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T system
Energy 37 (2012) 384e395
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Performance study and parametric analysis of a novel heat pipe PV/T system Pei Gang*, Fu Huide, Zhu Huijuan, Ji Jie* Department of Thermal Science and Energy Engineering, University of Science and Technology of China, #96 Jinzhai Road, Hefei City, Anhui Province 230026, People’s Republic of China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2011 Received in revised form 10 October 2011 Accepted 10 November 2011 Available online 14 December 2011
A novel heat pipe photovoltaic/thermal (PV/T) system that could simultaneously supply electrical and thermal energy was proposed. Compared with a traditional water-type PV/T system, the heat pipe PV/T system can be used in cold regions without becoming frozen. A dynamic model of the heat pipe PV/T system was presented, and a test rig was constructed. Experiments were conducted to validate the results of the simulation. Based on the validated model, the performances of the heat pipe PV/T system were studied under different parametric conditions, such as water flow rates, PV cell covering factor of the collector, tube space of heat pipes, and kinds of solar absorptive coatings of the absorber plate. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heat pipe Photovoltaic/thermal Solar collector
1. Introduction The photovoltaic/thermal (PV/T) collector is an integration of PV cells and a solar thermal collector in a single unit, which can simultaneously generate electrical and thermal energy. Heat carriers, such as water or air, take in heat extracted from PV cells. The cells are then cooled, thereby improving the yield of electricity. Several investigations on PV/T collector/systems have been previously carried out. Zondag [1] reported that Martin Wolf presented the first work on a flat-plate PV/T collector [2]. Other researchers have subsequently undertaken studies on the PV/T collector/system. Raghuraman [3] presented two separate 1D mathematical models to predict the performance of water and air PV/T flat-plate collectors. He then compared the results with the experimental data. Design recommendations were also made to maximize the total energy extracted from the collectors. Tripanagnostopoulos et al. [4] analyzed the performance of different types of PV/T systems, including PV/water with/without glazing, PV/air with/without glazing, and PV/T systems with/without booster diffuse reflectors. Their conclusion implied that PV/T systems with glazing could increase thermal efficiency, but reduce electrical efficiency. In addition, systems with booster diffuse reflectors could achieve an electrical output increase of 16% compared with those without booster diffuse reflectors. Similarly, Chow [5] proposed an explicit dynamic model to predict the
* Corresponding authors. Tel./fax: þ86 551 3607367. E-mail addresses: [email protected] (P. Gang), [email protected] (J. Jie). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.11.017
transient performance of PV/T collectors. Ji et al. [6] studied a PV/T collector adapted with a flat-box absorber design. They reported a daily thermal efficiency of above 45% in cases with natural water circulation. Chow and Pei et al. [7] used energy and exergy to analyze the performance of PV/T collectors with/without glass covers. Charalambous et al. [8] presented a comprehensive review on PV/T systems, which entailed a broad investigation of the studies of different researchers, especially their work on various parameters affecting PV/T performance. Many other studies on PV/T collector/systems have been conducted in recent years [9e13]. A traditional water-type PV/T collector/system is not used in cold regions because freezing breaks up the collectors. A heat pipe is a structure with very high thermal conduction, which allows heat transport almost without any temperature drop. Freezing can be eliminated by carefully selecting the working fluid. Corrosion can be reduced as well. Therefore, joining the evaporator of heat pipes to the back of the absorber plate and using the heat pipes to transport the thermal energy can be incorporated in a practical design for a PV/T collector. Several studies on heat pipes integrated with solar thermal collectors have been conducted. Hammad [14] studied flat-plate heat pipe collectors, and found that the thermal efficiency of a heat pipe collector is comparable with that of a water-cooled solar collector. Furthermore, the transient thermal performances of wickless heat pipe (a two-phase closed thermosiphon with a smooth inner face, with only the working fluid inside the heat pipe; the condensate travels back to the hot side through gravity) and flat-plate solar collectors are affected by various parameters, such as solar radiation intensity, temperature of cooling water,
P. Gang et al. / Energy 37 (2012) 384e395
Nomenclature A c D E G h k L M R T t u Ex Pr Nu Ra Re
area, m2 specific heat capacity, J/kg K diameter, m output electricity, W/m2 solar radiation intensity, W/m2 heat transfer coefficient, W/m2 K thermal conductivity, W/m K length, m mass, Kg thermal resistance, K/W temperature, C time, s flow velocity, m/s exergy, W/m2 Prandtl number, Nusselt number, Raleigh number, Reynolds number, -
Greek letters a absorptivity, g PV cell covering factor, d thickness, m ε emissivity, -, second-low efficiency h efficiency, -
absorber plate material and thickness, and the ratio of condenser section length to total wickless heat pipe length [15]. Hiroshi et al. [16] designed a vertical multiple-effect diffusion-type solar still coupled with a heat pipe solar collector. Theoretical research showed that the still could produce 21.8 kg/(m2 d) distilled water on a sunny autumn equinox day with a solar radiation of 22.4 MJ/ (m2 d). Esen [17] designed a solar cooker using a vacuum-tube collector with heat pipes. Experiments were conducted to examine the performance of the solar cooker when three different heat pipe working fluids were used. The result revealed that a cooking time between 27 and 70 min could be obtained using this type of cooker. Riffat [18] developed a theoretical model to investigate the thermal performance of a thin-membrane heat pipe solar collector. Bourdoukan [19] experimentally studied the potential of solar heat pipe vacuum collectors in the desiccantcooling process. Other investigations on heat pipe solar thermal collectors have been conducted in recent years as well [20,21]. However, heat pipes integrated with PV/T panels have not been examined so far. A novel integration of a PV/T flat-plate collector and heat pipe was designed and constructed in the present study. A dynamic model was presented to predict the performance of the heat pipe PV/T (HP-PV/T) system, and experiments were conducted to validate the simulation results. Based on the validated model, the performances of the HP-PV/T system were studied under the following conditions: different water flow rates through the collectors, different PV cell covering factors of the collectors, different tube space of heat pipes, and kinds of solar absorptive coatings of the absorber plate. 2. HP-PV/T solar collector The structure of the HP-PV/T solar collector is presented in Fig. 1. A piece of aluminum plate with an area of 780 1270 mm and a thickness of 1.16 mm was chosen as the base panel. Nine
q r s s (sa)
385
angle, degree density, kg/m3, reflectance, StefaneBoltzman constant, W/m2 K4 transmittance, transmittanceeabsorptance product, -
Subscripts a air, ambient b base panel c collector g glass cover i inner, differential node “i” j differential node “j” l liquid o outer p heat pipe s thermal insulating material v vapor w water, wall of the heat pipe ad adhesive layer con condenser section of heat pipe eva evaporator section of heat pipe pv PV cell sky sky TPT black tedlar-polyester-tellar groove groove
water-copper heat pipes, with dimensions of 4 8 0.7 (thickness) 1300 mm for the evaporator and 4 24 1 90 mm for the condenser, were joined together at the back of the aluminum plate. The condenser section was inserted into a heat exchanger (Fig. 2). The space between the two adjacent heat pipes was measured to be approximately 80 mm. Fig. 3 depicts a section of the HP-PV/T solar collector. Underneath the upper glass cover, there were layers of transparent tedlar-polyester-tellar (TPT, thickness: 0.2 mm), ethylene-vinyl acetate (EVA, thickness: 0.5 mm), PV cells (single-crystalline silicon), black TPT (thickness: 0.2 mm), and aluminum plate. EVA is an adhesive material, whereas TPT is an electrical insulating material. When the six layers were placed into a PV vacuum laminator, the TPT, EVA, and the PV cells were laminated on the surface of the aluminum plate. The black TPT between the PV cell and the aluminum plate plays a role in the electrical insulation of the PV cells and enhances the absorption of solar irradiation. A low-iron-tempered, textured glass plate was used as the upper glazing for the collector, which permitted sunlight passage. However, the textured glass plate prevented thermal loss and entry of dust particles and rain. The air gap between the glass cover and the PV plate was 21 mm. A thermal insulation layer 50 mm thick was placed behind the aluminum plate. The effective irradiation-collection area of the HP-PV/T solar collector was 0.967 m2, and the PV cell area was 0.555 m2. The PV module comprised 72 pieces of small PV cells positioned in two groups. The PV cells in the same groups were arranged in series, and the two groups were connected in parallel. The PV characteristics of the PV module under standard test conditions (at an irradiation intensity of 1000 W/m2 and a temperature of 25 C) are presented in Table 1. The working voltage of the PV module was 12 V when electricity was transported by a solar controller to an accumulator battery. Most radiation is absorbed by the PV cells and the black TPT layer when solar radiation passes through the glass cover and
386
P. Gang et al. / Energy 37 (2012) 384e395
Fig. 1. The HP-PV/T solar collector.
penetrates the PV layer. Part of this radiation is converted to electricity, whereas the rest are eventually converted to heat energy. Heat energy is conducted along the aluminum plate to the evaporator section of the heat pipes. The heat pipes then transfer this energy to the flowing water through the heat exchanger by their condenser sections.
For the glass cover, the heat-balance equation is as follows:
dg rg cg
vTg ¼ ha Ta Tg þ he;g Te Tg þ hg;pv Tpv Tg þ Gag ; vt (1)
and Te is given as follows [5]:
4 4 4 Te4 ¼ fsky $Tsky þ fgr $Tgr þ fsur $Tsur
3. Thermal analysis In the present study, a transient model was developed for an HPPV/T system. The mathematical model consists of six main equation sets as follows: (i) heat-balance equation of the glass cover; (ii) heat-balance equation of the PV module; (iii) uni-dimensional heat conduction of the base panel (aluminum plate); (iv) heat-balance equation of the heat pipe; (v) heat-balance equation for water in the heat exchanger; and (vi) heat-balance equation for water in the storage tank. The following assumptions were made in the model to simplify the calculation. Heat conduction in the longitudinal direction of the aluminum plate was neglected. The temperatures of the adhesive layer (EVA and TPT) and PV cells in the same direction were considered equal. The heat capacity of the adhesive layer (EVA and TPT) was neglected. Heat loss from the heat pipe condenser to the ambient was neglected.
Fig. 2. Schematic diagram of the heat exchanger.
(2)
where ha and he,g are convective and radiant heat transfer coefficients, respectively, between the glass cover and environments; hg,pv is the total heat transfer coefficient between the glass cover and the PV layer; Tsky, Tgr, and Tsur are the temperatures of the sky, ground, and surroundings, respectively; and fsky, fgr, and fsur are the view factors of the glass surface to the sky, ground, and surrounding, respectively. The convective and radiant heat transfer coefficients between the glass cover and the environments are respectively given as follows [22]:
ha ¼ 2:8 þ 3:0ua ;
(3)
and
he;g ¼ εg s Te2 þ Tg2 Te þ Tg :
(4)
By combining the radiation and convection heat transfer mechanisms, the heat transfer coefficient between the PV and the glass cover hg,pv could be derived as
Fig. 3. A section of the HP-PV/T solar collector.
P. Gang et al. / Energy 37 (2012) 384e395 Table 1 PV characteristics of the PV module at standard test conditions. ISC ¼ 5.25A, VSC ¼ 0 V IOC ¼ 0 A, VOC ¼ 21.9 V Imp ¼ 4.91 A, Vmp ¼ 18.0 V (E ¼ 88.4 W, h ¼ 15.9%)
At short-circuit current At open-circuit voltage At the maximum power point
to a heat pipe (heat pipe node) and the other is not (middle node). The heat conduction equations in these two types of grids are different and are given by Eqs. (11.a) and (11.b), respectively. The heat pipe node is expressed as
rb cb 2 hg;pv ¼ s Tpv þ Tg2 Tpv þ Tg þ
g 1=εpv þ g 1=εg 1
1g Nu$ka þ ; l 1=εTPT þ ð1 gÞ 1=εg 1
(5)
where g is the PV cell covering factor, and g ¼ Apv =Ac . For tilt angles ranging from 0 to 75 , Hollands et al. [23] presented the relationship between the Nusselt number and the Raleigh number as follows:
1708$ðsin1:8qÞ Ra$cosq 1=3 þ Ra$cosq þ 1 ; 5830
1:6
Nu ¼ 1 þ 1:14 1
! 1
1708 þ Ra$cosq
(6)
where Rb,pv is the thermal resistance between the PV layer and the base panel (aluminum plate) expressed as Rb;pv ¼ dad =kad . Epv is given by the instantaneous PV efficiency (hpv) expressed as
(8)
where hr is the reference cell efficiency at the reference operating temperature Tr ¼ 298.15 K; Br is the temperature coefficient 0.0045 K1; and s is the total transmittance of the covers, given by Eq. (9) [22]:
s ¼
1 2
"
so si 1 ro ri
t
so si 1 ro ri
þ
# ;
sa 1 ð1 aÞrd
;
rb cb
i
vTb v2 T 1h ðTa Tb Þ=Rb;a þ Tpv Tb Rb;pv ; ¼ kb 2b þ db vt vx
(11.b)
Rb,a is the thermal resistance between the base panel and the ambient air given by
(12)
Rp,b is the thermal resistance between the base panel and the heat pipe expressed as
(13)
where Apb and dpb are the contact area and thickness between the base panel and the evaporator section of the heat pipe, respectively. For the heat pipe, heat-balance equations were provided for the evaporator and the condenser sections, respectively. The heat transfer from the evaporator section to the condenser section was calculated using a total thermal resistance Reva,con. Given that the pressure drop caused by vapor flow along the axial length of the heat pipe is very small, the vapor space is assumed to operate at a constant saturation pressure. Therefore, the temperature gradient of the working fluid along the axial length of the heat pipe can be neglected. The value for Reva,con can be derived based on the resistance of the following components: conduction resistance across the pipe wall and thermal resistance associated with the grooves of the heat pipe evaporator, thermal resistance associated with the condensing process, and conduction resistance across the pipe wall of the heat pipe condenser expressed as follows:
Reva;con ¼ Reva;p þ Reva;groove þ Rcon;i þ Rcon;p ;
(14)
where !
(9)
k
where so and si are the transmittances of the outer cover (glass) and the inner cover (adhesive layer), respectively; ro and ri are the reflectances of the outer cover (glass) and the inner cover (adhesive layer), respectively; and t and k indicate the perpendicular and parallel components of unpolarized radiation passing through the covers, respectively. (sa)pv is the transmittanceeabsorptance product given as:
ðsaÞpv ¼
(11.a)
and the middle node is expressed as
Rp;b ¼ dpb = kp $Apb ;
vTpv ¼ hg;pv Tg Tpv þ Tb Tpv Rb;pv þ GðsaÞpv vt Epv ; (7)
Epv ¼ gGshr 1 Br Tpv Tr ;
vTb v2 T 1h ðTa Tb Þ=Rb;a þ Tpv Tb Rb;pv ¼ kb 2b þ d vt vx b i þ Tp;eva Tb Rp;b $Abi
Rb;a ¼ ds =ks þ 1=ha :
where the þ exponent indicates that only positive values for terms within the square brackets are to be used. In case of negative values, zero is used. Based on these assumptions, the heat-balance equation for the PV layer, which includes the PV cells, EVA, and TPT, is given by
gdpv rpv cpv
387
Reva;p ¼
ln Deva;o=D
eva;i
2pLeva kp
;
(15) !
Reva;groove ¼
ln Do;groove=D
i;groove
2pLeva kgroove
:
An axial groove structure was designed in the inner face of the heat pipe evaporator (Fig. 5). The equivalent thermal conductivity associated with the grooves can be calculated by [24]
(10)
where a is the effective absorptance of PV/T plate given by the weighted average of the absorptances of PV cell (apv) and black TPT (aTPT), a ¼ gapvþ(1g)aTPT; and rd is the reflectance of the inner cover for diffuse radiation, which can be estimated from rd ¼ 1 aad sad at a radiation incidence angle of 60 [22]. For the base panel, the differential grids were divided as shown in Fig. 4. Two types of grids are labeled, where one grid is connected
(16)
Fig. 4. Differential grid partition of the base panel.
388
P. Gang et al. / Energy 37 (2012) 384e395
kgroove ¼
wf kl kw d þ wkl 0:185wf kw þ kl d : w þ wf 0:185wf kw þ kl d
(17)
where wf is the rib width of the groove; w is the width of the groove; and d is the depth of the groove. Thermal resistance associated with the condensing process is defined as
1
Rcon;i ¼
pDcon;i Lcon hcon;i
;
(18)
where hcon,i is the condensing film coefficient obtained by [15]
i h 0:108 hcon;i ¼ 0:997 0:334ðcosqÞ "
gr2l k3l hfg ml DTcr Lcon
#0:25
0:254ðcosqÞ0:385 Lcon =Dcon;i ½ ;
(19)
Nu ¼ CRem Prn ðPrN =Prs Þ1=4
when Pr 10, n ¼ 3.7, and Pr > 10, n ¼ 3.6. The values of C and m depend on the Reynolds number. The differential grid partition for the water in the heat exchanger is shown in Fig. 6. The upwind scheme is used in the water differential equation. For grid (j), the equation can be expressed as
vTw;j _ w cw Tw;j Tw;j1 mw cw þm vt
¼ Ta Tw;j Rw;a þ Tp;con Tw;j Rw;con ;
Rcon;p ¼
ln Dcon;o=D
con;i
2pLcon kp
Mw;tank cw :
(20)
The heat-balance equation of the evaporator section is expressed as
Mp;eva cp
vTp;eva ¼ Tp;con Tp;eva Reva;con þ Tb Tp;eva Rp;b ; vt (21.a)
while that of the condenser section is expressed as
Mp;con cp
vTp;con ¼ Tp;eva Tp;con Reva;con þ Tw Tp;con Rw;con ; vt (21.b)
1 ; Aw hw
(22)
1 0 : Qw ¼ Mw;tank cw Tw;t Tw;t
kw D
(27)
To describe the total efficiency of the HP-PV/T system, an equation based on the first-law of thermodynamics (energy efficiency) is introduced as follows [26]:
Zt2
hpvt ¼
Qw þ Ac Epv dt
t1
¼ hw þ ghpv ;
Zt2
(28)
Ac Gdt
where Rct is the contact thermal resistance between the heat pipe condenser and the copper sleeve of the heat exchanger; and hw is the convection heat transfer coefficient between the heat exchanger and water obtained by [25]:
hw ¼ Nu
vTw;t _ w cw Tw;out Tw;in ; ¼ Ta Tw;t Ra;wt þ n$m vt (26)
where Mw,tank is the mass of water in the storage tank; Ra,wt is the equivalent thermal resistance between the water and the ambient air; Tw,in and Tw,out are the inlet and outlet water temperatures of solar collectors, respectively; and n is the number of solar collectors. The instantaneous useful heat gain of the system is expressed as
where Rw,con is the equivalent thermal resistance between the heat pipe condenser and water calculated by
Rw;con ¼ Rct þ
(25)
_ w is where mw is the mass of water in a single control volume; and m _ w ¼ rw uw A; and Rw,a is the mass flow rate of the water, that is, m the equivalent thermal resistance between water and ambient air. For the water in the storage tank, the heat-balance equation is given by
and !
(24)
t1
where Epv is calculated by Eq. (8). Based on the second-law of thermodynamics (exergy efficiency), another expression is introduced as follows [7]:
(23)
Zt2
and
εpvt ¼
_ pv dt Exw þ Ac Ex
t1
Zt2
¼ εw þ gεpv ;
(29)
_ sun dt Ac Ex
t1
and
_ pv ¼ Epv ; Ex
Fig. 5. Structure of the heat pipe evaporator.
Fig. 6. Differential grid partition of water in the heat exchanger.
(30)
P. Gang et al. / Energy 37 (2012) 384e395
Ta ; Tw;t
(31)
_ sun ¼ G 1 Ta ; Ex Tsun
(32)
Exw ¼ Qw 1
389
where Tsun is the solar radiation temperature at 6000 K. The relative error (RE) between the simulation values and experimental results is calculated by
RE ¼
Xexp Xsim 100%; Xexp
(33)
where Xsim and Xexp are the simulation and experimental values, respectively. 4. Results and analysis 4.1. Experimental validation Fig. 7 shows the schematic diagram of the HP-PV/T system test rig. The system was composed of a storage tank, circulation pump, and two HP-PV/T solar collectors. The two collectors were arranged parallel to each other at the water circulation loop. The water pump circulated the water between the water-storage tank and the collectors, such that the heat energy of the collectors was removed by the circulating water. The storage capacity of the water-storage tank was 200 L. The total irradiation-collection area for the two collectors was 1.934 m2, and the total PV cell area was 1.11 m2. Fig. 8 depicts the actual setup of the HP-PV/T system test rig. The experiment was carried out in Hefei, a city in the middle region of China (117.23 E and 31.87 N). The two solar collectors were installed facing south with a tilt angle of 45 . The experiment commenced at 8:00 and ended at 16:30 (September 17, 2010). During the experiment, the volume flow rate of the circulating water was set at an almost constant rate of (9.9e10.2) L/min, and the water temperature in the storage tank increased from (28.0 to 47.1) C. The ambient parameters during the experiment are shown in Fig. 9.
Fig. 8. Actual setup of the HP-PV/T system test rig.
The initial conditions for the simulation are obtained from the experimental data. The instantaneous boundary conditions, such as solar radiation, ambient temperature, and mass flow rate of circulating water are directly reported from the experimental data. The inlet temperature of the collectors is set to be equal to the outlet temperature of the storage tank. The inlet temperature of the storage tank is set to be equal to the outlet temperature of the collectors.
Fig. 7. Schematic diagram of the HP-PV/T system test rig.
P. Gang et al. / Energy 37 (2012) 384e395
Ta 38
700
36
600
34
500
32
400
30
300
28
200
8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Epv(exp)
ηpv(exp)
Epv(sim)
ηpv(sim)
14
45 12 40
2
800
50
Electrical gain ( W/m )
40
35
10
30 8 25 20
6
15 4
Electrical efficiencies (%)
G 900
Ambient temperature ( oC )
Intensity of the solar irradiation ( W/m2)
390
10
26
5
Time
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
2
Time Fig. 9. Solar radiation intensity and ambient temperature. Fig. 11. Electrical gain and efficiency.
Fig. 10 shows the temperature of the water in the storage tank. The water temperature in the storage tank increased gradually from (28.0 to 47.1) C. The simulation results agree well with the experimental data, with an RE within 1.0% to 1.5%. Figs. 11 and 12 show the electrical and heat gains per unit collecting area, respectively. Compared with Fig. 9, the electrical and heat gains had very similar patterns as the solar radiation intensity. Electrical gain increased from (13.0 to 48.1) W/m2 in the morning, and decreased to 10.2 W/m2 when the solar radiation decreased to 211 W/m2 in the late afternoon. Heat gain increased from (100.0 to 431.7) W/m2 in the morning, and then decreased to 12.0 W/m2 in the late afternoon. The average electrical and heat gains per unit collecting area during the test time were 34.6 and 269.5 W/m2, respectively. The average total values of the two collectors were 66.9 and 521.3 W, respectively, as shown in Table 2. The electrical and the thermal efficiencies of the HP-PV/T system are shown in Figs. 11 and 12, respectively. The solar radiation transmission through the covers induced the electrical efficiency to decrease relatively sharply in the early morning and in the late afternoon. However, the electrical efficiency had a stable value of approximately 10.3% from 9:00 to 15:00. The thermal efficiency fluctuated between 45.0% and 55.0% from 9:30 to 14:30, and then sharply decreased in the afternoon due to the relatively high water temperature in the afternoon resulting in large heat loss. Decreased solar radiation also led to decreased thermal efficiency. Based on the energy analysis, the average electrical and thermal energy efficiencies during the
test time were 10.2% and 45.7%, respectively. Applying Eq. (28), the average total first-law efficiency (energy efficiency) of the HP-PV/T system is 51.5% (Table 2). Based on the exergy analysis, the average electrical and thermal exergy efficiencies during the test time were 10.7% and 0.9%, respectively. Applying Eq. (29), the average total second-law efficiency (exergy efficiency) of the HP-PV/T system is 7.1%. Although the average thermal energy efficiency can reach a value of 45.7%, the thermal exergy efficiency (εw) is only 0.9%, much lower than the electrical exergy efficiency (εpv, 10.7%) because the thermal energy is low-grade energy, and its power conversion efficiency depends on the temperature difference between a heat and a cold source (ambient, currently). Yet the water temperature obtained by the HP-PV/T system is lower. Hence, only a small part of the thermal energy can be converted into work, and its exergy efficiency is low. Conversely, though the average electrical energy efficiency is only 10.2%, the electrical energy is high-grade energy. The subtotal electrical energy can be converted into work. Thus, its exergy efficiency is much higher than the thermal exergy efficiency. The simulated values are in approximate accordance with the experimental results. For the instantaneous values of electrical gain and efficiency, the REs are at 8.0%. For the instantaneous values of heat gain and thermal efficiency, the REs are within 20.0%. This deviation can be attributed to the fact that glass covers with textured inner surfaces were chosen in the solar collectors, and
Tw,t(exp)
48
500
Tw,t(sim)
Qw(exp)
ηw(exp)
Qw(sim)
ηw(sim)
70 60
2
42 39 36 33
50
300
40 200
30 20
100 30 27
10 8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 10. Temperature of the water in the storage tank.
0
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 12. Heat gain and efficiency.
0
Thermal efficiencies (%)
400
Heat gain ( W/m )
Water temperature ( C)
45 o
80
P. Gang et al. / Energy 37 (2012) 384e395
391
Table 2 The average electrical gain, heat gain, and efficiencies of the HP-PV/T system during the test duration from 8:00 to 16:30.
Per unit area
Total
269.5 W/m2 270.3 W/m2 0.3%
521.3 522.7 0.3%
34.6 W/m2 35.0 W/m2 1.2%
66.9 67.7 1.2%
dy vf dx1 vf dx2 vf dxn þ þ/þ ¼ y vx1 y vx2 y vxn y
(34)
where xi ; ði ¼ 1; .; nÞ are the independent variables of the dependent variable y; and vf =vxi is the error transferring coefficient of the variables. The experimental relative mean error (RME) during the test period can be expressed as [27]
PN RME ¼
jREj N
1
hpvt
εpvt
45.7% 45.8% 0.2%
10.2% 10.3% 1.0%
51.5% 51.7% 0.4%
7.1% 7.2% 1.4%
Epv
Qw
275
35.5
270 265
35.0
260 255 34.5 250 245 34.0
240 235 230 0.00
0.02
0.04
0.06
0.08
0.10
33.5
Mass flow rate of water (kg/s) Fig. 13. Average heat gain and electrical gain with water flow rate in each collector.
Fig. 13 shows the average heat gain and electrical gain per unit collecting area curves versus water flow rate. Heat gain and electrical gain increased with increased water flow rate. However, the increase of the heat gain and the electrical gain slowed down with the increase in water flow rate. The same variation tendency was also found in the total efficiencies (first- and second-law efficiencies) of the HP-PV/T system, as shown in Fig. 14. The influence of water flow rate on heat gain was much stronger than on the electrical gain. Heat gain increases from 233.8 to 262.1 W/ m2, and electrical gain increases from 33.9 to 34.8 W/m2 when the water mass flow rate increases from 0.01 to 0.04 kg/s. Heat gain and electrical gain increase to 271.4 and 35.1 W/m2, respectively, when the water mass flow rate increases to 0.1 kg/s because the increase in water mass flow rate results in decreased temperatures in the PV cells and the base panel. However, the influence of the temperature on the electrical gain is much weaker than that on the heat gain.
(35)
According to Eqs. (34) and (35), the RME of all variables are calculated, and the results are given in Table 3. 4.2. Different mass flow rates of the water
εpvt
ηpvt
53
7.2
52
First-law efficiency (%)
Numerical simulation was carried out to study the influence of water flow rate on the performance of the HP-PV/T system. The structural parameters of the HP-PV/T collector were set as follows: PV cell covering factor is 0.574 (Ac ¼ 0.967 m2, Apv ¼ 0.555 m2), and the tube space of heat pipes is 80 mm. The weather data given in Fig. 9 were used for the calculation in the simulation.
7.1
51 7.0
50
6.9
49 48
6.8
47 6.7
46 Table 3 The experimental RME of the variables.
45 0.00
Variable
Tw
Epv
Qw
hpv
hw
RME
0.064%
0.45%
23.1%
1.41%
24.1%
0.02
0.04
0.06
0.08
0.10
Second-law efficiency (%)
RE ¼
hpv
2
their influences on the transmission of solar radiation were different from the smooth glass plates. However, these differences were not considered in the model. Moreover, a global radiation on the collector surface was used for the simulation. The direct and diffuse radiations were not processed separately, which resulted in a deviation between the simulated values and experimental results. Copper-constantan thermocouples (T-type) with an accuracy of 0.2 C were used to measure the water temperatures, which resulted in a measured deviation of the water temperature. Therefore, for the instantaneous heat gain, the measured deviation is another reason for the deviation between the simulated values and the experimental results. The REs between simulated values and experimental results are all within 1.4% for the average values of electrical gain and efficiency, heat gain and thermal efficiency, and total efficiencies. The errors and inaccuracies in the test instrumentations led to some errors in the experimental data. In the present study, the experimental error of the independent variables, such as temperature, PV electric power, and solar radiation intensity, was determined by the accuracy of the corresponding test instrumentations. For the dependent variables, such as electrical gain, heat gain, and efficiencies, their experimental errors can be calculated from the experimental error of the independent variables. According to the literature by Ji et al. [27], the RE of dependent variable y can be calculated by
hw
Average electrical gain ( W/m )
590
Electrical gain Epv (W) Total
2
Experiment Simulation RE
Heat gain Qw (W) Per unit area
Average heat gain ( W/m )
Average G (W/m2)
Result
6.6
Mass flow rate of water (kg/s) Fig. 14. Total efficiencies of the HP-PV/T system with water flow rate in each collector.
P. Gang et al. / Energy 37 (2012) 384e395
4.3. Different PV cell covering factors
4.4. Different tube space of heat pipes The dimension of the space between two adjacent heat pipes has a significant influence on the heat transfer from the collectors to the water. In this section, a numerical simulation was carried out to study the performance of the HP-PV/T system under different tube spaces of heat pipes. The calculating parameters follow. The mass flow rate of the water in each collector was _ w ¼ 0:085kg=s. The solar irradiation collecting area of each m collector was Ac ¼ 0.967 m2. PV cell covering factor of the solar
Qw
52.4 8
52.2 52.0
6
51.8 51.6
4
51.4 51.2 51.0 0.0
2 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Coverage ratio of the PV cells Fig. 16. Total efficiencies of the HP-PV/T system with the PV cell covering factor.
collector was 0.574 (Apv ¼ 0.555 m2). The number of collectors was two. The weather data are shown in Fig. 9. Table 4 gives the tube space heat pipes and the number of the heat pipes in each collector. The average heat gain and electrical gain per unit collecting area are shown in Fig. 17. Heat gain and electrical gain exhibited a nearly linear decrease with increased tube space of heat pipes because the increased tube space of heat pipes resulted in increased thermal resistance between the base panel and the heat pipes. Moreover, when the tube space increases, the number of heat pipes in each collector will decrease (Table 4). The total heat transfer area will also decrease resulting in larger thermal resistance between the heat pipe condensers and the flowing water. Not all heat of the absorber plate is fully transferred to the flowing water, higher temperature of the absorber plate, and larger heat loss to the ambient. The heat gain decreases from 290.2 to 234.1 W/m2, and the electrical gain decreases from 35.8 to 33.9 W/m2 when the space between two adjacent heat pipes increases from 0.05 to 0.15 m.
Table 4 Space between two adjacent heat pipes and the number of the heat pipes in each collector. Space (m) Heat pipes (number) Energy efficiency (hpvt) Exergy efficiency (εpvt)
0.05 15 55.2% 7.5%
0.07 11 53.0% 7.3%
0.09 8 50.6% 7.1%
Qw
0.11 7 49.1% 7.0%
Epv
0.13 6 47.4% 6.8%
0.15 5 45.4% 6.7%
300
38
290
37
40 280 30 270 20 260
10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1.0
Coverage ratio of the PV cells Fig. 15. Average heat gain and electrical gain with the PV cell covering factor.
280 36 270 35 260 34 250 33
240 230 0.04
0.06
0.08
0.10
0.12
0.14
2
Average electrical gain ( W/m )
290
2
50
Average heat gain ( W/m )
2
Average electrical gain ( W/m )
60
2
Average heat gain ( W/m )
10
52.6
Epv
300
250 0.0
12
52.8
First-law efficiency (%)
The PV cell covering factor of the HP-PV/T collector (g) is an important parameter for an HP-PV/T system. To study the influence of parameter g on the performance of the HP-PV/T system, a numerical simulation was carried out under the following conditions: mass flow rate of the water in each collector is _ w ¼ 0:085kg=s; solar irradiation collecting area of each collector m is Ac ¼ 0.967 m2; and the number of collectors is two. The tube space of the heat pipes is 80 mm. The weather data are shown in Fig. 9. Fig. 15 shows the average heat gain and electrical gain per unit collecting area. Electrical gain linearly increases with increased PV cell covering factor. However, heat gain linearly decreases with increased PV cell covering factor because when the PV cell covering factor increases, the PV area of the collector increases. Hence, the electricity produced from the solar irradiation increases. Conversely, because solar irradiation converted into the electricity increases, the part converted into heat decreases. The total efficiencies of the HP-PV/T system are shown in Fig. 16. The second-law efficiency (exergy efficiency) of the HP-PV/T system linearly increases with increased PV cell covering factor from 1.3% to 11.6% when the PV cell covering factor increases from 0 to 1. The reason for the low exergy efficiency of 1.3% is that, when the PV cell covering factor is equal to zero, no PV cell is present on the collector. Thus, no electricity output is available except thermal energy. Thermal energy is low-grade energy. In the HP-PV/T system, the water temperature is lower, as seen in the Eq. (31). Thus, its total exergy output is low. Therefore, according to Eq. (29), the exergy efficiency of the HP-PV/T system is low. The first-law efficiency (energy efficiency) of the HP-PV/T system also increases with increased PV cell covering factor. The rate gradually rises because the increasing rate of the electricity output is higher than the decreasing rate of the heat gain when the PV cell covering factor increases.
εpvt
ηpvt
53.0
Second-law efficiency (%)
392
32 0.16
Tube space of heat pipes (m) Fig. 17. Average heat gain and electrical gain with the tube space of heat pipes.
P. Gang et al. / Energy 37 (2012) 384e395
ηpvt
56
εpvt
performances of the HP-PV/T system using the following three types of collectors:
7.6
52 7.2 50 7.0 48 6.8
46 44 0.04
0.06
0.08
0.10
0.12
0.14
6.6 0.16
Tube space of heat pipes (m) Fig. 18. Total efficiencies of the HP-PV/T system with the tube space of heat pipes.
The first- and the second-law efficiencies of the HP-PV/T system linearly decrease with increased tube space of heat pipes (Fig. 18). The first-law efficiency decreases from 55.2% to 45.4%, and the second-law efficiency decreases from 7.5% to 6.7% when the tube space of heat pipes increases from 0.05 to 0.15 m. Reducing the tube space of heat pipes can improve the performance of the HP-PV/T system as shown in Table 4. However, a small tube space will result in a collector requiring many heat pipes and will increase the cost of the collector. Hence, tube space of heat pipes smaller than 0.08 m was not used in our collector for economical reason. 4.5. Absorber plate with different kinds of solar absorptive coating Three different types of collectors are given in this section. Numerical simulations were carried out to calculate the
solar selective coating black pigment coating no coating
48
o
Water temperature ( C)
Type 1: Absorber plate with solar selective coating, absorbance of the coating is 0.95, and emittance is 0.05; Type 2: Absorber plate with black pigment coating, absorbance of the coating is 0.98, and emittance is 0.98; and Type 3: Absorber plate without any coating, PV cells are directly laminated onto an aluminum plate with surface polished, absorbance of the aluminum is 0.09, and emittance is 0.03.
7.4
Second-law efficiency (%)
First-law efficiency (%)
54
393
44 40 36 32 28
The calculating parameters follow. _ w ¼ 0:085kg=s. Mass flow rate of the water in each collector is m Solar irradiation collecting area of each collector is Ac ¼ 0.967 m2. PV cell covering factor of the solar collector is 0.574 (Apv ¼ 0.555 m2). The number of collector is two. Tube space of heat pipes is 80 mm. Weather data are shown in Fig. 9. Fig. 19 shows the water temperature of the storage tank. The water temperatures increase from 28.0 to 48.2 C and from 28.0 to 47.1 C, respectively, when using the collector with solar selective coating and that with black pigment coating. For the collector without any coating, the water temperature only increases from 28.0 to 41.3 C. The collector with solar selective coating has the best thermal performance. The average heat gain reaches 284.7 W/ m2 with a thermal efficiency of 48.2% as shown in Table 5. The collector with black pigment coating comes next, with an average heat gain of 270.3 W/m2 and a thermal efficiency of 45.8%. The thermal performance of the collector without any coating is the worst with an average heat gain of only 187.9 W/m2 and a thermal efficiency of 31.8%. However, the collector without any coating has the best electrical performance, with an average electrical gain reaching up to 36.5 W/m2 and an electrical efficiency of 10.8% because electrical efficiency of the PV module is affected by its temperature (Eq. (8)). When the temperature increases, electrical efficiency decreases. The collector without coating absorbs the least solar radiation, and its PV module temperature is lowest. Thus, its electrical efficiency is the highest. Similar to thermal performance, the best total PV/T efficiency is obtained by the HP-PV/T system using collectors with solar selective coating. The average total first-law efficiency (energy efficiency) is 54.1%, and the average total second-law efficiency (exergy efficiency) is 7.3%. The one using collectors with black pigment coating comes next which can reach an average total first-law efficiency of 51.7% and an average total second-law efficiency of 7.2%. The system using collectors without coating has average total first- and second-law efficiencies of only 38.0% and 6.8%, respectively. For a collector with a PV cell covering factor of 0.574, HP-PV/T system using the collectors with solar absorptive coating can greatly improve its total PV/T performance. 4.6. Cost analysis
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Increasing the PV cells covering factor and reducing the tube space of heat pipes can improve the overall performance of an HPPV/T system. However, these would lead to a rising cost of each HP-
Time Fig. 19. Water temperature of the storage tank.
Table 5 Average electrical gain, heat gain, and efficiencies of the HP-PV/T system using three different types of collectors (time: 8:00e16:30). Type
Selective coating Black TPT Without coating
Average G (W/m2) 590
Heat gain Qw (W)
Electrical gain Epv (W)
Per unit area
Total
Per unit area
Total
284.7 W/m2 270.3 W/m2 187.9 W/m2
550.6 522.7 363.3
34.8 W/m2 35.0 W/m2 36.5 W/m2
67.2 67.7 70.5
Total energy Qtotal (W)
Total exergy Extotal (W)
hw
hpv
hpvt
εpvt
617.8 590.4 433.8
78.7 77.7 74.0
48.2% 45.8% 31.8%
10.3% 10.3% 10.8%
54.1% 51.7% 38.0%
7.3% 7.2% 6.8%
394
P. Gang et al. / Energy 37 (2012) 384e395
Table 6 Cost of the PV cell of each HP-PV/T collector. PV cell covering factor PV cell area (m2) Cost of the PV cell ($)
0.0 0.0 0.0
0.2 0.2 19.5
0.4 0.4 39.0
0.6 0.6 58.5
0.8 0.8 78.0
1.0 1.0 97.5
Table 7 Cost of the heat pipe of each HP-PV/T collector. Tube space (m) Number of heat pipes Cost of the heat pipe ($)
0.05 15 104.1
0.07 11 76.4
0.09 8 55.5
0.11 7 48.6
0.13 6 41.6
0.15 5 34.7
PV/T collector. For example, in an HP-PV/T collector with a collecting area of 1 m2, the cost of the PV cell and heat pipes are calculated, as shown in Tables 6 and 7, respectively. When the area of the PV cell increases 0.2 m2, the cost of the PV cell of each collector will increase about 19.5$. The annual average electrical efficiency of the PV cell is about 10.0%. Take Hefei (China) as example, its annual average solar radiation is about 1295.53 kWh/(m2 year). Hence, the electricity output of per unit area PV cell will be about 129.55 kWh/ (m2 year). The average residential electrovalence of China is about 0.09$/kWh. Calculating based on this, then the payback period of the PV cell is about 8e9 years. If the government subsidy can reach 50% of its cost, the payback period will decrease to 4e5 years. The life of the PV cell can reach 20 years. Thus, higher PV covering factor has better economic benefit. The cost of a heat pipe is about 6.9$ when tube space of heat pipes is 0.09 m, producing a collector requiring eight heat pipes. The cost of the heat pipes is about 55.5$. However, when the tube space is 0.05 m, producing a collector will require 15 heat pipes. The cost of the heat pipes of each collector alone will reach 104.1$. Yet, the energy efficiency only increases with an absolute value of 4.6%. Hence, a tube space of 0.09 m is suitable for the HP-PV/T collector when considering cost. Overall, considering both cost and performance, high PV cell covering factor and tube space of about 0.09 m is beneficial for an HP-PV/T collector. 5. Conclusion A dynamic model of the HP-PV/T system was presented and validated by experimental results. Based on the validated model, the performances of the HP-PV/T system under the conditions of different water flow rates through the collectors, different PV cell covering factors of the collectors, different tube spaces of heat pipes, and absorber plate with three different kinds of solar absorptive coatings were studied. The results are summarized as follows: 1. The recorded data demonstrated that the simulated values agreed with the experimental results. For the instantaneous values of electrical gain and efficiency, the REs are at 8.0%. For the instantaneous values of heat gain and thermal efficiency, the REs are within 20.0%. The average total first- and secondlaw efficiencies of the HP-PV/T system in the test duration are 51.5% and 7.1%, respectively. 2. Heat gain, electrical gain, and total PV/T efficiencies (first- and second-law efficiencies) of the HP-PV/T system increase with increased water flow rate. However, the increasing rate will gradually decrease with increased water flow rate, and the increase of the electrical and heat gain will be very small when the water flow rate is larger than 0.07 kg/s. The influence of water flow rate on heat gain is much stronger than on electrical gain.
3. Electrical gain and total PV/T efficiencies of the HP-PV/T system increase with increased PV cell covering factor. However, the heat gain of the HP-PV/T system will decrease when the PV cell covering factor increases. Increasing the PV cell covering factor is beneficial for increasing solar radiation utilization and in improving the grade of the energy output. 4. Reducing the tube space of heat pipes can improve the heat gain, electrical gain, and total PV/T efficiencies of the HP-PV/T system. However, this reduction would increase the number of heat pipes in each collector resulting in high costs. 5. The HP-PV/T system using collectors with solar absorptive coating can increase heat gain and total PV/T efficiencies, but would decrease electricity output. Hence, collectors with solar absorptive coating are needed for the HP-PV/T system to obtain more thermal energy. However, collectors without solar absorptive coating are better from the standpoint of improving the electricity output. Acknowledgments The present study was sponsored by the National Science Foundation of China (50974150, 50978241, 50708105), the Excellence Youth Science Foundation of Anhui Province of China (10040606Y20), the Fundamental Research Funds for the Central Universities of China, and the Huo Yingdong Education Foundation (122029). References [1] Zondag HA. Flat-plate PV-thermal collectors and systems: a review. Renewable and Sustainable Energy Reviews 2008;12:891e959. [2] Wolf M. Performance analyses of combined heating and photovoltaic power systems for residences. Energy Conversion 1976;16:79e90. [3] Raghuraman P. Analytical predictions of liquid and air photovoltaic/thermal flat plate collector performance. Journal of Solar Energy Engineering 1981; 103:291e8. [4] Tripanagnostopoulos Y, Nousia TH, Souliotis M, Yianoulis P. Hybrid photovoltaic/thermal solar systems. Solar Energy 2002;72:217e34. [5] Chow TT. Performance analysis of photovoltaic-thermal collector by explicit dynamic model. Solar Energy 2003;75:143e52. [6] Ji J, Lu JP, Chow TT, He W, Pei G. Hybrid photovoltaic and thermal solarcollector designed for natural circulation of water. Applied Energy 2006;83: 199e210. [7] 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. Applied Energy 2009;86:310e6. [8] Charalambous PG, Maidment GG, Kalogirou SA, Yiakoumetti K. Photovoltaic thermal (PV/T) collectors: a review. Applied Thermal Engineering 2007;27: 275e86. [9] Tiwari Arvind, Sodha MS. Performance evaluation of solar PV/T system: an experimental validation. Solar Energy 2006;80:751e9. [10] Fraisse G, Me’ne’zo C, Johannes K. Energy performance of water hybrid PV/T collectors applied to combisystems of Direct Solar Floor type. Solar Energy 2007;81:1426e38. [11] Robles-Ocampo B, Ruı’z-Vasquezb E, Canseco-Sa’nchezb H, Cornejo-Mezac RC, Tra’paga-Martı’nezd G, Garcı’a-Rodrigueza FJ, et al. Photovoltaic/thermal solar hybrid system with bifacial PV module and transparent plane collector. Solar Energy Materials & Solar Cells 2007;91:1966e71. [12] Pei G, Ji J, Chow TT, He H, Liu K, Yi H. Comparative analysis of winter performance of PV-SAHP system with and without glass cover. Proceedings of the Institution of Mechanical Engineers, part A. Journal of Power and Energy 2008;222:179e87. [13] Pei G, Ji J, Liu KL, He HF, Jiang AG. Numerical study of PV/T-SAHP system. Journal of Zhejiang University SCIENCE 2008;A9:970e80. [14] Hammad M. Experimental study of the performance of a solar collector cooled by heat pipes. Energy Conversion 1995;36:197e203. [15] Husseina HMS, Mohamada MA, El-Asfouri AS. Optimization of a wickless heat pipe flat plate solar collector. Energy Conversion & Management 1999;40: 1949e61. [16] Tanaka Hiroshi, Nakatake Yasuhito. A vertical multiple-effect diffusion-type solar still coupled with a heat-pipe solar collector. Desalination 2004;160: 195e205. [17] Esen Mehmet. Thermal performance of a solar cooker integrated vacuum-tube collector with heat pipes containing different refrigerants. Solar Energy 2004; 76:751e7.
P. Gang et al. / Energy 37 (2012) 384e395 [18] Riffat SB, Zhao X, Doherty PS. Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector. Applied Thermal Engineering 2005;25:899e915. [19] Bourdoukan P, Wurtz E, Joubert P, Spe’randio M. Potential of solar heat pipe vacuum collectors in the desiccant cooling process: modelling and experimental results. Solar Energy 2008;82:1209e19. [20] Rittidech S, Wannapakne S. Experimental study of the performance of a solar collector by closed-end oscillating heat pipe (CEOHP). Applied Thermal Engineering 2007;27:1978e85. [21] Azad E. Theoretical and experimental investigation of heat pipe solar collector. Experimental Thermal and Fluid Science 2008;32:1666e72. [22] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. New York: John Wiley & Sons; 1991.
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[23] Hollands KGT, Unny TE, Raithby GD, konicek L. Free convection heat transfer across inclined air layers. Transactions of the American Society of Mechanical Engineers. Journal of Heat Transfer 1976;98:189e93. [24] Chi SW. Heat pipe theory and practice. New York: McGraw-Hill; 1976. [25] Incropera FP, DeWitt DP, Bergman TL, Lavine AS. Fundamentals of heat and mass transfer. 6th ed. New York: John Wiley & Sons; 2007. [26] Garg HP, Agarwal RK. Some aspects of a PV/T collector/forced circulation flat plate solar water heater with solar cells. Energy Conversion and Management 1995;36:87e99. [27] Ji J, He HF, Chow TT, Pei G, He W, Liu KL. Distributed dynamic modeling and experimental study of PV evaporator in a PV/T solar-assisted heat pump. International Journal of Heat and Mass Transfer 2009;52: 1365e73.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Performance study and parametric analysis of a novel heat pipe PV/T system Pei Gang*, Fu Huide, Zhu Huijuan, Ji Jie* Department of Thermal Science and Energy Engineering, University of Science and Technology of China, #96 Jinzhai Road, Hefei City, Anhui Province 230026, People’s Republic of China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2011 Received in revised form 10 October 2011 Accepted 10 November 2011 Available online 14 December 2011
A novel heat pipe photovoltaic/thermal (PV/T) system that could simultaneously supply electrical and thermal energy was proposed. Compared with a traditional water-type PV/T system, the heat pipe PV/T system can be used in cold regions without becoming frozen. A dynamic model of the heat pipe PV/T system was presented, and a test rig was constructed. Experiments were conducted to validate the results of the simulation. Based on the validated model, the performances of the heat pipe PV/T system were studied under different parametric conditions, such as water flow rates, PV cell covering factor of the collector, tube space of heat pipes, and kinds of solar absorptive coatings of the absorber plate. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heat pipe Photovoltaic/thermal Solar collector
1. Introduction The photovoltaic/thermal (PV/T) collector is an integration of PV cells and a solar thermal collector in a single unit, which can simultaneously generate electrical and thermal energy. Heat carriers, such as water or air, take in heat extracted from PV cells. The cells are then cooled, thereby improving the yield of electricity. Several investigations on PV/T collector/systems have been previously carried out. Zondag [1] reported that Martin Wolf presented the first work on a flat-plate PV/T collector [2]. Other researchers have subsequently undertaken studies on the PV/T collector/system. Raghuraman [3] presented two separate 1D mathematical models to predict the performance of water and air PV/T flat-plate collectors. He then compared the results with the experimental data. Design recommendations were also made to maximize the total energy extracted from the collectors. Tripanagnostopoulos et al. [4] analyzed the performance of different types of PV/T systems, including PV/water with/without glazing, PV/air with/without glazing, and PV/T systems with/without booster diffuse reflectors. Their conclusion implied that PV/T systems with glazing could increase thermal efficiency, but reduce electrical efficiency. In addition, systems with booster diffuse reflectors could achieve an electrical output increase of 16% compared with those without booster diffuse reflectors. Similarly, Chow [5] proposed an explicit dynamic model to predict the
* Corresponding authors. Tel./fax: þ86 551 3607367. E-mail addresses: [email protected] (P. Gang), [email protected] (J. Jie). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.11.017
transient performance of PV/T collectors. Ji et al. [6] studied a PV/T collector adapted with a flat-box absorber design. They reported a daily thermal efficiency of above 45% in cases with natural water circulation. Chow and Pei et al. [7] used energy and exergy to analyze the performance of PV/T collectors with/without glass covers. Charalambous et al. [8] presented a comprehensive review on PV/T systems, which entailed a broad investigation of the studies of different researchers, especially their work on various parameters affecting PV/T performance. Many other studies on PV/T collector/systems have been conducted in recent years [9e13]. A traditional water-type PV/T collector/system is not used in cold regions because freezing breaks up the collectors. A heat pipe is a structure with very high thermal conduction, which allows heat transport almost without any temperature drop. Freezing can be eliminated by carefully selecting the working fluid. Corrosion can be reduced as well. Therefore, joining the evaporator of heat pipes to the back of the absorber plate and using the heat pipes to transport the thermal energy can be incorporated in a practical design for a PV/T collector. Several studies on heat pipes integrated with solar thermal collectors have been conducted. Hammad [14] studied flat-plate heat pipe collectors, and found that the thermal efficiency of a heat pipe collector is comparable with that of a water-cooled solar collector. Furthermore, the transient thermal performances of wickless heat pipe (a two-phase closed thermosiphon with a smooth inner face, with only the working fluid inside the heat pipe; the condensate travels back to the hot side through gravity) and flat-plate solar collectors are affected by various parameters, such as solar radiation intensity, temperature of cooling water,
P. Gang et al. / Energy 37 (2012) 384e395
Nomenclature A c D E G h k L M R T t u Ex Pr Nu Ra Re
area, m2 specific heat capacity, J/kg K diameter, m output electricity, W/m2 solar radiation intensity, W/m2 heat transfer coefficient, W/m2 K thermal conductivity, W/m K length, m mass, Kg thermal resistance, K/W temperature, C time, s flow velocity, m/s exergy, W/m2 Prandtl number, Nusselt number, Raleigh number, Reynolds number, -
Greek letters a absorptivity, g PV cell covering factor, d thickness, m ε emissivity, -, second-low efficiency h efficiency, -
absorber plate material and thickness, and the ratio of condenser section length to total wickless heat pipe length [15]. Hiroshi et al. [16] designed a vertical multiple-effect diffusion-type solar still coupled with a heat pipe solar collector. Theoretical research showed that the still could produce 21.8 kg/(m2 d) distilled water on a sunny autumn equinox day with a solar radiation of 22.4 MJ/ (m2 d). Esen [17] designed a solar cooker using a vacuum-tube collector with heat pipes. Experiments were conducted to examine the performance of the solar cooker when three different heat pipe working fluids were used. The result revealed that a cooking time between 27 and 70 min could be obtained using this type of cooker. Riffat [18] developed a theoretical model to investigate the thermal performance of a thin-membrane heat pipe solar collector. Bourdoukan [19] experimentally studied the potential of solar heat pipe vacuum collectors in the desiccantcooling process. Other investigations on heat pipe solar thermal collectors have been conducted in recent years as well [20,21]. However, heat pipes integrated with PV/T panels have not been examined so far. A novel integration of a PV/T flat-plate collector and heat pipe was designed and constructed in the present study. A dynamic model was presented to predict the performance of the heat pipe PV/T (HP-PV/T) system, and experiments were conducted to validate the simulation results. Based on the validated model, the performances of the HP-PV/T system were studied under the following conditions: different water flow rates through the collectors, different PV cell covering factors of the collectors, different tube space of heat pipes, and kinds of solar absorptive coatings of the absorber plate. 2. HP-PV/T solar collector The structure of the HP-PV/T solar collector is presented in Fig. 1. A piece of aluminum plate with an area of 780 1270 mm and a thickness of 1.16 mm was chosen as the base panel. Nine
q r s s (sa)
385
angle, degree density, kg/m3, reflectance, StefaneBoltzman constant, W/m2 K4 transmittance, transmittanceeabsorptance product, -
Subscripts a air, ambient b base panel c collector g glass cover i inner, differential node “i” j differential node “j” l liquid o outer p heat pipe s thermal insulating material v vapor w water, wall of the heat pipe ad adhesive layer con condenser section of heat pipe eva evaporator section of heat pipe pv PV cell sky sky TPT black tedlar-polyester-tellar groove groove
water-copper heat pipes, with dimensions of 4 8 0.7 (thickness) 1300 mm for the evaporator and 4 24 1 90 mm for the condenser, were joined together at the back of the aluminum plate. The condenser section was inserted into a heat exchanger (Fig. 2). The space between the two adjacent heat pipes was measured to be approximately 80 mm. Fig. 3 depicts a section of the HP-PV/T solar collector. Underneath the upper glass cover, there were layers of transparent tedlar-polyester-tellar (TPT, thickness: 0.2 mm), ethylene-vinyl acetate (EVA, thickness: 0.5 mm), PV cells (single-crystalline silicon), black TPT (thickness: 0.2 mm), and aluminum plate. EVA is an adhesive material, whereas TPT is an electrical insulating material. When the six layers were placed into a PV vacuum laminator, the TPT, EVA, and the PV cells were laminated on the surface of the aluminum plate. The black TPT between the PV cell and the aluminum plate plays a role in the electrical insulation of the PV cells and enhances the absorption of solar irradiation. A low-iron-tempered, textured glass plate was used as the upper glazing for the collector, which permitted sunlight passage. However, the textured glass plate prevented thermal loss and entry of dust particles and rain. The air gap between the glass cover and the PV plate was 21 mm. A thermal insulation layer 50 mm thick was placed behind the aluminum plate. The effective irradiation-collection area of the HP-PV/T solar collector was 0.967 m2, and the PV cell area was 0.555 m2. The PV module comprised 72 pieces of small PV cells positioned in two groups. The PV cells in the same groups were arranged in series, and the two groups were connected in parallel. The PV characteristics of the PV module under standard test conditions (at an irradiation intensity of 1000 W/m2 and a temperature of 25 C) are presented in Table 1. The working voltage of the PV module was 12 V when electricity was transported by a solar controller to an accumulator battery. Most radiation is absorbed by the PV cells and the black TPT layer when solar radiation passes through the glass cover and
386
P. Gang et al. / Energy 37 (2012) 384e395
Fig. 1. The HP-PV/T solar collector.
penetrates the PV layer. Part of this radiation is converted to electricity, whereas the rest are eventually converted to heat energy. Heat energy is conducted along the aluminum plate to the evaporator section of the heat pipes. The heat pipes then transfer this energy to the flowing water through the heat exchanger by their condenser sections.
For the glass cover, the heat-balance equation is as follows:
dg rg cg
vTg ¼ ha Ta Tg þ he;g Te Tg þ hg;pv Tpv Tg þ Gag ; vt (1)
and Te is given as follows [5]:
4 4 4 Te4 ¼ fsky $Tsky þ fgr $Tgr þ fsur $Tsur
3. Thermal analysis In the present study, a transient model was developed for an HPPV/T system. The mathematical model consists of six main equation sets as follows: (i) heat-balance equation of the glass cover; (ii) heat-balance equation of the PV module; (iii) uni-dimensional heat conduction of the base panel (aluminum plate); (iv) heat-balance equation of the heat pipe; (v) heat-balance equation for water in the heat exchanger; and (vi) heat-balance equation for water in the storage tank. The following assumptions were made in the model to simplify the calculation. Heat conduction in the longitudinal direction of the aluminum plate was neglected. The temperatures of the adhesive layer (EVA and TPT) and PV cells in the same direction were considered equal. The heat capacity of the adhesive layer (EVA and TPT) was neglected. Heat loss from the heat pipe condenser to the ambient was neglected.
Fig. 2. Schematic diagram of the heat exchanger.
(2)
where ha and he,g are convective and radiant heat transfer coefficients, respectively, between the glass cover and environments; hg,pv is the total heat transfer coefficient between the glass cover and the PV layer; Tsky, Tgr, and Tsur are the temperatures of the sky, ground, and surroundings, respectively; and fsky, fgr, and fsur are the view factors of the glass surface to the sky, ground, and surrounding, respectively. The convective and radiant heat transfer coefficients between the glass cover and the environments are respectively given as follows [22]:
ha ¼ 2:8 þ 3:0ua ;
(3)
and
he;g ¼ εg s Te2 þ Tg2 Te þ Tg :
(4)
By combining the radiation and convection heat transfer mechanisms, the heat transfer coefficient between the PV and the glass cover hg,pv could be derived as
Fig. 3. A section of the HP-PV/T solar collector.
P. Gang et al. / Energy 37 (2012) 384e395 Table 1 PV characteristics of the PV module at standard test conditions. ISC ¼ 5.25A, VSC ¼ 0 V IOC ¼ 0 A, VOC ¼ 21.9 V Imp ¼ 4.91 A, Vmp ¼ 18.0 V (E ¼ 88.4 W, h ¼ 15.9%)
At short-circuit current At open-circuit voltage At the maximum power point
to a heat pipe (heat pipe node) and the other is not (middle node). The heat conduction equations in these two types of grids are different and are given by Eqs. (11.a) and (11.b), respectively. The heat pipe node is expressed as
rb cb 2 hg;pv ¼ s Tpv þ Tg2 Tpv þ Tg þ
g 1=εpv þ g 1=εg 1
1g Nu$ka þ ; l 1=εTPT þ ð1 gÞ 1=εg 1
(5)
where g is the PV cell covering factor, and g ¼ Apv =Ac . For tilt angles ranging from 0 to 75 , Hollands et al. [23] presented the relationship between the Nusselt number and the Raleigh number as follows:
1708$ðsin1:8qÞ Ra$cosq 1=3 þ Ra$cosq þ 1 ; 5830
1:6
Nu ¼ 1 þ 1:14 1
! 1
1708 þ Ra$cosq
(6)
where Rb,pv is the thermal resistance between the PV layer and the base panel (aluminum plate) expressed as Rb;pv ¼ dad =kad . Epv is given by the instantaneous PV efficiency (hpv) expressed as
(8)
where hr is the reference cell efficiency at the reference operating temperature Tr ¼ 298.15 K; Br is the temperature coefficient 0.0045 K1; and s is the total transmittance of the covers, given by Eq. (9) [22]:
s ¼
1 2
"
so si 1 ro ri
t
so si 1 ro ri
þ
# ;
sa 1 ð1 aÞrd
;
rb cb
i
vTb v2 T 1h ðTa Tb Þ=Rb;a þ Tpv Tb Rb;pv ; ¼ kb 2b þ db vt vx
(11.b)
Rb,a is the thermal resistance between the base panel and the ambient air given by
(12)
Rp,b is the thermal resistance between the base panel and the heat pipe expressed as
(13)
where Apb and dpb are the contact area and thickness between the base panel and the evaporator section of the heat pipe, respectively. For the heat pipe, heat-balance equations were provided for the evaporator and the condenser sections, respectively. The heat transfer from the evaporator section to the condenser section was calculated using a total thermal resistance Reva,con. Given that the pressure drop caused by vapor flow along the axial length of the heat pipe is very small, the vapor space is assumed to operate at a constant saturation pressure. Therefore, the temperature gradient of the working fluid along the axial length of the heat pipe can be neglected. The value for Reva,con can be derived based on the resistance of the following components: conduction resistance across the pipe wall and thermal resistance associated with the grooves of the heat pipe evaporator, thermal resistance associated with the condensing process, and conduction resistance across the pipe wall of the heat pipe condenser expressed as follows:
Reva;con ¼ Reva;p þ Reva;groove þ Rcon;i þ Rcon;p ;
(14)
where !
(9)
k
where so and si are the transmittances of the outer cover (glass) and the inner cover (adhesive layer), respectively; ro and ri are the reflectances of the outer cover (glass) and the inner cover (adhesive layer), respectively; and t and k indicate the perpendicular and parallel components of unpolarized radiation passing through the covers, respectively. (sa)pv is the transmittanceeabsorptance product given as:
ðsaÞpv ¼
(11.a)
and the middle node is expressed as
Rp;b ¼ dpb = kp $Apb ;
vTpv ¼ hg;pv Tg Tpv þ Tb Tpv Rb;pv þ GðsaÞpv vt Epv ; (7)
Epv ¼ gGshr 1 Br Tpv Tr ;
vTb v2 T 1h ðTa Tb Þ=Rb;a þ Tpv Tb Rb;pv ¼ kb 2b þ d vt vx b i þ Tp;eva Tb Rp;b $Abi
Rb;a ¼ ds =ks þ 1=ha :
where the þ exponent indicates that only positive values for terms within the square brackets are to be used. In case of negative values, zero is used. Based on these assumptions, the heat-balance equation for the PV layer, which includes the PV cells, EVA, and TPT, is given by
gdpv rpv cpv
387
Reva;p ¼
ln Deva;o=D
eva;i
2pLeva kp
;
(15) !
Reva;groove ¼
ln Do;groove=D
i;groove
2pLeva kgroove
:
An axial groove structure was designed in the inner face of the heat pipe evaporator (Fig. 5). The equivalent thermal conductivity associated with the grooves can be calculated by [24]
(10)
where a is the effective absorptance of PV/T plate given by the weighted average of the absorptances of PV cell (apv) and black TPT (aTPT), a ¼ gapvþ(1g)aTPT; and rd is the reflectance of the inner cover for diffuse radiation, which can be estimated from rd ¼ 1 aad sad at a radiation incidence angle of 60 [22]. For the base panel, the differential grids were divided as shown in Fig. 4. Two types of grids are labeled, where one grid is connected
(16)
Fig. 4. Differential grid partition of the base panel.
388
P. Gang et al. / Energy 37 (2012) 384e395
kgroove ¼
wf kl kw d þ wkl 0:185wf kw þ kl d : w þ wf 0:185wf kw þ kl d
(17)
where wf is the rib width of the groove; w is the width of the groove; and d is the depth of the groove. Thermal resistance associated with the condensing process is defined as
1
Rcon;i ¼
pDcon;i Lcon hcon;i
;
(18)
where hcon,i is the condensing film coefficient obtained by [15]
i h 0:108 hcon;i ¼ 0:997 0:334ðcosqÞ "
gr2l k3l hfg ml DTcr Lcon
#0:25
0:254ðcosqÞ0:385 Lcon =Dcon;i ½ ;
(19)
Nu ¼ CRem Prn ðPrN =Prs Þ1=4
when Pr 10, n ¼ 3.7, and Pr > 10, n ¼ 3.6. The values of C and m depend on the Reynolds number. The differential grid partition for the water in the heat exchanger is shown in Fig. 6. The upwind scheme is used in the water differential equation. For grid (j), the equation can be expressed as
vTw;j _ w cw Tw;j Tw;j1 mw cw þm vt
¼ Ta Tw;j Rw;a þ Tp;con Tw;j Rw;con ;
Rcon;p ¼
ln Dcon;o=D
con;i
2pLcon kp
Mw;tank cw :
(20)
The heat-balance equation of the evaporator section is expressed as
Mp;eva cp
vTp;eva ¼ Tp;con Tp;eva Reva;con þ Tb Tp;eva Rp;b ; vt (21.a)
while that of the condenser section is expressed as
Mp;con cp
vTp;con ¼ Tp;eva Tp;con Reva;con þ Tw Tp;con Rw;con ; vt (21.b)
1 ; Aw hw
(22)
1 0 : Qw ¼ Mw;tank cw Tw;t Tw;t
kw D
(27)
To describe the total efficiency of the HP-PV/T system, an equation based on the first-law of thermodynamics (energy efficiency) is introduced as follows [26]:
Zt2
hpvt ¼
Qw þ Ac Epv dt
t1
¼ hw þ ghpv ;
Zt2
(28)
Ac Gdt
where Rct is the contact thermal resistance between the heat pipe condenser and the copper sleeve of the heat exchanger; and hw is the convection heat transfer coefficient between the heat exchanger and water obtained by [25]:
hw ¼ Nu
vTw;t _ w cw Tw;out Tw;in ; ¼ Ta Tw;t Ra;wt þ n$m vt (26)
where Mw,tank is the mass of water in the storage tank; Ra,wt is the equivalent thermal resistance between the water and the ambient air; Tw,in and Tw,out are the inlet and outlet water temperatures of solar collectors, respectively; and n is the number of solar collectors. The instantaneous useful heat gain of the system is expressed as
where Rw,con is the equivalent thermal resistance between the heat pipe condenser and water calculated by
Rw;con ¼ Rct þ
(25)
_ w is where mw is the mass of water in a single control volume; and m _ w ¼ rw uw A; and Rw,a is the mass flow rate of the water, that is, m the equivalent thermal resistance between water and ambient air. For the water in the storage tank, the heat-balance equation is given by
and !
(24)
t1
where Epv is calculated by Eq. (8). Based on the second-law of thermodynamics (exergy efficiency), another expression is introduced as follows [7]:
(23)
Zt2
and
εpvt ¼
_ pv dt Exw þ Ac Ex
t1
Zt2
¼ εw þ gεpv ;
(29)
_ sun dt Ac Ex
t1
and
_ pv ¼ Epv ; Ex
Fig. 5. Structure of the heat pipe evaporator.
Fig. 6. Differential grid partition of water in the heat exchanger.
(30)
P. Gang et al. / Energy 37 (2012) 384e395
Ta ; Tw;t
(31)
_ sun ¼ G 1 Ta ; Ex Tsun
(32)
Exw ¼ Qw 1
389
where Tsun is the solar radiation temperature at 6000 K. The relative error (RE) between the simulation values and experimental results is calculated by
RE ¼
Xexp Xsim 100%; Xexp
(33)
where Xsim and Xexp are the simulation and experimental values, respectively. 4. Results and analysis 4.1. Experimental validation Fig. 7 shows the schematic diagram of the HP-PV/T system test rig. The system was composed of a storage tank, circulation pump, and two HP-PV/T solar collectors. The two collectors were arranged parallel to each other at the water circulation loop. The water pump circulated the water between the water-storage tank and the collectors, such that the heat energy of the collectors was removed by the circulating water. The storage capacity of the water-storage tank was 200 L. The total irradiation-collection area for the two collectors was 1.934 m2, and the total PV cell area was 1.11 m2. Fig. 8 depicts the actual setup of the HP-PV/T system test rig. The experiment was carried out in Hefei, a city in the middle region of China (117.23 E and 31.87 N). The two solar collectors were installed facing south with a tilt angle of 45 . The experiment commenced at 8:00 and ended at 16:30 (September 17, 2010). During the experiment, the volume flow rate of the circulating water was set at an almost constant rate of (9.9e10.2) L/min, and the water temperature in the storage tank increased from (28.0 to 47.1) C. The ambient parameters during the experiment are shown in Fig. 9.
Fig. 8. Actual setup of the HP-PV/T system test rig.
The initial conditions for the simulation are obtained from the experimental data. The instantaneous boundary conditions, such as solar radiation, ambient temperature, and mass flow rate of circulating water are directly reported from the experimental data. The inlet temperature of the collectors is set to be equal to the outlet temperature of the storage tank. The inlet temperature of the storage tank is set to be equal to the outlet temperature of the collectors.
Fig. 7. Schematic diagram of the HP-PV/T system test rig.
P. Gang et al. / Energy 37 (2012) 384e395
Ta 38
700
36
600
34
500
32
400
30
300
28
200
8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Epv(exp)
ηpv(exp)
Epv(sim)
ηpv(sim)
14
45 12 40
2
800
50
Electrical gain ( W/m )
40
35
10
30 8 25 20
6
15 4
Electrical efficiencies (%)
G 900
Ambient temperature ( oC )
Intensity of the solar irradiation ( W/m2)
390
10
26
5
Time
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
2
Time Fig. 9. Solar radiation intensity and ambient temperature. Fig. 11. Electrical gain and efficiency.
Fig. 10 shows the temperature of the water in the storage tank. The water temperature in the storage tank increased gradually from (28.0 to 47.1) C. The simulation results agree well with the experimental data, with an RE within 1.0% to 1.5%. Figs. 11 and 12 show the electrical and heat gains per unit collecting area, respectively. Compared with Fig. 9, the electrical and heat gains had very similar patterns as the solar radiation intensity. Electrical gain increased from (13.0 to 48.1) W/m2 in the morning, and decreased to 10.2 W/m2 when the solar radiation decreased to 211 W/m2 in the late afternoon. Heat gain increased from (100.0 to 431.7) W/m2 in the morning, and then decreased to 12.0 W/m2 in the late afternoon. The average electrical and heat gains per unit collecting area during the test time were 34.6 and 269.5 W/m2, respectively. The average total values of the two collectors were 66.9 and 521.3 W, respectively, as shown in Table 2. The electrical and the thermal efficiencies of the HP-PV/T system are shown in Figs. 11 and 12, respectively. The solar radiation transmission through the covers induced the electrical efficiency to decrease relatively sharply in the early morning and in the late afternoon. However, the electrical efficiency had a stable value of approximately 10.3% from 9:00 to 15:00. The thermal efficiency fluctuated between 45.0% and 55.0% from 9:30 to 14:30, and then sharply decreased in the afternoon due to the relatively high water temperature in the afternoon resulting in large heat loss. Decreased solar radiation also led to decreased thermal efficiency. Based on the energy analysis, the average electrical and thermal energy efficiencies during the
test time were 10.2% and 45.7%, respectively. Applying Eq. (28), the average total first-law efficiency (energy efficiency) of the HP-PV/T system is 51.5% (Table 2). Based on the exergy analysis, the average electrical and thermal exergy efficiencies during the test time were 10.7% and 0.9%, respectively. Applying Eq. (29), the average total second-law efficiency (exergy efficiency) of the HP-PV/T system is 7.1%. Although the average thermal energy efficiency can reach a value of 45.7%, the thermal exergy efficiency (εw) is only 0.9%, much lower than the electrical exergy efficiency (εpv, 10.7%) because the thermal energy is low-grade energy, and its power conversion efficiency depends on the temperature difference between a heat and a cold source (ambient, currently). Yet the water temperature obtained by the HP-PV/T system is lower. Hence, only a small part of the thermal energy can be converted into work, and its exergy efficiency is low. Conversely, though the average electrical energy efficiency is only 10.2%, the electrical energy is high-grade energy. The subtotal electrical energy can be converted into work. Thus, its exergy efficiency is much higher than the thermal exergy efficiency. The simulated values are in approximate accordance with the experimental results. For the instantaneous values of electrical gain and efficiency, the REs are at 8.0%. For the instantaneous values of heat gain and thermal efficiency, the REs are within 20.0%. This deviation can be attributed to the fact that glass covers with textured inner surfaces were chosen in the solar collectors, and
Tw,t(exp)
48
500
Tw,t(sim)
Qw(exp)
ηw(exp)
Qw(sim)
ηw(sim)
70 60
2
42 39 36 33
50
300
40 200
30 20
100 30 27
10 8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 10. Temperature of the water in the storage tank.
0
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 12. Heat gain and efficiency.
0
Thermal efficiencies (%)
400
Heat gain ( W/m )
Water temperature ( C)
45 o
80
P. Gang et al. / Energy 37 (2012) 384e395
391
Table 2 The average electrical gain, heat gain, and efficiencies of the HP-PV/T system during the test duration from 8:00 to 16:30.
Per unit area
Total
269.5 W/m2 270.3 W/m2 0.3%
521.3 522.7 0.3%
34.6 W/m2 35.0 W/m2 1.2%
66.9 67.7 1.2%
dy vf dx1 vf dx2 vf dxn þ þ/þ ¼ y vx1 y vx2 y vxn y
(34)
where xi ; ði ¼ 1; .; nÞ are the independent variables of the dependent variable y; and vf =vxi is the error transferring coefficient of the variables. The experimental relative mean error (RME) during the test period can be expressed as [27]
PN RME ¼
jREj N
1
hpvt
εpvt
45.7% 45.8% 0.2%
10.2% 10.3% 1.0%
51.5% 51.7% 0.4%
7.1% 7.2% 1.4%
Epv
Qw
275
35.5
270 265
35.0
260 255 34.5 250 245 34.0
240 235 230 0.00
0.02
0.04
0.06
0.08
0.10
33.5
Mass flow rate of water (kg/s) Fig. 13. Average heat gain and electrical gain with water flow rate in each collector.
Fig. 13 shows the average heat gain and electrical gain per unit collecting area curves versus water flow rate. Heat gain and electrical gain increased with increased water flow rate. However, the increase of the heat gain and the electrical gain slowed down with the increase in water flow rate. The same variation tendency was also found in the total efficiencies (first- and second-law efficiencies) of the HP-PV/T system, as shown in Fig. 14. The influence of water flow rate on heat gain was much stronger than on the electrical gain. Heat gain increases from 233.8 to 262.1 W/ m2, and electrical gain increases from 33.9 to 34.8 W/m2 when the water mass flow rate increases from 0.01 to 0.04 kg/s. Heat gain and electrical gain increase to 271.4 and 35.1 W/m2, respectively, when the water mass flow rate increases to 0.1 kg/s because the increase in water mass flow rate results in decreased temperatures in the PV cells and the base panel. However, the influence of the temperature on the electrical gain is much weaker than that on the heat gain.
(35)
According to Eqs. (34) and (35), the RME of all variables are calculated, and the results are given in Table 3. 4.2. Different mass flow rates of the water
εpvt
ηpvt
53
7.2
52
First-law efficiency (%)
Numerical simulation was carried out to study the influence of water flow rate on the performance of the HP-PV/T system. The structural parameters of the HP-PV/T collector were set as follows: PV cell covering factor is 0.574 (Ac ¼ 0.967 m2, Apv ¼ 0.555 m2), and the tube space of heat pipes is 80 mm. The weather data given in Fig. 9 were used for the calculation in the simulation.
7.1
51 7.0
50
6.9
49 48
6.8
47 6.7
46 Table 3 The experimental RME of the variables.
45 0.00
Variable
Tw
Epv
Qw
hpv
hw
RME
0.064%
0.45%
23.1%
1.41%
24.1%
0.02
0.04
0.06
0.08
0.10
Second-law efficiency (%)
RE ¼
hpv
2
their influences on the transmission of solar radiation were different from the smooth glass plates. However, these differences were not considered in the model. Moreover, a global radiation on the collector surface was used for the simulation. The direct and diffuse radiations were not processed separately, which resulted in a deviation between the simulated values and experimental results. Copper-constantan thermocouples (T-type) with an accuracy of 0.2 C were used to measure the water temperatures, which resulted in a measured deviation of the water temperature. Therefore, for the instantaneous heat gain, the measured deviation is another reason for the deviation between the simulated values and the experimental results. The REs between simulated values and experimental results are all within 1.4% for the average values of electrical gain and efficiency, heat gain and thermal efficiency, and total efficiencies. The errors and inaccuracies in the test instrumentations led to some errors in the experimental data. In the present study, the experimental error of the independent variables, such as temperature, PV electric power, and solar radiation intensity, was determined by the accuracy of the corresponding test instrumentations. For the dependent variables, such as electrical gain, heat gain, and efficiencies, their experimental errors can be calculated from the experimental error of the independent variables. According to the literature by Ji et al. [27], the RE of dependent variable y can be calculated by
hw
Average electrical gain ( W/m )
590
Electrical gain Epv (W) Total
2
Experiment Simulation RE
Heat gain Qw (W) Per unit area
Average heat gain ( W/m )
Average G (W/m2)
Result
6.6
Mass flow rate of water (kg/s) Fig. 14. Total efficiencies of the HP-PV/T system with water flow rate in each collector.
P. Gang et al. / Energy 37 (2012) 384e395
4.3. Different PV cell covering factors
4.4. Different tube space of heat pipes The dimension of the space between two adjacent heat pipes has a significant influence on the heat transfer from the collectors to the water. In this section, a numerical simulation was carried out to study the performance of the HP-PV/T system under different tube spaces of heat pipes. The calculating parameters follow. The mass flow rate of the water in each collector was _ w ¼ 0:085kg=s. The solar irradiation collecting area of each m collector was Ac ¼ 0.967 m2. PV cell covering factor of the solar
Qw
52.4 8
52.2 52.0
6
51.8 51.6
4
51.4 51.2 51.0 0.0
2 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Coverage ratio of the PV cells Fig. 16. Total efficiencies of the HP-PV/T system with the PV cell covering factor.
collector was 0.574 (Apv ¼ 0.555 m2). The number of collectors was two. The weather data are shown in Fig. 9. Table 4 gives the tube space heat pipes and the number of the heat pipes in each collector. The average heat gain and electrical gain per unit collecting area are shown in Fig. 17. Heat gain and electrical gain exhibited a nearly linear decrease with increased tube space of heat pipes because the increased tube space of heat pipes resulted in increased thermal resistance between the base panel and the heat pipes. Moreover, when the tube space increases, the number of heat pipes in each collector will decrease (Table 4). The total heat transfer area will also decrease resulting in larger thermal resistance between the heat pipe condensers and the flowing water. Not all heat of the absorber plate is fully transferred to the flowing water, higher temperature of the absorber plate, and larger heat loss to the ambient. The heat gain decreases from 290.2 to 234.1 W/m2, and the electrical gain decreases from 35.8 to 33.9 W/m2 when the space between two adjacent heat pipes increases from 0.05 to 0.15 m.
Table 4 Space between two adjacent heat pipes and the number of the heat pipes in each collector. Space (m) Heat pipes (number) Energy efficiency (hpvt) Exergy efficiency (εpvt)
0.05 15 55.2% 7.5%
0.07 11 53.0% 7.3%
0.09 8 50.6% 7.1%
Qw
0.11 7 49.1% 7.0%
Epv
0.13 6 47.4% 6.8%
0.15 5 45.4% 6.7%
300
38
290
37
40 280 30 270 20 260
10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1.0
Coverage ratio of the PV cells Fig. 15. Average heat gain and electrical gain with the PV cell covering factor.
280 36 270 35 260 34 250 33
240 230 0.04
0.06
0.08
0.10
0.12
0.14
2
Average electrical gain ( W/m )
290
2
50
Average heat gain ( W/m )
2
Average electrical gain ( W/m )
60
2
Average heat gain ( W/m )
10
52.6
Epv
300
250 0.0
12
52.8
First-law efficiency (%)
The PV cell covering factor of the HP-PV/T collector (g) is an important parameter for an HP-PV/T system. To study the influence of parameter g on the performance of the HP-PV/T system, a numerical simulation was carried out under the following conditions: mass flow rate of the water in each collector is _ w ¼ 0:085kg=s; solar irradiation collecting area of each collector m is Ac ¼ 0.967 m2; and the number of collectors is two. The tube space of the heat pipes is 80 mm. The weather data are shown in Fig. 9. Fig. 15 shows the average heat gain and electrical gain per unit collecting area. Electrical gain linearly increases with increased PV cell covering factor. However, heat gain linearly decreases with increased PV cell covering factor because when the PV cell covering factor increases, the PV area of the collector increases. Hence, the electricity produced from the solar irradiation increases. Conversely, because solar irradiation converted into the electricity increases, the part converted into heat decreases. The total efficiencies of the HP-PV/T system are shown in Fig. 16. The second-law efficiency (exergy efficiency) of the HP-PV/T system linearly increases with increased PV cell covering factor from 1.3% to 11.6% when the PV cell covering factor increases from 0 to 1. The reason for the low exergy efficiency of 1.3% is that, when the PV cell covering factor is equal to zero, no PV cell is present on the collector. Thus, no electricity output is available except thermal energy. Thermal energy is low-grade energy. In the HP-PV/T system, the water temperature is lower, as seen in the Eq. (31). Thus, its total exergy output is low. Therefore, according to Eq. (29), the exergy efficiency of the HP-PV/T system is low. The first-law efficiency (energy efficiency) of the HP-PV/T system also increases with increased PV cell covering factor. The rate gradually rises because the increasing rate of the electricity output is higher than the decreasing rate of the heat gain when the PV cell covering factor increases.
εpvt
ηpvt
53.0
Second-law efficiency (%)
392
32 0.16
Tube space of heat pipes (m) Fig. 17. Average heat gain and electrical gain with the tube space of heat pipes.
P. Gang et al. / Energy 37 (2012) 384e395
ηpvt
56
εpvt
performances of the HP-PV/T system using the following three types of collectors:
7.6
52 7.2 50 7.0 48 6.8
46 44 0.04
0.06
0.08
0.10
0.12
0.14
6.6 0.16
Tube space of heat pipes (m) Fig. 18. Total efficiencies of the HP-PV/T system with the tube space of heat pipes.
The first- and the second-law efficiencies of the HP-PV/T system linearly decrease with increased tube space of heat pipes (Fig. 18). The first-law efficiency decreases from 55.2% to 45.4%, and the second-law efficiency decreases from 7.5% to 6.7% when the tube space of heat pipes increases from 0.05 to 0.15 m. Reducing the tube space of heat pipes can improve the performance of the HP-PV/T system as shown in Table 4. However, a small tube space will result in a collector requiring many heat pipes and will increase the cost of the collector. Hence, tube space of heat pipes smaller than 0.08 m was not used in our collector for economical reason. 4.5. Absorber plate with different kinds of solar absorptive coating Three different types of collectors are given in this section. Numerical simulations were carried out to calculate the
solar selective coating black pigment coating no coating
48
o
Water temperature ( C)
Type 1: Absorber plate with solar selective coating, absorbance of the coating is 0.95, and emittance is 0.05; Type 2: Absorber plate with black pigment coating, absorbance of the coating is 0.98, and emittance is 0.98; and Type 3: Absorber plate without any coating, PV cells are directly laminated onto an aluminum plate with surface polished, absorbance of the aluminum is 0.09, and emittance is 0.03.
7.4
Second-law efficiency (%)
First-law efficiency (%)
54
393
44 40 36 32 28
The calculating parameters follow. _ w ¼ 0:085kg=s. Mass flow rate of the water in each collector is m Solar irradiation collecting area of each collector is Ac ¼ 0.967 m2. PV cell covering factor of the solar collector is 0.574 (Apv ¼ 0.555 m2). The number of collector is two. Tube space of heat pipes is 80 mm. Weather data are shown in Fig. 9. Fig. 19 shows the water temperature of the storage tank. The water temperatures increase from 28.0 to 48.2 C and from 28.0 to 47.1 C, respectively, when using the collector with solar selective coating and that with black pigment coating. For the collector without any coating, the water temperature only increases from 28.0 to 41.3 C. The collector with solar selective coating has the best thermal performance. The average heat gain reaches 284.7 W/ m2 with a thermal efficiency of 48.2% as shown in Table 5. The collector with black pigment coating comes next, with an average heat gain of 270.3 W/m2 and a thermal efficiency of 45.8%. The thermal performance of the collector without any coating is the worst with an average heat gain of only 187.9 W/m2 and a thermal efficiency of 31.8%. However, the collector without any coating has the best electrical performance, with an average electrical gain reaching up to 36.5 W/m2 and an electrical efficiency of 10.8% because electrical efficiency of the PV module is affected by its temperature (Eq. (8)). When the temperature increases, electrical efficiency decreases. The collector without coating absorbs the least solar radiation, and its PV module temperature is lowest. Thus, its electrical efficiency is the highest. Similar to thermal performance, the best total PV/T efficiency is obtained by the HP-PV/T system using collectors with solar selective coating. The average total first-law efficiency (energy efficiency) is 54.1%, and the average total second-law efficiency (exergy efficiency) is 7.3%. The one using collectors with black pigment coating comes next which can reach an average total first-law efficiency of 51.7% and an average total second-law efficiency of 7.2%. The system using collectors without coating has average total first- and second-law efficiencies of only 38.0% and 6.8%, respectively. For a collector with a PV cell covering factor of 0.574, HP-PV/T system using the collectors with solar absorptive coating can greatly improve its total PV/T performance. 4.6. Cost analysis
8:00
9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Increasing the PV cells covering factor and reducing the tube space of heat pipes can improve the overall performance of an HPPV/T system. However, these would lead to a rising cost of each HP-
Time Fig. 19. Water temperature of the storage tank.
Table 5 Average electrical gain, heat gain, and efficiencies of the HP-PV/T system using three different types of collectors (time: 8:00e16:30). Type
Selective coating Black TPT Without coating
Average G (W/m2) 590
Heat gain Qw (W)
Electrical gain Epv (W)
Per unit area
Total
Per unit area
Total
284.7 W/m2 270.3 W/m2 187.9 W/m2
550.6 522.7 363.3
34.8 W/m2 35.0 W/m2 36.5 W/m2
67.2 67.7 70.5
Total energy Qtotal (W)
Total exergy Extotal (W)
hw
hpv
hpvt
εpvt
617.8 590.4 433.8
78.7 77.7 74.0
48.2% 45.8% 31.8%
10.3% 10.3% 10.8%
54.1% 51.7% 38.0%
7.3% 7.2% 6.8%
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Table 6 Cost of the PV cell of each HP-PV/T collector. PV cell covering factor PV cell area (m2) Cost of the PV cell ($)
0.0 0.0 0.0
0.2 0.2 19.5
0.4 0.4 39.0
0.6 0.6 58.5
0.8 0.8 78.0
1.0 1.0 97.5
Table 7 Cost of the heat pipe of each HP-PV/T collector. Tube space (m) Number of heat pipes Cost of the heat pipe ($)
0.05 15 104.1
0.07 11 76.4
0.09 8 55.5
0.11 7 48.6
0.13 6 41.6
0.15 5 34.7
PV/T collector. For example, in an HP-PV/T collector with a collecting area of 1 m2, the cost of the PV cell and heat pipes are calculated, as shown in Tables 6 and 7, respectively. When the area of the PV cell increases 0.2 m2, the cost of the PV cell of each collector will increase about 19.5$. The annual average electrical efficiency of the PV cell is about 10.0%. Take Hefei (China) as example, its annual average solar radiation is about 1295.53 kWh/(m2 year). Hence, the electricity output of per unit area PV cell will be about 129.55 kWh/ (m2 year). The average residential electrovalence of China is about 0.09$/kWh. Calculating based on this, then the payback period of the PV cell is about 8e9 years. If the government subsidy can reach 50% of its cost, the payback period will decrease to 4e5 years. The life of the PV cell can reach 20 years. Thus, higher PV covering factor has better economic benefit. The cost of a heat pipe is about 6.9$ when tube space of heat pipes is 0.09 m, producing a collector requiring eight heat pipes. The cost of the heat pipes is about 55.5$. However, when the tube space is 0.05 m, producing a collector will require 15 heat pipes. The cost of the heat pipes of each collector alone will reach 104.1$. Yet, the energy efficiency only increases with an absolute value of 4.6%. Hence, a tube space of 0.09 m is suitable for the HP-PV/T collector when considering cost. Overall, considering both cost and performance, high PV cell covering factor and tube space of about 0.09 m is beneficial for an HP-PV/T collector. 5. Conclusion A dynamic model of the HP-PV/T system was presented and validated by experimental results. Based on the validated model, the performances of the HP-PV/T system under the conditions of different water flow rates through the collectors, different PV cell covering factors of the collectors, different tube spaces of heat pipes, and absorber plate with three different kinds of solar absorptive coatings were studied. The results are summarized as follows: 1. The recorded data demonstrated that the simulated values agreed with the experimental results. For the instantaneous values of electrical gain and efficiency, the REs are at 8.0%. For the instantaneous values of heat gain and thermal efficiency, the REs are within 20.0%. The average total first- and secondlaw efficiencies of the HP-PV/T system in the test duration are 51.5% and 7.1%, respectively. 2. Heat gain, electrical gain, and total PV/T efficiencies (first- and second-law efficiencies) of the HP-PV/T system increase with increased water flow rate. However, the increasing rate will gradually decrease with increased water flow rate, and the increase of the electrical and heat gain will be very small when the water flow rate is larger than 0.07 kg/s. The influence of water flow rate on heat gain is much stronger than on electrical gain.
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