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Maximizing the energy output of a photovoltaic–thermal solar collector incorporating phase change materials
Energy and Buildings 153 (2017) 382–391
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Maximizing the energy output of a photovoltaic–thermal solar collector incorporating phase change materials Di Su, Yuting Jia, Yaxue Lin, Guiyin Fang ∗ School of Physics, Nanjing University, Nanjing 210093, China
a r t i c l e
i n f o
Article history: Received 26 April 2017 Received in revised form 11 July 2017 Accepted 10 August 2017 Keywords: Solar energy Photovoltaic–thermal collector Electrical efficiency Phase change material Thermal energy storage Energy output
a b s t r a c t Photovoltaic–thermal collector can simultaneously generate both electricity and heat, making full use of the solar energy. It is worth to increase the electrical output by reducing the operating temperature. An effective method of cooling the cell temperature is incorporating phase change materials into the collector. In order to maximize the energy output and improve the performance of the collector, we perform comparative analyses on a hybrid photovoltaic–thermal solar collector incorporating phase change materials with different melting point. Solar cell temperature, electrical power, electrical efficiency, outlet temperature of water, thermal power output of the collector by varying melting point and thickness of phase change material layer are evaluated using one dimensional energy balance method. The corresponding graphical representations are described to explain the way of maximizing the electrical and thermal energy output of this system. And the numerical results have provided guidance for further experiment. In this theoretical work, it is found that phase change material layer with lower melting point has better electrical properties of the collector, while the heat stored in phase change material layer is more difficult to utilize. The results show that the photovoltaic–thermal solar collector gets a maximum of overall energy output by incorporating 3.4cm-thick phase change material layer with 40 ◦ C melting point. By contrast of the electrical power of 30 ◦ C melting point case and no phase change material case, the biggest value of difference is 16.12 W at 12:00. It means that the electrical power of the collector has increased around 13.6% by incorporating phase change material layer with 30 ◦ C melting point. © 2017 Elsevier B.V. All rights reserved.
1. Introduction As a clean renewable source, solar energy has good prospects for solving the energy and environment problems in the future. The photovoltaic (PV) technology is currently the most common way of converting the solar energy to electricity directly by using solar cells. For every 1 ◦ C rise in solar cell temperature, the electrical efficiency drops by around 0.45% [1]. Typically, the solar cells using silicon technology convert about 15%–25% of the solar radiation into electricity, and the remaining incident solar energy is converted to heat [2]. In order to enhance the solar cell efficiency and the energy output, it requires a device to remove this waste heat [3]. A practical method to prevent overheating of PV modules is embedding a thermal absorber to remove the exhaust heat. This combined system is known as the photovoltaic thermal (PV/T) col-
∗ Corresponding author. E-mail address: [email protected] (G. Fang). http://dx.doi.org/10.1016/j.enbuild.2017.08.027 0378-7788/© 2017 Elsevier B.V. All rights reserved.
lector, which can simultaneously generate both electricity and heat [4]. According to the type of working fluids used in absorber, the PV/T collectors can be divided into three types: air–based PV/T collector, water–based collector and combination of water/air collector. Up to now, several experimental, analytical and numerical studies on the performance evaluation of PV/T collectors have been performed by many researchers. Herrando et al. [5] developed a model to estimate the performance of PV/T systems based on domestic water, and achieved a higher overall efficiency than air–based systems. Slimani et al. [6] presented a PV/T solar collector embedded in an indirect solar dryer system. The calculation results showed that the hybrid PV/T collector provided a more suitable air temperature for drying agricultural products. Shan et al. [7] assessed the performance of a PV/T collector for water heating in building through numerical simulation methods, and the results showed that more number of series–connected PV cells lead to higher outlet temperature and lower electrical efficiency. The configurations of the PV/T collector have profound effects on the system performances. A comparative study was carried out in four solar devices: PV module, conventional hybrid solar air collector,
D. Su et al. / Energy and Buildings 153 (2017) 382–391
Nomenclature c D F h I K L ˙ m T U
v W x ␣ ı
Specific heat capacity (kJ/kg K) Diameter of the pipe (m) Packing factor Convective heat transfer coefficient (W/m2 K) Solar radiation intensity (W/m2 ) Overall heat transfer coefficient (W/m2 K) Length (m) Mass flow rate (kg/s) Temperature (K) Overall heat transfer coefficient (W/m2 K) Flow velocity (m/s) Width (m) Distance in flowing direction (m) Absorption coefficient Thickness (m) Dynamic viscosity Photovoltaic efficiency Thermal conductivity (W/m K) Transmission coefficient Kinematic viscosity (m2 /s)
Subscripts b Backplane c Solar cell e Environment Glass cover g i Insulation layer PCM layer p t Tube w Water flow ref Reference value at reference conditions
glazed hybrid solar air collector and glazed double–pass hybrid solar air collector. The fourth configuration reached the highest daily average of overall energy efficiency at 74% [8]. Su et al. [9] compared four configurations of the PV/T collector with dual channels, in which water and air were used as working fluids. This work gives guidance to select a suitable working fluid depending on different needs. Water is a good working fluid for the PV/T systems, due to its high heat conductivity and high specific heat capacity. Furthermore, to increase the efficiency of the PV/T systems, it seems to be a useful way to improve the thermal properties of the working fluid [10]. Another effective method of cooling the cell temperature is increasing thermal capacitance of the collector [11]. Phase change material (PCM) integrated into a PV module helps to limit the temperature of PV cells by absorbing heat when melting, because of its high latent heat capacity [12]. In fact, the PCM layer not only maintains appropriate temperature of the PV cells, but also acts as a heat sink storing the exhaust heat for a later use [13]. It is known that solar energy is intermittent, therefore thermal energy storage used in the PV/T collector can ameliorate this problem, by storing the heat during the day and releasing it at night. Over the years, the potential of the PV/T collector incorporating PCM has been demonstrated in theoretical simulations and experimental tests by researchers. A schematic diagram of the PV/T collectors with PCM is illustrated in Fig. 1. Stropnik et al. [14] designed a novel photovoltaic/thermal collector with PCM and investigated the thermal performance of this system. Results indicated that the addition of PCM was an effective means to enhance heat exchange between PV cells and absorber in a PV/T collector, and the maxi-
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mum temperature difference on the surface of PV cells without PCM was 35.6 ◦ C higher than on a system with PCM. Al Imam et al. [15] examined energy storage incorporating PCM in the PV/T collector system with compound parabolic concentrator. For system with PCM, up to around 3 m from entrance, the plate temperature rose and then it stayed almost steady. But in case of applying same system without PCM, the plate temperature was sharp. Japs et al. [16] conducted an experimental analysis of two different PCMs used in PV/T system considering actual electricity prices. At the tests, the PCM with a higher thermal conductivity had a corresponding higher yield. Su et al. [17] performed comparative analyses on an air–based PV/T collector with PCM, and it was demonstrated that 3cm–thick PCM layer glued to PV cells was optimum both in electrical and thermal performance. Navarro et al. [18] tried to integrate PCM into a PV/T collector. The prototype was tested in the outdoors, and it was demonstrated that the PCM layer could achieve about 20% of energy savings compared to the PV/T collector with no PCM layer. Serale et al. [19] developed a physical–mathematical model for a solar collector with slurry–PCM, which increased the latent heat of the heat carrier fluid. Simulation results showed the PCM slurry could improve the efficiency of system about 20%–40%. Photovoltaic systems integrated PCM are often used in building, providing benefits of generating electricity and thermal management [20]. Lin et al. [21] compared the three types of buildings using PV/T collector only, using PCM only, and without using PV/T collectors and PCMs. The results showed that these two methods could effectively improve the indoor thermal performance of the house. However, few studies have been devoted to improve the energy output, especially the heat stored in PCM layers, of the PV/T collector integrated with PCMs. In this work, panels with water fluid are embedded to PCM layer to make full use of the heat. A theoretical model of PV/T collector with PCM layer is presented to maximize its energy output. In addition, the thermal and electrical energy output and heat stored in PCM are presented. The influence of melting point and thickness of PCM on the energy output of the systems are analyzed in detail. The goals of this article are: (1) to analyze the electrical and thermal performance of the PV/T collector with PCM, (2) to evaluate the influences of the melting point of the PCM layer, and (3) to determine the optimal melting point and thickness of PCM layer to maximize electrical and thermal energy outputs. 2. Mathematical models The sectional view of the PV/T collectors with PCM is shown in Fig. 2, and the collector is mainly made up of: a protective tempered glass cover exposed to the ambient, an aluminum–alloy backplane, a PCM layer with embedded 2.54 cm diameter copper pipes through which the water flows, and an insulation layer. The thickness of tubes is 0.8 mm with center to center distance 6.66 cm. In order to simplify the calculation, the following assumptions have been made: (1) Mean temperature is assumed across each layer. (2) Horizontal temperature in each layer is uniform except for the water in pipes. (3) The radiant heat transfer and reflection of sunlight are neglected. (4) Heat capacities of the PV/T components are neglected. It is mainly because the equivalent heat capacity of the PCM in melting process is much larger than heat capacity of the PV/T components. The equivalent heat capacity of PCM using in this work is greater than 105 kJ/kg K when phase transition temperature variation range is less than 2 ◦ C. For PV/T components, the specific heat capacities rang from 0.5–1.25 kJ/kg K [22].
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D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 1. The schematic diagram of the PV/T collector with PCM.
Fig. 2. The sectional view of the PV/T collector with PCM.
Table 1 Design parameters for the PV/T collector used in the numerical model.
In this article, h represents the overall heat transfer coefficient between the component and fluid, for layer A and fluid B, it can be calculated as:
Parameters
Symbol
Value
Length of the PV module Width of the PV module Diameter of the pipe Thermal conductivity of the pipe Thickness of the pipe Packing factor of the solar cell Wind velocity Mass flow rate of water Specific heat capacity of water Thickness of the PCM Reference value Average efficiency of power plants
L W D t ıt F v ˙ m cw ıp ref , ˇref and Tref Tpower
1.8 m 1m 0.0254 m [15] 383 W/m K 0.0008 m 0.83 [23] 2 m/s [24,25] 0.03 kg/s 4.18 kJ/kg K 0.05 m 0.12, 0.0045 and 293 K 0.4
(5) The PV/T components reach quasi–steady state immediately while the environment temperature and solar radiation intensity change, except for the PCM layer. According to the above assumptions, a proposed numerical model of water–based PV/T collector incorporating PCM have been developed using one dimensional energy balance method. Furthermore, the convective heat transfer coefficient inside the pipes is taken into account, different from some References [7,23]. This work aims to acquire the parameters of PV/T collector incorporating PCM varied with time and evaluate thermal and electrical performance of system. Table 1 shows design parameters of the PV/T collector in this work. 2.1. Components of the PV/T collector
ıA 1 + A hB
−1 (2)
In addition, U is the overall heat transfer coefficient of two components. For consecutive layers C and D, they can be given as:
UCD =
ıD ıC + C D
−1 (3)
For PV cells, energy inflow happens through both incident energy and the heat transfer occurring between cover and PV module, and from the total inflow energy, one part is converted to electricity and the other part is transmitted to the backplane, it can be given by:
F˛c g I + Ugc Tg − Tc = F˛c g I + Ucb (Tc − Tb )
(1)
(4)
where F is the packing factor of the system. An empirical relationship between the cell temperature and the photovoltaic efficiency is given by Ref. [26]: = ref [1 − ˇref (Tc − Tref )]
(5)
For the backplane, it is similar to PV cells. Before the sunlight reaches backplane, a part of light passes through glass cover and PV cells, another part passes though only the cover. It can be described as:
Of the heat absorbed by glass cover from the incident sunlight, one part is lost to the ambient air and the other part is conducted to the PV cell. The energy balance equation can be described as: ˛g I = hge Tg − Te + Ugc Tg − Tc
hAB =
F˛b c g I + (1 − F) · ˛b g I + Ucb (Tc − Tb ) = Ubp Tb − Tp
(6)
For insulation layer, the energy balance equation is presented as follow:
Upi Tp − Ti = hie (Ti − Te )
(7)
D. Su et al. / Energy and Buildings 153 (2017) 382–391 Table 2 Thermo-physical parameters of the photovoltaic modules [23,27]. Materials
(W/m K)
˛
ı (m)
Glass Solar cell Backplane Insulation
1 145 0.36 0.034
0.91 0.09 0.00039 –
0.05 0.9 0.5 –
0.005 0.0003 0.0001 0.05
Table 3 The value of thermo-physical properties of the PCM [29].
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could be tailored to meet the application requirements by adjusting the mass ratio of PEG, and the melting point of PEG/MCS composites was range from 34.16 to 58.95 ◦ C. In addition, the melting point of alkane increases with the increasing number of carbon atoms while the heat of fusion remained approximately constant [31]. 2.3. The water flow The heat transfer from the PCM layer to the pipes increases the flowing water temperature. In can be written as:
Thermal property
Symbol
Value
Thermal conductivity (solid) Thermal conductivity (liquid) Specific heat capacity (solid) Specific heat capacity (liquid) Density (solid) Density (liquid) Latent heat
PCMs PCM cPCMs cPCMl PCMs PCM LH
0.24 W/m K 0.15 W/m K 2.9 kJ/kg K 2.1 kJ/kg K 860 kg/m3 780 kg/m3 210 kJ/kg
For the windward face of the glass cover, the convective heat transfer coefficient depends on the wind speed, and it is described by an empirical relationship as follows [24]: he = 5.7 + 3.8v
(8)
The heat conductivity (), transmissivity (), absorptivity (␣) and thickness (ı) of PV components are listed in Table 2. Design parameters of the PV/T collector for simulation are outlined in Table 2.
˙ · dTw Kpw Tp − Tw · D · dx = cw m
where Kpw is the overall heat transfer coefficient, and it can describe as:
1 ı ıt + PCMl + h t PCMl
Kpw =
−1 (11)
Form Eq. (10) the temperature of water Tw (x) can be obtained, described as:
Tw (x) = Tw,in − Tp e−Px + Tp
(12)
Dh
where P = c m˙ pw , is a factor introduced to simplify the equation. w w Tw,in is the inlet temperature of water. Suppose the flow distance x = L, the outlet temperature of water can be described as: Tw (L) = Tw,in Q + Tp (1 − Q )
2.2. PCM layer In the melting process, the heat transfer from the PV module to PCM layer is in the forms of heat conduction and natural convection. Rayleigh’s number determines the dominant heat transfer mode phase transition of PCM layer. When Ra ≤ 103 , the main heat transfer mode is heat conduction [28]. Table 3 shows a list of the PCM thermal parameters used by the simulation. According to Table 3, thermal properties of PCM in solid and liquid phase are different. During the latent phase, the thermal conductivity of the PCM depends on the ratio of the solid and liquid phases [29]. ıQPCM = WL · [Ubp (Tb − Tp )] − hpw (Tp − Tw ) − Upi (Tp − Ti )]ıt
(9)
If QPCM < Qsol ,
If Qsol < QPCM < Qliq , Tp = Tmp , p = PCMs ·
Qliq − QPCM Qliq − Qsol
+ PCMl ·
QPCM − Qsol Qliq − Qsol
T¯ w =
1 L
Tp = Tmp −
cPCMl
L
Tw (x) · dx = Tw,in R + Tp (1 − R)
where R = 1−Q is introduced to simplify the equation. RL In this work, hw is calculated according to flow regime, and it changes with the water temperature. The relational expressions are as follows. The forced convective heat transfer coefficient of water in pipes can be described as:
f · D
(15)
where represents kinematic viscosity and D is the diameter of channel. After a quantitative calculation, the water in channel is in transition state in present work. The Nusselt number of water flow can be estimated by:
Nu = 1.86 × Ref · Pr f · ,
P = PCMl
where QPCM is the cumulative heat flow into the PCM layer, and Qsol and Qliq refer to the cumulative heat flows required to complete solid and liquid phase changes respectively, and Tmp is the PCM melting point. In this work, the effect of phase change temperature on the output of the PV/T collector incorporating PCMs is analyzed, with an assumption that the PCMs have the same thermo-physical properties except melting point. There are two main reasons for making this assumption. One is that the effect of that single variable can be determined easily. Besides, this is a reasonable assumption. Qian et al. [30] found that thermal properties of PEG/MCS composites
(14)
0
If Qliq < QPCM , QPCM − Qliq
(13)
where Q = e−PL . Based on Eqs. (10) and (12), the mean temperature of water in the pipes is:
Re =
Q − QPCM Tp = Tmp − sol , P = PCMs cPCMs
(10)
D L
1/3 0.14 f
t
(16)
where Pr is the Prandtl number. The subscript f refers to the mean water temperature and t denotes the wall temperature of the tube. This correlation is able to meet the requirement of accuracy for engineering calculation under the following conditions: Re < 2200, Pr = 0.5∼1700,
f t
= 0.044∼9.8, Re · Pr ·
D > 10 (17) L
Hence, the convective heat transfer coefficient between water and PCM layer can be described by: hw = Nu ·
w D
(18)
386
D. Su et al. / Energy and Buildings 153 (2017) 382–391 Table 4 The design parameters of the PV/T collector with PCM [34]. Parameters
Value
Length of the PV module Width of the PV module Length of the container Width of the container Thickness of the PCM Volume of the PCM Latent heat of PCM Melting peak of the PCM Thermal conductivity of the PCM Specific heat capacity of the PCM (solid) Specific heat capacity of the PCM (liquid)
1200 mm 508 mm 1000 mm 471 mm 65 mm 28 L 210 kJ/kg 22.8 ◦ C 0.143 W/m K 1.45 kJ/kg 1.65 kJ/kg
Fig. 3. The hourly variation of solar radiation intensity and ambient temperature in a typical summer day of August 2014 in Nanjing.
2.4. Evaluation of performance parameters According to Ref. [23,32], the thermal power output of systems is given by: ˙ (L) − Tw,in ] Q˙ t = cw m[T
(19)
The electrical power of the PV/T collector is given by: Q˙ p = ˛c g FAI
(20)
where represents conversion efficiency of the solar cell, referred to as photovoltaic efficiency. The photovoltaic efficiency can be calculated from Eq. (5). In addition, electrical efficiency, which represents the efficiency converting solar into electricity by the PV/T systems, is also used in assessing the electrical performance of PV/T collector incorporating PCM. And electrical efficiencies can be calculated as [33]: p =
Q˙ p AI
(21)
3. Results and discussion Fig. 3 displays the values of solar radiation intensity and ambient temperature that can change over time in a typical summer day of August 2014 in Nanjing. Solar radiation intensity increases to a peak value at 12:00, and then tends to reduce to 0 after 19:00. Ambient temperature rises before 14:00, then decreases over time and finally keeps relative stability. This work assumes that the PV panel could be adjusted perpendicular to the direction of radiation, and the inclination angle of incident light and PV cells are neglected. During the daytime, PCM layer absorbs heat and brings down temperature of PV modules. The PV/T systems typically generate thermal energy in daylight, when most hot water demand is the lowest. In order to use the limited water resources efficiently, after 5 PM, water begins to be pumped into pipes with a stable flow velocity to extract the heat. In other words, the systems don’t supply hot water before 5 PM, because the fact that night will be a better time for pre-heated water supply than midday. The inlet temperature of water is 25 ◦ C. And the initial temperature of PCM layer is 25 ◦ Cat 7:00. The wind speeds on front and back of PV/T collector are 2 m/s and 0 m/s, respectively. It is an average speed throughout the day, determined in accordance with references, such as V = 1.5 [24] and V = 2.4 [25]. Considering the poor thermal conductivity of the insulation layer (0.034 W/m K), the wind speed on the back of the collector is assumed to be zero in order to simplify the calculation. The design parameters of the PV/T collector with PCM are shown
Fig. 4. The hourly variation of solar radiation intensity and ambient temperature in Dublin [34].
in Tables 1–3. In this work, MATLAB software is used to construct numerical models and to carry out numerical simulation. The water-based collector provides a higher real-time efficiency and the warmer outlet water at day, while the latter can effectively store energy and provides warmer outlet water at night. The advantage of a PV/T collector with PCM over a PV/T collector is the potential to shift the time of availability of thermal energy [34]. Making direct comparison between the collector in present work and a PV/T collector with all-day water cooling is unlikely to be reasonable. As a comparison, the thermal and electrical performance of a PV/T collector, whose PCMs layer is replaced by a same size copper plate with embedded tubes, is estimated. This system is also pumped into water after 5 PM for each of comparison studies. All calculation results, including the cell temperature, the electrical power, the electrical efficiency and thermal power output will be analyzed in detail. 3.1. Model validation Browne et al. [34] constructed and tested a PV/T system integrated a container filled by PCM eutectic (capric acid:palmitic acid = 75%:25%, weight) in Dublin, Ireland. Under the same conditions (shown in Table 4 and Fig. 4), a simulation on the temperature of the back of PV panel is carried out, using numerical method in present work. Comparison of the calculation and the actual experimental data is shown in Fig. 5. Two curves keep the same trend, which rises from 8:00 to 13:00 and then drops. For the temperature of the back of PV panel, the calculation results by the model present in this work are slightly higher than the experiment ones before 12:00. A big reason for the difference is that the melting point of PCM layer is assumed to be a fixed value, while the PCM melts from 17.7 ◦ C to 22.8 ◦ C. This assumption makes the tempera-
D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 5. Comparisons of the calculated results with experimental results.
Fig. 6. Variation of solar cell temperature with different melting point of PCM.
ture of PCM a little high during the melting process. The simulation results nicely follow the experiment data during 12:00 to 18:00, when the assumed and experimental values of melting point of PCM are close. After 18:00, the experiment results are little above the calculations. One possibility is that the heat exchange parameter between the collector side and the ambient has been neglected. As shown in Fig. 4, the ambient temperature is large while the solar radiation intensity is weak during this period, it indicates that the effect of heat transfer coefficient on the PV temperature is more obvious than at any other time. In general, simulation result is consistent with the experiment result. And the correlation coefficient between two curves is 0.988. 3.2. Electrical performance of PV/T collector incorporating PCM with different melting point The curves of solar cell temperature varying with time are represented in Fig. 6. Before 12:00, all curves are in an upward trend. In more detail, cell temperatures of the collectors with PCM layer have an entirely uniform trend up till around 9:00 AM, but then onwards the curves begin to separate slowly one by one due to their difference in melting points. The PCM layer melts at different time instances during the day and this leads to different PV cell temperatures. The higher melting point of PCM layer leads to higher cell temperature. From 12:00 to 17:00, curves decline obviously, and
387
Fig. 7. Variation of photovoltaic efficiency with different melting point of PCM.
the gap between the curves decreases. The key difference of 60 ◦ C melting point mode is that the cell temperature increases slightly up till around 13:00. It indicated that the 60 ◦ C melting point mode is more easily influenced by the ambient temperature, whose peak value at 14:00 as seen in Fig. 3. The curve of no PCM is much higher than that of other four kinds. It demonstrated that the cell temperature can be effectively decreased by incorporating PCM layer. After 17:00, higher the melting point, faster the decline. The reason is that temperature difference between PCM layer and flowing water influences heat transfer, and the thermal energy stored in PCM with higher meting point can be extracted more easily. Hence the cell temperature of PV/T collector with higher meting point PCM has more marked downward trend. For the 30 ◦ C melting point mode, it seems the cell temperature keeps stable after 20:00. That may be because the melting point of PCM layer is at lower temperature, due to which there is poor heat transfer rate with water. The curves of the 50 ◦ Cand 60 ◦ C melting point mode become flat after 21:00, it is because much of the heat in the PCM layer has been carried away within first 4 h. The 40 ◦ C melting point curve is the highest of the five curves from around 19:15–22:45, it seems that the temperature of PCM layer with 40 ◦ C melting point is the highest during this period. It is noting that the curve of no PCM almost vertical, due to the high thermal conductivity and low specific heat capacity of copper. The photovoltaic efficiency curves with respect to time are illustrated in Fig. 7. After 19:00, the solar radiation intensity drops to almost zero, so the photovoltaic efficiency is meaningless and can be ignored. The negative correlation between photovoltaic efficiency and the cell temperature is given by Eq. (5). The variation of photovoltaic efficiency is opposite to the variation of cell temperature. On the whole, the photovoltaic efficiency decreases as the melting point of PCM layer rises. For the collector with PCM layer, there curves drop from 7:00 to 12:00 and rise from 12:00 to 19:00, besides, the curve of 60 ◦ C melting point mode reached a minimum value of 8.66% at about 12:30. The average difference between 30 ◦ C and 60 ◦ C melting point mode is 0.26%, and the maximum difference in photovoltaic efficiency is 0.5% at 18:00. The photovoltaic efficiency of the collector without PCM layer get its valley value of 7.95% at 12:00. The changing curves of electrical power with respect to time are drawn in Fig. 8. The changing trends for different curves are the same, but with different degree of variations. Electrical power of the PV/T collector with PCMs increases from 7:00 to 12:00, obtains maximum at 12:00, then decreases from 12:00 to 17:00. It means the solar radiation intensity has greater influence on elec-
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Fig. 8. Variation of electrical power with different melting point of PCM.
Fig. 10. Variation of outlet temperature with different value of melting point. Fig. 9. Variation of electrical efficiency with different melting point of PCM.
trical power than ambient temperature. As shown in Eq. (20), the electrical power depends heavily on radiation intensity when the changes in photovoltaic efficiency are not obvious according to Fig. 7. The PV/T collector using PCM layer with a low melting point has high electrical power. Moreover, the electrical power differences between the four curves with PCM are much more significant at midday than other time period. And the maximum difference between the highest and lowest curves with PCM layer is 5.44 W at around 12:30. The differences of both photovoltaic efficiency and electrical power between those two curves reach the peak at the same time. It means increasing conversion efficiency of PV cells can still enhance the electrical power, especially at midday. By contrast of the two curve of 30 ◦ C melting point mode and no PCM mode, the biggest value of difference is 16.12 W at 12:00. In other words, the electrical power of the PV/T collector has increased around 13.6% by incorporating PCM layer with 30 ◦ C melting point. Variation of electrical efficiency with time is shown in Fig. 9. The curves of electrical efficiency obviously keep pace with changes of photovoltaic efficiency. The reason is that this variable only depends on photovoltaic efficiency according to Eqs. (20) and (21). Two curves intersect at around 18:00. It seems that the tempera-
ture of PCM layer with 60 ◦ C melting point already decreases, and it is in accordance with that of 50 ◦ C melting point case. A similar situation is also found for other intersections. In short, integrating PCM layer with low melting point into the PV/T collector has better electrical performance than high melting point mode. 3.3. Thermal performance of PV/T collector incorporating PCM with different melting point Variation of outlet temperature of water and thermal power output with time are shown in Figs. 10 and 11, respectively. All curves of thermal power output keep in step with the variation of outlet temperature, because these two parameters are positive correlation according to Eq. (19). As we all known, greater the difference in temperature, faster the heat flow rate. Between 17:00–18:00, the outlet water provided by 60 ◦ C melting point of PCM mode is the warmest than all other cases. But PCM with 60 ◦ C melting point loses thermal energy quickly, which leads to quick falling of PCM temperature. Further, with the PCM temperature falling, the outlet temperature of 60 ◦ C melting point mode declines at a slower rate than before, and almost keeps at a constant level after 21:00. The
D. Su et al. / Energy and Buildings 153 (2017) 382–391
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Fig. 11. Variation of thermal power output with different melting point of PCM.
Fig. 12. Variation of heat stored in PCM with different melting point of PCM.
curve of 40 ◦ C and 50 ◦ C melting point mode is in the same situation. Each curves of PCM mode have a trend of rise over a period of time. The reason for the phenomenon is that the PCM layer maintains in phase transition state. The heat loss caused by water flow leads to an increase in the ratio of PCM in the solid state, and thermal conductivity of PCM goes up, as seen in Eq. (9) and Table 3. Hence, all curves are rising slowly during the phase change process. The evolution of curve of 30 ◦ C melting point mode has distinct different with that of others PCM mode after pumping in water. The outlet temperature of 30 ◦ C melting point mode firstly decreases from 17:00 to 18:00, and then increases. The cause of this decline is that the temperature of PCM is warmer than its melting point during this period. And the heat exchange between PCM layer and the flowing water slows down, as the temperature of PCM layer cools to melting point. The curves of no PCM mode decreases for the whole time, and the decrease tendency is more and more slow. It changes with the solar radiation intensity, as seen in Fig. 3. The heat is mainly from the PV module, due to the low specific heat capacity and the high thermal conductivity of copper. According to Figs. 10 and 11, the 60 ◦ C melting point case can provide the warmest water for a while, and the outlet temperature and thermal power reach peaks
of 30.24 ◦ C and 1096 W, respectively, at 17:30. The 40 ◦ C melting point case can provide maximum up time with warm water from 17:00 to 22:00. In general, the 40 ◦ C, 50 ◦ C and 60 ◦ C melting point case provide warmer water than no PCM mode. The curves of thermal energy stored in PCM with respect to time are drawn in Fig. 12. It is concluded that PCM layer with lower melting point can store more thermal energy before 17:00, however, it is more difficult to extract the heat. The curves except 60 ◦ C melting point mode rise from 7:00 to 17:00, and drop from 17:00 to 24:00. The curve of 60 ◦ C melting point mode drop slightly before 17:00. The reason for this decline is that the PCM layer transmits heat to PV cell, due to the fact that the temperature of PCM in phase transition state is higher than the PV temperature at that time. As shown in Fig. 6, the solar cell temperature of 60 ◦ C melting point case is less than 60 ◦ C. Thermal energy obtained by 30 ◦ C melting point mode reaches a peak value of 10.6 MJ at 17:00 while this part of energy is still around 7.84 MJ at 24:00. It means the utilization ratio of thermal energy is so low in this case. In addition, the maximal rate of storing heat occurs at midday during energy storage process. The curves of thermal energy output with respect to time are shown in Fig. 13. Between 17:00–19:00, higher melting point mode
Fig. 13. Variation of thermal energy output with different melting point of PCM.
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D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 14. Variation of thermal energy output with different thickness of PCM.
gets higher thermal energy output. All curves rarely rise in a straight line for a while. After a period of time, the curves of 50 ◦ C and 60 ◦ C melting point mode rise slowly and intersect each other at around 19:00. The curves of 30 ◦ C melting point mode almost maintains a tendency of straight climb until 24:00. Ultimately, the PV/T collector incorporating PCM with 40 ◦ C melting point obtains a maximal thermal energy output, and the value is 8.21 MJ. The minimum value of energy output at midnight is 2.90 MJ, obtained by 30 ◦ C melting point case. The thermal energy output of no PCM mode is higher than that of 30 ◦ C melting point case. It is concluded that 30 ◦ C melting point case has little usefulness for the thermal energy output of the PV/T collector. The thumbnail graph represents the electrical energy output throughout a day. The variation trend of electrical energy in each mode is similar to the others. All curves rise with the time, and theirs change rates increase firstly and then decrease. The peak value of the maximum difference between the highest curve and lowest curve is 0.29 MJ. In order to maximize the thermal energy output, the PCM layer with 40 ◦ C melting point is optimal for the PV/T collector in this work. 3.4. Influence of thickness of PCM on energy output of PV/T collector with PCM layer For further enhancing the energy output of the PV/T system, the next step of simulation is performed by changing the thickness of the PCM layer to choose an appropriate size of PCM layer. The relation curves that thermal energy outputs vary with thickness of PCM are illustrated in Fig. 14. For the curves of 40 ◦ C and 50 ◦ C melting point mode, a period of increased trend is observed, following by a decreased period with the thickness increasing. If thickness of PCM layer equals to the optimal, the PCM layer absorbs enough heat from 7:00 to 17:00 and release amount of heat from 17:00 to 24:00, which the difference value between absorbing heat and releasing heat is the largest. The thermal energy output of 60 ◦ C melting point mode remains almost no changes. Particularly, the thermal energy output in 30 ◦ C melting point case is steadily falling with the thickness increasing. It is too slow for the heat exchange between PCM layer with 30 ◦ C melting point and the flowing water. Increasing of thickness further reduces the heat transfer coefficient between PCM and water. 3.4cm-thick PCM layer with 40 ◦ C melting point reaches a maximum of thermal energy output, and the value is 8.54 MJ. The relation curves that electrical energy outputs vary with thickness of PCM are illustrated in Fig. 15. The PV/T collector inte-
Fig. 15. Variation of electrical energy output with different thickness of PCM.
Fig. 16. Variation of equivalent energy output with different thickness of PCM.
grating PCM with low melting point has higher electrical energy output. The larger the thickness of the PCM layer, the larger thermal capacity of the PCM layer, but the smaller the heat transfer coefficient between PV module and PCM layer. 3.6cm-thick PCM layer with 30 ◦ C melting point gets a maximum of electrical energy output, and the value is 3.56 MJ. It is necessary to choose the appropriate thickness of the PCM layer for a PV/T collector, considering simultaneously electrical and thermal energy outputs. Besides, it is essential to introduce a conversion factor to compare the two outputs, due to electricity is in a higher grade form than thermal energy [3,33,35], given by: Q =
Qe + Qt power
(22)
where Q is the equivalent energy, introduced to compare electrical and thermal energy conveniently. power represents the average efficiency of power plants at national level and is taken as 0.4 in this work, because the efficiency of thermal power plant in China is around 40% to 42%. Variation of the equivalent energy output with thickness is shown in Fig. 16. The curves of the equivalent energy are similar to those of thermal energy outputs, as seen in Fig. 14. It is mainly because the electrical energy output maintains within a narrow range from 3.36 MJ to 3.56 MJ. In conclusion, the PV/T solar collec-
D. Su et al. / Energy and Buildings 153 (2017) 382–391
tor gets a maximum of energy output by incorporating 3.4cm-thick PCM layer with 40 ◦ C melting point in present work. 3.5. A simple estimation method for the power of the pump The motor power of the pump can be calculated by: N=
VHg pump
(23)
where V and H are the volumetric flow rate (m3 /s) and the pump head (m). The letter g is the gravitational acceleration, which has a value of 9.81 (m2 /s). And represents the density of working fluid, which the value is taken as 995 kg/m3 . pump is the pump efficiency and is taken as 0.8 in present work. The order of magnitude of the pump head is 1, due to the length of the PV module and the angle between the PV collector and the ground. According to the design of the PV/T collector in the calculation, the estimate result of the pump power is about 0.6 W. As seen in Fig. 11, all thermal power outputs are greater than this value, and the PV/T collector has a wide application prospect. 4. Conclusions In this work, the influences of PCM layer’s parameters, like melting point and thickness, on electrical and thermal performance of the PV/T collector incorporating PCM are simulated and discussed. Based on the above results, the following conclusions can be drawn: (1) The PV/T collector with PCM of 30 ◦ C melting point has the best electrical performance. In this case, the solar cell temperature increased to 80.0 ◦ C, which is the minimum value among all cases at 12:00. And the electrical power increased to 135 W, while the electrical efficiency decreased to 7.4% at midday. (2) The 60 ◦ C melting point case can provide the warmest water for a while, and the outlet temperature and thermal power reach peaks of 30.24 ◦ C and 1096 W, respectively, at 17:30. The 40 ◦ C melting point case can provide maximum up time with warm water from 17:00 to 22:00. (3) To maximize the thermal energy outputs, the PCM layer with 40 ◦ C melting point is optimal for the PV/T collector in this work. (4) The PV/T collector gets a maximum of overall energy output by incorporating 3.4cm-thick phase change material layer with 40 ◦ C melting point. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant nos. 51376087, 51676095). References [1] E. Skoplaki, J.A. Palyvos, Operating temperature of photovoltaic modules: a survey of pertinent correlations, Renew. Energy 34 (2009) 23–29. [2] M.H. Vishkasougheh, B. Tunaboylu, Simulation of high efficiency silicon solar cells with a hetero–junction microcrystalline intrinsic thin layer, Energy Convers. Manage. 72 (2013) 141–146. [3] T.T. Chow, A review on photovoltaic/thermal hybrid solar technology, Appl. Energy 87 (2010) 365–379. [4] A.N. Al-Shamani, K. Sopian, S. Mat, H.A. Hasan, A.M. Abed, M.H. Ruslan, Experimental studies of rectangular tube absorber photovoltaic thermal collector with various types of nanofluids under the tropical climate conditions, Energy Convers. Manage. 124 (2016) 528–542. [5] M. Herrando, C.N. Markides, K.A. Hellgardt, UK–based assessment of hybrid PV and solar–thermal systems for domestic heating and power: system performance, Appl. Energy 122 (2014) 288–309. [6] M.E.A. Slimani, M. Amirat, S. Bahria, I. Kurucz, M. Aouli, R. Sellami, Study and modeling of energy performance of a hybrid photovoltaic/thermal solar collector: configuration suitable for an indirect solar dryer, Energy Convers. Manage. 125 (2016) 209–221.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Maximizing the energy output of a photovoltaic–thermal solar collector incorporating phase change materials Di Su, Yuting Jia, Yaxue Lin, Guiyin Fang ∗ School of Physics, Nanjing University, Nanjing 210093, China
a r t i c l e
i n f o
Article history: Received 26 April 2017 Received in revised form 11 July 2017 Accepted 10 August 2017 Keywords: Solar energy Photovoltaic–thermal collector Electrical efficiency Phase change material Thermal energy storage Energy output
a b s t r a c t Photovoltaic–thermal collector can simultaneously generate both electricity and heat, making full use of the solar energy. It is worth to increase the electrical output by reducing the operating temperature. An effective method of cooling the cell temperature is incorporating phase change materials into the collector. In order to maximize the energy output and improve the performance of the collector, we perform comparative analyses on a hybrid photovoltaic–thermal solar collector incorporating phase change materials with different melting point. Solar cell temperature, electrical power, electrical efficiency, outlet temperature of water, thermal power output of the collector by varying melting point and thickness of phase change material layer are evaluated using one dimensional energy balance method. The corresponding graphical representations are described to explain the way of maximizing the electrical and thermal energy output of this system. And the numerical results have provided guidance for further experiment. In this theoretical work, it is found that phase change material layer with lower melting point has better electrical properties of the collector, while the heat stored in phase change material layer is more difficult to utilize. The results show that the photovoltaic–thermal solar collector gets a maximum of overall energy output by incorporating 3.4cm-thick phase change material layer with 40 ◦ C melting point. By contrast of the electrical power of 30 ◦ C melting point case and no phase change material case, the biggest value of difference is 16.12 W at 12:00. It means that the electrical power of the collector has increased around 13.6% by incorporating phase change material layer with 30 ◦ C melting point. © 2017 Elsevier B.V. All rights reserved.
1. Introduction As a clean renewable source, solar energy has good prospects for solving the energy and environment problems in the future. The photovoltaic (PV) technology is currently the most common way of converting the solar energy to electricity directly by using solar cells. For every 1 ◦ C rise in solar cell temperature, the electrical efficiency drops by around 0.45% [1]. Typically, the solar cells using silicon technology convert about 15%–25% of the solar radiation into electricity, and the remaining incident solar energy is converted to heat [2]. In order to enhance the solar cell efficiency and the energy output, it requires a device to remove this waste heat [3]. A practical method to prevent overheating of PV modules is embedding a thermal absorber to remove the exhaust heat. This combined system is known as the photovoltaic thermal (PV/T) col-
∗ Corresponding author. E-mail address: [email protected] (G. Fang). http://dx.doi.org/10.1016/j.enbuild.2017.08.027 0378-7788/© 2017 Elsevier B.V. All rights reserved.
lector, which can simultaneously generate both electricity and heat [4]. According to the type of working fluids used in absorber, the PV/T collectors can be divided into three types: air–based PV/T collector, water–based collector and combination of water/air collector. Up to now, several experimental, analytical and numerical studies on the performance evaluation of PV/T collectors have been performed by many researchers. Herrando et al. [5] developed a model to estimate the performance of PV/T systems based on domestic water, and achieved a higher overall efficiency than air–based systems. Slimani et al. [6] presented a PV/T solar collector embedded in an indirect solar dryer system. The calculation results showed that the hybrid PV/T collector provided a more suitable air temperature for drying agricultural products. Shan et al. [7] assessed the performance of a PV/T collector for water heating in building through numerical simulation methods, and the results showed that more number of series–connected PV cells lead to higher outlet temperature and lower electrical efficiency. The configurations of the PV/T collector have profound effects on the system performances. A comparative study was carried out in four solar devices: PV module, conventional hybrid solar air collector,
D. Su et al. / Energy and Buildings 153 (2017) 382–391
Nomenclature c D F h I K L ˙ m T U
v W x ␣ ı
Specific heat capacity (kJ/kg K) Diameter of the pipe (m) Packing factor Convective heat transfer coefficient (W/m2 K) Solar radiation intensity (W/m2 ) Overall heat transfer coefficient (W/m2 K) Length (m) Mass flow rate (kg/s) Temperature (K) Overall heat transfer coefficient (W/m2 K) Flow velocity (m/s) Width (m) Distance in flowing direction (m) Absorption coefficient Thickness (m) Dynamic viscosity Photovoltaic efficiency Thermal conductivity (W/m K) Transmission coefficient Kinematic viscosity (m2 /s)
Subscripts b Backplane c Solar cell e Environment Glass cover g i Insulation layer PCM layer p t Tube w Water flow ref Reference value at reference conditions
glazed hybrid solar air collector and glazed double–pass hybrid solar air collector. The fourth configuration reached the highest daily average of overall energy efficiency at 74% [8]. Su et al. [9] compared four configurations of the PV/T collector with dual channels, in which water and air were used as working fluids. This work gives guidance to select a suitable working fluid depending on different needs. Water is a good working fluid for the PV/T systems, due to its high heat conductivity and high specific heat capacity. Furthermore, to increase the efficiency of the PV/T systems, it seems to be a useful way to improve the thermal properties of the working fluid [10]. Another effective method of cooling the cell temperature is increasing thermal capacitance of the collector [11]. Phase change material (PCM) integrated into a PV module helps to limit the temperature of PV cells by absorbing heat when melting, because of its high latent heat capacity [12]. In fact, the PCM layer not only maintains appropriate temperature of the PV cells, but also acts as a heat sink storing the exhaust heat for a later use [13]. It is known that solar energy is intermittent, therefore thermal energy storage used in the PV/T collector can ameliorate this problem, by storing the heat during the day and releasing it at night. Over the years, the potential of the PV/T collector incorporating PCM has been demonstrated in theoretical simulations and experimental tests by researchers. A schematic diagram of the PV/T collectors with PCM is illustrated in Fig. 1. Stropnik et al. [14] designed a novel photovoltaic/thermal collector with PCM and investigated the thermal performance of this system. Results indicated that the addition of PCM was an effective means to enhance heat exchange between PV cells and absorber in a PV/T collector, and the maxi-
383
mum temperature difference on the surface of PV cells without PCM was 35.6 ◦ C higher than on a system with PCM. Al Imam et al. [15] examined energy storage incorporating PCM in the PV/T collector system with compound parabolic concentrator. For system with PCM, up to around 3 m from entrance, the plate temperature rose and then it stayed almost steady. But in case of applying same system without PCM, the plate temperature was sharp. Japs et al. [16] conducted an experimental analysis of two different PCMs used in PV/T system considering actual electricity prices. At the tests, the PCM with a higher thermal conductivity had a corresponding higher yield. Su et al. [17] performed comparative analyses on an air–based PV/T collector with PCM, and it was demonstrated that 3cm–thick PCM layer glued to PV cells was optimum both in electrical and thermal performance. Navarro et al. [18] tried to integrate PCM into a PV/T collector. The prototype was tested in the outdoors, and it was demonstrated that the PCM layer could achieve about 20% of energy savings compared to the PV/T collector with no PCM layer. Serale et al. [19] developed a physical–mathematical model for a solar collector with slurry–PCM, which increased the latent heat of the heat carrier fluid. Simulation results showed the PCM slurry could improve the efficiency of system about 20%–40%. Photovoltaic systems integrated PCM are often used in building, providing benefits of generating electricity and thermal management [20]. Lin et al. [21] compared the three types of buildings using PV/T collector only, using PCM only, and without using PV/T collectors and PCMs. The results showed that these two methods could effectively improve the indoor thermal performance of the house. However, few studies have been devoted to improve the energy output, especially the heat stored in PCM layers, of the PV/T collector integrated with PCMs. In this work, panels with water fluid are embedded to PCM layer to make full use of the heat. A theoretical model of PV/T collector with PCM layer is presented to maximize its energy output. In addition, the thermal and electrical energy output and heat stored in PCM are presented. The influence of melting point and thickness of PCM on the energy output of the systems are analyzed in detail. The goals of this article are: (1) to analyze the electrical and thermal performance of the PV/T collector with PCM, (2) to evaluate the influences of the melting point of the PCM layer, and (3) to determine the optimal melting point and thickness of PCM layer to maximize electrical and thermal energy outputs. 2. Mathematical models The sectional view of the PV/T collectors with PCM is shown in Fig. 2, and the collector is mainly made up of: a protective tempered glass cover exposed to the ambient, an aluminum–alloy backplane, a PCM layer with embedded 2.54 cm diameter copper pipes through which the water flows, and an insulation layer. The thickness of tubes is 0.8 mm with center to center distance 6.66 cm. In order to simplify the calculation, the following assumptions have been made: (1) Mean temperature is assumed across each layer. (2) Horizontal temperature in each layer is uniform except for the water in pipes. (3) The radiant heat transfer and reflection of sunlight are neglected. (4) Heat capacities of the PV/T components are neglected. It is mainly because the equivalent heat capacity of the PCM in melting process is much larger than heat capacity of the PV/T components. The equivalent heat capacity of PCM using in this work is greater than 105 kJ/kg K when phase transition temperature variation range is less than 2 ◦ C. For PV/T components, the specific heat capacities rang from 0.5–1.25 kJ/kg K [22].
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Fig. 1. The schematic diagram of the PV/T collector with PCM.
Fig. 2. The sectional view of the PV/T collector with PCM.
Table 1 Design parameters for the PV/T collector used in the numerical model.
In this article, h represents the overall heat transfer coefficient between the component and fluid, for layer A and fluid B, it can be calculated as:
Parameters
Symbol
Value
Length of the PV module Width of the PV module Diameter of the pipe Thermal conductivity of the pipe Thickness of the pipe Packing factor of the solar cell Wind velocity Mass flow rate of water Specific heat capacity of water Thickness of the PCM Reference value Average efficiency of power plants
L W D t ıt F v ˙ m cw ıp ref , ˇref and Tref Tpower
1.8 m 1m 0.0254 m [15] 383 W/m K 0.0008 m 0.83 [23] 2 m/s [24,25] 0.03 kg/s 4.18 kJ/kg K 0.05 m 0.12, 0.0045 and 293 K 0.4
(5) The PV/T components reach quasi–steady state immediately while the environment temperature and solar radiation intensity change, except for the PCM layer. According to the above assumptions, a proposed numerical model of water–based PV/T collector incorporating PCM have been developed using one dimensional energy balance method. Furthermore, the convective heat transfer coefficient inside the pipes is taken into account, different from some References [7,23]. This work aims to acquire the parameters of PV/T collector incorporating PCM varied with time and evaluate thermal and electrical performance of system. Table 1 shows design parameters of the PV/T collector in this work. 2.1. Components of the PV/T collector
ıA 1 + A hB
−1 (2)
In addition, U is the overall heat transfer coefficient of two components. For consecutive layers C and D, they can be given as:
UCD =
ıD ıC + C D
−1 (3)
For PV cells, energy inflow happens through both incident energy and the heat transfer occurring between cover and PV module, and from the total inflow energy, one part is converted to electricity and the other part is transmitted to the backplane, it can be given by:
F˛c g I + Ugc Tg − Tc = F˛c g I + Ucb (Tc − Tb )
(1)
(4)
where F is the packing factor of the system. An empirical relationship between the cell temperature and the photovoltaic efficiency is given by Ref. [26]: = ref [1 − ˇref (Tc − Tref )]
(5)
For the backplane, it is similar to PV cells. Before the sunlight reaches backplane, a part of light passes through glass cover and PV cells, another part passes though only the cover. It can be described as:
Of the heat absorbed by glass cover from the incident sunlight, one part is lost to the ambient air and the other part is conducted to the PV cell. The energy balance equation can be described as: ˛g I = hge Tg − Te + Ugc Tg − Tc
hAB =
F˛b c g I + (1 − F) · ˛b g I + Ucb (Tc − Tb ) = Ubp Tb − Tp
(6)
For insulation layer, the energy balance equation is presented as follow:
Upi Tp − Ti = hie (Ti − Te )
(7)
D. Su et al. / Energy and Buildings 153 (2017) 382–391 Table 2 Thermo-physical parameters of the photovoltaic modules [23,27]. Materials
(W/m K)
˛
ı (m)
Glass Solar cell Backplane Insulation
1 145 0.36 0.034
0.91 0.09 0.00039 –
0.05 0.9 0.5 –
0.005 0.0003 0.0001 0.05
Table 3 The value of thermo-physical properties of the PCM [29].
385
could be tailored to meet the application requirements by adjusting the mass ratio of PEG, and the melting point of PEG/MCS composites was range from 34.16 to 58.95 ◦ C. In addition, the melting point of alkane increases with the increasing number of carbon atoms while the heat of fusion remained approximately constant [31]. 2.3. The water flow The heat transfer from the PCM layer to the pipes increases the flowing water temperature. In can be written as:
Thermal property
Symbol
Value
Thermal conductivity (solid) Thermal conductivity (liquid) Specific heat capacity (solid) Specific heat capacity (liquid) Density (solid) Density (liquid) Latent heat
PCMs PCM cPCMs cPCMl PCMs PCM LH
0.24 W/m K 0.15 W/m K 2.9 kJ/kg K 2.1 kJ/kg K 860 kg/m3 780 kg/m3 210 kJ/kg
For the windward face of the glass cover, the convective heat transfer coefficient depends on the wind speed, and it is described by an empirical relationship as follows [24]: he = 5.7 + 3.8v
(8)
The heat conductivity (), transmissivity (), absorptivity (␣) and thickness (ı) of PV components are listed in Table 2. Design parameters of the PV/T collector for simulation are outlined in Table 2.
˙ · dTw Kpw Tp − Tw · D · dx = cw m
where Kpw is the overall heat transfer coefficient, and it can describe as:
1 ı ıt + PCMl + h t PCMl
Kpw =
−1 (11)
Form Eq. (10) the temperature of water Tw (x) can be obtained, described as:
Tw (x) = Tw,in − Tp e−Px + Tp
(12)
Dh
where P = c m˙ pw , is a factor introduced to simplify the equation. w w Tw,in is the inlet temperature of water. Suppose the flow distance x = L, the outlet temperature of water can be described as: Tw (L) = Tw,in Q + Tp (1 − Q )
2.2. PCM layer In the melting process, the heat transfer from the PV module to PCM layer is in the forms of heat conduction and natural convection. Rayleigh’s number determines the dominant heat transfer mode phase transition of PCM layer. When Ra ≤ 103 , the main heat transfer mode is heat conduction [28]. Table 3 shows a list of the PCM thermal parameters used by the simulation. According to Table 3, thermal properties of PCM in solid and liquid phase are different. During the latent phase, the thermal conductivity of the PCM depends on the ratio of the solid and liquid phases [29]. ıQPCM = WL · [Ubp (Tb − Tp )] − hpw (Tp − Tw ) − Upi (Tp − Ti )]ıt
(9)
If QPCM < Qsol ,
If Qsol < QPCM < Qliq , Tp = Tmp , p = PCMs ·
Qliq − QPCM Qliq − Qsol
+ PCMl ·
QPCM − Qsol Qliq − Qsol
T¯ w =
1 L
Tp = Tmp −
cPCMl
L
Tw (x) · dx = Tw,in R + Tp (1 − R)
where R = 1−Q is introduced to simplify the equation. RL In this work, hw is calculated according to flow regime, and it changes with the water temperature. The relational expressions are as follows. The forced convective heat transfer coefficient of water in pipes can be described as:
f · D
(15)
where represents kinematic viscosity and D is the diameter of channel. After a quantitative calculation, the water in channel is in transition state in present work. The Nusselt number of water flow can be estimated by:
Nu = 1.86 × Ref · Pr f · ,
P = PCMl
where QPCM is the cumulative heat flow into the PCM layer, and Qsol and Qliq refer to the cumulative heat flows required to complete solid and liquid phase changes respectively, and Tmp is the PCM melting point. In this work, the effect of phase change temperature on the output of the PV/T collector incorporating PCMs is analyzed, with an assumption that the PCMs have the same thermo-physical properties except melting point. There are two main reasons for making this assumption. One is that the effect of that single variable can be determined easily. Besides, this is a reasonable assumption. Qian et al. [30] found that thermal properties of PEG/MCS composites
(14)
0
If Qliq < QPCM , QPCM − Qliq
(13)
where Q = e−PL . Based on Eqs. (10) and (12), the mean temperature of water in the pipes is:
Re =
Q − QPCM Tp = Tmp − sol , P = PCMs cPCMs
(10)
D L
1/3 0.14 f
t
(16)
where Pr is the Prandtl number. The subscript f refers to the mean water temperature and t denotes the wall temperature of the tube. This correlation is able to meet the requirement of accuracy for engineering calculation under the following conditions: Re < 2200, Pr = 0.5∼1700,
f t
= 0.044∼9.8, Re · Pr ·
D > 10 (17) L
Hence, the convective heat transfer coefficient between water and PCM layer can be described by: hw = Nu ·
w D
(18)
386
D. Su et al. / Energy and Buildings 153 (2017) 382–391 Table 4 The design parameters of the PV/T collector with PCM [34]. Parameters
Value
Length of the PV module Width of the PV module Length of the container Width of the container Thickness of the PCM Volume of the PCM Latent heat of PCM Melting peak of the PCM Thermal conductivity of the PCM Specific heat capacity of the PCM (solid) Specific heat capacity of the PCM (liquid)
1200 mm 508 mm 1000 mm 471 mm 65 mm 28 L 210 kJ/kg 22.8 ◦ C 0.143 W/m K 1.45 kJ/kg 1.65 kJ/kg
Fig. 3. The hourly variation of solar radiation intensity and ambient temperature in a typical summer day of August 2014 in Nanjing.
2.4. Evaluation of performance parameters According to Ref. [23,32], the thermal power output of systems is given by: ˙ (L) − Tw,in ] Q˙ t = cw m[T
(19)
The electrical power of the PV/T collector is given by: Q˙ p = ˛c g FAI
(20)
where represents conversion efficiency of the solar cell, referred to as photovoltaic efficiency. The photovoltaic efficiency can be calculated from Eq. (5). In addition, electrical efficiency, which represents the efficiency converting solar into electricity by the PV/T systems, is also used in assessing the electrical performance of PV/T collector incorporating PCM. And electrical efficiencies can be calculated as [33]: p =
Q˙ p AI
(21)
3. Results and discussion Fig. 3 displays the values of solar radiation intensity and ambient temperature that can change over time in a typical summer day of August 2014 in Nanjing. Solar radiation intensity increases to a peak value at 12:00, and then tends to reduce to 0 after 19:00. Ambient temperature rises before 14:00, then decreases over time and finally keeps relative stability. This work assumes that the PV panel could be adjusted perpendicular to the direction of radiation, and the inclination angle of incident light and PV cells are neglected. During the daytime, PCM layer absorbs heat and brings down temperature of PV modules. The PV/T systems typically generate thermal energy in daylight, when most hot water demand is the lowest. In order to use the limited water resources efficiently, after 5 PM, water begins to be pumped into pipes with a stable flow velocity to extract the heat. In other words, the systems don’t supply hot water before 5 PM, because the fact that night will be a better time for pre-heated water supply than midday. The inlet temperature of water is 25 ◦ C. And the initial temperature of PCM layer is 25 ◦ Cat 7:00. The wind speeds on front and back of PV/T collector are 2 m/s and 0 m/s, respectively. It is an average speed throughout the day, determined in accordance with references, such as V = 1.5 [24] and V = 2.4 [25]. Considering the poor thermal conductivity of the insulation layer (0.034 W/m K), the wind speed on the back of the collector is assumed to be zero in order to simplify the calculation. The design parameters of the PV/T collector with PCM are shown
Fig. 4. The hourly variation of solar radiation intensity and ambient temperature in Dublin [34].
in Tables 1–3. In this work, MATLAB software is used to construct numerical models and to carry out numerical simulation. The water-based collector provides a higher real-time efficiency and the warmer outlet water at day, while the latter can effectively store energy and provides warmer outlet water at night. The advantage of a PV/T collector with PCM over a PV/T collector is the potential to shift the time of availability of thermal energy [34]. Making direct comparison between the collector in present work and a PV/T collector with all-day water cooling is unlikely to be reasonable. As a comparison, the thermal and electrical performance of a PV/T collector, whose PCMs layer is replaced by a same size copper plate with embedded tubes, is estimated. This system is also pumped into water after 5 PM for each of comparison studies. All calculation results, including the cell temperature, the electrical power, the electrical efficiency and thermal power output will be analyzed in detail. 3.1. Model validation Browne et al. [34] constructed and tested a PV/T system integrated a container filled by PCM eutectic (capric acid:palmitic acid = 75%:25%, weight) in Dublin, Ireland. Under the same conditions (shown in Table 4 and Fig. 4), a simulation on the temperature of the back of PV panel is carried out, using numerical method in present work. Comparison of the calculation and the actual experimental data is shown in Fig. 5. Two curves keep the same trend, which rises from 8:00 to 13:00 and then drops. For the temperature of the back of PV panel, the calculation results by the model present in this work are slightly higher than the experiment ones before 12:00. A big reason for the difference is that the melting point of PCM layer is assumed to be a fixed value, while the PCM melts from 17.7 ◦ C to 22.8 ◦ C. This assumption makes the tempera-
D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 5. Comparisons of the calculated results with experimental results.
Fig. 6. Variation of solar cell temperature with different melting point of PCM.
ture of PCM a little high during the melting process. The simulation results nicely follow the experiment data during 12:00 to 18:00, when the assumed and experimental values of melting point of PCM are close. After 18:00, the experiment results are little above the calculations. One possibility is that the heat exchange parameter between the collector side and the ambient has been neglected. As shown in Fig. 4, the ambient temperature is large while the solar radiation intensity is weak during this period, it indicates that the effect of heat transfer coefficient on the PV temperature is more obvious than at any other time. In general, simulation result is consistent with the experiment result. And the correlation coefficient between two curves is 0.988. 3.2. Electrical performance of PV/T collector incorporating PCM with different melting point The curves of solar cell temperature varying with time are represented in Fig. 6. Before 12:00, all curves are in an upward trend. In more detail, cell temperatures of the collectors with PCM layer have an entirely uniform trend up till around 9:00 AM, but then onwards the curves begin to separate slowly one by one due to their difference in melting points. The PCM layer melts at different time instances during the day and this leads to different PV cell temperatures. The higher melting point of PCM layer leads to higher cell temperature. From 12:00 to 17:00, curves decline obviously, and
387
Fig. 7. Variation of photovoltaic efficiency with different melting point of PCM.
the gap between the curves decreases. The key difference of 60 ◦ C melting point mode is that the cell temperature increases slightly up till around 13:00. It indicated that the 60 ◦ C melting point mode is more easily influenced by the ambient temperature, whose peak value at 14:00 as seen in Fig. 3. The curve of no PCM is much higher than that of other four kinds. It demonstrated that the cell temperature can be effectively decreased by incorporating PCM layer. After 17:00, higher the melting point, faster the decline. The reason is that temperature difference between PCM layer and flowing water influences heat transfer, and the thermal energy stored in PCM with higher meting point can be extracted more easily. Hence the cell temperature of PV/T collector with higher meting point PCM has more marked downward trend. For the 30 ◦ C melting point mode, it seems the cell temperature keeps stable after 20:00. That may be because the melting point of PCM layer is at lower temperature, due to which there is poor heat transfer rate with water. The curves of the 50 ◦ Cand 60 ◦ C melting point mode become flat after 21:00, it is because much of the heat in the PCM layer has been carried away within first 4 h. The 40 ◦ C melting point curve is the highest of the five curves from around 19:15–22:45, it seems that the temperature of PCM layer with 40 ◦ C melting point is the highest during this period. It is noting that the curve of no PCM almost vertical, due to the high thermal conductivity and low specific heat capacity of copper. The photovoltaic efficiency curves with respect to time are illustrated in Fig. 7. After 19:00, the solar radiation intensity drops to almost zero, so the photovoltaic efficiency is meaningless and can be ignored. The negative correlation between photovoltaic efficiency and the cell temperature is given by Eq. (5). The variation of photovoltaic efficiency is opposite to the variation of cell temperature. On the whole, the photovoltaic efficiency decreases as the melting point of PCM layer rises. For the collector with PCM layer, there curves drop from 7:00 to 12:00 and rise from 12:00 to 19:00, besides, the curve of 60 ◦ C melting point mode reached a minimum value of 8.66% at about 12:30. The average difference between 30 ◦ C and 60 ◦ C melting point mode is 0.26%, and the maximum difference in photovoltaic efficiency is 0.5% at 18:00. The photovoltaic efficiency of the collector without PCM layer get its valley value of 7.95% at 12:00. The changing curves of electrical power with respect to time are drawn in Fig. 8. The changing trends for different curves are the same, but with different degree of variations. Electrical power of the PV/T collector with PCMs increases from 7:00 to 12:00, obtains maximum at 12:00, then decreases from 12:00 to 17:00. It means the solar radiation intensity has greater influence on elec-
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D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 8. Variation of electrical power with different melting point of PCM.
Fig. 10. Variation of outlet temperature with different value of melting point. Fig. 9. Variation of electrical efficiency with different melting point of PCM.
trical power than ambient temperature. As shown in Eq. (20), the electrical power depends heavily on radiation intensity when the changes in photovoltaic efficiency are not obvious according to Fig. 7. The PV/T collector using PCM layer with a low melting point has high electrical power. Moreover, the electrical power differences between the four curves with PCM are much more significant at midday than other time period. And the maximum difference between the highest and lowest curves with PCM layer is 5.44 W at around 12:30. The differences of both photovoltaic efficiency and electrical power between those two curves reach the peak at the same time. It means increasing conversion efficiency of PV cells can still enhance the electrical power, especially at midday. By contrast of the two curve of 30 ◦ C melting point mode and no PCM mode, the biggest value of difference is 16.12 W at 12:00. In other words, the electrical power of the PV/T collector has increased around 13.6% by incorporating PCM layer with 30 ◦ C melting point. Variation of electrical efficiency with time is shown in Fig. 9. The curves of electrical efficiency obviously keep pace with changes of photovoltaic efficiency. The reason is that this variable only depends on photovoltaic efficiency according to Eqs. (20) and (21). Two curves intersect at around 18:00. It seems that the tempera-
ture of PCM layer with 60 ◦ C melting point already decreases, and it is in accordance with that of 50 ◦ C melting point case. A similar situation is also found for other intersections. In short, integrating PCM layer with low melting point into the PV/T collector has better electrical performance than high melting point mode. 3.3. Thermal performance of PV/T collector incorporating PCM with different melting point Variation of outlet temperature of water and thermal power output with time are shown in Figs. 10 and 11, respectively. All curves of thermal power output keep in step with the variation of outlet temperature, because these two parameters are positive correlation according to Eq. (19). As we all known, greater the difference in temperature, faster the heat flow rate. Between 17:00–18:00, the outlet water provided by 60 ◦ C melting point of PCM mode is the warmest than all other cases. But PCM with 60 ◦ C melting point loses thermal energy quickly, which leads to quick falling of PCM temperature. Further, with the PCM temperature falling, the outlet temperature of 60 ◦ C melting point mode declines at a slower rate than before, and almost keeps at a constant level after 21:00. The
D. Su et al. / Energy and Buildings 153 (2017) 382–391
389
Fig. 11. Variation of thermal power output with different melting point of PCM.
Fig. 12. Variation of heat stored in PCM with different melting point of PCM.
curve of 40 ◦ C and 50 ◦ C melting point mode is in the same situation. Each curves of PCM mode have a trend of rise over a period of time. The reason for the phenomenon is that the PCM layer maintains in phase transition state. The heat loss caused by water flow leads to an increase in the ratio of PCM in the solid state, and thermal conductivity of PCM goes up, as seen in Eq. (9) and Table 3. Hence, all curves are rising slowly during the phase change process. The evolution of curve of 30 ◦ C melting point mode has distinct different with that of others PCM mode after pumping in water. The outlet temperature of 30 ◦ C melting point mode firstly decreases from 17:00 to 18:00, and then increases. The cause of this decline is that the temperature of PCM is warmer than its melting point during this period. And the heat exchange between PCM layer and the flowing water slows down, as the temperature of PCM layer cools to melting point. The curves of no PCM mode decreases for the whole time, and the decrease tendency is more and more slow. It changes with the solar radiation intensity, as seen in Fig. 3. The heat is mainly from the PV module, due to the low specific heat capacity and the high thermal conductivity of copper. According to Figs. 10 and 11, the 60 ◦ C melting point case can provide the warmest water for a while, and the outlet temperature and thermal power reach peaks
of 30.24 ◦ C and 1096 W, respectively, at 17:30. The 40 ◦ C melting point case can provide maximum up time with warm water from 17:00 to 22:00. In general, the 40 ◦ C, 50 ◦ C and 60 ◦ C melting point case provide warmer water than no PCM mode. The curves of thermal energy stored in PCM with respect to time are drawn in Fig. 12. It is concluded that PCM layer with lower melting point can store more thermal energy before 17:00, however, it is more difficult to extract the heat. The curves except 60 ◦ C melting point mode rise from 7:00 to 17:00, and drop from 17:00 to 24:00. The curve of 60 ◦ C melting point mode drop slightly before 17:00. The reason for this decline is that the PCM layer transmits heat to PV cell, due to the fact that the temperature of PCM in phase transition state is higher than the PV temperature at that time. As shown in Fig. 6, the solar cell temperature of 60 ◦ C melting point case is less than 60 ◦ C. Thermal energy obtained by 30 ◦ C melting point mode reaches a peak value of 10.6 MJ at 17:00 while this part of energy is still around 7.84 MJ at 24:00. It means the utilization ratio of thermal energy is so low in this case. In addition, the maximal rate of storing heat occurs at midday during energy storage process. The curves of thermal energy output with respect to time are shown in Fig. 13. Between 17:00–19:00, higher melting point mode
Fig. 13. Variation of thermal energy output with different melting point of PCM.
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D. Su et al. / Energy and Buildings 153 (2017) 382–391
Fig. 14. Variation of thermal energy output with different thickness of PCM.
gets higher thermal energy output. All curves rarely rise in a straight line for a while. After a period of time, the curves of 50 ◦ C and 60 ◦ C melting point mode rise slowly and intersect each other at around 19:00. The curves of 30 ◦ C melting point mode almost maintains a tendency of straight climb until 24:00. Ultimately, the PV/T collector incorporating PCM with 40 ◦ C melting point obtains a maximal thermal energy output, and the value is 8.21 MJ. The minimum value of energy output at midnight is 2.90 MJ, obtained by 30 ◦ C melting point case. The thermal energy output of no PCM mode is higher than that of 30 ◦ C melting point case. It is concluded that 30 ◦ C melting point case has little usefulness for the thermal energy output of the PV/T collector. The thumbnail graph represents the electrical energy output throughout a day. The variation trend of electrical energy in each mode is similar to the others. All curves rise with the time, and theirs change rates increase firstly and then decrease. The peak value of the maximum difference between the highest curve and lowest curve is 0.29 MJ. In order to maximize the thermal energy output, the PCM layer with 40 ◦ C melting point is optimal for the PV/T collector in this work. 3.4. Influence of thickness of PCM on energy output of PV/T collector with PCM layer For further enhancing the energy output of the PV/T system, the next step of simulation is performed by changing the thickness of the PCM layer to choose an appropriate size of PCM layer. The relation curves that thermal energy outputs vary with thickness of PCM are illustrated in Fig. 14. For the curves of 40 ◦ C and 50 ◦ C melting point mode, a period of increased trend is observed, following by a decreased period with the thickness increasing. If thickness of PCM layer equals to the optimal, the PCM layer absorbs enough heat from 7:00 to 17:00 and release amount of heat from 17:00 to 24:00, which the difference value between absorbing heat and releasing heat is the largest. The thermal energy output of 60 ◦ C melting point mode remains almost no changes. Particularly, the thermal energy output in 30 ◦ C melting point case is steadily falling with the thickness increasing. It is too slow for the heat exchange between PCM layer with 30 ◦ C melting point and the flowing water. Increasing of thickness further reduces the heat transfer coefficient between PCM and water. 3.4cm-thick PCM layer with 40 ◦ C melting point reaches a maximum of thermal energy output, and the value is 8.54 MJ. The relation curves that electrical energy outputs vary with thickness of PCM are illustrated in Fig. 15. The PV/T collector inte-
Fig. 15. Variation of electrical energy output with different thickness of PCM.
Fig. 16. Variation of equivalent energy output with different thickness of PCM.
grating PCM with low melting point has higher electrical energy output. The larger the thickness of the PCM layer, the larger thermal capacity of the PCM layer, but the smaller the heat transfer coefficient between PV module and PCM layer. 3.6cm-thick PCM layer with 30 ◦ C melting point gets a maximum of electrical energy output, and the value is 3.56 MJ. It is necessary to choose the appropriate thickness of the PCM layer for a PV/T collector, considering simultaneously electrical and thermal energy outputs. Besides, it is essential to introduce a conversion factor to compare the two outputs, due to electricity is in a higher grade form than thermal energy [3,33,35], given by: Q =
Qe + Qt power
(22)
where Q is the equivalent energy, introduced to compare electrical and thermal energy conveniently. power represents the average efficiency of power plants at national level and is taken as 0.4 in this work, because the efficiency of thermal power plant in China is around 40% to 42%. Variation of the equivalent energy output with thickness is shown in Fig. 16. The curves of the equivalent energy are similar to those of thermal energy outputs, as seen in Fig. 14. It is mainly because the electrical energy output maintains within a narrow range from 3.36 MJ to 3.56 MJ. In conclusion, the PV/T solar collec-
D. Su et al. / Energy and Buildings 153 (2017) 382–391
tor gets a maximum of energy output by incorporating 3.4cm-thick PCM layer with 40 ◦ C melting point in present work. 3.5. A simple estimation method for the power of the pump The motor power of the pump can be calculated by: N=
VHg pump
(23)
where V and H are the volumetric flow rate (m3 /s) and the pump head (m). The letter g is the gravitational acceleration, which has a value of 9.81 (m2 /s). And represents the density of working fluid, which the value is taken as 995 kg/m3 . pump is the pump efficiency and is taken as 0.8 in present work. The order of magnitude of the pump head is 1, due to the length of the PV module and the angle between the PV collector and the ground. According to the design of the PV/T collector in the calculation, the estimate result of the pump power is about 0.6 W. As seen in Fig. 11, all thermal power outputs are greater than this value, and the PV/T collector has a wide application prospect. 4. Conclusions In this work, the influences of PCM layer’s parameters, like melting point and thickness, on electrical and thermal performance of the PV/T collector incorporating PCM are simulated and discussed. Based on the above results, the following conclusions can be drawn: (1) The PV/T collector with PCM of 30 ◦ C melting point has the best electrical performance. In this case, the solar cell temperature increased to 80.0 ◦ C, which is the minimum value among all cases at 12:00. And the electrical power increased to 135 W, while the electrical efficiency decreased to 7.4% at midday. (2) The 60 ◦ C melting point case can provide the warmest water for a while, and the outlet temperature and thermal power reach peaks of 30.24 ◦ C and 1096 W, respectively, at 17:30. The 40 ◦ C melting point case can provide maximum up time with warm water from 17:00 to 22:00. (3) To maximize the thermal energy outputs, the PCM layer with 40 ◦ C melting point is optimal for the PV/T collector in this work. (4) The PV/T collector gets a maximum of overall energy output by incorporating 3.4cm-thick phase change material layer with 40 ◦ C melting point. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant nos. 51376087, 51676095). References [1] E. Skoplaki, J.A. Palyvos, Operating temperature of photovoltaic modules: a survey of pertinent correlations, Renew. Energy 34 (2009) 23–29. [2] M.H. Vishkasougheh, B. Tunaboylu, Simulation of high efficiency silicon solar cells with a hetero–junction microcrystalline intrinsic thin layer, Energy Convers. Manage. 72 (2013) 141–146. [3] T.T. Chow, A review on photovoltaic/thermal hybrid solar technology, Appl. Energy 87 (2010) 365–379. [4] A.N. Al-Shamani, K. Sopian, S. Mat, H.A. Hasan, A.M. Abed, M.H. Ruslan, Experimental studies of rectangular tube absorber photovoltaic thermal collector with various types of nanofluids under the tropical climate conditions, Energy Convers. Manage. 124 (2016) 528–542. [5] M. Herrando, C.N. Markides, K.A. Hellgardt, UK–based assessment of hybrid PV and solar–thermal systems for domestic heating and power: system performance, Appl. Energy 122 (2014) 288–309. [6] M.E.A. Slimani, M. Amirat, S. Bahria, I. Kurucz, M. Aouli, R. Sellami, Study and modeling of energy performance of a hybrid photovoltaic/thermal solar collector: configuration suitable for an indirect solar dryer, Energy Convers. Manage. 125 (2016) 209–221.
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