [J/kg.K]
K [W/m.K]
µ [kg/m.s]
L [J/kg]
𝜷 [1/K]
RT35
29-36
815
2000
0.2
0.023
170000
0.6e-3
HTF
Inlet Temperature [ ℃]
𝝆 [kg/m3]
𝑪𝒑 [J/kg.K]
K [W/m.K]
µ [kg/m.s]
Water
60
983.3
4185
0.654
0.467e-3
116
2.2. Assumptions
117
In order to derive the governing physical and mathematical equations the following assumptions are
118
considered:
119
Flow is assumed to be laminar, transient, incompressible and three-dimensional.
120
Viscous dissipation is assumed to be negligible.
121
The thermophysical properties of the materials are assumed to be constant as the temperature varies.
122
Heat is transferred due to conduction and convection mechanisms.
123
2.3. Numerical model
124
In order to simulated the melting process in the latent heat storage system, the enthalpy-porosity method
125
[28,29] is implemented for a three dimensional model. Considering the assumptions made in section 2.2,
126
the continuity, momentum and energy equations can be presented as below:
127
For the HTF:
128
Continuity: (1)
∇.𝑉𝑓 = 0 129
Momentum: ∂𝑉𝑓 ∂𝑡
130
+ 𝑉𝑓 (∇.𝑉𝑓) =
1 ( ‒ ∇𝑃𝑓 + 𝜇𝑓∇2𝑉𝑓 + 𝜌𝑓𝑔) 𝜌𝑓
(2)
Energy: ∂𝐻𝑓 ∂𝑡
(
+ ∇ ∙ (𝑉𝐻𝑓) = ∇
𝑘𝑓
)
∇ℎ 𝜌𝑓𝐶𝑝,𝑓 𝑓
(3)
131 132 133
For the PCM: 5
ACCEPTED MANUSCRIPT
134
Continuity: ∇.𝑉𝑝𝑐𝑚 = 0
(4)
Momentum: ∂𝑉𝑝𝑐𝑚 ∂𝑡 135
+ 𝑉𝑝𝑐𝑚 (∇.𝑉𝑝𝑐𝑚) =
1
( ‒ ∇𝑃𝑝𝑐𝑚 + 𝜇𝑝𝑐𝑚∇2𝑉𝑝𝑐𝑚 + 𝜌𝑝𝑐𝑚𝑔𝛽(𝑇 ‒ 𝑇𝑟𝑒𝑓)) + 𝑆
𝜌𝑝𝑐𝑚
(5)
Energy: ∂𝐻𝑝𝑐𝑚 ∂𝑡
(
+ ∇ ∙ (𝑉𝐻𝑝𝑐𝑚) = ∇
𝑘𝑝𝑐𝑚 𝜌𝑝𝑐𝑚𝐶𝑝,𝑝𝑐𝑚
)
∇ℎ𝑝𝑐𝑚
(6)
136
The PCM’s enthalpy can be represented as a summation of sensible enthalpy, ℎ𝑝𝑐𝑚, and latent enthalpy,
137
𝛥𝐻. 𝐻𝑝𝑐𝑚 = ℎ𝑝𝑐𝑚 + 𝛥𝐻
138
(7)
where 𝑇
ℎ𝑝𝑐𝑚 = ℎ𝑟𝑒𝑓 +
∫𝑇
𝐶𝑝,𝑝𝑐𝑚 𝑑𝑇
(8)
𝑟𝑒𝑓
139
in which thermal capacity, 𝐶𝑝,𝑝𝑐𝑚, is a constant factor that can be drawn outside the integral. The value of
140
the latent heat can be calculated using the PCM’s latent heat, 𝐿. (9)
𝛥𝐻 = 𝜆𝐿 141
where liquid fraction 𝜆 varies in the range of zero (solid) to one (liquid) and is defined as below [30].
{
𝛥𝐻 =0 𝐿 𝛥𝐻 =1 𝜆= 𝐿 𝑇 ‒ 𝑇𝑠 𝛥𝐻 = 𝐿 𝑇𝑙𝑖𝑞 ‒ 𝑇𝑠
𝑖𝑓 𝑇 < 𝑇𝑠 𝑖𝑓 𝑇 > 𝑇𝑙𝑖𝑞
(10)
𝑖𝑓 𝑇𝑠 < 𝑇 < 𝑇𝑙𝑖𝑞
142
where 𝑇𝑙𝑖𝑞 and 𝑇𝑠 are the two ends of the melting range of the PCM. Considering equation 2, 𝑆 is the
143
Darcy’s law damping term which is added to the momentum equation to include convection heat transfer
144
in this equation. (1 ‒ 𝜆)2 𝑆= ‒ 3 𝐴𝑚𝑢𝑠ℎ𝑉 𝜆 +𝜀
(11)
145
𝐴𝑚𝑢𝑠ℎ is the mushy zone constant which is conventionally a large number in the range of 104 to 107. A
146
comparatively larger value of the constant is equivalent to higher rate of velocity damping. As this value
147
becomes excessively large, the solution will fluctuate. In the current paper, Amush constant is set on 106
148
and 𝜀 is a very small value parameter which is designated to prevent division to zero. 6
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149
The effect of mushy zone variation on the melting time of the triple-fin arranged in 120 degree angle is
150
shown in Fig. 3.
151
Fig. 3- Liquid fraction versus time for different mushy zone constant. 152 153
2.4. Numerical schemes and verification
154
The system’s governing equations have been solved employing SIMPLE algorithm via a 3D in-house
155
developed code [31]. In order to discretize the energy and momentum equations the QUICK
156
differentiating scheme is implemented. The pressure equation has been corrected using the PRESTO
157
scheme. In order to achieve a stable solution, under relaxation factors are considered which are 0.3, 0.6, 1
158
and 0.9 respectively for pressure, velocity, energy and volumetric liquid fraction. The convergence
159
tolerances for the continuity equation, momentum equation and energy equation are 10-5, 10-5 and 10-6.
160
In order to study the independency of the numerical solution to the mash grids and the time step, the
161
liquid fraction is studied for varying number of cells and different values of time step. The result of which
162
is summarized in tables 2 and 3. The selected values of the two parameters are highlighted for all the
163
cases. The process of the grid size and time step selection of one of the cases (case of 90°) can be
164
observed in Fig. 4 and the numerical mesh grid is shown in Fig. 5 for this case.
165
The results of the current CFD model has been compared with the experimental analysis on a simple
166
double pipe heat exchanger of Hosseini et al. [31] to validate the employed model. An acceptable match 7
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167
is observed between the two studied from which the average temperature versus time is chosen to be
168
presented in Fig. 6. Moreover a number of validations is also presented for specific points by which the
169
temperatures resulted from the current simulation are compared with the experimental data presented by
170
Jesumathy et al. [32]. As can be seen in Fig. 7, a fine match between the simulation results and the
171
experiment outputs of Jesumathy et al.’s.
172 173
Table 2. Selected cell numbers for different cases. Case
Cell Numbers
Without fin 60°-3 fins 90°-3 fins 120°-3 fins
51400 45190 36080 38000
72000 85100 54400 55130
94620 105000 98960 102200
110190 131078 121840 138200
174 175
Table 3. Selected time steps for different cases. Case
Time steps
Without fin 60°-3 fins 90°-3 fins 120°-3 fins
0.05 0.05 0.05 0.01
0.1 0.1 0.1 0.05
0.5 0.5 0.5 0.1
176 177
(a)
(b)
Fig. 4. Numerical independence (a) grid size (b) time step for the case of 90°. 178
8
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179
180
Fig. 5. Numerical mesh grid for the case of 90°.
Fig. 6. Comparison of average temperature profile between the present work and Hosseini et al. [31].
181 182 183 9
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Fig. 7. The comparison of temperature profiles at different locations between this study and Jesumathy et al.’s [32]. 184 185
3. Results and discussion
186
3.1. Melting process in a triple-fin heat exchanger
187
Melting process of the simple and triple-fin heat exchangers in midway along the length of cylindrical
188
shell are shown in Fig.8 for different fins angles, considering the bare tube heat exchanger, at the
189
beginning of the melting process, a small amount of the PCM has been melted just around the central
190
tube. During this stage, the dominated mechanism of heat transfer is conduction. As time passes, the
191
volumetric fraction of the melt increases which strengthens the buoyancy effect in the melt. The effect
192
pushes the hot liquid upwardly which brings about the superiority of the convection mechanism.
193
However, due to the existence of fins in finned cases, conduction plays a more important role in the
194
melting process. The presence of the fins is so effective that after 30 minutes of the process initiation,
195
upper half of the shell is completely melted in the enhanced cases. It can be seen in the figure that among
196
the finned cases, the one whose fins penetrate to the lower half of the shell (120°) performs more
197
acceptably in melting the PCM. This observation is due to the intrinsic behavior of the buoyancy effect
198
which pushes the hot liquid upwardly. Therefore the presence of fins in the lower half of the heat storage
199
system exposes a larger part of the shell to the buoyancy forces. 10
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200
θ =60°
θ =90°
θ =120°
130 min
80 min
30 min
20 min
10 min
5 min
Without fins
Fig. 8. Liquid fraction contours in midway along the length of the triple-fin cases and the bare tube. case.
11
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201
The variation of liquid fraction versus time for the triple-fin cases and the bare tube one is shown in Fig.9.
202
As the angles 60°, 90° and 120° is used, 6, 10 and 22.5 percent reduction in melting time is observed with
203
respect to the base case. As can be seen until 25 minutes, the rate of heat transfer in the case of 60° is
204
slightly more than others which can be explained via the small space between the three fins. In fact, the
205
limited amount of PCM between the fins melts in this portion and the presence of two hot surfaces next to
206
each other leads to an improved fluid movement and faster melting process. However as the process
207
continues, due to the largest distance between the fins and the lower half of the shell, this case becomes
208
the least capable to melt the remaining solid PCM at the bottom of the shell.
Fig.9. Liquid fraction versus time for the triple-fin cases and the base case. 209
Fig. 10 shows the amount of heat gain in term of time for all the finned tubes. At the initial stages of the
210
melting process, the heat absorption potential is maximum which results in the largest heat storage rate.
211
As the process continues, the PCM temperature rises and the temperature difference between the heat
212
transfer fluid and the PCM diminishes which results in a decrease in heat exchanger’s heat absorption
213
potential. During the above mentioned intervals the absorbed heat is mainly via sensible form. However
214
as the temperature approaches melting temperature, the mechanism of heat absorption changes from
215
sensible to latent and a slight increment in the heat absorption potential is observed (5 to 15 minutes).
216
Afterward, as the melt occupies the upper half of the shell, the mechanism of heat absorption becomes
217
sensible. Therefore the PCM temperature ascends that reduces the thermal potential between the two
218
media. As the thermal potential reduces the rate of heat absorption decreases. The figure also shows that
12
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219
after 25 minutes, the case 120° is able to absorb higher rate of energy due to the existence of two fins in
220
the lower half of the shell in this case.
Fig. 10. Rate of heat storage in the triple-fin heat storage systems. 221
Fig. 11 shows the temperature contours and streamlines for the triple-fin cases in which the angles
222
between the fins vary. As can be seen at the initial minutes of the process, small vortices form just next to
223
the fins surfaces and around the HTF carrying tube. As time passes, due to the buoyancy effect the
224
vortices move upwards. Considering the case 120°, the form of the two lower fins leads to vortices formed
225
between the two to be trapped. As 30 minutes passes, the trapped vortices can join other vortices due to
226
the expansion of the liquid zone which results in larger and stronger vortices with respect to the two other
227
cases. Considering the temperature contours shown on the left half of the figures, after a short time of
228
conduction domination period, the convection mechanism holds the superiority which results in upper
229
half higher temperature with respect to the lower one. In fact the temperature difference between these
230
upper parts plays an important role on creation of the vortices. Considering the temperature contours, it
231
can also be stated that the lower half average temperature of the case 120° , regardless of the moment
232
taken into account exceeds the average temperature of the two other cases due to the presence of
233
extended surface exclusively in the lower half of the shell.
234 235
13
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θ =90°
θ =120°
130 min
80 min
30 min
20 min
10 min
5 min
θ =60°
Fig. 11. temperature contours and streamlines at the midsection of the triplefin heat exchangers. 14
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236
Due to the reduction of the heat transfer fluid temperature as it flows along the heat exchanger, the
237
temperature difference between the two media reduces. This reduction in the thermal potential results in
238
lower values of melt fraction near the HTF outlet. Therefore in order to study the variations along the heat
239
exchanger a horizontal section at the height of y=28mm has been considered and the solid and liquid
240
fronts at the section are demonstrated at 15 minutes after the experiment initiation (Fig. 12). It is
241
noteworthy that the red and blue colors are utilized to show molten and solid PCM. Moreover, the melt
242
penetration length and its rate of increase are shown in Table 4. Results indicate that the increase in the
243
fins’ angle results in longer length of penetration. In other words, when the fins’ angle changes from 60°
244
to 90° and afterward to 120°, the melt penetration increases from 49.6% to 199.2%.
245
15
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Fig. 12. Solid and melt fronts at the height of y=28mm and at 15 minutes after the initiation. 246
16
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247
Table 4: Comparison of penetration length at certain time with changing angle. θ
Δx (mm)
ηΔx= (( Δxθ= 90° & 120°– Δx60°) / Δx60°) ×100
60°
133
_
90°
199
49.6%
120°
398
199.2%
248
The obtained results show that the fins presence in the lower half of the shell influences the complete
249
melting time noticeably while the upper one, although changes the process at the initiation, does not affect
250
the total rate of heat transfer . Therefore, according to Fig. 13, the upper fin in the case 120° has been
251
removed and its length has been added to the two lower fins. Afterward the effect of the angle is studied
252
for the double fin heat exchanger.
Fig. 13. Improvement of triple-fin heat exchanger to double-fin heat exchanger. 253
3.2. melting process in a double-fin heat exchanger
254
The total melting time of the double-fin heat exchanger for different angles is shown in Fig. 14. It is clear
255
that there is an optimum value. In other words as the angle between the two fins diminishes from 150 to
256
45, a decreasing trend is observed which results in 53.5% reduction tin total melting time. However extra
257
reduction in the fins angle leads to longer melting time. It is interesting that at the best case, 45°, 62%
258
total melting time reduction is observed with respect to bare tube heat exchanger.
17
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Fig. 14. total melting time of double-fin cases as the angle changes 259
The melt fraction contours and streamlines of the double-fin heat exchanger for 15, 45, 75 and 120 degree
260
angle are shown in Fig. 15. As can be seen, after 5 minutes a thin layer melt covers the internal tube
261
surface the fins which is due to the conduction mechanism. As the angle between the fins increases, a
262
larger space trapped between the fins prevents the melt from moving to the upper parts of the shell which
263
in turn reduces the natural convection consequences. At 45°, a balance is achieved between both the heat
264
penetration of fins to the lowest parts of the shell and the natural convection. So, in this case, the solid
265
PCM easily melts in the region between than can freely move upwards. Considering the streamlines
266
presented in the figure, at the initial stages of the melting process, small vortices forms at all over the
267
inner tube and the fins. An exception for the space between the fins of the case 15° is due to the small
268
space provided. After some time, except the trapped vortices between the fins that cannot penetrate to the
269
upper half solid front, these vortices merge together because of the buoyancy effect. Moreover, it can be
270
concluded that as the angle reduces to 45°, the melting zone in which the vortices are formed expands
271
which results in accelerated melting process.
272
Results reported in Fig. 16 indicates that for the case of 45°, the 76 percent of the PCM melts in the first
273
30 minutes while the remaining 24 percent requires 35 minutes to melt. Considering the case in which the
274
angle is 120°, the same amount of PCM melts in the first 30 minutes, however in this case in order to melt
275
the remaining 24% percent, double time is essential.
276 277 18
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θ =45°
θ =75°
θ =120°
65 min
45 min
30 min
15 min
10 min
5 min
θ =15°
Fig. 15. liquid fraction contours and streamlines of double-fin heat exchangers. 19
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278
Fig. 16. liquid fraction versus time for two cases of double-fin heat exchangers. 279
Conclusion
280
In this paper, the melting process of a PCM in a thermally enhanced heat exchanger is studied. Thus, the
281
effects of variation of longitudinal fins angles is studied on the melting front boundaries, total melting
282
time, rate of melting and the temperature distribution. The obtained results are summarized as below:
283
Considering the triple-fin cases, at initial steps, the highest rate of melting process is related to the
284
case in which the fins' angle is 60 degree. As the process progresses, larger angles improve the
285
melting process and decrease the total melting time.
286
In all the triple-fin cases, the upper half temperature is larger than the lower one. By increasing
287
the fins angle from 60° to 120°, the formation of melting front in lower half of the heat exchanger
288
accelerates and the temperature of this half is the highest when 120° case is considered.
289
Since the natural convection improves the melting process of the upper half of the heat exchanger
290
more than the lower part. Presence of fins in the lower part is more effective on lowering the total
291
melting time.
292 293
Among the double-fin cases, the optimum orientation of fins is related to the case of 45°. Increasing the angle results in blockage of the natural convection streams. While reduction of the
20
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294
angle to less than 45°prevents the vortices formation between the two fins and increases the total
295
melting time.
296
Nomenclatures
297
𝑐𝑝
Specific heat capacity (J/kg. K)
298
𝑔
Gravity (m/s2)
299
ℎ
Enthalpy (J/kg)
300
𝐻
Total enthalpy (J)
301
𝑘
Thermal conductivity (W/m. K)
302
𝐿
Latent heat (J/kg)
303
𝑃
Pressure (Pa)
304
𝑆
Source term
305
𝑇
Temperature (K)
306
𝑉
Velocity vector (m/s)
307
𝐴
Mushy zone constant (kg/m3. s)
308
Greek symbols
309
𝛽
Expansion coefficient (1/K)
310
𝜆
Liquid fraction
311
𝜇
Dynamic viscosity (Pa. s)
312
𝜌
Density (kg/m3)
313
θ
Fins angle
314
𝜀
Numerical constant
315
η
Efficiency
316
Δx
Penetration length (m)
317
Subscripts
318
lat
Latent
319
ref
Reference
320
s
Solid
321
𝑙𝑖𝑞
Liquid
322
𝑚𝑢𝑠ℎ Mushy zone
323
𝑓
Fluid
324
𝑝𝑐𝑚
Phase change material
325
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