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Using air flow to alleviate temperature elevation in solar cells within asymmetric compound parabolic concentrators
Solar Energy 81 (2007) 173–184 www.elsevier.com/locate/solener
Using air flow to alleviate temperature elevation in solar cells within asymmetric compound parabolic concentrators Tapas K. Mallick a
a,*
, Philip C. Eames
a,1
, Brian Norton
b,2
Centre for Sustainable Technologies, School of Built Environment, University of Ulster, Newtownabbey BT37 0QB, Northern Ireland, UK b Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland Received 4 August 2005; received in revised form 7 April 2006; accepted 11 April 2006 Available online 2 June 2006 Communicated by: Associate Editor Hansjo¨rg Gabler
Abstract Air filled asymmetric compound parabolic photovoltaic concentrators (ACPPVC) have been studied using a comprehensive validated unified model for optics and heat transfer in line-axis solar energy systems. The heat transfer that occurs within the cavity of a single concentrator, multiple concentrators, the space between adjacent concentrators and in an air duct behind the photovoltaics was simulated and is presented. For a range of insolation intensities incident at the aperture cover the maximum PV cell operating temperatures are determined. From the simulations undertaken the effects on solar cell surface temperatures resulting from air flow in the air filled space at the front of the system and in the air duct to the rear of the solar cells are clearly evident. 2006 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic concentrator; Heat transfer; Temperature elevation
1. Introduction For photovoltaics to achieve wide-scale implementation as a building fac¸ade element it is essential that their cost is reduced while maintaining or exceeding the present level of solar to electrical conversion performance. Concentrating solar energy onto a smaller area allows a reduction in the output electricity cost if the cost of the concentrator is less than that of the displaced photovoltaic materials. A truncated asymmetric compound parabolic non-imaging (Welford and Winston, 1978) concentrator has been designed and characterised experimentally for south-facing building fac¸ade integration in the UK (Mallick, 2003). Truncation *
Corresponding author. Tel.: +44 2890 368568; fax: +44 2890 368239. E-mail addresses: [email protected], [email protected] (T.K. Mallick), [email protected] (P.C. Eames), [email protected] (B. Norton). 1 Tel.: +44 2890 368244; fax: +44 2890 368239. 2 Tel.: +353 1 402 7135; fax: +353 1 402 7099. 0038-092X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.04.003
allows a significant reduction in the materials required for the reflectors and thus cost (Rabl, 1976). Abdel-Khalik et al. (1978) developed a vorticity-based triangular finite element model for natural convection inside the cavity of a flat-plate-absorber CPC that assumed isothermal absorber and cover plate surfaces and adiabatic reflectors. A conduction Nusselt number was defined and a critical Rayleigh number was obtained by extrapolating from the convective Nusselt number obtained to the conduction limit. The effect of varying the ratio of Nusselt number to the conduction Nusselt number on the ratio of Rayleigh number to the critical Rayleigh number were given for full CPCs of different concentration ratios. Several studies (Hseih, 1981; Prapas et al., 1987; Chew et al., 1989; Eames and Norton, 1993a,b, 1995; Eames et al., 2001) have examined natural convection in the air-filled cavity of tubular-absorber CPC’s and inverted-flat-plate absorber CPC’s. The thermal analysis of tubular-absorber CPC’s undertaken by Hseih (1981) did not account for the effect of long-wave radiation at the system reflectors and
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Nomenclature h G H R1 R2 T V W a, b g u
heat transfer coefficient (W m2 K1) insolation (W m2) height (m) left parabola right parabola temperature (K) velocity (m s1) width (m) acceptance half angle () efficiency solar incidence angle ()
Subscripts amb ambient apt aperture c convective eff effective elec electrical max maximum out outlet 2 half pv surface of the solar cells rear rear of the absorber
assumed that the reflector, absorber, and cover plate were all at different constant temperatures. This assumption is not realistic. Prapas et al. (1987) performed a more thorough heat transfer analysis of different CPC configurations, taking into account energy absorbed at the reflector. The model assumed unrealistically that the reflector, absorber and cover plates were all at constant temperatures. The temperature at the absorber, reflector and the aperture cover were also non-uniform to an extent depending on the interaction between the flux intensity, thermal conduc-
Exterior convection: Specified boundary conditions hc=1Wm-2K-1
tivity and heat removal or loss. A model using triangular finite elements was presented by Chew et al. (1989) for a tubular-absorber CPC that predicted a uni-cellular flow for vertical CPC orientation. Their model did not allow for conduction in the reflector and the aperture cover glass. Such short-comings were addressed in the ‘unified’ model developed by Eames and Norton (1993a); and their subsequent ‘comprehensive unified’ model (Eames et al., 2001). Eames and Norton (1993b), carried out detailed analysis, validated experimentally, of the thermophysical behaviour
Glass aperture cover: Specified boundary conditions hc = 12 Wm-2K-1, Insolation =1000 Wm-2 unless specified otherwise.
Aluminium back plate: Specified boundary conditions hc=9Wm-2K-1
Internal convection: Specified flow boundary conditions
Inter-trough convection Vertical φ
Incident solar radiation: Optics of solar energy conversion, ray trace analysis. Horizontal φ = Solar incidence angle
Solar cell: ηelec=15% Reflector
Conduction in all boundaries: PV, reflector, aperture cover and back plate Back conductive loss: Specified boundary conditions. Heat transfer to working fluid, free and forced convection.
Energy Conversion: Specified boundary conditions, electrical output, heat generation
Long-wave radiative exchange via elementary view factors, CFD for convective fluid behaviour specified in the ‘unified’ model (Eames and Norton, 1993b).
Convective loss: Specified boundary conditions
Fig. 1. Schematic diagram of a five trough asymmetric compound parabolic photovoltaic concentrator showing energy transfer mechanisms.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
of tubular-absorber CPC’s and tubular-absorber CPC’s with modified reflectors for 30, 45 and 60 acceptance half angles over a range of inclinations. Long-wave radiative exchange between the absorber, reflectors and aperture cover was taken into account through a view factor analysis for the element faces. For a 60 half-acceptance angle CPC the internal convective flow was forced to change from a bi-cellular flow to a uni-cellular flow at an inclination angle greater than 45. To date no reports of such similar detailed analysis of the heat transfer within asymmetric compound parabolic concentrators and their possible application to photovoltaic systems have been produced. The work presented in this paper details optics and heat transfer analysis for an asymmetric compound parabolic concentrator suitable for building integrated photovoltaic applications. The modelled asymmetric compound parabolic photovoltaic concentrator (ACPPVC) system consists of a 3 mm thick aluminium back plate, to which an array of 6 mm thick aluminium reflector supports are attached. A 0.15 mm thick stainless steel reflector substrate covered with a 68 lm thick mirror reflector was glued to the reflector supports. The solar cells were attached to the rear aluminium plate via an intermediate layer of Ethylene Vinyl Acetate (EVA). The PV concentrator system consists of 40 half-size (50 mm · 125 mm) BP Saturn solar cells (Eager et al., 2002) with eight strings of five cells connected in series. The detailed design and fabrication of the photovoltaic concentrator has been reported previously (Mallick et al., 2004). An extensive experimental characterisation of this ACPPVC system showed an increase of the maximum power point by 62% compared to its non-concentrating counterpart (Mallick et al., 2006).
heat loss from the rear aluminium plate. The thermophysical properties of the materials used in the simulations are given in Table 2. The fluid properties of air at 293 K and atmospheric pressure were used in the simulations. As the reflecting film (3M, 2001) thickness was less than 68.6 · 106m, conduction within it was considered negligible compared with that of the 0.15 mm thick stainless steel reflector substrate. In the absence of forced convective heat transfer from the aperture cover the heat transfer is mainly due to free convection and long-wave radiation. For free convection, Table 1 System geometry and dimensions
Acceptance half angles (hs, ha) Absorber width (mm) Aperture width (mm) Length of lower reflector (R1 mm) Length of upper reflector (R2 mm) Concentration ratio Truncation (%) R1, R2 System aperture dimensions
Untruncated system
Truncated system
50 and 0 50.0 116 154.0
– 50.0 100.4 71.0
84.4 2.32 – Single-trough Five trough
84.5 2.01 54, 0 0.10 m · 0.625 m 1.0 m · 0.650 m
Table 2 Thermophysical properties assumed in the simulations Component Absorber
Material and properties Material Thermal conductivity Thickness Absorptance
2. System modelling A ‘comprehensive unified’ model for optics and heat transfer in line-axis concentrating solar energy collectors (Eames et al., 2001) was employed in the analysis of the designed concentrating systems illustrated in Fig. 1. This extensively experimentally validated model allows the detailed analysis of the spatial variation of the solar energy flux in the system and the resulting convective, conductive and long-wave radiative heat transfer for both solar thermal or photovoltaic applications. Using this model the thermophysical behaviour of single-trough, and five trough asymmetric compound parabolic photovoltaic concentrators have been evaluated. Natural and forced convection conditions within the air ducts between the aperture cover and the front of the reflectors (front) and between the back plate and the building wall (rear) were simulated and techniques to reduce solar cell temperature elevation implemented. The system geometry and dimensions used in the simulations are given in Table 1. The energy transfer mechanisms are illustrated in Fig. 1 for a five trough system. This includes the exterior heat loss from the reflector boundary, heat loss from the glass aperture cover and the
175
Back plate
Silicon solar cell (Bruton et al., 2002) 148 W m1 K1 0.3 mm 1
Material Thermal conductivity Thickness
Aluminium 238 W m1 K1
Material Thermal conductivity Thickness
Stainless steel 15.1 W m1 K1
Reflector
Material Thickness Reflectance Absorptance
VM2000 (3M, 2001) 68.6 · 106 m 0.98 0.02
Aperture cover
Material Heat loss coefficient Thermal conductivity Thickness Extinction coefficient Insolation
Low-iron glass 12 W m2 K1
Reflector substrate
3 mm
0.15 mm
1.05 W m1 K1 4 mm 0.00003512 m1 1000 W m2 unless specified otherwise
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A representative value of 12 W m2 K1 was therefore employed for the aperture glass cover heat loss coefficient. The rear of the mirror was 0.15 mm thick stainless steel. The heat loss co-efficient through the stainless steel was 0.75 W m2 K1. The overall heat loss coefficient for the aluminium substrate was calculated assuming the system
the predicted heat transfer coefficient is between 2.8 W m2 K1 and 5.7 W m2 K1 (Duffie and Beckman, 1991). In the presence of forced convection assuming a wind velocity of 2 m s1 to 3 m s1 the heat loss coefficient lies in the range of 8.8 W m2 K1 to 16.1 W m2 K1 (Duffie and Beckman, 1991).
Solar incidence angle 60° 45
50
Solar incidence angle (o) 55 60
65
70
7000
Reflector 1
Absorbed energy (Wm-2)
6000
5000
4000
3000
2000
1000
0 0
Reflector 2 (a)
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Distance across solar cell (from lower reflector) (m)
(b)
Fig. 2. (a) Illustrative ray trace diagram for a single-trough system, (b) energy distribution at the solar cell for 1000 W m2 solar radiation incident at various incidence angles on the glass aperture cover.
Fig. 3. Example of a finite element mesh employed for the simulations of a five trough system: (a) enlargement of reflective fins, (b) enlargement of reflector back plate junction (c) enlargement of inter-reflector space.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
31
35
PV cell
27
36
27
28
25
37
35 29
26
28
40
34
30
36
22
23
27
25
24
28
32
28
Aluminium back plate
Aperture cover
30
29
25
-1
Reference vector = 0.05 ms Upper reflector
26
PV cell Aluminium back plate
Aperture cover
26
Reference vector = 0.05 ms-1 Upper reflector
at the back of aluminium substrate the heat transfer coefficient from the back of the aluminium substrate was calculated using
30
was integrated onto a vertical building wall and the overall thermal resistance of the building was 1.462 m2 K W1 (CIBSE, 1999). For a convective flow
177
27
Air
34
38
26
26
Air 33
26
23
25
26
26
Lower reflector
25
26
27
28
32
36
(b)
(a) 35
38
36
48
PV cell 33
51
Aluminium back plate
34
44
Aperture cover
-1
Reference vector =0.05 ms Upper reflector
30
41
PV cell 45
Aperture cover
52 52
Reference vector = 0.05 ms-1 Upper reflector
Aluminium back plate
Lower reflector
32
35
26
25
29
32
40
30
26
32
40
30
29
40
26
26
31
26
26
30
27
29
51
43
42
29 55
35 34
57
49
42
46
29
42
41
49 58
40
Air
59
41
33
45
46
60
30
38
38
52
38
32
44
42
Lower reflector
44 38
40
41
47
51
49
(d)
43
60
50
Aluminium back plate
37
67
56
66
6 64 4
41
44 43
75
40 38
57
37
65
56
68
67
7271
63
64
49
59
67
70
59
65
68
60
59
5255
42
60 61
66
62
Aperture cover
68
67
37
59
65
PV cell
48
58
PV cell
61
56
55
56
58
Reference vector = 0.05 ms-1 Upper reflector 62
41
Aperture cover
51
Reference vector = 0.05 ms-1 Upper reflector
66
42
43
(c)
Aluminium back plate
Lower reflector
44
54
34
37
44
42
60
37
49
48
47
35
37
49
40
49
Air
29
54 4548 49
30
22
30
47
54 61
(e)
55
56
50
56
Lower reflector
54
44
58
77 75 67
48
60
59
40
53
53 51
5960 6624
62 59
4343 49
41
56
41 57
56
56 56
70 80
50
52
41
42
38 80
51
63
62
Air 60
58
51 50
61
76 78
37
50 50
70 70
80 77
45
54
54
52
69
54
63
62
47
Air 5555
61
67 58
56
70
55
56 63
73
66
60 67
56
59 64
5455
45 48 553 3
Lower reflector
(f)
Fig. 4. The theoretically predicted isotherms and velocity vectors for a single-trough system with boundary conditions given in Fig. 1. The isotherms are at 1 C interval. The solar radiation incident at an angle 60 at the aperture cover was (a) 200 W m2, (b) 400 W m2, (c) 600 W m2, (d) 800 W m2, (e) 1000 W m2 and (f) 1200 W m2.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184 Solar radiation -2 = 600 Wm
0.6 28
66
Reflector substrate
0.55 59
38
32
0.5
0.5 52
67
0.45
59
0.2
28
39
50
72
68
90
0.2
70
Air 68
Aluminium back plate
65
0.15
88
32
74
38
47 64
Aperture cover
0.1
61
0
24
Support frame
36
38
0
32
46 76
28
0.05
24
52
22
0
80
84
34
0
0.05
31
Support frame
Support frame
86
0.05 30
Aperture cover
56
45
38
72
56
0.1
32
Aluminium back plate
34
Aperture cover
0.1
0.05
0.25
PV cell
52
0.15
70
70
Air 47
0.15
76
0.3
40
31
66
System dimension (m)
45 38
0.25
PV cell
80
84
70
Aluminium back plate
59
45
Air
0.3
0.35
48
0.2
59
78
38
0.35
42
PV cell
34 36
0.25
70
54
0.3
System dimension (m)
26
40
34
System dimension (m)
0.35
Air
Air
36
52
34
86
0.4
0.4
Air 33
38 46
70
74 36
0.4
Reflector substrate
78 78 90
0.45
78
0.5
Reflector substrate
38
0.45
44 34 62
45
0.55
40
38
36
68 82
52
39
0.55
Solar radiation -2 = 1000 Wm
0.6
31
29
44
Solar radiation = 200 Wm-2
0.6
32
178
0.1
0.15
System dimension (m)
0
0.05
0.1
0.15
System dimension (m)
(a)
0
0.05
0.1
0.15
System dimension (m)
(b)
(c)
Fig. 5. The theoretically predicted isotherms and velocity vectors for a five trough system with the boundary conditions given in Fig. 1 for solar radiation of (a) 200 W m2, (b) 600 W m2, (c) 1000 W m2. The air gap between the concentrator and the aperture cover is 20 mm and the isotherms are at 1 C intervals.
hrear Apv T pv T amb ¼ GAapt ð1 gÞ
ð1Þ
For a ‘SATURN’ solar cell of 15% electrical conversion efficiency (Bruton et al., 2002), a temperature difference of 60 K and an insolation of 1000 W m2, assuming all heat flows to the rear then the value of hrear, the overall heat transfer coefficient would be 21.3 W m2 K1. Allowing for heat loss from the aperture cover of 12 W m2 K1 gives a heat transfer coefficient from the rear of the aluminium back plate to ambient of 9 W m2 K1. Ray tracing was used to predict the solar flux absorbed at the aperture cover, at the reflectors and at the PV surface (Mallick et al., 2002). Reflective losses at the glass aperture cover have been included. An illustrative ray trace diagram is presented in Fig. 2a for solar radiation incident at an angle of 60 to the vertical. The predicted energy distributions incident at the solar cell surface are presented in Fig. 2b for 1000 W m2 solar radiation incident at the glass cover. At low solar incidence angles (e.g., less than 45 to the vertical), the primary peak in the incident energy occurs adjacent to reflector 1 due to reflections from reflector 2. The location of the peak energy intensity moves from the left side to the right side (i.e., from reflector 1 towards
reflector 2) as the solar incidence angle increases. In addition to the primary peak energy intensities, secondary peaks can be seen for solar incidence angles of 45, 50 and 55. It can be seen from Fig. 2b that two peaks occur for a 60 incidence angle as would be expected from the ray trace diagram illustrated in Fig. 2a. Energy distributions determined using ray trace analysis for a solar incidence angle of 60 were used in the thermal analysis. The finite element mesh used for this analysis uses eight node isoparametric quadrilateral elements. An example of the finite ele-
Table 3 Average predicted PV surface and aperture cover temperatures for different incident insolation intensities Incident insolation (W m2)
Average PV surface temperature (C)
Average aperture cover temperature (C)
200 400 600 800 1000 1200
30.4 40.8 51.3 61.7 71.8 82.0
22.0 25.0 28.2 31.4 34.7 38.3
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
ment mesh employed for the five trough simulation is shown in Fig. 3. The stainless steel reflector substrate (shown in Fig. 3a) acts as a fin within the system and increases the heat transfer from the PV which leads to reduced PV cell operating temperature. 3. Predicted thermofluid behaviour for 50 effective acceptance half angle single-trough system Simulations were undertaken for 200, 400, 600, 800, 1000 and 1200 W m2 insolation incident at 60 from the vertical on to the aperture cover of a 50 acceptance half angle single-trough system truncated by 54% with a constant heat loss from the aluminium back plate to the ambient. Isotherms at intervals of 1C and velocity vector diagrams are presented in Fig. 4. The velocity vectors are scaled to the reference vector of magnitude 0.05 m s1. The predicted average PV surface temperatures and average aperture cover temperature are shown in Table 3. The photovoltaic concentrator has a concentration ratio of 2.0, thus 1000 W m2 incident insolation was concentrated to 2000 W m2 at the PV cells. For a mono-crystalline Si-based flat non-concentrating PV panel a solar cell temperature of 75 C has been reported at 1000 W m2 incident insolation (Brinkworth et al., 1997). Thus the predicted average PV surface temperature of 71.8 C (when incident insolation was 1000 W m2 as shown in Table 3) is comparable to that reported previously (Brinkworth et al., 1997) when heat is lost from the rear of the concentrating panel. Although the predicted velocity profiles are similar for all solar radiation intensities, at higher solar radiation intensities the air velocity adjacent to the boundary increases as the mean temperature difference between the aperture and the solar cell increases. The fluid flow can be seen from Fig. 4 to consist of a major circulation surrounded by three smaller secondary circulations resulting due to heat loss from the reflectors. Due to the heat trans-
fer adjacent to the boundaries predicted air flow is significant, however in the central region of the cavity the air velocity is low. 4. Theoretically predicted thermofluid behaviour of a five trough system Simulations were undertaken for 200, 400, 600, 800 and 1000 W m2 insolation incident on a 50 acceptance half angle five trough system truncated by 54%. The predicted isotherms for solar radiation intensities of 200, 600 and 1000 W m2 incident at the aperture are shown in Fig. 5. The design included an air gap of 20 mm between the aperture cover glass and the tips of the individual reflector troughs. The isotherms are at 1 C intervals. The predicted maximum temperature at the PV surface was 95 C when the incident solar radiation was 1000 W m2. The heat loss from the rear aluminium plate depends on wind velocity and ambient temperature. Providing an air gap adjacent to the aperture glass cover and at the rear plate enables a significant temperature reduction achieved. This can be seen inside all individual troughs, however only a minor change in isotherm pattern occurred for higher solar radiation intensities. Increased insolation intensity leads to higher temperatures which cause the thermal plume to be thinner compared to those predicted for lower insolation intensities. For these simulations although the predicted velocity profile is similar in form for all insolation intensities, at higher insolation intensities the air velocity near to the boundaries increases as the mean temperature difference between the aperture cover and the PV cell increases. The air flow adjacent to the glass cover is downwards where it is being cooled, with a upward flow predicted at the tip of the reflectors were consecutive concentrators join together. Heat transfer from the hot PV surfaces to the air causes it to flow upwards in the system towards the upper reflector. The predicted maximum temperature rise
Average PV cell temperature
100
95
Average aperture cover temperature
90
80
80
Temperature (oC)
179
66
70 53
60 50
39
40 30
35
32
29
27
24
20 10 0 200
400
600
800
1000
Incident solar radiation intensity (Wm-2)
Fig. 6. The predicted average PV cell temperature and average aperture cover temperature for different insolation intensities incident at the aperture cover for a five trough concentrator system.
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of the PV cells was 39 K. For this five trough system the fluid flow consists of in each collector trough a major circulation surrounded by three smaller secondary circulations. The lengths of the upper and lower reflectors of each trough are of different lengths this leads to unequal rates of heat transfer from the reflectors to the air which in turn
helps promote a reverse circulation adjacent to the lower reflector. The reverse circulation intensity increases as incident solar radiation intensity increases from 200 W m2 to 1000 W m2. The predicted thermal plumes are thinner at higher solar radiation intensity due to the mean temperature of the air and the temperature difference between the
Fig. 7. The predicted isotherms in the five trough concentrator system for (a) 10 mm, (b) 20 mm, and (c) 30 mm wide front channels adjacent to the aperture cover with an inlet air velocity of 1.0 m s1. The isotherms are at 2 C intervals and the solar radiation incident at the aperture cover was 1000 W m2.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
glass aperture cover and PV cell temperature being larger. Higher temperatures at the PV surface leading to higher air temperatures and thus increased buoyancy leads to the air flow velocity inside each individual reflector trough increasing. When compared to those in other regions, the magnitude of air flow in the space between consecutive concentrator troughs is small for all insolation levels, a consequence of this region being surrounded completely by boundaries at nearly the same temperature leading to minimal force for fluid motion. From Fig. 5 it can be seen that the upper reflector has a higher temperature compared to the lower reflector for all solar radiation intensities. The maximum predicted velocity of magnitude 0.125 m s1 occurs near to the central region of the third trough (from lower position) for a solar radiation intensity of 1000 W m2. Fig. 6 shows the predicted average PV cell and aperture cover temperatures for different solar radiation intensities incident at the aperture cover. The predicted temperature difference between the aperture cover and the solar cell was 60 K at 1000 W m2 incident insolation. 5. Predictions of the thermofluid behaviour of a five trough system with different widths of front air channel adjacent to the aperture cover with different inlet air velocities A major change in the predicted air flow occurred inside the five trough ACPPVC system with a consequent change in the predicted PV cell temperatures when an open air channel was incorporated between the front of the reflectors and the glass aperture cover (i.e., front air channel). Cold air that enters the inlet channel (at the bottom of the concentrator system) removes heat from the reflector substrate and the hot PV cell, the heated air leaves the concentrator through the open outlet channel. Increasing the inlet air velocity increases the convective heat removal from the system and results in a significant reduction in solar cell temperature. The zero inlet air velocity condition signifies a recirculating natural convective flow with only low fluid velocity resulting due to the temperature gradients estab-
181
lished within the system. Systems with front channel widths of 10 mm, 20 mm, and 30 mm were simulated for inlet air velocities of 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 m s1. An additional air channel of length 100 mm was incorporated at the inlet and outlet to reduce simulation convergence time. A constant heat loss coefficient of 9 W m2 K1 from the rear aluminium plate to the ambient was used for all of these simulations with the boundary conditions as stated in Fig. 1, the ambient temperature was 20 C. The isotherms for the five trough concentrator system with 10 mm, 20 mm and 30 mm wide front air channels for inlet air velocities of 1.0 m s1 are shown in Fig. 7. For the five trough system with 10 mm front air channel, the highest predicted temperature at the PV cell of 95.2 C (i.e., no through flow condition) was reduced to 72 C for an inlet air flow velocity of 1.0 m s1. For forced convection conditions when the inlet air velocity increases from 0.2 m s1 to 1.0 m s1, the increased flow velocity over the reflector surface and PV cell surface leads to an increased rate of heat transfer to the air. This reduces the solar cell operating temperature improving the electrical conversion efficiency of the PV system. Table 4 presents the average PV cell temperatures for 10, 20 and 30 mm wide air spaces adjacent to the aperture cover for different air velocities. For a front air gap of 10 mm, when the inlet air velocity was zero a maximum temperature difference of 5.2 K was predicted between the inlet and outlet of the front channel whereas the predicted average Table 4 Average temperatures at the PV surface for 10, 20 and 30 mm wide air gap adjacent to aperture cover Inlet velocity (m s1)
Average PV cell temperature (in C) for front air gap of 10 mm
20 mm
30 mm
0.0 0.2 0.4 0.6 0.8 1.0
95.2 80.2 78.0 75.3 73.8 72.0
91.2 76.8 75.2 73.1 71.2 69.8
94.0 79.8 77.4 76.2 74.8 73.0
Average PV temperature (oC)
100.0 95.0 10 mm
90.0
Front air gap 20 mm
30 mm
85.0 80.0 75.0 70.0 65.0 60.0 0
0.2
0.4
0.6
0.8
1
-1
Inlet air velocity (ms )
Fig. 8. Predicted average PV temperature with inlet air velocity for different air gaps adjacent to the aperture cover.
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temperature difference between the PV cell surface and the aperture cover was 57.2 K. The temperature difference between the aperture cover and the solar cell surface reduces to 48.4 K for an inlet air velocity of 1.0 m s1. Since the ratio of the channel depth to its length is higher when compared to systems with 10 mm or 20 mm channel depths, the air flow interaction with the CPC cavity is reduced. The predicted velocity vector diagram is similar to that for the smaller channel depths, the peak velocities inside the outlet channel increase. Due to heat transfer to the air from the hot PV and reflector surfaces the air flow inside the channel develops due to buoyancy effects. The air adjacent to the aperture cover is cooler than for the ‘no flow through’ case, a reverse circulation near to the lower reflector for all reflector troughs is predicted. The maximum solar cell temperature is reduced by 21 K for an inlet air velocity of 1.0 m s1 which is 0.4 K lower then the corresponding temperature reduction for a 20 mm wide air channel. The variation of average PV temperature with inlet air velocity is shown in Fig. 8 for air gaps of 10, 20 and 30 mm adjacent to the aperture cover. The predicted solar cell surface temperature decreased by 2.2 K when the air channel depth increased from 10 mm to 20 mm for similar inlet flow velocity of 1 m s1, an air gap of 30 mm however leads to an increase the PV cell operating temperature by 3.2 K, confirming that an optimum front channel width exists in between 10 and 30 mm that will lead to a minimum PV cell operating temperature.
into two distinct thermal plumes. For an inlet velocity of 0.1 m s1 the major circulation within the fifth trough is surrounded by secondary circulations, this results in a tem-
6. The theoretical predictions of thermofluid behaviour of five trough system with 10 mm and 20 mm front and rear air gap for different inlet air velocities In addition to the front air channel an air channel at the rear aluminium plate increases the heat loss and decreases the aluminium back plate and photovoltaic temperature. Similar to the front channel, an additional 100 mm long inlet and outlet air channel was included at the rear of the aluminium back plate in all simulations. Channel widths of 10 mm and 20 mm have been simulated with inlet air velocities of 0.1 m s1, 0.5 m s1 and 1.0 m s1. 1000 W m2 insolation was incident at the aperture cover at an angle of 60, the boundary conditions used are those in Fig. 1. The left side of the rear air channel (adjacent to the building wall) had a fixed constant heat loss coefficient of 5 W m2 K1. The predicted isotherms in the concentrator system for front and rear open channels of depth 10 mm and 20 mm for an inlet velocity of 0.1 m s1 are shown in Fig. 9. The isotherms are at 2 C intervals. From Fig. 9a it can be seen that for an inlet air velocity of 0.1 m s1, the central region of the first ACPPVC reflector trough maintained an average temperature of 27 C. A major difference in isotherms was evident inside the corresponding reflector troughs for different inlet air velocities. For higher inlet velocities, the isotherms became thinner and the central isotherm divided
Fig. 9. The isotherms of a five trough concentrator system with the (a) 10 mm and (b) 20 mm wide front and rear open channels for an inlet air velocity of magnitude 0.1 m s1. The isotherms are at 2 C intervals and the solar radiation incident at the aperture cover was 1000 W m2.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
183
Table 5 Predicted temperatures and air velocities for different configurations for 1000 W m2 insolation incident at the aperture cover and ambient temperature was 20 C
Without front and rear air channel
Average PV temperature (C)
Average aperture cover temperature (C)
Maximum predicted air velocity inside the system (m s1)
95
35
0.12
72.0 69.8 62 60.8
21.4 21.4 20.8 20.2
1.32 1.33 1.35 1.38
1
Channel inlet air velocity of 1.0 m s Front channel of width Front and rear channel of width
10 mm 20 mm 10 mm 20 mm
perature reduction of 25 K at the photovoltaic surface. The maximum temperature rise at the solar cell surface reduced from 73 C at an inlet air velocity of 0.1 m s1 to 60.8 C at an inlet air velocity of 1.0 m s1. The highest temperature rise of 55 K between the inlet and outlet of the rear channel occurs for an inlet air velocity of 0.1 m s1 whereas the temperature rise reduces to 44 K for an inlet air velocity of 1.0 m s1. From Fig. 9b it can be seen that the increasing the width of the back channel leads to the centre of the reverse circulation being located towards the upper reflector, and the reverse circulation in the ACPC cavities adjacent to the PV disappearing. A further increase of inlet air velocity reduced the solar cell temperature, leading to increased electrical conversion efficiency. Table 5 shows the reduction of solar cell surface temperature for different system configurations. The maximum predicted temperature of the solar cell surface was 60.8 C for an inlet air velocity of 1.0 m s1, a temperature reduction of 34.2 K compared to the system without any air channels. This is predicted to increase solar to electrical conversion efficiency of the ACPPVC system by approximately 17%.
7. Conclusions A detailed parametric analysis of the heat transfer in an experimentally characterised asymmetric compound parabolic photovoltaic concentrator suitable for building fac¸ade integration in the UK has been undertaken. Examples of natural convection within a single-trough, and a five trough photovoltaic concentrator have been presented. Free and forced convection at the rear of the PV concentrator provides a significant temperature reduction in the PV. A maximum possible solar cell temperature of 95 C was predicted for an incident insolation of 1000 W m2, this will decrease solar cell efficiency by 25% compared to a PV panel operating at the standard characterising conditions. An inlet air velocity of 1.0 m s1 in a 20 mm wide channel between the aperture cover and the reflector, decreased the PV cell temperature by 25.4 K. A further reduction of temperature was achieved by providing an air channel to the rear of the aluminium back plate. Both 10 and 20 mm wide air gaps were simu-
lated at the front and rear channels for inlet velocities of 0.1, 0.5 and 1.0 m s1. The predicted air velocity in the space formed between the reflector troughs is very small, due to the enclosed nature of the boundary and near uniform boundary temperatures. For all conditions the predicted temperature gradients are maximum at the aperture cover and at the solar cell surface. A maximum temperature reduction of 34.2 K is predicted for a front and rear air gap of 20 mm with an inlet air velocity of 1.0 m s1. Acknowledgements This work was supported by the Engineering and Physical Sciences Resource Council, Swindon, UK. Thanks are also extended to BP Solar for supply of the photovoltaic cells and EVA used in this work. References 3M, 2001. Technical data for ‘Radiant VM2000’ reflector film. 3M United Kingdom PLC, Berkshire, UK. Abdel-Khalik, S.I., Li, H.W., Randall, K.R., 1978. Natural convection in compound parabolic concentrators – a finite element solution. ASME J. Heat Transfer 100, 199–204. Brinkworth, B.J., Cross, B.M., Marshall, R.H., Hongxing, Y., 1997. Thermal regulation of photovoltaic cladding. Solar Energy 61 (3), 169–178. Bruton, T.M., Sherborne, J., Heasman K C., Ramsdale, C.M., 2002. Concepts for the manufacturing of silicon solar cell modules for use in concentrating systems up to 5X. In: 29th IEEE Photovoltaic Specialists Conference, New Orleans, USA. Chew, T.C., Tay, A.O., Wijeysundera, N.E., 1989. A numerical study of the natural convection in CPC solar collector cavities with tubular absorbers. Trans. ASME J. Solar Energy Eng. 111, 16–23. CIBSE, 1999. Small-scale Combined Heat and Power for Buildings. London, UK. Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Process. John Wiley and Sons, New York. Eager, S., Mason, N., Bruton, T., Sherborne, J., Russell, R., 2002. Environmentally friendly processes in the manufacture of Saturn solar cells. In: 29th IEEE Photovoltaic Specialists Conference, New Orleans, USA. Eames, P.C., Norton, B., 1993a. Validated unified model for optics and heat transfer in line-axis concentrating solar energy collectors. Solar Energy 50 (4), 339–355. Eames, P.C., Norton, B., 1993b. Detailed parametric analysis of heat transfer in CPC solar energy collectors. Solar Energy 50 (4), 321–338.
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Eames, P.C., Norton, B., 1995. Thermal and optical consequences of the introduction of baffles into compound parabolic concentrating solar energy collector cavities. Solar Energy 55 (2), 139–150. Eames, P.C., Smyth, M., Norton, B., 2001. The experimental validation of a comprehensive unified model for optics and heat transfer in line-axis solar energy systems. Solar Energy 71 (2), 121–133. Hseih, C.K., 1981. Thermal analysis of CPC collectors. Solar Energy 27, 19–29. Mallick, T.K., 2003. Optics and heat transfer for asymmetric compound parabolic photovoltaic concentrators for building integrated photovoltaics. Ph.D. Thesis, University of Ulster, UK. Mallick, T.K., Eames, P.C., Norton, B., 2002. Asymmetric compound parabolic photovoltaic concentrators for building integration in the UK: an optical analysis. World Renewable Energy Congress, Ko¨ln, Germany.
Mallick, T.K., Eames, P.C., Hyde, T.J., Norton, B., 2004. The design and experimental characterisation of an asymmetric compound parabolic photovoltaic concentrator for building fac¸ade integration in the UK. Solar Energy 77 (33), 19–327. Mallick, T.K., Eames, P.C., Norton, B., 2006. Non-concentrating and asymmetric compound parabolic concentrating building fac¸ade integrated photovoltaics: an experimental comparison. Solar Energy 80 (7), 834–849. Prapas, D.E., Norton, B., Probert, S.D., 1987. Thermal design of compound parabolic concentrating solar energy collectors. ASME J. Solar Energy Eng. 109, 161–168. Rabl, A., 1976. Optical and thermal properties of compound parabolic concentrators. Solar Energy 18, 497–511. Welford, W.T., Winston, R., 1978. The Optics of Non-imaging Concentrators: Light and Solar Energy. Academic Press, London.
Using air flow to alleviate temperature elevation in solar cells within asymmetric compound parabolic concentrators Tapas K. Mallick a
a,*
, Philip C. Eames
a,1
, Brian Norton
b,2
Centre for Sustainable Technologies, School of Built Environment, University of Ulster, Newtownabbey BT37 0QB, Northern Ireland, UK b Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland Received 4 August 2005; received in revised form 7 April 2006; accepted 11 April 2006 Available online 2 June 2006 Communicated by: Associate Editor Hansjo¨rg Gabler
Abstract Air filled asymmetric compound parabolic photovoltaic concentrators (ACPPVC) have been studied using a comprehensive validated unified model for optics and heat transfer in line-axis solar energy systems. The heat transfer that occurs within the cavity of a single concentrator, multiple concentrators, the space between adjacent concentrators and in an air duct behind the photovoltaics was simulated and is presented. For a range of insolation intensities incident at the aperture cover the maximum PV cell operating temperatures are determined. From the simulations undertaken the effects on solar cell surface temperatures resulting from air flow in the air filled space at the front of the system and in the air duct to the rear of the solar cells are clearly evident. 2006 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic concentrator; Heat transfer; Temperature elevation
1. Introduction For photovoltaics to achieve wide-scale implementation as a building fac¸ade element it is essential that their cost is reduced while maintaining or exceeding the present level of solar to electrical conversion performance. Concentrating solar energy onto a smaller area allows a reduction in the output electricity cost if the cost of the concentrator is less than that of the displaced photovoltaic materials. A truncated asymmetric compound parabolic non-imaging (Welford and Winston, 1978) concentrator has been designed and characterised experimentally for south-facing building fac¸ade integration in the UK (Mallick, 2003). Truncation *
Corresponding author. Tel.: +44 2890 368568; fax: +44 2890 368239. E-mail addresses: [email protected], [email protected] (T.K. Mallick), [email protected] (P.C. Eames), [email protected] (B. Norton). 1 Tel.: +44 2890 368244; fax: +44 2890 368239. 2 Tel.: +353 1 402 7135; fax: +353 1 402 7099. 0038-092X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.04.003
allows a significant reduction in the materials required for the reflectors and thus cost (Rabl, 1976). Abdel-Khalik et al. (1978) developed a vorticity-based triangular finite element model for natural convection inside the cavity of a flat-plate-absorber CPC that assumed isothermal absorber and cover plate surfaces and adiabatic reflectors. A conduction Nusselt number was defined and a critical Rayleigh number was obtained by extrapolating from the convective Nusselt number obtained to the conduction limit. The effect of varying the ratio of Nusselt number to the conduction Nusselt number on the ratio of Rayleigh number to the critical Rayleigh number were given for full CPCs of different concentration ratios. Several studies (Hseih, 1981; Prapas et al., 1987; Chew et al., 1989; Eames and Norton, 1993a,b, 1995; Eames et al., 2001) have examined natural convection in the air-filled cavity of tubular-absorber CPC’s and inverted-flat-plate absorber CPC’s. The thermal analysis of tubular-absorber CPC’s undertaken by Hseih (1981) did not account for the effect of long-wave radiation at the system reflectors and
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T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
Nomenclature h G H R1 R2 T V W a, b g u
heat transfer coefficient (W m2 K1) insolation (W m2) height (m) left parabola right parabola temperature (K) velocity (m s1) width (m) acceptance half angle () efficiency solar incidence angle ()
Subscripts amb ambient apt aperture c convective eff effective elec electrical max maximum out outlet 2 half pv surface of the solar cells rear rear of the absorber
assumed that the reflector, absorber, and cover plate were all at different constant temperatures. This assumption is not realistic. Prapas et al. (1987) performed a more thorough heat transfer analysis of different CPC configurations, taking into account energy absorbed at the reflector. The model assumed unrealistically that the reflector, absorber and cover plates were all at constant temperatures. The temperature at the absorber, reflector and the aperture cover were also non-uniform to an extent depending on the interaction between the flux intensity, thermal conduc-
Exterior convection: Specified boundary conditions hc=1Wm-2K-1
tivity and heat removal or loss. A model using triangular finite elements was presented by Chew et al. (1989) for a tubular-absorber CPC that predicted a uni-cellular flow for vertical CPC orientation. Their model did not allow for conduction in the reflector and the aperture cover glass. Such short-comings were addressed in the ‘unified’ model developed by Eames and Norton (1993a); and their subsequent ‘comprehensive unified’ model (Eames et al., 2001). Eames and Norton (1993b), carried out detailed analysis, validated experimentally, of the thermophysical behaviour
Glass aperture cover: Specified boundary conditions hc = 12 Wm-2K-1, Insolation =1000 Wm-2 unless specified otherwise.
Aluminium back plate: Specified boundary conditions hc=9Wm-2K-1
Internal convection: Specified flow boundary conditions
Inter-trough convection Vertical φ
Incident solar radiation: Optics of solar energy conversion, ray trace analysis. Horizontal φ = Solar incidence angle
Solar cell: ηelec=15% Reflector
Conduction in all boundaries: PV, reflector, aperture cover and back plate Back conductive loss: Specified boundary conditions. Heat transfer to working fluid, free and forced convection.
Energy Conversion: Specified boundary conditions, electrical output, heat generation
Long-wave radiative exchange via elementary view factors, CFD for convective fluid behaviour specified in the ‘unified’ model (Eames and Norton, 1993b).
Convective loss: Specified boundary conditions
Fig. 1. Schematic diagram of a five trough asymmetric compound parabolic photovoltaic concentrator showing energy transfer mechanisms.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
of tubular-absorber CPC’s and tubular-absorber CPC’s with modified reflectors for 30, 45 and 60 acceptance half angles over a range of inclinations. Long-wave radiative exchange between the absorber, reflectors and aperture cover was taken into account through a view factor analysis for the element faces. For a 60 half-acceptance angle CPC the internal convective flow was forced to change from a bi-cellular flow to a uni-cellular flow at an inclination angle greater than 45. To date no reports of such similar detailed analysis of the heat transfer within asymmetric compound parabolic concentrators and their possible application to photovoltaic systems have been produced. The work presented in this paper details optics and heat transfer analysis for an asymmetric compound parabolic concentrator suitable for building integrated photovoltaic applications. The modelled asymmetric compound parabolic photovoltaic concentrator (ACPPVC) system consists of a 3 mm thick aluminium back plate, to which an array of 6 mm thick aluminium reflector supports are attached. A 0.15 mm thick stainless steel reflector substrate covered with a 68 lm thick mirror reflector was glued to the reflector supports. The solar cells were attached to the rear aluminium plate via an intermediate layer of Ethylene Vinyl Acetate (EVA). The PV concentrator system consists of 40 half-size (50 mm · 125 mm) BP Saturn solar cells (Eager et al., 2002) with eight strings of five cells connected in series. The detailed design and fabrication of the photovoltaic concentrator has been reported previously (Mallick et al., 2004). An extensive experimental characterisation of this ACPPVC system showed an increase of the maximum power point by 62% compared to its non-concentrating counterpart (Mallick et al., 2006).
heat loss from the rear aluminium plate. The thermophysical properties of the materials used in the simulations are given in Table 2. The fluid properties of air at 293 K and atmospheric pressure were used in the simulations. As the reflecting film (3M, 2001) thickness was less than 68.6 · 106m, conduction within it was considered negligible compared with that of the 0.15 mm thick stainless steel reflector substrate. In the absence of forced convective heat transfer from the aperture cover the heat transfer is mainly due to free convection and long-wave radiation. For free convection, Table 1 System geometry and dimensions
Acceptance half angles (hs, ha) Absorber width (mm) Aperture width (mm) Length of lower reflector (R1 mm) Length of upper reflector (R2 mm) Concentration ratio Truncation (%) R1, R2 System aperture dimensions
Untruncated system
Truncated system
50 and 0 50.0 116 154.0
– 50.0 100.4 71.0
84.4 2.32 – Single-trough Five trough
84.5 2.01 54, 0 0.10 m · 0.625 m 1.0 m · 0.650 m
Table 2 Thermophysical properties assumed in the simulations Component Absorber
Material and properties Material Thermal conductivity Thickness Absorptance
2. System modelling A ‘comprehensive unified’ model for optics and heat transfer in line-axis concentrating solar energy collectors (Eames et al., 2001) was employed in the analysis of the designed concentrating systems illustrated in Fig. 1. This extensively experimentally validated model allows the detailed analysis of the spatial variation of the solar energy flux in the system and the resulting convective, conductive and long-wave radiative heat transfer for both solar thermal or photovoltaic applications. Using this model the thermophysical behaviour of single-trough, and five trough asymmetric compound parabolic photovoltaic concentrators have been evaluated. Natural and forced convection conditions within the air ducts between the aperture cover and the front of the reflectors (front) and between the back plate and the building wall (rear) were simulated and techniques to reduce solar cell temperature elevation implemented. The system geometry and dimensions used in the simulations are given in Table 1. The energy transfer mechanisms are illustrated in Fig. 1 for a five trough system. This includes the exterior heat loss from the reflector boundary, heat loss from the glass aperture cover and the
175
Back plate
Silicon solar cell (Bruton et al., 2002) 148 W m1 K1 0.3 mm 1
Material Thermal conductivity Thickness
Aluminium 238 W m1 K1
Material Thermal conductivity Thickness
Stainless steel 15.1 W m1 K1
Reflector
Material Thickness Reflectance Absorptance
VM2000 (3M, 2001) 68.6 · 106 m 0.98 0.02
Aperture cover
Material Heat loss coefficient Thermal conductivity Thickness Extinction coefficient Insolation
Low-iron glass 12 W m2 K1
Reflector substrate
3 mm
0.15 mm
1.05 W m1 K1 4 mm 0.00003512 m1 1000 W m2 unless specified otherwise
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T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
A representative value of 12 W m2 K1 was therefore employed for the aperture glass cover heat loss coefficient. The rear of the mirror was 0.15 mm thick stainless steel. The heat loss co-efficient through the stainless steel was 0.75 W m2 K1. The overall heat loss coefficient for the aluminium substrate was calculated assuming the system
the predicted heat transfer coefficient is between 2.8 W m2 K1 and 5.7 W m2 K1 (Duffie and Beckman, 1991). In the presence of forced convection assuming a wind velocity of 2 m s1 to 3 m s1 the heat loss coefficient lies in the range of 8.8 W m2 K1 to 16.1 W m2 K1 (Duffie and Beckman, 1991).
Solar incidence angle 60° 45
50
Solar incidence angle (o) 55 60
65
70
7000
Reflector 1
Absorbed energy (Wm-2)
6000
5000
4000
3000
2000
1000
0 0
Reflector 2 (a)
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Distance across solar cell (from lower reflector) (m)
(b)
Fig. 2. (a) Illustrative ray trace diagram for a single-trough system, (b) energy distribution at the solar cell for 1000 W m2 solar radiation incident at various incidence angles on the glass aperture cover.
Fig. 3. Example of a finite element mesh employed for the simulations of a five trough system: (a) enlargement of reflective fins, (b) enlargement of reflector back plate junction (c) enlargement of inter-reflector space.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184
31
35
PV cell
27
36
27
28
25
37
35 29
26
28
40
34
30
36
22
23
27
25
24
28
32
28
Aluminium back plate
Aperture cover
30
29
25
-1
Reference vector = 0.05 ms Upper reflector
26
PV cell Aluminium back plate
Aperture cover
26
Reference vector = 0.05 ms-1 Upper reflector
at the back of aluminium substrate the heat transfer coefficient from the back of the aluminium substrate was calculated using
30
was integrated onto a vertical building wall and the overall thermal resistance of the building was 1.462 m2 K W1 (CIBSE, 1999). For a convective flow
177
27
Air
34
38
26
26
Air 33
26
23
25
26
26
Lower reflector
25
26
27
28
32
36
(b)
(a) 35
38
36
48
PV cell 33
51
Aluminium back plate
34
44
Aperture cover
-1
Reference vector =0.05 ms Upper reflector
30
41
PV cell 45
Aperture cover
52 52
Reference vector = 0.05 ms-1 Upper reflector
Aluminium back plate
Lower reflector
32
35
26
25
29
32
40
30
26
32
40
30
29
40
26
26
31
26
26
30
27
29
51
43
42
29 55
35 34
57
49
42
46
29
42
41
49 58
40
Air
59
41
33
45
46
60
30
38
38
52
38
32
44
42
Lower reflector
44 38
40
41
47
51
49
(d)
43
60
50
Aluminium back plate
37
67
56
66
6 64 4
41
44 43
75
40 38
57
37
65
56
68
67
7271
63
64
49
59
67
70
59
65
68
60
59
5255
42
60 61
66
62
Aperture cover
68
67
37
59
65
PV cell
48
58
PV cell
61
56
55
56
58
Reference vector = 0.05 ms-1 Upper reflector 62
41
Aperture cover
51
Reference vector = 0.05 ms-1 Upper reflector
66
42
43
(c)
Aluminium back plate
Lower reflector
44
54
34
37
44
42
60
37
49
48
47
35
37
49
40
49
Air
29
54 4548 49
30
22
30
47
54 61
(e)
55
56
50
56
Lower reflector
54
44
58
77 75 67
48
60
59
40
53
53 51
5960 6624
62 59
4343 49
41
56
41 57
56
56 56
70 80
50
52
41
42
38 80
51
63
62
Air 60
58
51 50
61
76 78
37
50 50
70 70
80 77
45
54
54
52
69
54
63
62
47
Air 5555
61
67 58
56
70
55
56 63
73
66
60 67
56
59 64
5455
45 48 553 3
Lower reflector
(f)
Fig. 4. The theoretically predicted isotherms and velocity vectors for a single-trough system with boundary conditions given in Fig. 1. The isotherms are at 1 C interval. The solar radiation incident at an angle 60 at the aperture cover was (a) 200 W m2, (b) 400 W m2, (c) 600 W m2, (d) 800 W m2, (e) 1000 W m2 and (f) 1200 W m2.
T.K. Mallick et al. / Solar Energy 81 (2007) 173–184 Solar radiation -2 = 600 Wm
0.6 28
66
Reflector substrate
0.55 59
38
32
0.5
0.5 52
67
0.45
59
0.2
28
39
50
72
68
90
0.2
70
Air 68
Aluminium back plate
65
0.15
88
32
74
38
47 64
Aperture cover
0.1
61
0
24
Support frame
36
38
0
32
46 76
28
0.05
24
52
22
0
80
84
34
0
0.05
31
Support frame
Support frame
86
0.05 30
Aperture cover
56
45
38
72
56
0.1
32
Aluminium back plate
34
Aperture cover
0.1
0.05
0.25
PV cell
52
0.15
70
70
Air 47
0.15
76
0.3
40
31
66
System dimension (m)
45 38
0.25
PV cell
80
84
70
Aluminium back plate
59
45
Air
0.3
0.35
48
0.2
59
78
38
0.35
42
PV cell
34 36
0.25
70
54
0.3
System dimension (m)
26
40
34
System dimension (m)
0.35
Air
Air
36
52
34
86
0.4
0.4
Air 33
38 46
70
74 36
0.4
Reflector substrate
78 78 90
0.45
78
0.5
Reflector substrate
38
0.45
44 34 62
45
0.55
40
38
36
68 82
52
39
0.55
Solar radiation -2 = 1000 Wm
0.6
31
29
44
Solar radiation = 200 Wm-2
0.6
32
178
0.1
0.15
System dimension (m)
0
0.05
0.1
0.15
System dimension (m)
(a)
0
0.05
0.1
0.15
System dimension (m)
(b)
(c)
Fig. 5. The theoretically predicted isotherms and velocity vectors for a five trough system with the boundary conditions given in Fig. 1 for solar radiation of (a) 200 W m2, (b) 600 W m2, (c) 1000 W m2. The air gap between the concentrator and the aperture cover is 20 mm and the isotherms are at 1 C intervals.
hrear Apv T pv T amb ¼ GAapt ð1 gÞ
ð1Þ
For a ‘SATURN’ solar cell of 15% electrical conversion efficiency (Bruton et al., 2002), a temperature difference of 60 K and an insolation of 1000 W m2, assuming all heat flows to the rear then the value of hrear, the overall heat transfer coefficient would be 21.3 W m2 K1. Allowing for heat loss from the aperture cover of 12 W m2 K1 gives a heat transfer coefficient from the rear of the aluminium back plate to ambient of 9 W m2 K1. Ray tracing was used to predict the solar flux absorbed at the aperture cover, at the reflectors and at the PV surface (Mallick et al., 2002). Reflective losses at the glass aperture cover have been included. An illustrative ray trace diagram is presented in Fig. 2a for solar radiation incident at an angle of 60 to the vertical. The predicted energy distributions incident at the solar cell surface are presented in Fig. 2b for 1000 W m2 solar radiation incident at the glass cover. At low solar incidence angles (e.g., less than 45 to the vertical), the primary peak in the incident energy occurs adjacent to reflector 1 due to reflections from reflector 2. The location of the peak energy intensity moves from the left side to the right side (i.e., from reflector 1 towards
reflector 2) as the solar incidence angle increases. In addition to the primary peak energy intensities, secondary peaks can be seen for solar incidence angles of 45, 50 and 55. It can be seen from Fig. 2b that two peaks occur for a 60 incidence angle as would be expected from the ray trace diagram illustrated in Fig. 2a. Energy distributions determined using ray trace analysis for a solar incidence angle of 60 were used in the thermal analysis. The finite element mesh used for this analysis uses eight node isoparametric quadrilateral elements. An example of the finite ele-
Table 3 Average predicted PV surface and aperture cover temperatures for different incident insolation intensities Incident insolation (W m2)
Average PV surface temperature (C)
Average aperture cover temperature (C)
200 400 600 800 1000 1200
30.4 40.8 51.3 61.7 71.8 82.0
22.0 25.0 28.2 31.4 34.7 38.3
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ment mesh employed for the five trough simulation is shown in Fig. 3. The stainless steel reflector substrate (shown in Fig. 3a) acts as a fin within the system and increases the heat transfer from the PV which leads to reduced PV cell operating temperature. 3. Predicted thermofluid behaviour for 50 effective acceptance half angle single-trough system Simulations were undertaken for 200, 400, 600, 800, 1000 and 1200 W m2 insolation incident at 60 from the vertical on to the aperture cover of a 50 acceptance half angle single-trough system truncated by 54% with a constant heat loss from the aluminium back plate to the ambient. Isotherms at intervals of 1C and velocity vector diagrams are presented in Fig. 4. The velocity vectors are scaled to the reference vector of magnitude 0.05 m s1. The predicted average PV surface temperatures and average aperture cover temperature are shown in Table 3. The photovoltaic concentrator has a concentration ratio of 2.0, thus 1000 W m2 incident insolation was concentrated to 2000 W m2 at the PV cells. For a mono-crystalline Si-based flat non-concentrating PV panel a solar cell temperature of 75 C has been reported at 1000 W m2 incident insolation (Brinkworth et al., 1997). Thus the predicted average PV surface temperature of 71.8 C (when incident insolation was 1000 W m2 as shown in Table 3) is comparable to that reported previously (Brinkworth et al., 1997) when heat is lost from the rear of the concentrating panel. Although the predicted velocity profiles are similar for all solar radiation intensities, at higher solar radiation intensities the air velocity adjacent to the boundary increases as the mean temperature difference between the aperture and the solar cell increases. The fluid flow can be seen from Fig. 4 to consist of a major circulation surrounded by three smaller secondary circulations resulting due to heat loss from the reflectors. Due to the heat trans-
fer adjacent to the boundaries predicted air flow is significant, however in the central region of the cavity the air velocity is low. 4. Theoretically predicted thermofluid behaviour of a five trough system Simulations were undertaken for 200, 400, 600, 800 and 1000 W m2 insolation incident on a 50 acceptance half angle five trough system truncated by 54%. The predicted isotherms for solar radiation intensities of 200, 600 and 1000 W m2 incident at the aperture are shown in Fig. 5. The design included an air gap of 20 mm between the aperture cover glass and the tips of the individual reflector troughs. The isotherms are at 1 C intervals. The predicted maximum temperature at the PV surface was 95 C when the incident solar radiation was 1000 W m2. The heat loss from the rear aluminium plate depends on wind velocity and ambient temperature. Providing an air gap adjacent to the aperture glass cover and at the rear plate enables a significant temperature reduction achieved. This can be seen inside all individual troughs, however only a minor change in isotherm pattern occurred for higher solar radiation intensities. Increased insolation intensity leads to higher temperatures which cause the thermal plume to be thinner compared to those predicted for lower insolation intensities. For these simulations although the predicted velocity profile is similar in form for all insolation intensities, at higher insolation intensities the air velocity near to the boundaries increases as the mean temperature difference between the aperture cover and the PV cell increases. The air flow adjacent to the glass cover is downwards where it is being cooled, with a upward flow predicted at the tip of the reflectors were consecutive concentrators join together. Heat transfer from the hot PV surfaces to the air causes it to flow upwards in the system towards the upper reflector. The predicted maximum temperature rise
Average PV cell temperature
100
95
Average aperture cover temperature
90
80
80
Temperature (oC)
179
66
70 53
60 50
39
40 30
35
32
29
27
24
20 10 0 200
400
600
800
1000
Incident solar radiation intensity (Wm-2)
Fig. 6. The predicted average PV cell temperature and average aperture cover temperature for different insolation intensities incident at the aperture cover for a five trough concentrator system.
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of the PV cells was 39 K. For this five trough system the fluid flow consists of in each collector trough a major circulation surrounded by three smaller secondary circulations. The lengths of the upper and lower reflectors of each trough are of different lengths this leads to unequal rates of heat transfer from the reflectors to the air which in turn
helps promote a reverse circulation adjacent to the lower reflector. The reverse circulation intensity increases as incident solar radiation intensity increases from 200 W m2 to 1000 W m2. The predicted thermal plumes are thinner at higher solar radiation intensity due to the mean temperature of the air and the temperature difference between the
Fig. 7. The predicted isotherms in the five trough concentrator system for (a) 10 mm, (b) 20 mm, and (c) 30 mm wide front channels adjacent to the aperture cover with an inlet air velocity of 1.0 m s1. The isotherms are at 2 C intervals and the solar radiation incident at the aperture cover was 1000 W m2.
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glass aperture cover and PV cell temperature being larger. Higher temperatures at the PV surface leading to higher air temperatures and thus increased buoyancy leads to the air flow velocity inside each individual reflector trough increasing. When compared to those in other regions, the magnitude of air flow in the space between consecutive concentrator troughs is small for all insolation levels, a consequence of this region being surrounded completely by boundaries at nearly the same temperature leading to minimal force for fluid motion. From Fig. 5 it can be seen that the upper reflector has a higher temperature compared to the lower reflector for all solar radiation intensities. The maximum predicted velocity of magnitude 0.125 m s1 occurs near to the central region of the third trough (from lower position) for a solar radiation intensity of 1000 W m2. Fig. 6 shows the predicted average PV cell and aperture cover temperatures for different solar radiation intensities incident at the aperture cover. The predicted temperature difference between the aperture cover and the solar cell was 60 K at 1000 W m2 incident insolation. 5. Predictions of the thermofluid behaviour of a five trough system with different widths of front air channel adjacent to the aperture cover with different inlet air velocities A major change in the predicted air flow occurred inside the five trough ACPPVC system with a consequent change in the predicted PV cell temperatures when an open air channel was incorporated between the front of the reflectors and the glass aperture cover (i.e., front air channel). Cold air that enters the inlet channel (at the bottom of the concentrator system) removes heat from the reflector substrate and the hot PV cell, the heated air leaves the concentrator through the open outlet channel. Increasing the inlet air velocity increases the convective heat removal from the system and results in a significant reduction in solar cell temperature. The zero inlet air velocity condition signifies a recirculating natural convective flow with only low fluid velocity resulting due to the temperature gradients estab-
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lished within the system. Systems with front channel widths of 10 mm, 20 mm, and 30 mm were simulated for inlet air velocities of 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 m s1. An additional air channel of length 100 mm was incorporated at the inlet and outlet to reduce simulation convergence time. A constant heat loss coefficient of 9 W m2 K1 from the rear aluminium plate to the ambient was used for all of these simulations with the boundary conditions as stated in Fig. 1, the ambient temperature was 20 C. The isotherms for the five trough concentrator system with 10 mm, 20 mm and 30 mm wide front air channels for inlet air velocities of 1.0 m s1 are shown in Fig. 7. For the five trough system with 10 mm front air channel, the highest predicted temperature at the PV cell of 95.2 C (i.e., no through flow condition) was reduced to 72 C for an inlet air flow velocity of 1.0 m s1. For forced convection conditions when the inlet air velocity increases from 0.2 m s1 to 1.0 m s1, the increased flow velocity over the reflector surface and PV cell surface leads to an increased rate of heat transfer to the air. This reduces the solar cell operating temperature improving the electrical conversion efficiency of the PV system. Table 4 presents the average PV cell temperatures for 10, 20 and 30 mm wide air spaces adjacent to the aperture cover for different air velocities. For a front air gap of 10 mm, when the inlet air velocity was zero a maximum temperature difference of 5.2 K was predicted between the inlet and outlet of the front channel whereas the predicted average Table 4 Average temperatures at the PV surface for 10, 20 and 30 mm wide air gap adjacent to aperture cover Inlet velocity (m s1)
Average PV cell temperature (in C) for front air gap of 10 mm
20 mm
30 mm
0.0 0.2 0.4 0.6 0.8 1.0
95.2 80.2 78.0 75.3 73.8 72.0
91.2 76.8 75.2 73.1 71.2 69.8
94.0 79.8 77.4 76.2 74.8 73.0
Average PV temperature (oC)
100.0 95.0 10 mm
90.0
Front air gap 20 mm
30 mm
85.0 80.0 75.0 70.0 65.0 60.0 0
0.2
0.4
0.6
0.8
1
-1
Inlet air velocity (ms )
Fig. 8. Predicted average PV temperature with inlet air velocity for different air gaps adjacent to the aperture cover.
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temperature difference between the PV cell surface and the aperture cover was 57.2 K. The temperature difference between the aperture cover and the solar cell surface reduces to 48.4 K for an inlet air velocity of 1.0 m s1. Since the ratio of the channel depth to its length is higher when compared to systems with 10 mm or 20 mm channel depths, the air flow interaction with the CPC cavity is reduced. The predicted velocity vector diagram is similar to that for the smaller channel depths, the peak velocities inside the outlet channel increase. Due to heat transfer to the air from the hot PV and reflector surfaces the air flow inside the channel develops due to buoyancy effects. The air adjacent to the aperture cover is cooler than for the ‘no flow through’ case, a reverse circulation near to the lower reflector for all reflector troughs is predicted. The maximum solar cell temperature is reduced by 21 K for an inlet air velocity of 1.0 m s1 which is 0.4 K lower then the corresponding temperature reduction for a 20 mm wide air channel. The variation of average PV temperature with inlet air velocity is shown in Fig. 8 for air gaps of 10, 20 and 30 mm adjacent to the aperture cover. The predicted solar cell surface temperature decreased by 2.2 K when the air channel depth increased from 10 mm to 20 mm for similar inlet flow velocity of 1 m s1, an air gap of 30 mm however leads to an increase the PV cell operating temperature by 3.2 K, confirming that an optimum front channel width exists in between 10 and 30 mm that will lead to a minimum PV cell operating temperature.
into two distinct thermal plumes. For an inlet velocity of 0.1 m s1 the major circulation within the fifth trough is surrounded by secondary circulations, this results in a tem-
6. The theoretical predictions of thermofluid behaviour of five trough system with 10 mm and 20 mm front and rear air gap for different inlet air velocities In addition to the front air channel an air channel at the rear aluminium plate increases the heat loss and decreases the aluminium back plate and photovoltaic temperature. Similar to the front channel, an additional 100 mm long inlet and outlet air channel was included at the rear of the aluminium back plate in all simulations. Channel widths of 10 mm and 20 mm have been simulated with inlet air velocities of 0.1 m s1, 0.5 m s1 and 1.0 m s1. 1000 W m2 insolation was incident at the aperture cover at an angle of 60, the boundary conditions used are those in Fig. 1. The left side of the rear air channel (adjacent to the building wall) had a fixed constant heat loss coefficient of 5 W m2 K1. The predicted isotherms in the concentrator system for front and rear open channels of depth 10 mm and 20 mm for an inlet velocity of 0.1 m s1 are shown in Fig. 9. The isotherms are at 2 C intervals. From Fig. 9a it can be seen that for an inlet air velocity of 0.1 m s1, the central region of the first ACPPVC reflector trough maintained an average temperature of 27 C. A major difference in isotherms was evident inside the corresponding reflector troughs for different inlet air velocities. For higher inlet velocities, the isotherms became thinner and the central isotherm divided
Fig. 9. The isotherms of a five trough concentrator system with the (a) 10 mm and (b) 20 mm wide front and rear open channels for an inlet air velocity of magnitude 0.1 m s1. The isotherms are at 2 C intervals and the solar radiation incident at the aperture cover was 1000 W m2.
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Table 5 Predicted temperatures and air velocities for different configurations for 1000 W m2 insolation incident at the aperture cover and ambient temperature was 20 C
Without front and rear air channel
Average PV temperature (C)
Average aperture cover temperature (C)
Maximum predicted air velocity inside the system (m s1)
95
35
0.12
72.0 69.8 62 60.8
21.4 21.4 20.8 20.2
1.32 1.33 1.35 1.38
1
Channel inlet air velocity of 1.0 m s Front channel of width Front and rear channel of width
10 mm 20 mm 10 mm 20 mm
perature reduction of 25 K at the photovoltaic surface. The maximum temperature rise at the solar cell surface reduced from 73 C at an inlet air velocity of 0.1 m s1 to 60.8 C at an inlet air velocity of 1.0 m s1. The highest temperature rise of 55 K between the inlet and outlet of the rear channel occurs for an inlet air velocity of 0.1 m s1 whereas the temperature rise reduces to 44 K for an inlet air velocity of 1.0 m s1. From Fig. 9b it can be seen that the increasing the width of the back channel leads to the centre of the reverse circulation being located towards the upper reflector, and the reverse circulation in the ACPC cavities adjacent to the PV disappearing. A further increase of inlet air velocity reduced the solar cell temperature, leading to increased electrical conversion efficiency. Table 5 shows the reduction of solar cell surface temperature for different system configurations. The maximum predicted temperature of the solar cell surface was 60.8 C for an inlet air velocity of 1.0 m s1, a temperature reduction of 34.2 K compared to the system without any air channels. This is predicted to increase solar to electrical conversion efficiency of the ACPPVC system by approximately 17%.
7. Conclusions A detailed parametric analysis of the heat transfer in an experimentally characterised asymmetric compound parabolic photovoltaic concentrator suitable for building fac¸ade integration in the UK has been undertaken. Examples of natural convection within a single-trough, and a five trough photovoltaic concentrator have been presented. Free and forced convection at the rear of the PV concentrator provides a significant temperature reduction in the PV. A maximum possible solar cell temperature of 95 C was predicted for an incident insolation of 1000 W m2, this will decrease solar cell efficiency by 25% compared to a PV panel operating at the standard characterising conditions. An inlet air velocity of 1.0 m s1 in a 20 mm wide channel between the aperture cover and the reflector, decreased the PV cell temperature by 25.4 K. A further reduction of temperature was achieved by providing an air channel to the rear of the aluminium back plate. Both 10 and 20 mm wide air gaps were simu-
lated at the front and rear channels for inlet velocities of 0.1, 0.5 and 1.0 m s1. The predicted air velocity in the space formed between the reflector troughs is very small, due to the enclosed nature of the boundary and near uniform boundary temperatures. For all conditions the predicted temperature gradients are maximum at the aperture cover and at the solar cell surface. A maximum temperature reduction of 34.2 K is predicted for a front and rear air gap of 20 mm with an inlet air velocity of 1.0 m s1. Acknowledgements This work was supported by the Engineering and Physical Sciences Resource Council, Swindon, UK. Thanks are also extended to BP Solar for supply of the photovoltaic cells and EVA used in this work. References 3M, 2001. Technical data for ‘Radiant VM2000’ reflector film. 3M United Kingdom PLC, Berkshire, UK. Abdel-Khalik, S.I., Li, H.W., Randall, K.R., 1978. Natural convection in compound parabolic concentrators – a finite element solution. ASME J. Heat Transfer 100, 199–204. Brinkworth, B.J., Cross, B.M., Marshall, R.H., Hongxing, Y., 1997. Thermal regulation of photovoltaic cladding. Solar Energy 61 (3), 169–178. Bruton, T.M., Sherborne, J., Heasman K C., Ramsdale, C.M., 2002. Concepts for the manufacturing of silicon solar cell modules for use in concentrating systems up to 5X. In: 29th IEEE Photovoltaic Specialists Conference, New Orleans, USA. Chew, T.C., Tay, A.O., Wijeysundera, N.E., 1989. A numerical study of the natural convection in CPC solar collector cavities with tubular absorbers. Trans. ASME J. Solar Energy Eng. 111, 16–23. CIBSE, 1999. Small-scale Combined Heat and Power for Buildings. London, UK. Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Process. John Wiley and Sons, New York. Eager, S., Mason, N., Bruton, T., Sherborne, J., Russell, R., 2002. Environmentally friendly processes in the manufacture of Saturn solar cells. In: 29th IEEE Photovoltaic Specialists Conference, New Orleans, USA. Eames, P.C., Norton, B., 1993a. Validated unified model for optics and heat transfer in line-axis concentrating solar energy collectors. Solar Energy 50 (4), 339–355. Eames, P.C., Norton, B., 1993b. Detailed parametric analysis of heat transfer in CPC solar energy collectors. Solar Energy 50 (4), 321–338.
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