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T) collector
Renewable Energy 77 (2015) 43e50
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A numerical investigation of a photovoltaic thermal (PV/T) collector Oussama Rejeb*, Houcine Dhaou, Abdelmajid Jemni Laboratoire d'Etudes des Syst emes Thermiques et Energ etiques, Rue Ibn Eljazzar, Ecole Nationale d'Ing enieurs de Monastir, Universit e de Monastir, Monastir 5019, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 July 2014 Accepted 4 December 2014 Available online
The photovoltaic thermal collector can provide thermal and heat power at the same time. In this paper, a photovoltaic/thermal sheet and tube collector has been numerically investigated. The paper focuses on the development of a hybrid solar collector PV/T. This model will be applied to optimize the operation of the PVT collector in the semi-arid climate. A mathematical model has been developed to determine the dynamic behavior of the collector, based on the energy balance of six main components namely a transparent cover, a PV module, a plate absorber, a tube, water in the tube and insulation. It has been validated by comparing the obtained simulation results with experimental results available in literature, where good agreement has been noted. Using our developed model, the heat and electrical power of sheet and tube collector has been analyzed for four typical days of year with the meteorological parameters of Monastir, Tunisia. Furthermore, the effect of solar radiation, the inlet water temperature, the number of glazing covers and the conductive heat transfer coefficient between plate absorber and PV module have been involved to identify their influence on the thermal and electrical efficiencies. The monthly thermal and electrical energies is also evaluated. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic thermal Electrical-performance Thermal-performance
1. Introduction The photovoltaic/thermal collector (PV/T) has been elaborated to provide both heat and electrical energies at the same time. The heat extracted from the PV modules by (cooling fluid) causes the cooling of the photovoltaic panels to stabilize its performances. It provides too useful heat that can be used for water heating. Raghuraman el al [1]. proposed a numerical model for liquid and air (PV/T) collector. A thermal efficiency of about 42% is obtained when air is used as a working fluid. Bergene [2] proposed a detailed model of the solar flat-plate with integrated Solar cells. The total efficiency of the system (electric þ thermal) was found in the range of 60e80%. Chow [3] developed an explicit dynamic model. The modeling gives a detailed analysis of the instantaneous thermal and electrical efficiencies. The performance of the collector is evaluated in terms of conduction heat transfer coefficients between the plate absorber and tubes and between the absorber and the PV module. A yield of 70% was obtained in the
* Corresponding author. Tel.: þ216 53918682; fax: þ216 73501579. E-mail addresses: [email protected], [email protected] (O. Rejeb). http://dx.doi.org/10.1016/j.renene.2014.12.012 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
event where the contacts are ideals. He el al [4]. carried out an experimental study of hybrid (PV/T) of an area of 1.34 m2.They used silicon polycrystalline PV cells, with a conversion effectiveness of 13%. The daily thermal efficiency obtained was approximately about 40%. Shan el al [5]. developed a numerical model to predict the transient performance of photovoltaicethermal collector with water heating in buildings for the environmental conditions of Jiangsu, China. They analyzed the effects of water mass flow rate and series-connected PVT module number on the performance of PV/T collector. They observed that when the mass flow of water increases and the PV modules connected in series decreases the performance of the collector PV/T improved. Dupeyrat el al. [6] made a numerical and experimental comparison between a thermal photovoltaic system, a conventional solar system and a conventional PV system. They pointed out that the (PVT) is the most advantageous system, in terms of energy and primary energy saving. Touafek el al. [7] designed and developed a mathematical model of a photovoltaic thermal collector for domestic air heating and electricity production. The maximum useful thermal power and thermal efficiency, for a sunny day studied, obtained were respectively 290 W and 48%. Several investigations on the effect of the thermal and electrical efficiencies of PV/T collector were carried out. Chow el al. [8]
44
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
Nomenclature A C k Pac G h Nu Ra Pr Pe t : m
surface area (m2) specific heat (JKg1 K 1 ) thermal conductivity (Wm1 K 1 ) packing factor solar irradiation (Wm2 ) heat transfer coefficient (Wm2 K 1 ) Nusselt number Rayleigh number Prandtl number perimeter (m) time (s) RMS mass flow rate (kgs1 ) root mean square percentage deviation
Greek
b d r
solar cell temperature coefficient (K 1 ) thickness (m) density (Kgm3 )
evaluated the performance of glazed PV/T and unglazed one. They showed that the exergetic efficiency of the unglazed collector is better than the glazed collector. Fujisawa el al. [9] evaluated experimentally the performance of PV/T single cover, uncover PV/T, PV module and flat plate collector. Their results showed that the electrical energy of the unglazed PV/T collector is better than the glazed PV/T collector. However, the thermal energy gain of cover PV/T is better than the PV/T uncover. Efficiency of (PV/T) collector is affected by the meteorological condition climatic (Solar radiation, ambient temperature and wind speed). Several studies were carried out in Hong Kong with a humid subtropical climate and in Europe. To the best knowledge of the authors, no attempt has been made in the previous works for the semi-arid climatic with hot summer and mild winter. The paper
h t ε
efficiency transmittance emissivity
Subscripts amb ambient env environnement g glazing PV photovoltaic module Pab absorber plate t tube w water i insulation cond conduction conv convection elec electrical out outlet in inlet th thermal Wi wind
focuses on the development of a hybrid solar collector PVT. This model will be applied to optimize the operation of the PVT collector in the semi-arid climate. The main objective of the present study is to state the evolution of heat and electrical gain under Monastir (Tunisia) climatic conditions. Furthermore, a parametric study has been conducted in order to analyze the electrical and thermal performances of PV/T collector. The monthly thermal and electrical energies is also evaluated. 2. Mathematical model The PV/T sheet and tube considered, in the current study, is shown in Fig. 1. It consists of glazing, PV module which has as a
Fig. 1. PV/T collector water.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
role of converting sunlight into electrical energy, a copper plate which has a role of absorbing sunlight, six tubes were attached to the absorber plate, in these tubes circulate coolant (water) which has a role of evacuating the heat stored by the absorber plate. Glass wool is used to minimize heat loss from the absorber plate and tubes. Various assumptions have been made to facilitate the theoretical analysis: The physical properties of the collector components are constant. The water flow rate in the tubes is presumably uniform. The temperature of the tube and the working fluid vary along with the y direction. The sky is assimilated as a blackbody.
For Plate absorber
rpab dpab Cpab
dTpab ¼ hcond;pv/pab Tpv Tpab dt Apab;t hcond;pab/t Tt Tpab þ Apab þ hcond;pab/i Ti Tpab þ kpab dpab
v2 Tpab ðx; yÞ
rt dt At dyCt
dTt ¼ Apab;t hcond;pab/t Tpab Tt dt þ Pehconv;t/f dy Tf Tt
ri di Ci
(4)
v2 y
(5)
Ai;t dTi ¼ hcond;t/i ðTt Ti Þ þ hcond;pab/i Tpab Ti dt Ai v2 Ti ðx; yÞ v2 Ti ðx; yÞ þ vx2 vy2
! (6)
The heat transfer coefficients used in the different energy balances equations cited above are given as follows: 2.1. Heat transfer coefficients 2.1.1. Radiative coefficients The radiation heat transfer coefficient between the glazing and sky, after assuming that the sky is a black body with a temperature of Tsky is obtained by using the following equation.
2 Tg þ Tsky hray;g/env ¼ εg s Tg2 þ Tsky
Table 1 Parameters used in simulations. Components
Parameters
Value
Unit
PV/T collector
Area, Ac Slope Thickness, dg Specific heat, Cg Density, rg Thermal conductivity, kg Emissivity, εg Specific heat, Cpv Thermal conductivity, kpv Emissivity, εpv Reference cell efficiency, h0 Packing factor, Pac Solar cell temperature coefficient, b Density, rpab Thermal conductivity, kpab Density, rt Thermal conductivity, kt Tube number Diameter of tube, D Thickness, dt Thickness, di Density, ri Thermal conductivity, kpv
1.5 35 0.004 670 2200 0.9 0.88 900 140 0.93 17.8 0.8 0.405 2702 310 2702 310 6 0.008 0.0012 0.05 20 0.030
m2 e m ðJ=kgKÞ ðkg=m3 Þ ðW=mKÞ ———— ðJ=kgKÞ ðW=mKÞ
Insulation
!
For Insulation
(1)
(2)
Tube
v2 Tt
dTf : ¼ Pehconv;t/f dy Tt Tf mCf DTf dt
þ hwi ðTamb Ti Þ þ ki di
Absorber Plate
vy2 (3)
þ Ai;t hcond;t/i ðTi Tt Þ þ kt dt
rf Af dyCf
dTpv ¼ apv Gtg þ hray;pv/g þ hconv;pv/g Tg Tpv rpv dpv Cpv dt Eelec þ hcond;pv/pab Tpab Tpv ! v2 Tpv ðx; yÞ v2 Tpv ðx; yÞ þ þ kpv dpv vx2 vy2
PV module
þ
Water in the tube
For PV module
Glazing
vx2
! v2 Tpab ðx; yÞ
For Tube
Considering these assumptions, the equations governing the heat transfer in various components of PV/T collector are given as follows: For glass cover
dTg ¼ av G þ hray;g/env Tsky Tg þ hwi Tamb Tg rg dg Cg dt þ hray;pv/g þ hconv;pv/g Tpv Tg ! v2 Tg ðx; yÞ v2 Tg ðx; yÞ þ kg dg þ vx2 vy2
45
(7)
% K1 ðkg=m3 Þ ðW=mKÞ ðkg=m3 Þ ðW=mKÞ e m m m ðkg=m3 Þ ðW=mKÞ
Fig. 2. Comparisons of numerical results of thermal and electrical efficiencies according to the reduced temperature ðTin Tamb Þ=G with experimental results [16].
46
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
Table 2 RMS values.
hwi ¼ 2:8 þ 3Vwi
RMS
Thermal efficiency
Electrical efficiency
0.575%
2.31224%
where s is the Stefan Boltzmann constant and εg is the emissivity of the glazing Swinbank [10] suggest a simple relation, between the sky temperature and the ambient temperature. 1:5 Tsky ¼ 0:0522*Tamb
(8)
The heat transfer radiation hray;pv/g between the glazing and the photovoltaic module is reported in Ref. [11]:
hray;pv/g ¼
2 s Tg2 þ Tpv Tg þ Tpv 1 εpv
þ ε1g 1
(9)
2.1.2. Conductive coefficients The convection heat transfer due to wind is estimated by the following correlation [12]:
(10)
The convective heat transfer coefficient hconv;pv/g between glass cover and PV is reported in Ref [13]:
hconv;pv/g ¼
Nua ka da
(11)
where ka ; da are respectively the thermal conductivity of air gap and the distance between the glass and the PV module. Nua is the Nusselt number, expressed by the following correlation [13]
# " 1708 1708ðsin qÞ1:66 * 1 Rada cos q Rada cos q " # ðRada cos qÞ0:33 þ 1 * 5830
Nua ¼ 1 þ 1:44 1
(12)
This expression is valid for tilt angles ranging from 0 to 75 The convective heat transfer coefficient,hconv;t/f , within the tube, Bejan [14] proposed a relation which is used in the current research.
Fig. 3. Variations of ambient temperature and the horizontal solar radiation of four topical days of meteorological parameters of Monastir namely 3 January, 20 April, 17 July and 8 October.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
47
Fig. 4. Variations of thermal and electrical power of PV/T collector.
0.17
0.80
0.8
0.20
0.16 0.60
0.16
Electrical efficiency
0.14
0.20
0.12 0.4 0.08
Electrical efficiency
Thermal efficiency
0.40
Thermal efficiency
0.15
Electrical efficiency
Thermal efficiency
0.6
0.2 0.04
0.13
0.12
0.00 20
40
60
80
Photovoltaic temperature (°C)
100
Fig. 5. Variations of thermal and electrical efficiencies with the PV temperature.
0.0
0.00 0
10
20
30
40
Inlet water temperature (°C)
Fig. 6. Variations of thermal and electrical efficiencies with the inlet water temperature.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50 0.20
0.80
0.80
0.16
0.16
Electrical efficiency
0.12 0.40 0.08
Thermal efficiency
0.60
0.60
Thermal efficiency
0.20
Electrical efficiency
48
0.12 0.40 0.08
0.20 0.04
0.20 0.04 0.00
0.00 0.2
0.4
200
400
600
Solar irradiance (W/m²)
800
0.8
1.0
Packing factor
0.00
0.00
0.6
1000
Fig. 9. Variation of the thermal and electrical efficiency with the packing factor.
Fig. 7. Variations of thermal and electrical efficiencies with solar radiation. :
Re < 23000Nut ¼ 4:364
(13)
Re > 23000Nut ¼ 0:023Re0:8 Pr0:4
(14)
2.1.3. Conduction coefficients The conduction heat transfer coefficient between two neighboring component layers m and n can be expressed by the following correlation [11]:
hcond;m/n ¼
1 dm km
(15)
þ kdn
hel ¼ h0 1 b Tpv 298
(17)
where h0 and b respectively represent the coefficient for photovoltaic conversion efficiency and coefficient for photovoltaic conversion efficiency at reference temperature (298 K). 3. Results and discussion
n
2.2. Expression of energy analysis In order to evaluate the performance of the PV/T system, the thermal and electrical efficiencies are calculated. The thermal efficiency of the PV/T can be described as [15] :
hth
m,Cp;f G and Ac are water flow rate, specific heat of water, solar radiation and area of collector, respectively. The electrical efficiency of the photovoltaic thermal collector is stated as [16]
mCp;f ðTout Tin Þ ¼ Ac G
(16)
In order to investigate the dynamic thermal and electrical behavior of PV/T collector, a finite volume method has been adopted to solve numerically the above system of equations (1)e(6). We have programmed our simulation in FORTRAN 90. The simulation carried out for the parameters values is summarized in Table 1. 3.1. Verification In order to validate the mathematical model proposed in this work, a comparison between our numerical results and experimental
0.8
0.20 0.60
0.20
0.16
0.4 0.08
0.40 0.12
0.08 0.20
Electrical effciency
0.12
Thermal effciency
0.16
Electrical efficiency
Thermal efficiency
0.6
0.2 0.04
0.0
0.00 0
1
2
Number of glass cover
Fig. 8. Variations of the thermal and electrical efficiencies for different numbers of glazing covers.
0.04
0.00
0.00
0
100
200
300
400
500
Conductive heat transfer coefficienct between module photovoltaic and plate absorber (W/m²K)
Fig. 10. Variations of the thermal and electrical efficiencies with the conductive heat transfer coefficient between the plate absorber and the PV module.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
49
Fig. 11. The predicted monthly electrical and thermal energy-outputs of PV/T sheet and tube collector.
results available in literature has been conducted. We have tested the validity of our numerical model under the same condition given by Bhattary [17]. A mean root square percentage deviation (RMS) is utilized. It is given by [18,19].
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP 2 u ½100X exp;i Xnum;i = Xexp;i t RMS ¼ nexp
(18)
where Xnum;i ,Xexp;i represent respectively the numerical and experimental values, nexp is the number of the experiments carried out. In Fig. 2, we have plotted the thermal and electrical efficiencies given by Bhattary [17] and our model. We have observed that the result of the current research is in good agreement with experimental results. In detail, the (RMS) are tabulated in Table 2. We have also noticed that our model is effective and it can be used to predict the performance of PV/T collector. 3.2. Results and discussion To study the PV/T collector behavior under Monastir climatic conditions, the numerical calculations have been carried out on four typical days of the year for meteorological parameters of Monastir namely 3 January, 20 April, 17 July and 8 October. The variations of ambient temperature and the horizontal solar radiation of four topical days are depicted in Fig. 3. With regard to these parameters, the variations of electrical and heat power are presented in Fig. 4. The maximum thermal and electrical power occurred in summer day and the minimum thermal and electrical power is observed in winter day. It's explained by the higher solar radiation in summer day and the lower solar radiation in winter day. The electrical and thermal powers are synchronized to the evolution of the solar radiation. Fig. 5 shows the variation of the thermal and electrical efficiencies with the PV temperature. The increase of the PV temperature decrease the electrical efficiency. However, the increase of PV temperature increase the thermal efficiency. Fig. 6 reports the variation of the thermal and electrical efficiencies with the inlet water temperature. Increasing the inlet temperature of water leads to an increase in the temperature of the PV module and therefore, its electrical efficiency decreases. Similarly, the thermal efficiency decreases according to an increase in
water inlet temperature. This is due to an increase in the level of the absorber temperature, consequently the thermal losses is on the rise. Fig. 7 shows the variation of the thermal and electrical efficiencies with solar radiation. The more of the solar radiation increases the temperature of PV, rises consequently, the electrical efficiency decreases. However, increasing the solar radiation leads to an increase in solar heat gain and hence thermal efficiency increases. solar energy due to high reflection and low transmisstance. The choice of a single glazed solar collector provides the best compatibility between electrical and thermal efficiencies. Fig. 8 illustrates the variations of the thermal and electrical efficiencies for different numbers of glazing covers. When the number of the glazing covers is increased, an increase and decrease of thermal efficiency and electrical efficiency are respectively observed. This could be explained by the fact that raising the number of glazing covers contributes, on one hand, to reduce heat losses and on the other hand, to minimizing the amount of absorbed solar energy due to high reflection and low transmisstance. The choice of a single glazed solar collector provides the best compatibility between electrical and thermal efficiencies. Fig. 9 shows the variation of the thermal and electrical efficiencies with the packing factor. An increase in the packing factor entails an increase in electrical efficiency. However, an increase in the packing factor leads to a decrease in thermal efficiency. The more the surface area of photovoltaic modules increases the more the electrical performance and hence the thermal efficiency decreases. Fig. 10 illustrates the variations of the thermal and electrical efficiencies with the conductive heat transfer coefficient between the plate absorber and the PV module. Increasing the conductive heat transfer between the plate absorber and the PV module leads to an increase in thermal and electrical efficiencies. Fig. 10 also shows that the increase of the conductive heat transfer between the plate absorber and the PV module, beyond 300 W/m2K vale, does not provide a significant improvement in thermal and electrical efficiencies. The monthly electrical and thermal output energies of photovoltaic thermal sheet and tube collector (see Fig. 1) by considering the Monastir climatic conditions are shown in Fig. 11. It can be seen that the maximum electrical and thermal output energy were respectively of 8.119 kWh/m2 and 49.44 kWh/m2. These results have been obtained in the month of July; which is characterized by the highest solar radiation in the year.
50
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
4. Conclusion In summary, a mathematical model for a solar photovoltaic thermal (PV/T) has been developed. The validity of this model is tested by comparing simulation results to experimental ones found in the literature [17]. A good agreement was obtained. A sensitivity analysis of same parameters has been made. Numerical results show that the increase of packing factor and heat conduction coefficient between the photovoltaic module and the plate absorber enhances electrical efficiency while both decreases with the increase of the inlet water temperature and the solar radiation. The thermal efficiency of the PV/T water collector increases with the solar radiation and heat conduction coefficient between the photovoltaic module and the plate absorber. However, it decreases with the rise of the inlet water temperature and the packing factor. The single cover glazing is a favorable choice to retain between the electrical and thermal efficiencies. Moreover, the monthly electrical and thermal output energies of photovoltaic thermal sheet and tube collector are examined under Monastir (Tunisia) climatic conditions. It is concluded that the uncovered PV/T yields the best electrical performance, payback period and economic efficiency. It has found that the maximum electrical and thermal output energy were respectively of 8119 kWh/m2 and 49,44 kWh/m2. Acknowledgments ne zo Head of the The first author would thank Pr. Christophe Me Chair INSA de Lyon/EDF «Habitats and Energy Innovations» e (CETHIL) for helpful discussions. References [1] Raghuraman P. Analytical predictions of liquid and air photovoltaic/thermal flat plate collector performance. J Sol Energy Eng 1981:103291e8.
[2] Bergene T, Lovvik OM. Model calculations on a flat-plate solar heat collector with integrated solar cells. Sol Energy 1995;55:453e462 55. [3] Chow TT. Performance analysis of photovoltaic-thermal collector by explicit dynamic model. Sol Energy 2003;75:143e52. [4] He W, Chow TT, Ji J, Lu J, Pei G, Chan LS. Hybrid photovoltaic and thermal solar collector designed for natural circulation of water. Appl Energy 2006;83: 199e210. [5] Shan F, Cao L, Fang GY. Dynamic performances modeling of a photovoltaicethermal collector with water heating in buildings. Energy Build 2013;66:485e94. ne zo C, Fortuinc S. Study of the thermal and electrical [6] Dupeyrat P, Me performances of PVT solar hot water system. Energy Build 2014;68: 751e5. [7] Touafek K, Haddadi M, Malek A. Design and modeling of a photovoltaic thermal collector for domestic air heating. Energy Build 2013;59:21e8. [8] Chow TT, Pei G, Fong KF, Lin Z, Chan ALS, Ji J. Energy and exergy analysis of photovoltaic-thermal collector with and without glass cover. Appl Energy 2009;86:310e6. [9] Fujisawa T, Tani T. Annual exergy evaluation on photovoltaicethermal hybrid collector. Sol Energy Mater Sol Cells 1997;47:135e48. [10] Swinbank WC, Roy QJ. Long-wave radiation from clear skies. Metereol Soc 1963;89:339. [11] Duffie JA, Beckman WA. Solar engineering of thermal processes. John Wiley &Sons, Inc; 1990. [12] Watmuff JH, Charters WWS, Proctor D. Solar and wind induced external coefficients solar collectors 2nd quarter. Rev Int d'Helio-technique 1977: 56. [13] Hollands KGT, Unny TE, Raithby GD, Konicek L. Free convective heat transfer across inclined air layers. J Heat Transfer ASME Trans 1976;98:189e93. [14] Bejan A. Heat transfer. New York: Wiley; 1993. [15] Sardarabadi M, Passandideh-Fard M, Zeinali Heris S. Experimental investigation of the effects of silica/water nanofluid on PV/T (photovoltaic thermal units). Energy 2014;66:264e72. [16] Evans DL. Simplified method for predicting photovoltaic array output. Sol Energy 1981;27:555e6. [17] Bhattarai S, Ohb JH, Euh SH, Kaflea GK, Kima DH. Simulation and model validation of sheet and tube type photovoltaic thermal solar system and conventional solar collecting system in transient states. Sol Energy Mater Sol Cells 2012;103:184e93. [18] Sobhnamayan F, Sarhaddi F, Alavi MA, Farahat S, Ajam H, Yazdanpanahi J. Optimization of a solar photovoltaic thermal (PV/T) water collector based on exergy concept. Renew Energy 2014;68:356e65. [19] Amori KE, Mustafa AAA. Field study of various air based photovoltaic/thermal hybrid solar collectors. Renew Energy 2014;63:402e14.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A numerical investigation of a photovoltaic thermal (PV/T) collector Oussama Rejeb*, Houcine Dhaou, Abdelmajid Jemni Laboratoire d'Etudes des Syst emes Thermiques et Energ etiques, Rue Ibn Eljazzar, Ecole Nationale d'Ing enieurs de Monastir, Universit e de Monastir, Monastir 5019, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 July 2014 Accepted 4 December 2014 Available online
The photovoltaic thermal collector can provide thermal and heat power at the same time. In this paper, a photovoltaic/thermal sheet and tube collector has been numerically investigated. The paper focuses on the development of a hybrid solar collector PV/T. This model will be applied to optimize the operation of the PVT collector in the semi-arid climate. A mathematical model has been developed to determine the dynamic behavior of the collector, based on the energy balance of six main components namely a transparent cover, a PV module, a plate absorber, a tube, water in the tube and insulation. It has been validated by comparing the obtained simulation results with experimental results available in literature, where good agreement has been noted. Using our developed model, the heat and electrical power of sheet and tube collector has been analyzed for four typical days of year with the meteorological parameters of Monastir, Tunisia. Furthermore, the effect of solar radiation, the inlet water temperature, the number of glazing covers and the conductive heat transfer coefficient between plate absorber and PV module have been involved to identify their influence on the thermal and electrical efficiencies. The monthly thermal and electrical energies is also evaluated. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic thermal Electrical-performance Thermal-performance
1. Introduction The photovoltaic/thermal collector (PV/T) has been elaborated to provide both heat and electrical energies at the same time. The heat extracted from the PV modules by (cooling fluid) causes the cooling of the photovoltaic panels to stabilize its performances. It provides too useful heat that can be used for water heating. Raghuraman el al [1]. proposed a numerical model for liquid and air (PV/T) collector. A thermal efficiency of about 42% is obtained when air is used as a working fluid. Bergene [2] proposed a detailed model of the solar flat-plate with integrated Solar cells. The total efficiency of the system (electric þ thermal) was found in the range of 60e80%. Chow [3] developed an explicit dynamic model. The modeling gives a detailed analysis of the instantaneous thermal and electrical efficiencies. The performance of the collector is evaluated in terms of conduction heat transfer coefficients between the plate absorber and tubes and between the absorber and the PV module. A yield of 70% was obtained in the
* Corresponding author. Tel.: þ216 53918682; fax: þ216 73501579. E-mail addresses: [email protected], [email protected] (O. Rejeb). http://dx.doi.org/10.1016/j.renene.2014.12.012 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
event where the contacts are ideals. He el al [4]. carried out an experimental study of hybrid (PV/T) of an area of 1.34 m2.They used silicon polycrystalline PV cells, with a conversion effectiveness of 13%. The daily thermal efficiency obtained was approximately about 40%. Shan el al [5]. developed a numerical model to predict the transient performance of photovoltaicethermal collector with water heating in buildings for the environmental conditions of Jiangsu, China. They analyzed the effects of water mass flow rate and series-connected PVT module number on the performance of PV/T collector. They observed that when the mass flow of water increases and the PV modules connected in series decreases the performance of the collector PV/T improved. Dupeyrat el al. [6] made a numerical and experimental comparison between a thermal photovoltaic system, a conventional solar system and a conventional PV system. They pointed out that the (PVT) is the most advantageous system, in terms of energy and primary energy saving. Touafek el al. [7] designed and developed a mathematical model of a photovoltaic thermal collector for domestic air heating and electricity production. The maximum useful thermal power and thermal efficiency, for a sunny day studied, obtained were respectively 290 W and 48%. Several investigations on the effect of the thermal and electrical efficiencies of PV/T collector were carried out. Chow el al. [8]
44
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
Nomenclature A C k Pac G h Nu Ra Pr Pe t : m
surface area (m2) specific heat (JKg1 K 1 ) thermal conductivity (Wm1 K 1 ) packing factor solar irradiation (Wm2 ) heat transfer coefficient (Wm2 K 1 ) Nusselt number Rayleigh number Prandtl number perimeter (m) time (s) RMS mass flow rate (kgs1 ) root mean square percentage deviation
Greek
b d r
solar cell temperature coefficient (K 1 ) thickness (m) density (Kgm3 )
evaluated the performance of glazed PV/T and unglazed one. They showed that the exergetic efficiency of the unglazed collector is better than the glazed collector. Fujisawa el al. [9] evaluated experimentally the performance of PV/T single cover, uncover PV/T, PV module and flat plate collector. Their results showed that the electrical energy of the unglazed PV/T collector is better than the glazed PV/T collector. However, the thermal energy gain of cover PV/T is better than the PV/T uncover. Efficiency of (PV/T) collector is affected by the meteorological condition climatic (Solar radiation, ambient temperature and wind speed). Several studies were carried out in Hong Kong with a humid subtropical climate and in Europe. To the best knowledge of the authors, no attempt has been made in the previous works for the semi-arid climatic with hot summer and mild winter. The paper
h t ε
efficiency transmittance emissivity
Subscripts amb ambient env environnement g glazing PV photovoltaic module Pab absorber plate t tube w water i insulation cond conduction conv convection elec electrical out outlet in inlet th thermal Wi wind
focuses on the development of a hybrid solar collector PVT. This model will be applied to optimize the operation of the PVT collector in the semi-arid climate. The main objective of the present study is to state the evolution of heat and electrical gain under Monastir (Tunisia) climatic conditions. Furthermore, a parametric study has been conducted in order to analyze the electrical and thermal performances of PV/T collector. The monthly thermal and electrical energies is also evaluated. 2. Mathematical model The PV/T sheet and tube considered, in the current study, is shown in Fig. 1. It consists of glazing, PV module which has as a
Fig. 1. PV/T collector water.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
role of converting sunlight into electrical energy, a copper plate which has a role of absorbing sunlight, six tubes were attached to the absorber plate, in these tubes circulate coolant (water) which has a role of evacuating the heat stored by the absorber plate. Glass wool is used to minimize heat loss from the absorber plate and tubes. Various assumptions have been made to facilitate the theoretical analysis: The physical properties of the collector components are constant. The water flow rate in the tubes is presumably uniform. The temperature of the tube and the working fluid vary along with the y direction. The sky is assimilated as a blackbody.
For Plate absorber
rpab dpab Cpab
dTpab ¼ hcond;pv/pab Tpv Tpab dt Apab;t hcond;pab/t Tt Tpab þ Apab þ hcond;pab/i Ti Tpab þ kpab dpab
v2 Tpab ðx; yÞ
rt dt At dyCt
dTt ¼ Apab;t hcond;pab/t Tpab Tt dt þ Pehconv;t/f dy Tf Tt
ri di Ci
(4)
v2 y
(5)
Ai;t dTi ¼ hcond;t/i ðTt Ti Þ þ hcond;pab/i Tpab Ti dt Ai v2 Ti ðx; yÞ v2 Ti ðx; yÞ þ vx2 vy2
! (6)
The heat transfer coefficients used in the different energy balances equations cited above are given as follows: 2.1. Heat transfer coefficients 2.1.1. Radiative coefficients The radiation heat transfer coefficient between the glazing and sky, after assuming that the sky is a black body with a temperature of Tsky is obtained by using the following equation.
2 Tg þ Tsky hray;g/env ¼ εg s Tg2 þ Tsky
Table 1 Parameters used in simulations. Components
Parameters
Value
Unit
PV/T collector
Area, Ac Slope Thickness, dg Specific heat, Cg Density, rg Thermal conductivity, kg Emissivity, εg Specific heat, Cpv Thermal conductivity, kpv Emissivity, εpv Reference cell efficiency, h0 Packing factor, Pac Solar cell temperature coefficient, b Density, rpab Thermal conductivity, kpab Density, rt Thermal conductivity, kt Tube number Diameter of tube, D Thickness, dt Thickness, di Density, ri Thermal conductivity, kpv
1.5 35 0.004 670 2200 0.9 0.88 900 140 0.93 17.8 0.8 0.405 2702 310 2702 310 6 0.008 0.0012 0.05 20 0.030
m2 e m ðJ=kgKÞ ðkg=m3 Þ ðW=mKÞ ———— ðJ=kgKÞ ðW=mKÞ
Insulation
!
For Insulation
(1)
(2)
Tube
v2 Tt
dTf : ¼ Pehconv;t/f dy Tt Tf mCf DTf dt
þ hwi ðTamb Ti Þ þ ki di
Absorber Plate
vy2 (3)
þ Ai;t hcond;t/i ðTi Tt Þ þ kt dt
rf Af dyCf
dTpv ¼ apv Gtg þ hray;pv/g þ hconv;pv/g Tg Tpv rpv dpv Cpv dt Eelec þ hcond;pv/pab Tpab Tpv ! v2 Tpv ðx; yÞ v2 Tpv ðx; yÞ þ þ kpv dpv vx2 vy2
PV module
þ
Water in the tube
For PV module
Glazing
vx2
! v2 Tpab ðx; yÞ
For Tube
Considering these assumptions, the equations governing the heat transfer in various components of PV/T collector are given as follows: For glass cover
dTg ¼ av G þ hray;g/env Tsky Tg þ hwi Tamb Tg rg dg Cg dt þ hray;pv/g þ hconv;pv/g Tpv Tg ! v2 Tg ðx; yÞ v2 Tg ðx; yÞ þ kg dg þ vx2 vy2
45
(7)
% K1 ðkg=m3 Þ ðW=mKÞ ðkg=m3 Þ ðW=mKÞ e m m m ðkg=m3 Þ ðW=mKÞ
Fig. 2. Comparisons of numerical results of thermal and electrical efficiencies according to the reduced temperature ðTin Tamb Þ=G with experimental results [16].
46
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
Table 2 RMS values.
hwi ¼ 2:8 þ 3Vwi
RMS
Thermal efficiency
Electrical efficiency
0.575%
2.31224%
where s is the Stefan Boltzmann constant and εg is the emissivity of the glazing Swinbank [10] suggest a simple relation, between the sky temperature and the ambient temperature. 1:5 Tsky ¼ 0:0522*Tamb
(8)
The heat transfer radiation hray;pv/g between the glazing and the photovoltaic module is reported in Ref. [11]:
hray;pv/g ¼
2 s Tg2 þ Tpv Tg þ Tpv 1 εpv
þ ε1g 1
(9)
2.1.2. Conductive coefficients The convection heat transfer due to wind is estimated by the following correlation [12]:
(10)
The convective heat transfer coefficient hconv;pv/g between glass cover and PV is reported in Ref [13]:
hconv;pv/g ¼
Nua ka da
(11)
where ka ; da are respectively the thermal conductivity of air gap and the distance between the glass and the PV module. Nua is the Nusselt number, expressed by the following correlation [13]
# " 1708 1708ðsin qÞ1:66 * 1 Rada cos q Rada cos q " # ðRada cos qÞ0:33 þ 1 * 5830
Nua ¼ 1 þ 1:44 1
(12)
This expression is valid for tilt angles ranging from 0 to 75 The convective heat transfer coefficient,hconv;t/f , within the tube, Bejan [14] proposed a relation which is used in the current research.
Fig. 3. Variations of ambient temperature and the horizontal solar radiation of four topical days of meteorological parameters of Monastir namely 3 January, 20 April, 17 July and 8 October.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
47
Fig. 4. Variations of thermal and electrical power of PV/T collector.
0.17
0.80
0.8
0.20
0.16 0.60
0.16
Electrical efficiency
0.14
0.20
0.12 0.4 0.08
Electrical efficiency
Thermal efficiency
0.40
Thermal efficiency
0.15
Electrical efficiency
Thermal efficiency
0.6
0.2 0.04
0.13
0.12
0.00 20
40
60
80
Photovoltaic temperature (°C)
100
Fig. 5. Variations of thermal and electrical efficiencies with the PV temperature.
0.0
0.00 0
10
20
30
40
Inlet water temperature (°C)
Fig. 6. Variations of thermal and electrical efficiencies with the inlet water temperature.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50 0.20
0.80
0.80
0.16
0.16
Electrical efficiency
0.12 0.40 0.08
Thermal efficiency
0.60
0.60
Thermal efficiency
0.20
Electrical efficiency
48
0.12 0.40 0.08
0.20 0.04
0.20 0.04 0.00
0.00 0.2
0.4
200
400
600
Solar irradiance (W/m²)
800
0.8
1.0
Packing factor
0.00
0.00
0.6
1000
Fig. 9. Variation of the thermal and electrical efficiency with the packing factor.
Fig. 7. Variations of thermal and electrical efficiencies with solar radiation. :
Re < 23000Nut ¼ 4:364
(13)
Re > 23000Nut ¼ 0:023Re0:8 Pr0:4
(14)
2.1.3. Conduction coefficients The conduction heat transfer coefficient between two neighboring component layers m and n can be expressed by the following correlation [11]:
hcond;m/n ¼
1 dm km
(15)
þ kdn
hel ¼ h0 1 b Tpv 298
(17)
where h0 and b respectively represent the coefficient for photovoltaic conversion efficiency and coefficient for photovoltaic conversion efficiency at reference temperature (298 K). 3. Results and discussion
n
2.2. Expression of energy analysis In order to evaluate the performance of the PV/T system, the thermal and electrical efficiencies are calculated. The thermal efficiency of the PV/T can be described as [15] :
hth
m,Cp;f G and Ac are water flow rate, specific heat of water, solar radiation and area of collector, respectively. The electrical efficiency of the photovoltaic thermal collector is stated as [16]
mCp;f ðTout Tin Þ ¼ Ac G
(16)
In order to investigate the dynamic thermal and electrical behavior of PV/T collector, a finite volume method has been adopted to solve numerically the above system of equations (1)e(6). We have programmed our simulation in FORTRAN 90. The simulation carried out for the parameters values is summarized in Table 1. 3.1. Verification In order to validate the mathematical model proposed in this work, a comparison between our numerical results and experimental
0.8
0.20 0.60
0.20
0.16
0.4 0.08
0.40 0.12
0.08 0.20
Electrical effciency
0.12
Thermal effciency
0.16
Electrical efficiency
Thermal efficiency
0.6
0.2 0.04
0.0
0.00 0
1
2
Number of glass cover
Fig. 8. Variations of the thermal and electrical efficiencies for different numbers of glazing covers.
0.04
0.00
0.00
0
100
200
300
400
500
Conductive heat transfer coefficienct between module photovoltaic and plate absorber (W/m²K)
Fig. 10. Variations of the thermal and electrical efficiencies with the conductive heat transfer coefficient between the plate absorber and the PV module.
O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
49
Fig. 11. The predicted monthly electrical and thermal energy-outputs of PV/T sheet and tube collector.
results available in literature has been conducted. We have tested the validity of our numerical model under the same condition given by Bhattary [17]. A mean root square percentage deviation (RMS) is utilized. It is given by [18,19].
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP 2 u ½100X exp;i Xnum;i = Xexp;i t RMS ¼ nexp
(18)
where Xnum;i ,Xexp;i represent respectively the numerical and experimental values, nexp is the number of the experiments carried out. In Fig. 2, we have plotted the thermal and electrical efficiencies given by Bhattary [17] and our model. We have observed that the result of the current research is in good agreement with experimental results. In detail, the (RMS) are tabulated in Table 2. We have also noticed that our model is effective and it can be used to predict the performance of PV/T collector. 3.2. Results and discussion To study the PV/T collector behavior under Monastir climatic conditions, the numerical calculations have been carried out on four typical days of the year for meteorological parameters of Monastir namely 3 January, 20 April, 17 July and 8 October. The variations of ambient temperature and the horizontal solar radiation of four topical days are depicted in Fig. 3. With regard to these parameters, the variations of electrical and heat power are presented in Fig. 4. The maximum thermal and electrical power occurred in summer day and the minimum thermal and electrical power is observed in winter day. It's explained by the higher solar radiation in summer day and the lower solar radiation in winter day. The electrical and thermal powers are synchronized to the evolution of the solar radiation. Fig. 5 shows the variation of the thermal and electrical efficiencies with the PV temperature. The increase of the PV temperature decrease the electrical efficiency. However, the increase of PV temperature increase the thermal efficiency. Fig. 6 reports the variation of the thermal and electrical efficiencies with the inlet water temperature. Increasing the inlet temperature of water leads to an increase in the temperature of the PV module and therefore, its electrical efficiency decreases. Similarly, the thermal efficiency decreases according to an increase in
water inlet temperature. This is due to an increase in the level of the absorber temperature, consequently the thermal losses is on the rise. Fig. 7 shows the variation of the thermal and electrical efficiencies with solar radiation. The more of the solar radiation increases the temperature of PV, rises consequently, the electrical efficiency decreases. However, increasing the solar radiation leads to an increase in solar heat gain and hence thermal efficiency increases. solar energy due to high reflection and low transmisstance. The choice of a single glazed solar collector provides the best compatibility between electrical and thermal efficiencies. Fig. 8 illustrates the variations of the thermal and electrical efficiencies for different numbers of glazing covers. When the number of the glazing covers is increased, an increase and decrease of thermal efficiency and electrical efficiency are respectively observed. This could be explained by the fact that raising the number of glazing covers contributes, on one hand, to reduce heat losses and on the other hand, to minimizing the amount of absorbed solar energy due to high reflection and low transmisstance. The choice of a single glazed solar collector provides the best compatibility between electrical and thermal efficiencies. Fig. 9 shows the variation of the thermal and electrical efficiencies with the packing factor. An increase in the packing factor entails an increase in electrical efficiency. However, an increase in the packing factor leads to a decrease in thermal efficiency. The more the surface area of photovoltaic modules increases the more the electrical performance and hence the thermal efficiency decreases. Fig. 10 illustrates the variations of the thermal and electrical efficiencies with the conductive heat transfer coefficient between the plate absorber and the PV module. Increasing the conductive heat transfer between the plate absorber and the PV module leads to an increase in thermal and electrical efficiencies. Fig. 10 also shows that the increase of the conductive heat transfer between the plate absorber and the PV module, beyond 300 W/m2K vale, does not provide a significant improvement in thermal and electrical efficiencies. The monthly electrical and thermal output energies of photovoltaic thermal sheet and tube collector (see Fig. 1) by considering the Monastir climatic conditions are shown in Fig. 11. It can be seen that the maximum electrical and thermal output energy were respectively of 8.119 kWh/m2 and 49.44 kWh/m2. These results have been obtained in the month of July; which is characterized by the highest solar radiation in the year.
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O. Rejeb et al. / Renewable Energy 77 (2015) 43e50
4. Conclusion In summary, a mathematical model for a solar photovoltaic thermal (PV/T) has been developed. The validity of this model is tested by comparing simulation results to experimental ones found in the literature [17]. A good agreement was obtained. A sensitivity analysis of same parameters has been made. Numerical results show that the increase of packing factor and heat conduction coefficient between the photovoltaic module and the plate absorber enhances electrical efficiency while both decreases with the increase of the inlet water temperature and the solar radiation. The thermal efficiency of the PV/T water collector increases with the solar radiation and heat conduction coefficient between the photovoltaic module and the plate absorber. However, it decreases with the rise of the inlet water temperature and the packing factor. The single cover glazing is a favorable choice to retain between the electrical and thermal efficiencies. Moreover, the monthly electrical and thermal output energies of photovoltaic thermal sheet and tube collector are examined under Monastir (Tunisia) climatic conditions. It is concluded that the uncovered PV/T yields the best electrical performance, payback period and economic efficiency. It has found that the maximum electrical and thermal output energy were respectively of 8119 kWh/m2 and 49,44 kWh/m2. Acknowledgments ne zo Head of the The first author would thank Pr. Christophe Me Chair INSA de Lyon/EDF «Habitats and Energy Innovations» e (CETHIL) for helpful discussions. References [1] Raghuraman P. Analytical predictions of liquid and air photovoltaic/thermal flat plate collector performance. J Sol Energy Eng 1981:103291e8.
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