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Factors influencing solar energy collector efficiency
Applied Energy 8 (1981) 205 213
FACTORS
INFLUENCING SOLAR EFFICIENCY
ENERGY
COLLECTOR
P. K. C. PILLA! and R. C. AGARWAL
Department of Physics, Indian Institute of Technology, New Delhi 110 029 (India)
SUMMARY The effects of glazing, solar flux, emissivity and absorptivity of the absorber surface on collector performance have been predicted for different plate temperatures (60 °C and IO0°C). At low solar flux levels (200-600 Wm -2) double- or triple-glazed collectors are superior to single-glazed collectors. For collectors with selective absorber coatings, the optimal number of glazing panes is two. Higher values of absorptivity and lower values of emissivity are more effective for single-glazed than for double-glazed collectors.
NOMENCLATURE ai
Ratio of the overall loss coefficient to the loss coefficient from the ith cover to the surroundings. C1 Constant of proportionality. D Dirt factor. F Collector efficiency factor. hw Convective heat loss coefficient. Hr Total solar flux incident on the tilted collector. k Extinction coefficient of the cover material (i.e. glass). K Thermal conductivity of glass wool. L Thickness of each glazing. N Number of glass covers. Qa Overall absorption by the absorber plate. Qu Useful energy available from a collector. S Shading coefficient. Ta Ambient air temperature. Tp Average plate temperature. Ub Bottom loss coefficient. UL Overall loss coefficient. 205 Applied Energy 0306-2619/81/0008-0205/$02"50© Applied Science Publishers Ltd, England, 1981 Printed in Great Britain
206
P. K. C. P I L L A I , R. C. A G A R W A L
U, V X
Top loss coefficient. Wind velocity. Thickness of the base insulation. Absorptivity of the absorber plate for solar radiation. (c~r)e Effective absorptance transmittance product. c Emissivity of the absorber plate for thermal radiation. % Infrared emittance of glass. r/ Efficiency of the collector. p~ Reflection of the cover plate for incident diffuse radiation. a Stephan-Boltzmann constant. r Overall transmittance of glass covers. r,, Transmittance of a single cover (ra = e x p ( - k L ) ) . INTRODUCTION
When an object is exposed to solar radiation, its temperature rises. This rise depends on the projected exposed area of the object, its material, its radiation absorbing property, the sun's altitude, the latitude and azimuth of the location and the energy losses, t Optical and thermal losses depend upon the number of glazing covers, their material, the plate temperature, the ambient temperature, the wind velocity and the emissivity of the absorber surface. All the influencing factors are controlled in such a way that heat collection is optimised. This is achieved by maximising energy absorption and, at the same time, minimising energy losses. This paper describes parametric studies undertaken to determine the effects of a number of glazing covers and solar flux, as well as emissivity and absorptivity of the absorber surface, on collector performance for different plate temperatures (60 °C and 100 °C). C O L L E C T O R EFFICIENCY
Collector efficiency may be written as: r/ -
Q.
(1)
H 7, where: Q, = F[Q~ -
Ut~(T v -
Ta) ]
(2)
Using Whillier's 2 approximation and applying corrections for the reduction in transmittance due to the accumulation of dirt on the glass cover and to shading of the absorber plate by the side walls supporting the glass cover, the overall absorption is given by: Q. = 0-98H~(~r)e(1 - D)(1 - S)
(3)
The effective absorptance-transmittance product (c~)e for a cover system of N identical plates is given 3 as:
207
FACTORS I N F L U E N C I N G S O L A R E N E R G Y C O L L E C T O R EFFICIENCY N
(~z)e - 1 - (1 -
~)Pa + (1 - za)
(4)
ai'r ' - 1 i=1
The value of Padepends upon the number of glass covers used. In the present study the values ofpa have been taken as 0.16, 0.24 and 0.29 for one, two and three glazing covers, respectively? The overall loss coefficient (UL) is the sum of the top and b o t t o m loss coefficients, i.e.; UL = U, + Ub
(5)
Following the basic procedure of Hottel and Woertz, 4 Klein 5'6 developed an empirical equation for the top loss coefficient for a collector inclined at 45 ° to the horizontal as:
U,
T p - T.'~
344
7¢7-7 ) + [~ + 0.0425N(1 - e)]-1 ..[_
2N+f-
1
(6)
N
/39
where f is given as: f=
(1.0 - 0.04hw + 5-0 x 10-4h~)(1 + 0.058N)
(7)
h w being the convective heat loss coefficient due to wind which can be determined, following McAdams, 7 from: hw = 5.7 + 3.8V
(8)
The b o t t o m loss coefficient ( U b) is given as: K Uh = ~
(9)
Edge loss coefficients have not been considered in the present study. Values of various parameters used in the present study are given below: Collector efficiency factor (F) = 0-9 Thickness of each glazing cover (L) = 0.3 cm Refractive index of glass (/t) = 1.526 Extinction coefficient of glass (k) = 0-123 c m - 1 Wind velocity (V) = 5.0 m s - 1 Reflectivity of cover plate system for incident diffuse radiation N = 1, 0.24 for N = 2 and 0-29 for N = 3. Infrared emittance of glass (%) = 0.88
(Pa) = 0.16 for
208
P. K. C. PILLAI, R. C. AGARWAL Ambient air temperature (T,) = 293 K Thermal conductivity o f glass wool used as insulation (K) = 0.047 W m - 1 C - 1 Thickness of glass wool at the b o t t o m (X) = 0.10m Shading coefficient (S) = 0.03 Dirt coefficient (D) = 0.02.
EFFECT OF NUMBER OF GLAZINGCOVERS Figures 1 to 4 present comparisons of the performances of single-, double- and triple-glazed collectors with non-selective absorber surfaces (e --0.95, ~ - - 0 . 9 5 ) 0.110
0.S0
0.~1
,/,//// //
r 0.3( >.-
//
1/
O Z
u_
/I/ff///I/
U.
1,1. uJ
0.70
0.10
000
0.0
/S/ ,(/ 700.0
,/
,
,.,
t.O0.O 600.0 800.0 SOLAR FLUX ( H r ). Wm"2
1000.0
Fig. 1. Effects of number of glazing covers and solar flux on collector performance (, = 0.95, at = 0.95, T, = 333 K).
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
209
0.$0
OJ.O
N, ~ . . - J
p., U
0.30
/
_u
7
2 ,/"
-
/ p
/
W
J
•
/
/"
/
/ 0.10
s
I
t I
/ I
I
/
/
I
I
I
I
I
/
/
f
,
,
,!
1
I
o.o
~oo.o
-
I
¢,~ . 0
600.0
8oo,o
"~00.0
SOLAR FLUX ( H.r }. Wm"2 Fig. 2.
Effects of number of glazing covers and solar flux on collector performance (e = 0.95, ct = 0.95, Tp = 373 K).
(Figs. 1 and 2) and selective a b s o r b e r surfaces (e = 0.10, ~ = 0-95) (Figs 3 and 4) for solar fluxes varying f r o m zero to 1000 W m - 2. The considerable benefits offered by m o r e than one glazing cover are a p p a r e n t , especially for higher emittance values (Figs 1 and 2). It is observed that for a collector with selective a b s o r b e r coatings, the o p t i m a l n u m b e r of glass covers is two (Figs 3 and 4). F o r collectors with selective a b s o r b e r coatings operating at low temperatures, say 60 °C, m o r e than one glazing cover has no effect on collector p e r f o r m a n c e (Fig. 3).
EFFECT OF SOLAR FLUX
T h e effect of solar flux on collector p e r f o r m a n c e is very significant, As the incident solar flux increases, the overall collection efficiency also increases (Figs 1 to 4). The p e r f o r m a n c e of a double- or triple-glazed collector is seen to be far superior to that o f a single-glazed collector, particularly at lower solar flux levels (200-600 W m - 2).
210
P. K. C. PILLAI, R. C. AGARWAL 0.I0 -
Nil
O.Sl
s' i
sS
S
o.i(
/;
i 0.30 ill
0.20
// +/
,!/
0.1C -
o.o
0.0
L'
i
,q
204
)
I 600.0
I $00.0
'1 iO00.O
SOLAR FLUX ( HT), Wm "2 Fig. 3.
Effects of number of glazing covers and solar flux on collector performance (e = 0 . 1 0 , ct = 0 . 9 5 , Tp = 333K).
EFFECTS OF EMISSIVITY AND ABSORPTIVITY
The effects of the variation of emissivity and absorptivity on collector performance under typical operating conditions are shown in Figs 5 and 6. It is found that for a single-glazed collector an increase in ct is more effective than for a double-glazed collector. F o r example, if~ is increased by a factor of, say, 0.10, i.e. from 0.80 to 0.90 or from 0.90 to 1.00, the increase in efficiency of a single-glazed collector is about 6.5 per cent, irrespective of plate temperature. For the same increase in ~, the increase in the efficiency of a double-glazed collector is about 5 per cent. Figures 5 and 6 show that a low emittance value is more effective for a single-glazed collector than for a
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
211
0.50 -
0.40
F" >.-
0.30 -
r,) Z
ca h
bd 0.20 --
0.10 --
0.0 200.0
//,/ 400.0
, 600.0
, 800.0
, 1000.0
SOLAR FLUX( HT),Wrn "2 Fig. 4.
Effectsof number of glazingcoversand solar fluxon collectorperformance(~ = Tp = 373 K).
0.10,
~ = 0.95,
double-glazed collector. It is also observed that there is a linear relationship between efficiency and absorptivity for ~ > 0.80, i.e. A~/= C1A~. However, there is no such linear relationship between efficiency and emittance. For example, for a doubleglazed collector an increase in emissivity from 0.10 to 0.20 leads to a decrease in efficiency of 1.1 per cent. At the same time, if the emissivity is increased from 0-40 to 0.50, the decrease in efficiency is about 0.5 per cent (Fig. 5). For higher emissivity values, the change in the e value has a slight effect on efficiency (Figs 5 and 6).
CONCLUSIONS
(i)
For collectors with selective absorber coatings the optimal number of glass covers is two.
0.70~
O
.
S
O
~
~
0.30
0.20 0.0 Fig. 5.
I 0.l
I I O.L O.B EMISSIVITY,£
I 1.0
Effect of variation of the emissivity and absorptivity on collector performance 1 0 0 0 W m -2, Tp = 333 K). - one glass cover, - - - - two glass covers.
O.t,O X
.030
z
~-~
~-.
"~_
ool oo
(Hr
,/,:l.O
0.90
o_~o......
- .......
3.80
0.10
Fig. 6.
I O.B
= o~
, o~
= os
EMISSIVITY,E
i ~ 08
= 1o
Effect of variation of the emissivity and absorptivity on collector performance ( H r 1000Wm -2, Tp = 373 K). - one glass cover, - - - - two glass covers.
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
213
(ii)
At low solar flux levels (200-600 W m - 2), double- or triple-glazed collectors are more efficient than single-glazed collectors. (iii) An increase in • is more effective for a single-glazed than for a double-glazed collector. (iv) There is an approximately linear relationship between the efficiency of a fiat plate collector and the absorptance of the absorber surface (for ct >_ 0-80), i.e. A t / = C~A~.
(v)
A low value of emittance is more effective for a single-glazed than for a double-glazed collector.
REFERENCES 1. P.K.C. PILLAIand R. C. AGARWAL,Spectrally selective surfaces for photothermal conversion of solar energy, Physica Status Solidi (a), 60 (1980). 2. A. WHmUER, Low temperature engineering applications of solar energy, ASHRAE, New York, 1967. 3. J.A. DUFFLEand W. A. BECKMANN,Solar energy thermalprocesses, John Wiley & Sons, New York, 1974. 4. H. C. HOTTEL and B. B. WOERTZ, Trans. Am. Soc. Mec. Eng., 64 (1942), p.91. 5. S. A. KLEIN, The effects of thermal capacitance upon the performance of flat-plate collectors, M.S. Thesis, University of Wisconsin, 1973. 6. S. A. KLEIN, Calculation of fiat plate collector loss coefficients, Solar Energy, 17 (1975), p. 79. 7. W. H. MCADA~S, Heat transmission, McGraw-Hill, New York, 1954.
FACTORS
INFLUENCING SOLAR EFFICIENCY
ENERGY
COLLECTOR
P. K. C. PILLA! and R. C. AGARWAL
Department of Physics, Indian Institute of Technology, New Delhi 110 029 (India)
SUMMARY The effects of glazing, solar flux, emissivity and absorptivity of the absorber surface on collector performance have been predicted for different plate temperatures (60 °C and IO0°C). At low solar flux levels (200-600 Wm -2) double- or triple-glazed collectors are superior to single-glazed collectors. For collectors with selective absorber coatings, the optimal number of glazing panes is two. Higher values of absorptivity and lower values of emissivity are more effective for single-glazed than for double-glazed collectors.
NOMENCLATURE ai
Ratio of the overall loss coefficient to the loss coefficient from the ith cover to the surroundings. C1 Constant of proportionality. D Dirt factor. F Collector efficiency factor. hw Convective heat loss coefficient. Hr Total solar flux incident on the tilted collector. k Extinction coefficient of the cover material (i.e. glass). K Thermal conductivity of glass wool. L Thickness of each glazing. N Number of glass covers. Qa Overall absorption by the absorber plate. Qu Useful energy available from a collector. S Shading coefficient. Ta Ambient air temperature. Tp Average plate temperature. Ub Bottom loss coefficient. UL Overall loss coefficient. 205 Applied Energy 0306-2619/81/0008-0205/$02"50© Applied Science Publishers Ltd, England, 1981 Printed in Great Britain
206
P. K. C. P I L L A I , R. C. A G A R W A L
U, V X
Top loss coefficient. Wind velocity. Thickness of the base insulation. Absorptivity of the absorber plate for solar radiation. (c~r)e Effective absorptance transmittance product. c Emissivity of the absorber plate for thermal radiation. % Infrared emittance of glass. r/ Efficiency of the collector. p~ Reflection of the cover plate for incident diffuse radiation. a Stephan-Boltzmann constant. r Overall transmittance of glass covers. r,, Transmittance of a single cover (ra = e x p ( - k L ) ) . INTRODUCTION
When an object is exposed to solar radiation, its temperature rises. This rise depends on the projected exposed area of the object, its material, its radiation absorbing property, the sun's altitude, the latitude and azimuth of the location and the energy losses, t Optical and thermal losses depend upon the number of glazing covers, their material, the plate temperature, the ambient temperature, the wind velocity and the emissivity of the absorber surface. All the influencing factors are controlled in such a way that heat collection is optimised. This is achieved by maximising energy absorption and, at the same time, minimising energy losses. This paper describes parametric studies undertaken to determine the effects of a number of glazing covers and solar flux, as well as emissivity and absorptivity of the absorber surface, on collector performance for different plate temperatures (60 °C and 100 °C). C O L L E C T O R EFFICIENCY
Collector efficiency may be written as: r/ -
Q.
(1)
H 7, where: Q, = F[Q~ -
Ut~(T v -
Ta) ]
(2)
Using Whillier's 2 approximation and applying corrections for the reduction in transmittance due to the accumulation of dirt on the glass cover and to shading of the absorber plate by the side walls supporting the glass cover, the overall absorption is given by: Q. = 0-98H~(~r)e(1 - D)(1 - S)
(3)
The effective absorptance-transmittance product (c~)e for a cover system of N identical plates is given 3 as:
207
FACTORS I N F L U E N C I N G S O L A R E N E R G Y C O L L E C T O R EFFICIENCY N
(~z)e - 1 - (1 -
~)Pa + (1 - za)
(4)
ai'r ' - 1 i=1
The value of Padepends upon the number of glass covers used. In the present study the values ofpa have been taken as 0.16, 0.24 and 0.29 for one, two and three glazing covers, respectively? The overall loss coefficient (UL) is the sum of the top and b o t t o m loss coefficients, i.e.; UL = U, + Ub
(5)
Following the basic procedure of Hottel and Woertz, 4 Klein 5'6 developed an empirical equation for the top loss coefficient for a collector inclined at 45 ° to the horizontal as:
U,
T p - T.'~
344
7¢7-7 ) + [~ + 0.0425N(1 - e)]-1 ..[_
2N+f-
1
(6)
N
/39
where f is given as: f=
(1.0 - 0.04hw + 5-0 x 10-4h~)(1 + 0.058N)
(7)
h w being the convective heat loss coefficient due to wind which can be determined, following McAdams, 7 from: hw = 5.7 + 3.8V
(8)
The b o t t o m loss coefficient ( U b) is given as: K Uh = ~
(9)
Edge loss coefficients have not been considered in the present study. Values of various parameters used in the present study are given below: Collector efficiency factor (F) = 0-9 Thickness of each glazing cover (L) = 0.3 cm Refractive index of glass (/t) = 1.526 Extinction coefficient of glass (k) = 0-123 c m - 1 Wind velocity (V) = 5.0 m s - 1 Reflectivity of cover plate system for incident diffuse radiation N = 1, 0.24 for N = 2 and 0-29 for N = 3. Infrared emittance of glass (%) = 0.88
(Pa) = 0.16 for
208
P. K. C. PILLAI, R. C. AGARWAL Ambient air temperature (T,) = 293 K Thermal conductivity o f glass wool used as insulation (K) = 0.047 W m - 1 C - 1 Thickness of glass wool at the b o t t o m (X) = 0.10m Shading coefficient (S) = 0.03 Dirt coefficient (D) = 0.02.
EFFECT OF NUMBER OF GLAZINGCOVERS Figures 1 to 4 present comparisons of the performances of single-, double- and triple-glazed collectors with non-selective absorber surfaces (e --0.95, ~ - - 0 . 9 5 ) 0.110
0.S0
0.~1
,/,//// //
r 0.3( >.-
//
1/
O Z
u_
/I/ff///I/
U.
1,1. uJ
0.70
0.10
000
0.0
/S/ ,(/ 700.0
,/
,
,.,
t.O0.O 600.0 800.0 SOLAR FLUX ( H r ). Wm"2
1000.0
Fig. 1. Effects of number of glazing covers and solar flux on collector performance (, = 0.95, at = 0.95, T, = 333 K).
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
209
0.$0
OJ.O
N, ~ . . - J
p., U
0.30
/
_u
7
2 ,/"
-
/ p
/
W
J
•
/
/"
/
/ 0.10
s
I
t I
/ I
I
/
/
I
I
I
I
I
/
/
f
,
,
,!
1
I
o.o
~oo.o
-
I
¢,~ . 0
600.0
8oo,o
"~00.0
SOLAR FLUX ( H.r }. Wm"2 Fig. 2.
Effects of number of glazing covers and solar flux on collector performance (e = 0.95, ct = 0.95, Tp = 373 K).
(Figs. 1 and 2) and selective a b s o r b e r surfaces (e = 0.10, ~ = 0-95) (Figs 3 and 4) for solar fluxes varying f r o m zero to 1000 W m - 2. The considerable benefits offered by m o r e than one glazing cover are a p p a r e n t , especially for higher emittance values (Figs 1 and 2). It is observed that for a collector with selective a b s o r b e r coatings, the o p t i m a l n u m b e r of glass covers is two (Figs 3 and 4). F o r collectors with selective a b s o r b e r coatings operating at low temperatures, say 60 °C, m o r e than one glazing cover has no effect on collector p e r f o r m a n c e (Fig. 3).
EFFECT OF SOLAR FLUX
T h e effect of solar flux on collector p e r f o r m a n c e is very significant, As the incident solar flux increases, the overall collection efficiency also increases (Figs 1 to 4). The p e r f o r m a n c e of a double- or triple-glazed collector is seen to be far superior to that o f a single-glazed collector, particularly at lower solar flux levels (200-600 W m - 2).
210
P. K. C. PILLAI, R. C. AGARWAL 0.I0 -
Nil
O.Sl
s' i
sS
S
o.i(
/;
i 0.30 ill
0.20
// +/
,!/
0.1C -
o.o
0.0
L'
i
,q
204
)
I 600.0
I $00.0
'1 iO00.O
SOLAR FLUX ( HT), Wm "2 Fig. 3.
Effects of number of glazing covers and solar flux on collector performance (e = 0 . 1 0 , ct = 0 . 9 5 , Tp = 333K).
EFFECTS OF EMISSIVITY AND ABSORPTIVITY
The effects of the variation of emissivity and absorptivity on collector performance under typical operating conditions are shown in Figs 5 and 6. It is found that for a single-glazed collector an increase in ct is more effective than for a double-glazed collector. F o r example, if~ is increased by a factor of, say, 0.10, i.e. from 0.80 to 0.90 or from 0.90 to 1.00, the increase in efficiency of a single-glazed collector is about 6.5 per cent, irrespective of plate temperature. For the same increase in ~, the increase in the efficiency of a double-glazed collector is about 5 per cent. Figures 5 and 6 show that a low emittance value is more effective for a single-glazed collector than for a
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
211
0.50 -
0.40
F" >.-
0.30 -
r,) Z
ca h
bd 0.20 --
0.10 --
0.0 200.0
//,/ 400.0
, 600.0
, 800.0
, 1000.0
SOLAR FLUX( HT),Wrn "2 Fig. 4.
Effectsof number of glazingcoversand solar fluxon collectorperformance(~ = Tp = 373 K).
0.10,
~ = 0.95,
double-glazed collector. It is also observed that there is a linear relationship between efficiency and absorptivity for ~ > 0.80, i.e. A~/= C1A~. However, there is no such linear relationship between efficiency and emittance. For example, for a doubleglazed collector an increase in emissivity from 0.10 to 0.20 leads to a decrease in efficiency of 1.1 per cent. At the same time, if the emissivity is increased from 0-40 to 0.50, the decrease in efficiency is about 0.5 per cent (Fig. 5). For higher emissivity values, the change in the e value has a slight effect on efficiency (Figs 5 and 6).
CONCLUSIONS
(i)
For collectors with selective absorber coatings the optimal number of glass covers is two.
0.70~
O
.
S
O
~
~
0.30
0.20 0.0 Fig. 5.
I 0.l
I I O.L O.B EMISSIVITY,£
I 1.0
Effect of variation of the emissivity and absorptivity on collector performance 1 0 0 0 W m -2, Tp = 333 K). - one glass cover, - - - - two glass covers.
O.t,O X
.030
z
~-~
~-.
"~_
ool oo
(Hr
,/,:l.O
0.90
o_~o......
- .......
3.80
0.10
Fig. 6.
I O.B
= o~
, o~
= os
EMISSIVITY,E
i ~ 08
= 1o
Effect of variation of the emissivity and absorptivity on collector performance ( H r 1000Wm -2, Tp = 373 K). - one glass cover, - - - - two glass covers.
FACTORS INFLUENCING SOLAR ENERGY COLLECTOR EFFICIENCY
213
(ii)
At low solar flux levels (200-600 W m - 2), double- or triple-glazed collectors are more efficient than single-glazed collectors. (iii) An increase in • is more effective for a single-glazed than for a double-glazed collector. (iv) There is an approximately linear relationship between the efficiency of a fiat plate collector and the absorptance of the absorber surface (for ct >_ 0-80), i.e. A t / = C~A~.
(v)
A low value of emittance is more effective for a single-glazed than for a double-glazed collector.
REFERENCES 1. P.K.C. PILLAIand R. C. AGARWAL,Spectrally selective surfaces for photothermal conversion of solar energy, Physica Status Solidi (a), 60 (1980). 2. A. WHmUER, Low temperature engineering applications of solar energy, ASHRAE, New York, 1967. 3. J.A. DUFFLEand W. A. BECKMANN,Solar energy thermalprocesses, John Wiley & Sons, New York, 1974. 4. H. C. HOTTEL and B. B. WOERTZ, Trans. Am. Soc. Mec. Eng., 64 (1942), p.91. 5. S. A. KLEIN, The effects of thermal capacitance upon the performance of flat-plate collectors, M.S. Thesis, University of Wisconsin, 1973. 6. S. A. KLEIN, Calculation of fiat plate collector loss coefficients, Solar Energy, 17 (1975), p. 79. 7. W. H. MCADA~S, Heat transmission, McGraw-Hill, New York, 1954.